# **Efficiency and Sustainability of the Distributed Renewable Hybrid Power Systems Based on the Energy Internet, Blockchain Technology and Smart Contracts**

Edited by Nicu Bizon Printed Edition of the Special Issue Published in *Sustainability*

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**Efficiency and Sustainability of the Distributed Renewable Hybrid Power Systems Based on the Energy Internet, Blockchain Technology and Smart Contracts**

## **Efficiency and Sustainability of the Distributed Renewable Hybrid Power Systems Based on the Energy Internet, Blockchain Technology and Smart Contracts**

Editor

**Nicu Bizon**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

*Editor* Nicu Bizon Faculty of Electronics, Communication and Computers University of Pitesti Pitesti Romania

*Editorial Office* MDPI St. Alban-Anlage 66 4052 Basel, Switzerland

This is a reprint of articles from the Special Issue published online in the open access journal *Sustainability* (ISSN 2071-1050) (available at: www.mdpi.com/journal/sustainability/special issues/ Distributed Renewable Hybrid Power Systems).

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## **Contents**




## **About the Editor**

## **Nicu Bizon**

Nicu Bizon (senior member, IEEE) was born in Albesti de Muscel, Arges county, Romania, in 1961. He received his 5-year B.S. degree in electronic engineering from the University "Polytechnic"of Bucharest, Romania, in 1986 and his Ph.D. degree in automatic systems and control from the same university in 1996. From 1996 to 1989, he was involved in hardware design with Dacia Renault SA, Romania. Since 2000, he has served as a professor with the University of Pitesti, Romania, and has received two awards from the Romanian Academy, in 2013 and 2016. He is the editor and author of 5 books published in Springer and the author of 206 scientific papers (including 7 and 84 papers in IEEE transactions and conferences, respectively) published in Scopus, which have been cited 1678 times, corresponding to an h-index = 29. His current research interests include power electronic converters, fuel cell and electric vehicles, renewable energy, energy storage system, microgrids, and control and optimization of these systems.

## **Preface to "Efficiency and Sustainability of the Distributed Renewable Hybrid Power Systems Based on the Energy Internet, Blockchain Technology and Smart Contracts"**

The very fast increase in the world's energy demand over the last decade, and the request for sustainable development, can be approached through micro- and nano-grids using hybrid power systems based on the energy internet, blockchain technology, and smart contracts.

This book includes innovative solutions and experimental research, as well as state-of-the-art studies, in the following challenging fields:











The climate changes that are visible today are a challenge for the global research community. The stationary applications sector is one of the most important energy consumers. Harnessing the potential of renewable energy worldwide is currently being considered to find alternatives to obtaining energy by using technologies that offer maximum efficiency and minimum pollution. In this context, renewable energy sources, fuel cell systems, and other energy generating sources must be optimally combined and connected to the grid system using advanced energy transaction methods.

The first chapter presents networked control systems (NCSs), which attract the attention of control system engineers. This chapter presents an extensive review of NCSs from the perspective of control system design. The evolution of NCSs is broadly divided in three phases, namely NCSs prior to 2000, NCSs during 2001–2010, and NCSs from 2011 onwards, which correspond to the initial status, intermediate status, and the recent status of the developments in the design of NCSs. The advancement of different control techniques during these phases has been discussed comprehensively. This chapter also describes the transition of control systems ffom a continuous domain to a networked domain, which makes it better than the traditional control systems.

The next three chapters, Chapters 2 to 4, present applications related to microgrids.

Chapter 2 introduces a new concept that allows for small energy producers to deliver excess energy to microgrids using smart transactions based on blockchain technology.

Chapter 3 investigates the power-sharing issues in networked-isolated microgrids containing multiple distributed generators (DGs) and loads connected to different common coupling points (CCPs) if the line parameters or mesh microgrid configuration are unknown. A decentralized droop control algorithm is proposed to achieve active and reactive sharing of different DGs in isolated microgrids with reconfigurable mesh.

Chapter 4 investigates the problems of improving the power factor through correction methods that reduce the load on the transformers and power conductors, leading to a reduction in losses in power supply and reduced costs by eliminating penalties (because they apply only at the common coupling point).

Chapters 5 and 6 present applications related to proton-exchange membrane fuel cell (PEMFC)-based hybrid power systems.

Chapter 5 proposes an effective control strategy to manage the distribution of energy from fuel cells and batteries to power a hybrid electric boat. The main objectives of this real-time control are to reduce hydrogen consumption and to improve the quality of energy transfer for a hybrid electric boat in various demand conditions.

Chapter 6 examines four fuel-saving strategies using power tracking control of the fuel cell boost converter and optimization of the PEMFC system by controlling power regulators. The performance and safe operation of the PEMFC system in the event of load disturbances and variations in renewable energy were estimated and compared with a reference strategy. The percentages of fuel economy are between 2.83% and 4.36% and between 7.69% and 12.94%, in the case of dynamic charging cycles with averages of 5 kW and 2.5 kW, respectively.

The last five chapters, Chapters 7 to 11, present applications related to microgrids based on energy internet, blockchain technology, and smart contracts.

Chapter 7 presents a new market model with social and commercial tiers for improved prosumer trading in microgrids. The proposal is based on a two-tier local market model oriented for prosumers and consumers connected in microgrids, based on the blockchain technologies and other technologies and concepts such as smart grids, crowdsourcing, and energy poverty.

Chapter 8 proposes the scheduled charging of electric vehicles in a secured manner by emphasizing cost minimization Using blockchain technology and an Inter-Planetary File System (IPFS). The charging of vehicles is performed in a Peer-to-Peer (P2P) manner, using Charging Stations (CSs) or Mobile Vehicles (MVs) that are not connected to a central entity.

Chapter 9 discusses carbon credits, which should reduce the environmental pollution and carbon emission of the Earth in the future, and shows that the market for carbon credits will become a critical issue from 2021 onwards. It proposes a market for carbon credits based on blockchain technology to measure carbon emission rights, making transactions more reliable by verifying carbon emissions rights among the UN-SDGs '(United Nations Sustainable Development Goals') 17 tasks.

Chapter 10 analyzes the blockchain-based Internet of Things (IoT) for a smart electric vehicle battery management system. The first implementation uses ethereum as the blockchain framework for developing smart contracts, while the second uses a directed acyclic graph (DAG), on top of the IOTA tangle. The two approaches are implemented and compared, demonstrating that both platforms can provide a viable solution for an efficient, semi-decentralized, data-driven BMS.

Chapter 11 proposes the implementation of blockchain technology in irrigation systems that integrate photovoltaic power generation systems. The efficiency of the proposed system is monitored not only through digital hardware connected to photovoltaic panels and water pumps but also by using the blockchain technology and smart contracts. A SolarCoin version similar to the Bitcoin cryptocurrency is proposed for energy and water trading.

As this book presents the latest solutions in the implementation of fuel cell and renewable energy in mobile and stationary applications such as hybrid and microgrid power systems based on energy internet, blockchain technology, and smart contracts, we hope that they are of interest to readers working in the related fields mentioned above.

> **Nicu Bizon** *Editor*

## *Review* **A Comprehensive Review of the Evolution of Networked Control System Technology and Its Future Potentials**

**Mayank Kumar Gautam <sup>1</sup> , Avadh Pati <sup>1</sup> , Sunil Kumar Mishra <sup>2</sup> , Bhargav Appasani <sup>2</sup> , Ersan Kabalci <sup>3</sup> , Nicu Bizon 4,5,6,7,\* and Phatiphat Thounthong 8,9**


5

**Abstract:** Networked control systems (NCSs) are attracting the attention of control system engineers. The NCS has created a paradigm shift in control system technology. An NCS consists of control loops joined through communication networks in which both the control signal and the feedback signal are exchanged between the system and the controller. However, its materialization faces several challenges as it requires the integration of advanced control and communication techniques. This paper presents an extensive review of NCSs from the perspective of control system design. The evolution of NCSs is broadly divided in three phases, namely NCSs prior to 2000, NCSs during 2001–2010, and NCSs from 2011 onwards. This division corresponds to the initial status, intermediate status, and the recent status of the developments in the design of NCSs. The advancement of different control techniques during these phases has been discussed comprehensively. This paper also describes the transition of control systems form continuous domain to networked domain, which makes it better than the traditional control systems. Some important practical applications, which have been implemented using NCSs, have also been discussed. The thrust areas for future research on NCS have also been identified.

**Keywords:** controller design analysis; networked control systems (NCSs); network security; delays; sampling

## **1. Introduction**

A networked control system (NCS) consists of control loops connected through communication networks, in which both the control signal and the feedback signal are exchanged between the system/plant and the controller. There are two types of approaches for design of NCSs, namely control of network approach and control over network approach. Only the control over network approach-based NCSs are considered in this review. A simple block diagram of this type of networked system is shown in Figure 1.

In an NCS, the plant output is measured using the sensors. These signals are converted into digital signals using the analog-digital (A/D) convertors, which are transmitted to the

**Citation:** Gautam, M.K.; Pati, A.; Mishra, S.K.; Appasani, B.; Kabalci, E.; Bizon, N.; Thounthong, P. A Comprehensive Review of the Evolution of Networked Control System Technology and Its Future Potentials. *Sustainability* **2021**, *13*, 2962. https://doi.org/10.3390/ su13052962

Academic Editors: Marc A. Rosen and Yuya Kajikawa

Received: 22 January 2021 Accepted: 28 February 2021 Published: 9 March 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

controller via a communication network. The controller determines the control signal based on the sensor output, which is transmitted back to the plant using same communication channel. The control signal before being fed to the actuator section of the plant, is converted from digital to analog signal using the digital-analog (D/A) convertor. In this manner, the plant dynamics can be controlled from a remote location. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 2 of 38

**Figure 1.** A simple block representation of a networked control system (NCS).

#### **Figure 1.** A simple block representation of a networked control system (NCS). *1.1. Advantages and Disadvantages of NCS*

In an NCS, the plant output is measured using the sensors. These signals are There are several underlying advantages of an NCS, which is termed as the next generation control system. Key merits of networked control systems (NCSs) are as follows:


exchanged easily using the communication networks, which helps in the design of

(iv) *Eliminates unnecessary wiring*: Today, it is possible to transmit data wirelessly at a very high speed. The wiring for interfacing controllers and plants can also be avoided. The wireless sensor networks are advanced enough to make the wireless

(v) *Simple to scale the networks by adding additional sensors, actuators, and controller*: The wireless sensors and actuators can be replaced easily, which reduces the maintenance cost of the NCS. The controllers can also be replaced economically as compared to the traditional wired controllers. The expansion of sensors, actuators

used to make intelligent decisions easily.

and controllers can also be achieved easily.

control algorithms.

control is a reality.

(vii) *Wide range of applications*: Applications in the area of distributed power systems, robots, unmanned aerial vehicles (UAVs), automobiles, space discovery, terrestrial discovery, industrial unit automation, remote problem-solving and troubleshooting, perilous environments, aircraft, production plant monitoring, and many more. More and more applications of NCS are coming into existence every day.

The NCS is also plagued by several problems. The disadvantages of NCS are:


#### *1.2. Designing of Control System from Continuous Domain to Networked Control Domain*

In the beginning, control signals were generated using analog computers. Frequency analysis and Laplace transform were the primary tools for analysis. The main drawbacks of this system are its limited accuracy, limited bandwidth, drift, noise, and limited capabilities to manage nonlinearities. Known delays could be handled at the time of control synthesis using the well-known Smith predictor.

Digital controllers replaced the analog technology with the advancement of processors. However, controlling an analog plant with a discrete electronic system inevitably introduces timing distortions. In particular, it will become necessary to sample and convert the sensor measurements to digital data and also convert them back to analog values. Sampling theory and z transform became the standard tools for the design and analysis of digital control systems analysis. For z transform, it is assumed that the sampling is uniform. Thus, for the design of digital controllers, periodic sampling became the standard. Note that, at the infancy of digital controls, as the computing power was poor and memory was expensive, it was vital to minimize the complexity of the controllers and the operating power. It is not obvious that the periodic sampling assumption is always the best choice. For example, adaptive sampling has been used in Reference [1], where the sampling frequency is changed based on the derivative of the error signal, and is far better than equidistant sampling in terms of computed samples (but possibly not in terms of disturbance rejection [2]). A summary of these efforts is provided in References [3,4]. However, with the decreasing computational costs, interest in adaptive sampling reduced, and the linearity preservation property of equidistant sampling has helped it to stay the undisputed standard.

From the computing side, real-time scheduling modeling and analysis were introduced in Reference [5]. This scheduling was based on restrictive assumptions, one of them being the periodicity of the tasks. Even if more assumptions were progressively introduced to cope with the practical problems, the periodicity presumption remains popular [6]. Moreover, the topology of the network can vary with time, allowing the mobility of the control devices. Hence, the whole control system can be highly adaptive in a dynamic environment. In particular, wireless communications allow for the rapid deployment of networks for connecting remotely located devices. However, networking also has problems, such as variable delays, message de-sequencing, and periodic data loss. These timing uncertainties and disturbances are in addition to the problems introduced by the digital controllers. Figure 2 shows the trade-off between control performance and the sampling rate.

performance and the sampling rate.

also has problems, such as variable delays, message de-sequencing, and periodic data loss. These timing uncertainties and disturbances are in addition to the problems introduced by the digital controllers. Figure 2 shows the trade-off between control

sampling rate from *P<sup>B</sup>* to *PC*. Increasing the sampling rate above *P<sup>C</sup>* increases the

network-induced delays. This will result in the degradation of control performance.

Figure 2 shows that the control performance is only applicable for a range of

**Figure 2.** Trade-off between control performance and the sampling rate. **Figure 2.** Trade-off between control performance and the sampling rate.

Based on the above discussion, the difference between the conventional control systems and the NCS is been summarized in Table 1 as: Figure 2 shows that the control performance is only applicable for a range of sampling rate from *P<sup>B</sup>* to *PC*. Increasing the sampling rate above *P<sup>C</sup>* increases the network-induced delays. This will result in the degradation of control performance.

**Table 1.** Differences between networked and conventional control systems. Based on the above discussion, the difference between the conventional control systems and the NCS is been summarized in Table 1 as:


and real-time computing. The increasing complexity of the computer systems, and their networks, requires advanced methods specifically suited for the NCS. The main issue to

sharing of common computing resources and communication bandwidths by competing control loops, alongside the other functions, introduces random delays and data losses.

**Table 1.** Differences between networked and conventional control systems.

#### *1.3. Co-Design Approach for the NCSs*

The design of an NCS integrates the domains of control system, communication, and real-time computing. The increasing complexity of the computer systems, and their networks, requires advanced methods specifically suited for the NCS. The main issue to be addressed is the achievement of the control objective (i.e., a combination of security, performance, and reliability requirements), despite the disturbances. For instance, sharing of common computing resources and communication bandwidths by competing control loops, alongside the other functions, introduces random delays and data losses. Moreover, the use of heterogeneous computers and communication systems increases the complexity of the NCS.

Control plays a significant role in interconnected complex systems for their reliable performance [7]. The interconnection of elements and sub-systems, coming from different technologies, and which are subject to various constraints, calls for a design that can solve the conflicting constraints. Besides achieving the desired performance in normal situations, the reliability and safety-related problems are of concern for the system developers. A fundamental concept that is dependability, which is the device property that features various attributes, such as access, reliability, safety, confidentiality, integrity, and maintainability [8]. Being confronted with faults, errors, and failures, a system's dependability could be achieved in numerous ways, i.e., fault prevention, fault threshold, and fault forecasting [9].

Except in the event of failures due to hardware or software components, most procedures run with nominal behavior, but, neither the process nor the execution resource parameters are completely known or modeled. One method is to allocate the system resources conservatively, which results in the wastage of resources. From the control viewpoint, specific inadequacies to be considered include poor timing, delays, and data loss. Control usually deals with modeling uncertainty, powerful adaptation, and disturbance attenuation. More correctly, as shown with recent results obtained on NCS [10], control loops tend to be robust and can tolerate networking and computing disturbances, up to a certain level. Therefore, the timing deviations, such as jitter or data loss, as long as they remain within the bounds, may be viewed as the nominal features of the system, but not as exceptions. Robustness allows for provisioning the execution resources according to needs that are average than for worst cases, and to take into account system reconfiguration only once the failures surpass the abilities of the controller tolerance that is running.

An NCS is composed of a collection of heterogeneous devices and information subsystems. For designing the NCS, many conflicting constraints must be simultaneously fixed before reaching a satisfactory solution that is implementable. Issues related to networking control tracking performance, robustness, redundancy, reconfigurability, energy consumption, expense effectiveness, etc., are to be addressed. Traditional control usually deals with a procedure that requires a solitary computer, and the limitations of the communication links and computing resources usually do not notably affect its performance. Existing tools dealing with the modeling and identification, robust control, fault diagnosis and isolation, fault tolerant control, and flexible real-time scheduling need to be enhanced, adapted, and extended to handle the networked characteristics of the control system. Finally, the thought of a co-design system approach has emerged that allows the integration of control, as well as communication within the NCS design [10].

#### *1.4. Main Contributions*

The NCS is an emerging area of the control system. It is worth reviewing the state-ofthe-art developments in NCS. Although many review papers have been published in this area, to the best of the authors' knowledge, these focused only on a certain dimension of the NCS, and a comprehensive approach was lacking. In this paper, a comprehensive review on the evolution of NCSs in last the 30 years is discussed. The evolution of NCS is broadly divided in three phases as: (i) prior to 2000, (ii) 2001–2010, and (iii) 2011 onwards. The reason for this division is to understand the initial, the intermediate, and the latest developments related to NCS. The main focus of this discussion would be on the advancement

of different control techniques during these phases. Based on the extensive review, the different types of NCSs and their related challenges are described. At the end, this review paper highlights the following innovations in the field of NCS: new novel methods for selecting the best sampling time in the NCS, new jitter compensation techniques, developing the theory and practice for control systems operating in a distributed and asynchronous packet-based environment, stability analysis of networked control systems in the presence of network-induced delays and packet dropouts (due to propagation delay and also due to the network congestion), and developing of advanced networked control methods that provide the desired performance in the presence of uncertainties and adversaries. This review paper also highlights some important practical applications that are implemented using the NCSs. Lastly, the important future research areas for NCSs are discussed.

The remaining sections are as follows: Section 2 reviews the development of NCS prior to 2000 AD; The development of NCS from 2001 AD to 2010 AD is discussed in Section 3; The advancement of NCS in recent phase after 2011 AD is discussed in Section 4; Section 5 describes about different topologies of NCSs; Section 6 presents different types of NCSs and their related challenges; Section 7 discusses some of the vital practical applications of the NCSs; Section 8 is the conclusion, along with the observations and potential future developments.

#### **2. Initial Phase of NCS Prior to 2000**

The NCS concept is not a recent phenomenon. It emerged in the early 1970s, with the progress of computation, as well as communication, technologies. However, the computation and communication technologies were still in the nascent stages and so the NCSs were designed as decentralized control systems, which remained prominent for the next three decades. One of the earliest works on decentralized NCS was proposed by Reference [11], where algebraic and geometric methods were discussed to obtain stable results. A dual-mode decentralized scheme for the networked control of a commodity's flow has been presented in Reference [12]. First, local controllers located at network nodes, exchange simple messages with their neighbors to determine the confined optimum flows. Second, the local controllers adjust their flows to reach the optimal equilibrium state in finite time.

The stabilization of the decentralized linear time-invariant multivariable (LTI-MultiVar) system was proposed in Reference [13] by employing numerous local feedback control rules. A necessary and sufficient condition was obtained from the above rule for the stabilization of the given system. Later, in Reference [14], the properties of the closed loop were studied for both controllable and observable *k-channel* linear systems, by applying the consequences of decentralized feedback. In addition, the theory of a complete system was established. Complete systems can be made both controllable and observable for all channels by applying non-dynamic decentralized feedback.

Some development in the field of decentralized control was achieved in 1980s. In Reference [15], a new dynamic interaction measure was defined by using the perception of structured singular value (SSV) for multivariable systems under feedback. To predict the stability of the decentralized systems and to measure the loss of performance, dynamic interaction measure was used. Later, in Reference [16], F. Lin et al. presented several important studies on decentralized control systems. The decentralized regulation and synchronization for partially surveyed discrete-time-event systems was studied. In Reference [17], which was illustrated using a simple production system. This study was later extended in Reference [18], and it was concluded that decentralized supervision would be easier to design and use.

In the 1990s, several NCS-related ideas evolved based on the concepts developed in the recent years, such as smart networks for control, decentralized control of complex systems, supervisory control, control in multimedia wireless networks, quasi-decentralized control, scheduling, event-triggered control, stability analysis, and so on [19–31].

The decentralized control of systems, which is complex in nature, were described in Reference [19], wherein topics, such as stabilization, optimization, estimation and control, output control, decompositions, and reliable control, were discussed in detail. In Reference [20], the author discussed the role of distributed, as well as centralized, networks for control. The authors also differentiated the above two categories in different ways. It also discussed the benefits and drawbacks of data networks, as well as the control networks. In a discrete-time system [21], the events must be within the imposed time constraints. To achieve a given control objective, a controller can hinder, permit, or pressurize several events in the system. In Reference [22], the network-level management and control issues were discussed. The quasi-decentralized control for complex systems was analyzed in Reference [23] using the concept of power system stabilization to design a sample system.

Three types of data: periodic data, sporadic data, and messages, have been proposed in Reference [24] for the planning of the NCS. As a basic parameter, delay bound was used, which guarantees the stability of the given system using Lyapunov's theorem. The above method can adjust the sampling period to be as minimum as possible, allocating all the network bandwidth. The basic properties of real time distributed systems were compared in Reference [25]. In addition, the characteristics of time triggered and event-triggered distributed systems in robotics were discussed in References [26,27] using the artificial intelligence, particularly focusing on the predictability, resource utilization, extensibility, etc. In Reference [28], the authors achieved the asymptotic stability and improved controller performance by scheduling the use of the network.

At the end of 20th century, a basic controller called an event-based proportional– integral–derivative (PID) controller was described in Reference [29], decreasing the resource consumption, only with the deprivation in the performance of trivial control. The proposed work was validated with simulations on a double-tank process. Next, two types of algorithms were suggested in Reference [30] for approximating the plant operation: one was an open-loop arrangement analyst, and the other was a closed-loop arrangement analyst/predictor. Again, the NCS's stability was analyzed in Reference [31], showing the effects of sampling rate manipulation and network delay on the system stability.

The above historical developments are summarized in tabular form in Table 2 on the basis of area/network/parameter.


**Table 2.** Summarized discussion of development of NCS prior to 2000.

Table 2 shows the distribution of available papers in the different areas prior to year 2000: on decentralized-based networks, there are around 10 papers; on smart networkbased systems, there are around 9 papers (during this period, the smart networks are in development stage); stable and robust networks can be found in all types of networks. The table here describes about the evolution of networked systems from decentralization of the available conventional networks. As there are many shortcomings in decentralized systems, the evolution of smart/wireless networks/discreet event-based networks came into existence. The distribution of the papers prior to 2000 is shown in Figure 3. The majority of the works are related to decentralized networks, followed by smart networks, and only a small percentage of works dealt with stable/robust networks.

**Figure 3.** Distribution of focus areas of NCS research prior to 2000. **Figure 3.** Distribution of focus areas of NCS research prior to 2000.

#### **3. Development of NCS between 2001 to 2010 3. Development of NCS between 2001 to 2010**

During this period, the key concepts of NCS, which were proposed earlier, received more attention, and the volume of research increased tremendously. One of the main themes of this period was the controller design for NCS with stability analysis and time delay. An important work on scheduling method for NCS was proposed by Reference [32]. This method guaranteed the stability using Lyapunov method. Next, a work on the impact of modern networked architecture on control act of NCS was published by Reference [33]. In Reference [34], the procedures for selecting the message recognizers for vigorously scheduled networked systems were proposed and validated. In Reference [35], recital benefits were established by dispensing with queues and by vigorous traffic During this period, the key concepts of NCS, which were proposed earlier, received more attention, and the volume of research increased tremendously. One of the main themes of this period was the controller design for NCS with stability analysis and time delay. An important work on scheduling method for NCS was proposed by Reference [32]. This method guaranteed the stability using Lyapunov method. Next, a work on the impact of modern networked architecture on control act of NCS was published by Reference [33]. In Reference [34], the procedures for selecting the message recognizers for vigorously scheduled networked systems were proposed and validated. In Reference [35], recital benefits were established by dispensing with queues and by vigorous traffic scheduling on the network.

scheduling on the network. An uncomplicated and easy model of a network system was proposed in Reference [36], in which local controllers connected by a network was addressed. In Reference [37], it was discussed that any complex self-motivated communications network typically has several layers and executive units and would be at risk of several disturbances. Therefore, the requirement for efficient and intelligent control of the systems must be An uncomplicated and easy model of a network system was proposed in Reference [36], in which local controllers connected by a network was addressed. In Reference [37], it was discussed that any complex self-motivated communications network typically has several layers and executive units and would be at risk of several disturbances. Therefore, the requirement for efficient and intelligent control of the systems must be used [38]. In Reference [39], an original networked control protocol, called try once-discard, has been proposed for multiple-input and multiple-output (MIMO) NCSs.

used [38]. In Reference [39], an original networked control protocol, called try oncediscard, has been proposed for multiple-input and multiple-output (MIMO) NCSs. A style technique of memoryless-quantizers in sampled-data models was planned by Reference [40]. The objective was quadratic stability within the continuous time (CT) domain. In Reference [41] a general framework for the NCSs was given, where all elements were assumed to be connected through a communication network. They used A style technique of memoryless-quantizers in sampled-data models was planned by Reference [40]. The objective was quadratic stability within the continuous time (CT) domain. In Reference [41] a general framework for the NCSs was given, where all elements were assumed to be connected through a communication network. They used the uncertainty threshold principle to point out that, with the bound conditions, even in an undisturbed NCS there would be data rates that degrade the performance of networked control due to the network induced delays and can lead the system to the instability [42].

the uncertainty threshold principle to point out that, with the bound conditions, even in an undisturbed NCS there would be data rates that degrade the performance of networked control due to the network induced delays and can lead the system to the instability [42]. In Reference [43], web-based multi-rate control systems were presented. It was suggested that the effect of web time delay on the control performance can be reduced In Reference [43], web-based multi-rate control systems were presented. It was suggested that the effect of web time delay on the control performance can be reduced by using the time delay compensation. A novel networked control strategy developed by Reference [44], analyzes the soundness of the networked systems with unsystematic delay in the communication. It consisted of a network control predictor and a traditional controller. The soundness criteria of a networked system were analytically derived for random

by Reference [44], analyzes the soundness of the networked systems with unsystematic delay in the communication. It consisted of a network control predictor and a traditional controller. The soundness criteria of a networked system were analytically derived for random communication delays. In Reference [45] a state observer for the networked communication delays. In Reference [45] a state observer for the networked systems with a delay in the time period was designed. Authors claimed that the state observer supported the satisfactory performance of the NCS, even with delay in the time period. Another review paper [46], which appeared within the same year, was centered on network-induced delays, sampling amount, jitter, information packet dropout, network programming, and stability of Ss.

In Reference [47], authors studied the result of a network within the feedback circuit of an NCS. A random packet-loss model for the network was considered. A classical work on the design of robust H-infinity (H∞) controllers for NCSs with uncertainties was given by Reference [48] that additionally considered the network-induced delay and information dropout. Next, the delays due to the sensor-to-controller and to-actuator were sculptured as two Markov/stochastic chains in Reference [49]. Input/output delay approach was considered by Reference [50] to style the strong sampled-data strong control. Enough LMI conditions were obtained by Lyapunov–Krasovskii functionals. In Reference [51], the straight line stability and straight line persistent disturbance attenuation problems were investigated for NCSs under the effects of random access delays and packet dropout. A robust controller was designed in Reference [52] for the NCSs with random time-delays, using the linear matrix inequality (LMI). The performance analysis of the event-triggered control for the detector sampling in a NCS was carried out by Reference [53]. The analytical formula for analyzing the mean and, therefore, the rate of event-driven traffic versus the sampling resolution was obtained. The simulation results in support of the obtained formula were additionally discussed.

A fault detection technique for NCSs supporting the parity relation and Principal Component Analysis (PCA) was projected in Reference [54]. The projected methodology noticed an honest decoupling from the unknown and random network-induced delay. In Reference [55] a fault bearing control methodology for the nonlinear NCSs with communication constraints was given. In Reference [56], the Tagaki-Sugeno (T-S) model was utilized to design a networked system with completely different delays induced by the network. When analyzed with the existing system modeling methods, this approach does not need the data of the actual delays induced by the network. The work in Reference [57] focused on the networked system with random time delays and, additionally, bestowed a brand new modeling methodology for the linear and nonlinear NCS with time delays that are random in nature and named those models as similar T-S fuzzy models.

A system supported bionic principles was introduced by Reference [58] to demonstrate the information obtained from an oversized range of numerous sensors. By means of that structure symbolization, the quantity of data to be processed was considerably reduced. In Reference [59] the event-triggered control was revisited, from an input-to-output perspective. Review of many modern results on evaluation, investigation, and controller synthesis for networked systems were administered in Reference [60]. Another paper, by Reference [10], surveyed appropriate work from the areas of systems and process control, detection, and estimation. Input delay approach, during which the sample-and-hold circuit can be implanted into an analog system with an input delay which is time-varying, was revised in Reference [61]. The loss of data-packets in the NCSs was mentioned in Reference [62]. In Reference [63], a mathematical model of a small rotorcraft was presented. The identification methodology and state estimation using Extended Kalman Filter were discussed. Control algorithms, based on PI, LQG and SDRE approaches, focused on rotorcraft were also proposed.

In Reference [64], the impact of a network within the electrical circuit of a system was discussed. They used an unsystematic loss of data-packet model for the network, and showed the results for discrete-time period systems with stochastic process jumping constraints. In Reference [65] the exponential stability of Nonlinear Time Varying (NLTV) impulsive systems was established with the help of Lyapunov functions separated at the impulse times. In Reference [66], it was observed that for NCSs with delays and output feedback stabilization, there was a deviation in the mean-square stability due to the random

communication situations. In Reference [67], a state feedback controller was proposed for the stabilization of an uncertain linear networked control systems with random communication time delays, which differs from the Lyapunov–Razumikh methodology. In Reference [68], a sufficient condition was obtained for the exponential stability of the networked systems, and they also the mentioned relationship between the dropout rate of the data-packets. An occurrence-based discrete-time model (an exponential unsure system with delay) was proposed by Reference [69] that showed that the stability of the projected system can be achieved by finding an effect for a switched stochastic system with an additive norm delimited uncertainty.

In Reference [70], the state feedback controllers were considered for a closed-loop NCS that is represented as a delay in switched systems. A technical note involved with the stabilization drawback of NCS was revealed by Reference [71]. In Reference [72], compensation ways were studied, within the structure of NCS, while considering the protocol characteristics. A general framework was projected initially, wherever the zeroorder hold had the logical capability of selecting the most recent control input packet. A category of period of time control systems during which every control task triggers its next unleash supported the worth of the last sampled state were examined by Reference [73]. In Reference [74], a memory less quantizer for steadying a single-input discrete-time Linear Time Invariant (LTI) system with random loss in data-packets, was proposed within the sense of unsystematic quadratic stability. Nesic et al. [75] generalized and unified a variety of recent developments in the literature pertaining to quantized control systems (QCS) and NCS. They provided a unified framework for the controller style with division and time planning via an emulation-like approach. Improved stability conditions were derived in Reference [76] for sampled-data feedback control systems with falteringly Linear Time Variant (LTV) sampling intervals. The cause of robust *H*∞ control was researched by Reference [77] for sampled-data systems with probabilistic sampling. By Linear Matrix Inequality (LMI) approach, enough situations were produced, that bonded the robust mean-square exponential stability of the system.

An event-driven state-feedback type of control technique in which a control input generator mimicked a continuous feedback between two successive event times was published by Reference [78]. In Reference [79], focus was given on different factors, such as networking technology, delay network induced delay, resource allocation of networks, scheduling, fault bearing capacity, etc. In Reference [80], an original totally time period dependent Lyapunov function was proposed in the construction of the input delay that improves the existing results. In Reference [81], the cause of the NCSs having exponential stability with the increase in delay time-periods, was studied. The cause of robust fault calculation for a class of tentative networked systems with arbitrary communication delays induced by the network was inspected by Reference [82], which also described the delays by Markov processes. In Reference [83], wireless sensor networks for networked manufacturing systems were proposed.

The above historical development is summarized in tabular form in Table 3 on the basis of area/network/parameter as follows.

The above, Table 3, gives a structured information about the distribution of papers in different areas published during the phase from 2001 to 2010. On scheduled networks, there are around 6 papers; on stability analysis-based systems, there are around 15 papers; on complex and interactive networks, there are around 5 papers; on communication and event-based networks there are around 4 papers, etc. Event-based approach was still in the developmental phase as it was a new technique. Delay-based systems were popular during this stage that were used to overcome the drawbacks of the research prior to year 2000. So, scheduled, autonomous, event-based, and communication-based approaches came into existence during this phase. The major drawbacks prior to year 2000 were: security issues, effect of delay on networked systems, effect of packet dropouts in communication networks, etc. So, to overcome these issues, scheduled approach-based network came into existence. The distribution of the papers during this phase are shown in Figure 4. The

major focus was on delay-based approaches in networked system to improve the flow of information in networked system and make the system stable. The above, Table 3, gives a structured information about the distribution of papers


**Table 3.** Summarized discussion of development of NCS from 2001 to 2010. in different areas published during the phase from 2001 to 2010. On scheduled networks,

*Sustainability* **2021**, *13*, x FOR PEER REVIEW 11 of 38

system and make the system stable.

**Figure 4.** Distribution of focus areas of NCS research from 2001 to 2010. **Figure 4.** Distribution of focus areas of NCS research from 2001 to 2010.

#### **4. Development of NCS from 2011 Onwards 4. Development of NCS from 2011 Onwards**

In the last decade, highly developed control methods were employed for improving the performance of NCS in terms of system stability, delays, event-triggering algorithms, network security, etc. In addition, the discrete time NCSs have received a considerable In the last decade, highly developed control methods were employed for improving the performance of NCS in terms of system stability, delays, event-triggering algorithms, network security, etc. In addition, the discrete time NCSs have received a considerable amount of attention.

amount of attention. Model-based predictive NCSs (MBPNCSs) were proposed by Reference [84] that compensated for the random delays and for the data losses in data transmission. The performance of the system was improved with the help of a predictive control scheme. In Reference [85], an approach for stabilization via discontinuous Lyapunov function Model-based predictive NCSs (MBPNCSs) were proposed by Reference [84] that compensated for the random delays and for the data losses in data transmission. The performance of the system was improved with the help of a predictive control scheme. In Reference [85], an approach for stabilization via discontinuous Lyapunov function was proposed, where sampling intervals that varied in terms of their nature, the dropouts, and

control of random time delayed networked systems was proposed. In Reference [87], the stability investigation of a NCS was achieved, where the communication between the controller and the plant input is through a digital channel, with dropouts in data-packets and finite-level quantization. Again, in Reference [88], authors describe the stability of

NCSs with respect to time-varying transmission intervals.

network delays were taken into account. In Reference [86], a *H2/H*∞ control of random time delayed networked systems was proposed. In Reference [87], the stability investigation of a NCS was achieved, where the communication between the controller and the plant input is through a digital channel, with dropouts in data-packets and finite-level quantization. Again, in Reference [88], authors describe the stability of NCSs with respect to time-varying transmission intervals.

For discrete-time models, in Reference [89], the difficulty of the networking-based *H*∞ filtering method was described. A Markov jumping model based method was described to design *H*∞ filters, in which the filter gains depend on both the network delays and dropouts in data-packets. In Reference [90], a novel method was presented to calculate the stability of continuous linear systems with input containing the sampled data. In a technical note, Reference [91] presented a new method with control packet loss. In Reference [92], a networked control loop was considered in which the "slave" portion was a plant, and the "master" portion was the remote controller and observer. In networks, the fault detection of linear systems with restricted loss of data packets was proposed by Reference [93]. In Reference [94], a modern control system mapped on Networks-on-Chip was presented. The proposed architecture was supposed to play a pivotal role in real time applications like missile control system, robot trajectory, and satellite vehicle orbital trajectory control system. In Reference [95], a NCS framework for the coordinated control of distributed generation sources in smart power grids was proposed. The system measurements were transmitted to the controller through a real-time communication network and the effects of delays and packet dropouts due to the communication network were modeled.

An event-triggered transmission scheme was proposed by Reference [96] for a sampleddata control system. In Reference [97], an event-triggering method was designed to decrease the network communication load, which could also be used to decide the time moment of the sampled signals. In Reference [98], a methodology for the technological investigation of iterative learning control for sampled-data systems was proposed. In Reference [99], a new Lyapunov functional was constructed to drive some stability criteria. Then, a channel utilization-based switched controller was designed to asymptotically stabilize the networked system in the sense of mean-square. It was shown that the proposed approach enhances the robustness of the networked control system to data drift and external disturbances. In Reference [100], the cascade control was employed for stabilization of the singular NCSs. In Reference [101], a network-based output controlled T-S fuzzy system was investigated that is steadied using a delayed fuzzy static controller, and not by any non-delayed static controller. In Reference [102], a novel robust variable sampling period controller (RVSPC) was developed that takes into account random time delays and losses in data-packets. In Reference [103], a decentralized event-triggered dissipative control was studied for systems having diverse physical characteristics. In Reference [104], a distributed NCS scheme was proposed by considering the communication delays. The results were applied to reduce the inter-area swing oscillations in a power grid. A brief overview of NCSs was presented by Reference [105] regarding the system configurations, challenging issues, and the methodologies.

In Reference [106], a time-triggered zooming algorithm for the dynamic quantization at the sensor side was proposed that led to an exponentially stable closed-loop system. The algorithm included proper initialization of the zoom parameter. An exhaustive explanation of the various types of networked control techniques is given by Reference [107]. The *H*∞ output feedback control of NCSs with time delay and dropout in data-packets were considered in Reference [108], whereas Reference [109] discovered the nonlinear networked systems with tracking control problem. In Reference [110], the data that uses self-healing technology was reviewed as input and was justified as big data. In Reference [111] the method for time-delays in large-scale networked systems connecting sensors, controllers, and actuators was developed. A new sampling and control strategy was proposed by Reference [112] to search a sub-optimal sampling sequence and control input sequence to minimize the disordering of data-packets. Further, in Reference [113], an original state

space model was set up, in which both the tracking error and the state variables were combined and optimized. The optimal estimation problem in lossy NCSs with randomly dropped control data-packets was elaborated in Reference [114]. In Reference [115], the problem of Sliding Mode Controller (SMC) for NCSs was considered with semi-stochastic switching, popularly known as Markov or stochastic switching and having unsystematic dimensions. In Reference [116], a phenomenon of self-triggered sampling was proposed for a networked system with considerations of data losses and delay in communication. In Reference [117], both the *D*-stability, as well as the properties of finite *L***2**-gain, were studied for a class of uncertain discrete-time systems with time varying network-induced delays [118,119].

A summary of the distributed NCSs was presented by Reference [105]. In Reference [120], stochastic nonlinear time-delay systems were considered that take the help of observer-based fuzzy output-feedback control (OFOFC). In Reference [121], the stochastic linear systems with random data dropout designed by a Bernoulli random variable were described. In Reference [122], the state and fault estimation problem for Linear Time (LT) switched systems with immediate disturbances and faults, was considered. Also, the two types of observer-based approaches were considered.

A procedure to evaluate the wellbeing of Centralized Power Systems (CPSs) in the event of cyber-attacks was described by Reference [123]. The problem of switched type networked systems with external disturbance and faults was investigated in Reference [124]. In Reference [125], the main cause of *H*∞ control for uncertain discrete-time domain T-S fuzzy systems was considered.

The problem of state estimation for linear stochastic methods with event-triggered communication and packet loss was determined in Reference [126]. In Reference [127] event-triggered coordination for multi-agent structures/systems was elaborated. A survey on the distributed type of control and distributed type of filtering had been provided by Reference [128] for industrial CPSs, explained by different mathematical equations. In Reference [129], the problem of event-based network-induced time-varying delays with output tracking control for nonlinear NCSs approximated by type-2 fuzzy systems was investigated. In Reference [130], the authors addressed the concern for multi-layer, data-driven cyber-attacks, developed to boost ICS cyber security. In Reference [131], the control of automotive active suspension system using Proportional Integral Derivative (PID) and Linear Quadratic Regulator (LQR) methods was discussed. In Reference [132], a closed-loop controller model considering cyber-attacks and the mixed-triggering scheme, was proposed. In Reference [133], a robust fault detection scheme for networked control systems (NCSs) was developed with limited quality of services (QoS), such as networkinduced time delay, data dropout, and error sequence. In Reference [134], a survey on time-delay approach to networked control systems (NCSs) was provided, which discusses the fundamental network-induced issues in NCSs and the main approaches to the modeling of NCSs. Again, an investigation on distributed type of control and distributed type of filtering for CPSs described by dynamic mathematical modeling equations was presented by Reference [135]. In Reference [136], a scheme called robust approximation-based model predictive control (RAMPC) was developed for the constrained networked control systems (NCSs) subject to external disturbances. This paper also provides a roadmap to evaluate the permissible sampling period and also evaluates the necessary conditions for the feasibility of the RAMPC.

In Reference [137], a sampled-data control problem was investigated for connected vehicles subject to switching topologies, communication delays, and external disturbances. It used an advanced tracking error-based sampled-data platoon control method. In Reference [138], authors were concerned with the modeling and controlling using the mixed event-triggered mechanism (ETM) for NCSs with varying time-delays and uncertainties. In Reference [139], authors investigated about the switching-like event-triggered control for networked control systems (NCSs) under the malicious denial of service (DoS) attacks. In Reference [140] authors proposed an iterative learning control (ILC) scheme to synchronize an array of non-identical neural network systems based on time-varying delay in a repetitive environment. In Reference [141], authors considered a resilient event-triggered control problem for a class of networked systems subject to randomly occurring deception attacks. In Reference [142], a novel method is proposed for line selection and fault location in a distribution network based on a cloud-edge-terminal hierarchical fault monitoring and control system. Reference [143] focuses on the event-triggered control problem for networked switched systems with actuator saturation. Here, an event-triggering strategy is developed based on discrete event-triggered samplings.

In Reference [144], authors investigated the stability problem for networked control systems. They have taken into consideration the input delays and multiple communication imperfections containing time-varying transmission intervals and transmission protocols. Reference [145] focused on addressing the sliding mode control problem of continuoustime nonlinear networked control systems. In Reference [146], the problem of fault-tolerant sampled-data *H*∞ control for a networked control system with random time delays and actuator faults is investigated. In Reference [147], the problem of event-triggered finite-time control for networked switched control systems with extended dissipative performance was investigated. In Reference [148], the authors proposed a scheduling approach which can minimize the impact of delays and conflicts on the network, to improve the system stability, which results in an economical allocation of network resources, minimizes the traffic congestion, and improves the overall performance of the NCS.

In Reference [149], the authors discussed about the effect of limited bandwidth on the system's performance, particularly when the sampling period was small. In Reference [150], the authors discussed the amalgamation of control and communication in NCSs that offers remarkable achievement in the design and analysis of such controlled systems. In Reference [151], the authors discussed the LMI approach to effectively compensate for the random network-induced delays and provide the desired control performance. In Reference [152], a new ETM was proposed, under which data packets could be actively dropped within consecutive steps, thereby, saving more communication resources than the existing ETM. In Reference [153], the authors proposed the descriptive analysis about classification of cyber-attacks and threats related to security in industrial control systems. In Reference [154], the authors proposed a new quantization structure, and a mathematical treatment of this structure was given to illustrate the advantage for the quantization effects.

The above developments can be summarized in tabular form in Table 4 on the basis of area/network/parameter as follows.


**Table 4.** Summarized discussion of development of NCS from 2011 onwards.

Table 4 gives the structured information on the distribution of papers in different areas published from the year 2011 onwards. The major focus of research during this phase was on the delay-based networks. The difference between the works published in the earlier phases is that the security approach, model-based approach, and the sampledbased approach involve the incorporation of delays. Secondly, the advanced modelbased networked approaches, such as Model-Predictive Control (MPC), OFOFC networks, etc., were proposed, which make the networked system more stable and improve its performance. Figure 5 shows the distribution of papers during this phase. It can be clearly noticed that major focus is on the delay-based approach, which covers approximately 37% of the research contribution. The stability approach is also very important as the stability depends on delay. If the delay is maximum, the system has to be designed to make it stable. To achieve this purpose, many event-based techniques were developed. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 15 of 38 model-based networked approaches, such as Model-Predictive Control (MPC), OFOFC networks, etc., were proposed, which make the networked system more stable and improve its performance. Figure 5 shows the distribution of papers during this phase. It can be clearly noticed that major focus is on the delay-based approach, which covers approximately 37% of the research contribution. The stability approach is also very important as the stability depends on delay. If the delay is maximum, the system has to be designed to make it stable. To achieve this purpose, many event-based techniques were developed.

**Figure 5.** Distribution of focus areas of NCS research from 2011 onwards. **Figure 5.** Distribution of focus areas of NCS research from 2011 onwards.

#### **5. Topologies in NCSs 5. Topologies in NCSs**

Basically, there are three types of network topologies available in NCSs, namely centralized topology, decentralized topology, and distributed topology. A brief discussion on these topologies is given below. Basically, there are three types of network topologies available in NCSs, namely centralized topology, decentralized topology, and distributed topology. A brief discussion on these topologies is given below.

#### *5.1. Centralized Topology*

*5.1. Centralized Topology* The centralized topology is shown in Figure 6. Here, the sensed data is sent to a centralized controller for data fusion. Suitable data fusion methods are necessary to The centralized topology is shown in Figure 6. Here, the sensed data is sent to a centralized controller for data fusion. Suitable data fusion methods are necessary to obtain the fused data which are utilized for computing processes and executions.

obtain the fused data which are utilized for computing processes and executions.

**Figure 6.** Centralized topology. **Figure 6.** Centralized topology.

#### *5.2. Decentralized Topology 5.2. Decentralized Topology*

*5.2. Decentralized Topology* This topology is shown in Figure 7. Each controller node depends only on the local information that the controller possesses for making its local decision. In this topology, the controller nodes do not share their information with the corresponding neighboring This topology is shown in Figure 7. Each controller node depends only on the local information that the controller possesses for making its local decision. In this topology, the controller nodes do not share their information with the corresponding neighboring nodes. These types of topologies are helpful in reducing the time taken to analyze and synthesize the NCSs. Here, the controllers are decentralized controllers. This topology is shown in Figure 7. Each controller node depends only on the local information that the controller possesses for making its local decision. In this topology, the controller nodes do not share their information with the corresponding neighboring nodes. These types of topologies are helpful in reducing the time taken to analyze and synthesize the NCSs. Here, the controllers are decentralized controllers.

> A/ D

The pictorial representation of the distributed topology is shown in Figure 8. One

example of distributed topology can be found in Reference [155], where the load frequency control of a networked multi-area power system was discussed. There are two important characteristics of this topology: the subsystem's information is exchanged with the help of shared communication network, and the plant consists of a huge

example of distributed topology can be found in Reference [155], where the load frequency control of a networked multi-area power system was discussed. There are two important characteristics of this topology: the subsystem's information is exchanged with the help of shared communication network, and the plant consists of a huge

**Figure 7.** Decentralized topology. **Figure 7.** Decentralized topology.

*5.3. Distributed Topology*

*5.3. Distributed Topology*

**Figure 7.** Decentralized topology.

S Sensor

Communication Link

#### *5.3. Distributed Topology*

The pictorial representation of the distributed topology is shown in Figure 8. One example of distributed topology can be found in Reference [155], where the load frequency control of a networked multi-area power system was discussed. There are two important characteristics of this topology: the subsystem's information is exchanged with the help of shared communication network, and the plant consists of a huge number of simple interacting units that are interconnected to achieve a desired objective. In this topology, each controller is allowed to share its local information with the corresponding neighboring controllers. Thus, the distributed controllers are capable to coordinate their behavior by transmitting/receiving information to/from other controllers within their corresponding neighboring area. Here, the controllers are distributed controllers. Advantages of this type of topology are: modularity, scalability, and robustness. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 17 of 38 number of simple interacting units that are interconnected to achieve a desired objective. In this topology, each controller is allowed to share its local information with the corresponding neighboring controllers. Thus, the distributed controllers are capable to coordinate their behavior by transmitting/receiving information to/from other controllers within their corresponding neighboring area. Here, the controllers are distributed controllers. Advantages of this type of topology are: modularity, scalability, and robustness.

**Figure 8.** Distributed topology. **Figure 8.** Distributed topology.

#### *5.4. Distribution of Literature Based on the Topologies of NCSs*

*5.4. Distribution of Literature Based on the Topologies of NCSs* Table 5 gives a summary of the literature based on the topology. It can clearly be seen that the majority of research works use decentralized topology as the controller works independently for the given number of plants, and it has many advantages over the centralized topology, such as network time reduction in sending the data, less network congestion, maximum number of paths available for transmission, etc. The distributed topology is in the developmental stage and has tremendous applications in the NCSs. Focus is now shifting towards the distributed topologies of NCSs. Figure 9 clearly shows that the major focus has been on decentralized (i.e., 59%) topology, Table 5 gives a summary of the literature based on the topology. It can clearly be seen that the majority of research works use decentralized topology as the controller works independently for the given number of plants, and it has many advantages over the centralized topology, such as network time reduction in sending the data, less network congestion, maximum number of paths available for transmission, etc. The distributed topology is in the developmental stage and has tremendous applications in the NCSs. Focus is now shifting towards the distributed topologies of NCSs. Figure 9 clearly shows that the major focus has been on decentralized (i.e., 59%) topology, followed by the distributed topology, that has share of 32%. Centralized topology has been the least preferred topology, with a share of 9%.

followed by the distributed topology, that has share of 32%. Centralized topology has

3 Distributed Topology [20,25–27,46,58,83,95,104,105,107,111,118,126–129,134,135,142,155]

1 Centralized Topology [20,48,83,96,97,128]

**Table 5.** Summarized discussion of different types of NCS topologies.

2 Decentralized Topology [10,11–31,43,46,53,63,75,78,96,97,103,104,107,126,127,129,135,138,139,143,147,152,154]

been the least preferred topology, with a share of 9%.


**Table 5.** Summarized discussion of different types of NCS topologies.

**Figure 9.** Utilization of different topologies. **Figure 9.** Utilization of different topologies.

#### **6. Types and Challenges of NCS 6. Types and Challenges of NCS 6. Types and Challenges of NCS** Based on the above review, we have identified types of NCSs and the related

Based on the above review, we have identified types of NCSs and the related challenges, which are discussed in this section. Based on the above review, we have identified types of NCSs and the related challenges, which are discussed in this section. challenges, which are discussed in this section. *6.1. Types of NCS*

If all the control parts are placed in the similar venue, the resulting NCS is often considered to be a digital unit. Since the late 1950s, sampled data control theory has been very well developed for digital control systems. The strategy of delay in the input to this type of control, firstly planned in 1988 [79], has gained resurgent popularity, thanks to the advent of the LMI methodology and also to the advancement of network control technologies. The upper limit of two successive samples and the associated controller is

considered to be a digital unit. Since the late 1950s, sampled data control theory has been very well developed for digital control systems. The strategy of delay in the input to this type of control, firstly planned in 1988 [79], has gained resurgent popularity, thanks to the advent of the LMI methodology and also to the advancement of network control technologies. The upper limit of two successive samples and the associated controller is

Switched System Approach

#### *6.1. Types of NCS 6.1. Types of NCS* The types of NCS developed in the literature are shown in Figure 10.

The types of NCS developed in the literature are shown in Figure 10. The types of NCS developed in the literature are shown in Figure 10.

Jumping System Approach

**Figure 10.** Types of NCS.

6.1.1. Sampled-Data Control

6.1.2. Networked Control

6.1.1. Sampled-Data Control

6.1.2. Networked Control

often easily determined using the input delay technique.

often easily determined using the input delay technique.

#### 6.1.1. Sampled-Data Control

If all the control parts are placed in the similar venue, the resulting NCS is often considered to be a digital unit. Since the late 1950s, sampled data control theory has been very well developed for digital control systems. The strategy of delay in the input to this type of control, firstly planned in 1988 [79], has gained resurgent popularity, thanks to the advent of the LMI methodology and also to the advancement of network control technologies. The upper limit of two successive samples and the associated controller is often easily determined using the input delay technique.

#### 6.1.2. Networked Control

Delays caused by the network and the packet losses are still difficult issues for NCSs. Reckoning on managing the network delays and the packet dropouts, different ways to measure stability, and managing styles for NCSs have been developed over the past decade. A brief review of a few of them is discussed below.

#### 6.1.3. A Time-Delay System Approach

The delay in the input method for a sampled system motivates a time-delay system method [77]. Using this approach, the closed loop system is represented as a process with a time-varying lag. The delay in communicating the data from the sensors to the controller and from the controller to the actuators and the respective data-packet dropouts are indirectly incorporated within the input-delay. This approach obtains the maximum delay that the system can tolerate and still maintain its performance. On the other hand, it indicates the worst delay induced by the network and the corresponding packet dropouts that the networked system can tolerate. In the worst case scenario, the results obtained from this approach are definitely conservative [70].

#### 6.1.4. A Markovian-Jumping System Approach

This approach is developed for the investigation and control of the networked systems. Network delays were considered, where the closed-loop NCSs were represented as stochastic-process systems and associated with Linear Quadratic Gaussian (LQG) optimum controllers [66]. The stabilization issue in networked systems is mentioned employing this system approach [39]. Its price remarking that the conception of packets-dropout of data dependent Lyapunov functions is established [71], resulting in some less traditional stability criteria. The Markovian approach is planned for NCSs with delays induced by the network [86]. The key plan is to model the sensor to the controller and the controller to the actuator delays as Markov chains, thus reproducing the closed-loop NCSs as a Markovian process with two modes portrayed by two Markov chains.

#### 6.1.5. A Switched System Approach

This method with arbitrary switching is employed within the investigation and control of these systems. There are a variety of methods on how to build the networked system as a switched-system by means of arbitrary switching. Most of them support the discretetime method, whereas few of them on the continuous-time method. Based on the idea that the control signal varies with time, a discrete-time switched model is developed [92], where the sampling amount is split into a variety of subintervals on which the controller operates better than the sampling frequency. With this model, the stability and the chronic disturbance attenuation were investigated for the NCSs. It is to be noted that the constraint on delays due to the network is not simple for some NCSs. So, to get rid of this constraint, efforts are created; see, e.g., References [49,68,88].

#### 6.1.6. Event-Triggered Control

In this, the completion of control assignment is decided by the occurrence of an incident, instead of slip away of a fixed fundamental quantity as in the control of timetriggered systems. One of the main advantages of this type of control is the resource

consumption with less control performance degradation. This control technique has received plenty of interest and has become a booming topic within the field of NCSs; see, e.g., References [29,72,89]. A key purpose of this control technique is to style an acceptable triggering circumstance that decides whether or not a control task is accomplished. Because of the above benefits, this control approach involves the fore. A variety of problems for these type of systems is tackled, such as Euclidean Norm, *L*2, investigation and control style, tracking control, dynamic output feedback control, *H*∞ filtering, and accord of multi-agent systems. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 20 of 38 *6.2. Challenges of NCS* Apart from several advantages, there are many key challenges that have received a

#### *6.2. Challenges of NCS* considerable attention of the research community. Many solutions have been proposed

Apart from several advantages, there are many key challenges that have received a considerable attention of the research community. Many solutions have been proposed in the past, and many more are being proposed every day. Next, we will discuss some of the key challenges of NCS. Figure 11 presents a flow diagram of the challenges involved in the implementation of the NCS. in the past, and many more are being proposed every day. Next, we will discuss some of the key challenges of NCS. Figure 11 presents a flow diagram of the challenges involved in the implementation of the NCS.

**Figure 11.** Challenges of NCS. **Figure 11.** Challenges of NCS.

#### 6.2.1. Sampling

12).

6.2.1. Sampling Before being transmitted over a communication network, the continuous signals should be sampled for simplicity. For sampling the above continuous-time signals, there are basically two ways: one is time-triggered, and another is event-triggered. In timetriggered sampling also known as Riemann sampling, the sampling moment happens at fixed time intervals. Periodic sampling was usually employed in the early digital Before being transmitted over a communication network, the continuous signals should be sampled for simplicity. For sampling the above continuous-time signals, there are basically two ways: one is time-triggered, and another is event-triggered. In timetriggered sampling also known as Riemann sampling, the sampling moment happens at fixed time intervals. Periodic sampling was usually employed in the early digital management systems, as the analysis and style of these sampled systems is simple. At the instance the value of the sampled signal approaches zero, the output obtained is equivalent to the continuous-time system. Another sampling is event-triggered, which is generally denoted as Lebesgue sampling. In this the sampling occurs when an event is triggered. This sampling significantly reduces the network traffic volumes. Over the last decade, there

the instance the value of the sampled signal approaches zero, the output obtained is equivalent to the continuous-time system. Another sampling is event-triggered, which is generally denoted as Lebesgue sampling. In this the sampling occurs when an event is triggered. This sampling significantly reduces the network traffic volumes. Over the last decade, there has been an increasing interest in the control of NCSs through event-

triggering because of its advantage over time-triggering; see, e.g., References [59,73,78].

when the sampling period is small, thereby generating a lot of data that overloads the network and causes congestion. It may result in increased packet losses and longer delays, which degrades the performance. The relationship between the sampling period, the network load, and the system performance in an NCS is illustrated in Figure 12 [150]. For instance, decreasing the sampling period through the values corresponding to points "a" and "b," the device performance improves. In addition, the device performance deteriorates as a result of network congestion when the sampling period is reduced, as indicated by the values corresponding to points "b" to "c". An optimal sampling period exists at which the system performance is the best (point "b" in Figure

In NCSs, the limited bandwidth restricts the system performance [149]. This occurs

has been an increasing interest in the control of NCSs through event-triggering because of its advantage over time-triggering; see, e.g., References [59,73,78].

In NCSs, the limited bandwidth restricts the system performance [149]. This occurs when the sampling period is small, thereby generating a lot of data that overloads the network and causes congestion. It may result in increased packet losses and longer delays, which degrades the performance. The relationship between the sampling period, the network load, and the system performance in an NCS is illustrated in Figure 12 [150]. For instance, decreasing the sampling period through the values corresponding to points "a" and "b", the device performance improves. In addition, the device performance deteriorates as a result of network congestion when the sampling period is reduced, as indicated by the values corresponding to points "b" to "c". An optimal sampling period exists at which the system performance is the best (point "b" in Figure 12). *Sustainability* **2021**, *13*, x FOR PEER REVIEW 21 of 38

**Figure 12.** Relationship between system performance, network congestion and sampling period. **Figure 12.** Relationship between system performance, network congestion and sampling period.

Table 6 shows the quantitative data for the sampling rate considered in the different research works. There are mainly periodic and aperiodic sampling approaches. In periodic case, the lowest sampling rate considered was 22.1 ms [40], whereas the highest Table 6 shows the quantitative data for the sampling rate considered in the different research works. There are mainly periodic and aperiodic sampling approaches. In periodic case, the lowest sampling rate considered was 22.1 ms [40], whereas the highest sampling rate considered was 1730 ms [149]. For the case of aperiodic sampling, the lowest range is between 4 ms to 4.7 ms in Reference [119], whereas the highest range was between 30 ms to 1380 ms in Reference [96].

sampling rate considered was 1730 ms [149]. For the case of aperiodic sampling, the lowest range is between 4 ms to 4.7 ms in Reference [119], whereas the highest range

**Reference Type of Sampling Sampling Interval/Sampling Interval Range (***in ms***)**

In the literature, many delay induced network models have been proposed

[48,49,60,70,84,86,98–100,118]. In Reference [84], four main delay models were discussed, namely: (a) constant delay model, (b) stochastic delay model, (c) Markov chain model, and (d) hidden Markov model. Reasons for these types of delays are: limited bandwidth, network traffic, and transmission protocols [99]. Two types of delays mainly occur: (i) sensor to-the controller delays and (ii) controller to-the actuator delays. Since networkinduced delays depend on the networking circumstances [60], they are sometimes time-

[1] Aperiodic 16 to18

[4] Periodic 40, 80

[40] Periodic 22.1

[50] Periodic 785

[65] Periodic 132.77

[77] Aperiodic 10 to 11

[80] Aperiodic 104 to 169

[96] Aperiodic 30 to 1380

[103] Aperiodic 0 to 299

[119] Aperiodic 4 to 4.7

[146] Aperiodic 20 to 100

[137] Periodic 100

[149] Periodic 1730

6.2.2. Network-Induced Delay and Packet Dropout

[93] Periodic 40

was between 30 ms to 1380 ms in Reference [96].


**Table 6.** Sampling rate considered in different studies.

6.2.2. Network-Induced Delay and Packet Dropout

In the literature, many delay induced network models have been proposed [48,49,60, 70,84,86,98–100,118]. In Reference [84], four main delay models were discussed, namely: (a) constant delay model, (b) stochastic delay model, (c) Markov chain model, and (d) hidden Markov model. Reasons for these types of delays are: limited bandwidth, network traffic, and transmission protocols [99]. Two types of delays mainly occur: (i) sensor to-the controller delays and (ii) controller to-the actuator delays. Since network-induced delays depend on the networking circumstances [60], they are sometimes time-varying, unpredictable, and the upper bound is unknown. As a consequence, network-induced delays are ordinarily sculptured as interval time-varying delay [48,100] and a Markov chain with known transition chances [49,86], with partially transition chances [89] and with arbitrary shift [70]. As mentioned, in Reference [98], network-induced delays have been seen as a cause of degradation of performance of the system or possibly the cause for system instability. In Reference [118] authors proposed an algorithm based on the gradient push-sum method to solve the Electronic Data Processing (EDP) in a distributed manner over the communication networks with time-varying topologies and communication delays. This proposed algorithm is guaranteed to solve the EDP if the time-varying directed communication network is uniformly jointly strongly connected. There are some systems where the presence of communication delay may have a positive effect on the system performance as in Reference [119]. In Reference [151] authors proposed LMI approach to determine the two-mode-dependent static output feedback controller gains to compensate for the random network-induced delays efficiently and provide the desired control performance.

Table 7 shows the quantitative data for the delay range considered in the different studies carried out in the literature. The highest delay considered was 6 s [66].

Data-packet dropout is a vital issue, which is due to the defective transmission pathway. Limited bandwidth and bulk data transfer over one line are responsible for this defective transmission. Many studies have considered packet losses in the NCSs [41,63,69,75,88,92,94,109,113,114]. These issues often occur because of exchanging the data amongst the various devices, which degrades the performance and can destabilize the system. Due to traffic congestion, the data-packet loss is also a major concern. Mostly, the dropout effect is also known as a Bernoulli or Markov process. In most communication networks, different data packets suffer different delays, which produces a situation where a

data packet sent earlier may arrive at the destination later, or vice versa; see Figure 13 [46]. This phenomenon is referred to as data packet disorder. Table 8 shows the quantitative data of the packet loss rate considered in the different studies existing in the literature. The highest packet loss rate considered was 80% in Reference [63].


**Table 7.** Delay data considered in different studies.

**Reference Loss Rate/Loss Rate Range (in %)**

Security of NCSs is one in the various foremost challenges that is receiving much attention these days [123,130,132]. Any network is prone to interception, particularly the wireless networks. Hence, network security is usually involved. Attacks to the NCS (as shown in Figure 14) will be described in brief as: A1 and A3 symbolize deception attacks, where a person sends forged data from either the sensors or the controllers. The forged data consists of: faulty activity, like the incorrect time of activity or the incorrect sender id. The person will instigate these types of attacks by getting the key or by cooperating with some attacks on sensors (A1) or controllers (A3). Attacks A2 and A4 signifies Denial of Service (DoS) attacks, where the person is barred by the controller from attaining device measurements. To launch DoS attacks, the person jams the associated communication channels, negotiates the devices to stop, and attacks the routing protocols. Attack A5 symbolizes an on-the-spot attack against the actuators. So, attempts should be made to prevent the negotiation of the actuators and the other direct attacks against the physical system, for example, by securing the attacked-physical system, observation cameras, etc. In Reference [152], a new ETM is proposed, under which data packets could be actively dropped within consecutive steps, saving more communication resource than the existing ETM. Here, mainly the effect of DoS attacks obeying Bernoulli distribution is considered and analyzed. Figure 15 shows that the

[62] 0 to 80 [67] 26.39 [74] 25 to 31 [91] 25 [93] 10 [108] 30 to 70 [113] 20 to 40

**Figure 13.** Data packet dropouts/disorder in NCSs. **Figure 13.** Data packet dropouts/disorder in NCSs.

**Table 8.** Packet loss rate considered in different studies.

6.2.3. Network Security


**Table 8.** Packet loss rate considered in different studies.

#### 6.2.3. Network Security

Security of NCSs is one in the various foremost challenges that is receiving much attention these days [123,130,132]. Any network is prone to interception, particularly the wireless networks. Hence, network security is usually involved. Attacks to the NCS (as shown in Figure 14) will be described in brief as: A1 and A3 symbolize deception attacks, where a person sends forged data from either the sensors or the controllers. The forged data consists of: faulty activity, like the incorrect time of activity or the incorrect sender id. The person will instigate these types of attacks by getting the key or by cooperating with some attacks on sensors (A1) or controllers (A3). Attacks A2 and A4 signifies Denial of Service (DoS) attacks, where the person is barred by the controller from attaining device measurements. To launch DoS attacks, the person jams the associated communication channels, negotiates the devices to stop, and attacks the routing protocols. Attack A5 symbolizes an on-the-spot attack against the actuators. So, attempts should be made to prevent the negotiation of the actuators and the other direct attacks against the physical system, for example, by securing the attacked-physical system, observation cameras, etc. In Reference [152], a new ETM is proposed, under which data packets could be actively dropped within consecutive steps, saving more communication resource than the existing ETM. Here, mainly the effect of DoS attacks obeying Bernoulli distribution is considered and analyzed. Figure 15 shows that the numbers of security events have increased, which is reported by the industrial control systems (ICSs) cyber emergency response team. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 24 of 38 numbers of security events have increased, which is reported by the industrial control systems (ICSs) cyber emergency response team.

**Figure 14.** Cyber-attacks on NCSs. **Figure 14.** Cyber-attacks on NCSs.

**Figure 15.** Industrial control systems security incidents year by year.

2013 2014 2015 2016 2017 2018 2019 2020

**Years**

the NCSs are safer to operate [153].

6.2.4. Quantization

0

500

1000

**No. of incidents**

1500

2000

In Figure 15, it can be seen that in the beginning, the security incidents were on the rise, but there is a drastic decrease in the security incidents from 2017 to 2020 because of the protective measures taken and the development of advanced networked security approaches in NCSs. Advanced NCSs security techniques are being developed so that

In these systems, signals are typically quantified by a quantifier prior to sending over a communication network. A quantifier is the same as a nonlinear mapper that maps segments of real sets to completely diverse levels. The quantity of these levels is intimately joined for the flow of information between the physical plant and the filter. In step with the finite period of the word-quantization error, unit of measurement is ineluctable, that has negative effects on the NCS performance. For an NCS subject to quantization, associated random data-packet dropouts [74] were considered, where some relationship is disclosed between the magnitude of the quantization and datapacket dropout. For the NCS subject to finite-level quantization and dropouts in data

systems (ICSs) cyber emergency response team.

Physical System

A5

Controller

**Figure 14.** Cyber-attacks on NCSs.

A3 A2 A4

**Figure 15.** Industrial control systems security incidents year by year. **Figure 15.** Industrial control systems security incidents year by year.

In Figure 15, it can be seen that in the beginning, the security incidents were on the rise, but there is a drastic decrease in the security incidents from 2017 to 2020 because of the protective measures taken and the development of advanced networked security approaches in NCSs. Advanced NCSs security techniques are being developed so that In Figure 15, it can be seen that in the beginning, the security incidents were on the rise, but there is a drastic decrease in the security incidents from 2017 to 2020 because of the protective measures taken and the development of advanced networked security approaches in NCSs. Advanced NCSs security techniques are being developed so that the NCSs are safer to operate [153].

numbers of security events have increased, which is reported by the industrial control

A1

#### the NCSs are safer to operate [153]. 6.2.4. Quantization

6.2.4. Quantization In these systems, signals are typically quantified by a quantifier prior to sending over a communication network. A quantifier is the same as a nonlinear mapper that maps segments of real sets to completely diverse levels. The quantity of these levels is intimately joined for the flow of information between the physical plant and the filter. In step with the finite period of the word-quantization error, unit of measurement is ineluctable, that has negative effects on the NCS performance. For an NCS subject to quantization, associated random data-packet dropouts [74] were considered, where some relationship is disclosed between the magnitude of the quantization and datapacket dropout. For the NCS subject to finite-level quantization and dropouts in data In these systems, signals are typically quantified by a quantifier prior to sending over a communication network. A quantifier is the same as a nonlinear mapper that maps segments of real sets to completely diverse levels. The quantity of these levels is intimately joined for the flow of information between the physical plant and the filter. In step with the finite period of the word-quantization error, unit of measurement is ineluctable, that has negative effects on the NCS performance. For an NCS subject to quantization, associated random data-packet dropouts [74] were considered, where some relationship is disclosed between the magnitude of the quantization and data-packet dropout. For the NCS subject to finite-level quantization and dropouts in data packets, the results of the step-size quantifier and, additionally, the external variety of consecutive data-packet dropouts on the NCS attenuation level of disturbance are inspected [87]. An integrated generalized framework for the investigation and elegance of networked controlled systems is projected through an associated emulation-like approach that gives a distinct approach through the study of quantization effects on NCSs [75]. The uniform quantizer maps real-valued function to a finite number of quantization regions with arbitrary shape, as in Reference [106]. In Reference [154], the authors proposed a new quantization structure, and a mathematical treatment of this structure is given to illustrate the advantage for the quantization effects.

#### 6.2.5. Jitter

Jitter is generally defined as the distortion of a signal or image caused by poor synchronization. It is defined by the Institute of Electrical and Electronics Engineers (IEEE) [46] as "time-related, abrupt, spurious variations in the duration of any specified related interval", and it arises due to clock drift, branching in the code, scheduling, communication, and use of certain computer hardware structures, e.g., cache memory. Jitter can be classified into two types: delay jitter [156] and rate (sampling) jitter [157]. The goal of delay jitter is to minimize the difference between delay times of different packets. The goal of rate jitter is to minimize the difference between inter-arrive times [156].

#### **7. Practical Applications of NCS**

Apart from review of theoretical developments, many practical applications of NCS have been implemented to date. Some of the important areas of application of NCSs will be discussed briefly.

#### *7.1. Autonomous Mobile Robots/Controlled Networks*

For robots, the authority to perform and act dynamically is of vital importance. By itself, they comprise of mobile systems where the changes in environment activate changes in what purposes the system should convene the quality approach to structure the system, typically stated within the artificial intelligence literature because the behavior-based artificial intelligence framework [16,26,27]. Most plans are to spot completely different types of controllers and responses to sensory inputs, with desired mechanism performance. This practice of structuring the system into split behaviors, dedicated to playing bound responsibilities, has gained vital momentum in AI society. In Reference [158], implementation of a cloud service for remote control of a robotic manipulator is addressed, and an optimal control model restriction and control event-triggered communication are studied to be applied to a Robotic Manipulator as a Service. One more such example of the controlled network is the autonomous vehicular system designed by Toyota company called Prius, shown in Figure 16 [159]. This autonomous vehicular system consists of functions, such as automatic controlling the steering, acceleration, and brakes. This function is called Move-Box which is developed by Netherlands Organization for Applied Scientific Research. It functional system works as a line between the Peripheral Component Interface (PCI) extensions for Instrumentation (PXI) which is placed on the roof of vehicle. An eHorizon system designed by Continental company is proficient in controlling the vehicle by using Global Positioning System (GPS). *Sustainability* **2021**, *13*, x FOR PEER REVIEW 26 of 38

**Figure 16.** Components of autonomous vehicular system. **Figure 16.** Components of autonomous vehicular system.

#### *7.2. Power Systems and Smart Grids 7.2. Power Systems and Smart Grids*

Gradually proceeding to reliable information transmission to far-flung areas over Gradually proceeding to reliable information transmission to far-flung areas over communication networks, it is very difficult to reproduce the consequences of the commu-

communication system networks set up random variable time-delays and packetdropouts in the data being transmitted. There are so many approaches to check such type of communication systems, commonly known as NCS [60]. Intensive analysis persists in control system theory to model the consequences of data-packet delays and dropouts because of the transmission of sensor, as well as actuator, signals via a constrained communication network on desired system stability [39]. Power grids are amongst the biggest styles of systems that are made-up by the human. For performance and transient stability analysis functions, the facility network has to be studied as a full because of the extremely interactive nature of its parts. Another issue is that the growth of an influence network beside time that moves it aloof from its properly designed initial structure and causes degradation of performance, stability and dependableness. Supported by these facts, it is expected that a networked management theme is ready to realize a superior performance compared to the historically decentralized controllers

In Reference [95], a modern coordinated NCS framework is designed for grids to control distributed generation sources. Measurements of the system are being transmitted to the networked-controller through the above mentioned period of time communication system network. The consequences of data transmission delays and data-dropouts are because of the communication system network is sculptured. Because this modern communication system network has become vital for grids, future power

In Reference [155], a distributed supervisory strategy for load/frequency control problems in networked multi-area power systems is discussed. Coordination between the control center and the areas is accomplished via data networks subject to

Figure 17 shows the block diagram of networked control of smart grid [160]. The block "Power System" shows the open-loop power system which is to be controlled. To this effect, real-power deviations in some of the lines are measured in real-time using

that use solely the regionally measured info [104].

systems should be designed ready for instability.

communication latency, which is modeled by time-varying time-delay.

nication system in the situation of stability in power grids. These types of communication system networks set up random variable time-delays and packet-dropouts in the data being transmitted. There are so many approaches to check such type of communication systems, commonly known as NCS [60]. Intensive analysis persists in control system theory to model the consequences of data-packet delays and dropouts because of the transmission of sensor, as well as actuator, signals via a constrained communication network on desired system stability [39]. Power grids are amongst the biggest styles of systems that are made-up by the human. For performance and transient stability analysis functions, the facility network has to be studied as a full because of the extremely interactive nature of its parts. Another issue is that the growth of an influence network beside time that moves it aloof from its properly designed initial structure and causes degradation of performance, stability and dependableness. Supported by these facts, it is expected that a networked management theme is ready to realize a superior performance compared to the historically decentralized controllers that use solely the regionally measured info [104].

In Reference [95], a modern coordinated NCS framework is designed for grids to control distributed generation sources. Measurements of the system are being transmitted to the networked-controller through the above mentioned period of time communication system network. The consequences of data transmission delays and data-dropouts are because of the communication system network is sculptured. Because this modern communication system network has become vital for grids, future power systems should be designed ready for instability.

In Reference [155], a distributed supervisory strategy for load/frequency control problems in networked multi-area power systems is discussed. Coordination between the control center and the areas is accomplished via data networks subject to communication latency, which is modeled by time-varying time-delay.

Figure 17 shows the block diagram of networked control of smart grid [160]. The block "Power System" shows the open-loop power system which is to be controlled. To this effect, real-power deviations in some of the lines are measured in real-time using current transformers (CTs) and potential transformers (PTs), and represented by y(t) in the block diagram. They are sampled and sent over the communication network as discrete data-packets, y(k). User datagram protocol is used for packet transmission, and packet-loss occurs during transmission. The final data which is received at the control unit after packet loss is given by y'(k). The control unit consists of a LQG controller, which is a combination of a Kalman filter and a linear quadratic regulator (LQR). Kalman filter uses the reduced-power system model and the output data-packets arriving at the controller, y'(k), to estimate the states, x'(k). The state estimates are then multiplied by the LQR gain to produce the control signals, u(k), which are then sent with the help of communication network to the actuators.

#### *7.3. Manufacturing Systems*

With the growth in economic processes that specialize in high price with low volume, the producing system design is growing from ancient centralized model to the distributed model and then proceeds to the modern networked system/model. In present situations, the producing systems are designed as in a networked model framework with the help of networking communication systems which consist of the diverse collections of manufacturing devices. Such a type of modern networked producing system monitors and controls by provision of maximizing the standard of service provided by the prevailing manufacturing resources [83].

A typical Industrial Manufacturing Control System is shown in Figure 18 [161]. It consists of large number of control loops, Human-Machine Interface (HMIs), remote diagnostics section, sensors, and actuators, built on layered network architectures, with the help of networked layer. A control loop consists of sensors, actuators, and controllers to deploy certain controlled processes. A sensor is a device that produces a measurement of some physical property and then sends this information as controlled variables to the

controller. The controller interprets the signals and generates corresponding manipulated variables, based on a control algorithm and target set points, which it transmits to the actuators. Actuators are used to deploy the controlled processes based on the commands being received through the controller.

Although Radio-Frequency Identification (RFID) is widely used for the application of asset tracking, it requires a power supply for the operation. But, for some cases, where is no power supply available, such as monitoring the activities of the aircraft cabin's maintenance workers, wireless sensor networks (WSN) is the best choice for workers as it requires no power supply [83]. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 27 of 38

#### *7.4. Missiles* current transformers (CTs) and potential transformers (PTs), and represented by y(t) in

The system algorithms implementation in networks-on-chip is very helpful to address the varied problems with missile control systems, like power consumption, congestion management, and loss of data packets. Consideration of on-chip implementation of NCSs began to grow due to its potential in numerous applications; it conjointly provided several challenges for researchers to attain reliable and economical control. Moreover, the NCS has been analyzed for many years and has given rise to several necessary research topics in missile control systems [94]. With the progress in digital control systems, the data bus transmit scheme has secured more attention. However, communication networks inevitably introduce time delay. To compensate the time delay effects, an application of fuzzy controller to such a system was shown in Reference [162]. the block diagram. They are sampled and sent over the communication network as discrete data-packets, y(k). User datagram protocol is used for packet transmission, and packet-loss occurs during transmission. The final data which is received at the control unit after packet loss is given by y'(k). The control unit consists of a LQG controller, which is a combination of a Kalman filter and a linear quadratic regulator (LQR). Kalman filter uses the reduced-power system model and the output data-packets arriving at the controller, y'(k), to estimate the states, x'(k). The state estimates are then multiplied by the LQR gain to produce the control signals, u(k), which are then sent with the help of communication network to the actuators.

**Figure 17.** Layout of the networked control of the smart grid. **Figure 17.** Layout of the networked control of the smart grid.

With the growth in economic processes that specialize in high price with low volume, the producing system design is growing from ancient centralized model to the distributed model and then proceeds to the modern networked system/model. In present situations, the producing systems are designed as in a networked model framework with the help of networking communication systems which consist of the diverse collections of manufacturing devices. Such a type of modern networked

A typical Industrial Manufacturing Control System is shown in Figure 18 [161]. It consists of large number of control loops, Human-Machine Interface (HMIs), remote diagnostics section, sensors, and actuators, built on layered network architectures, with the help of networked layer. A control loop consists of sensors, actuators, and controllers to deploy certain controlled processes. A sensor is a device that produces a measurement of some physical property and then sends this information as controlled variables to the controller. The controller interprets the signals and generates corresponding manipulated variables, based on a control algorithm and target set points, which it transmits to the actuators. Actuators are used to deploy the controlled processes based

Although Radio-Frequency Identification (RFID) is widely used for the application of asset tracking, it requires a power supply for the operation. But, for some cases, where is no power supply available, such as monitoring the activities of the aircraft cabin's

*7.3. Manufacturing Systems*

on the commands being received through the controller.

service provided by the prevailing manufacturing resources [83].

it requires no power supply [83].

**Figure 18.** Industrial Manufacturing Control System. **Figure 18.** Industrial Manufacturing Control System.

#### *7.4. Missiles 7.5. UAVs*

*7.5. UAVs*

The system algorithms implementation in networks-on-chip is very helpful to address the varied problems with missile control systems, like power consumption, congestion management, and loss of data packets. Consideration of on-chip implementation of NCSs began to grow due to its potential in numerous applications; it conjointly provided several challenges for researchers to attain reliable and economical control. Moreover, the NCS has been analyzed for many years and has given rise to several necessary research topics in missile control systems [94]. With the progress in Today, unmanned aerial vehicles (UAVs) have become more and more well-liked in a wide field of applications. Though principally for military functions within the earlier period, it is noticed that there are various areas which may prove helpful [163]. For example, in the agriculture domain, they are applied in field observations or for chemical distributions. They patrol as a fireguard for forests or are used for traffic observation within the cities. They may also be used for automatic landscape photographing. They are terribly attention-grabbing, like in educational analysis, e.g., as flying laboratories, a workplace for control algorithms, or as an education gear for college scholars [63].

maintenance workers, wireless sensor networks (WSN) is the best choice for workers as

digital control systems, the data bus transmit scheme has secured more attention. However, communication networks inevitably introduce time delay. To compensate the time delay effects, an application of fuzzy controller to such a system was shown in Reference [162]. Figure 19 shows the diagram of an autonomous UAV. The block diagram consists of various control modules, sensors, actuators (valves, motors), communication modules, etc., which acts as a bridge between the remote access system and the UAV system. The remote control system can access the information, as well as send the useful commands to the UAV. The power available in the vehicle is calculated by the computing power module.

Today, unmanned aerial vehicles (UAVs) have become more and more well-liked in a wide field of applications. Though principally for military functions within the earlier

example, in the agriculture domain, they are applied in field observations or for

college scholars [63].

computing power module.

**Figure 19.** Flow diagram of autonomous unmanned aerial vehicles (UAV). **Figure 19.** Flow diagram of autonomous unmanned aerial vehicles (UAV).

#### *7.6. Quasi-Decentralized Control System 7.6. Quasi-Decentralized Control System*

In order to achieve robust stability for a wide range of power system operating conditions, there is a need to break the limit imposed by the decentralized controller structure by implementing a quasi-decentralized control structure. Figure 20 is a block In order to achieve robust stability for a wide range of power system operating conditions, there is a need to break the limit imposed by the decentralized controller structure by implementing a quasi-decentralized control structure. Figure 20 is a block diagram to represent such a scheme. Since time-synchronized phases of Alternating Current (AC) voltages and currents are essential for the coordinated control, synchronous sampling control units based on the Global Positioning System (GPS) are used for this purpose.

chemical distributions. They patrol as a fireguard for forests or are used for traffic observation within the cities. They may also be used for automatic landscape photographing. They are terribly attention-grabbing, like in educational analysis, e.g., as flying laboratories, a workplace for control algorithms, or as an education gear for

Figure 19 shows the diagram of an autonomous UAV. The block diagram consists of various control modules, sensors, actuators (valves, motors), communication modules, etc., which acts as a bridge between the remote access system and the UAV system. The remote control system can access the information, as well as send the useful commands to the UAV. The power available in the vehicle is calculated by the used for this purpose.

diagram to represent such a scheme. Since time-synchronized phases of Alternating Current (AC) voltages and currents are essential for the coordinated control, synchronous sampling control units based on the Global Positioning System (GPS) are

**Figure 20.** Quasi decentralized system for two synchronized plants. **Figure 20.** Quasi decentralized system for two synchronized plants.

#### *7.7. Cloud Computing*

*7.7. Cloud Computing* The cloud and networked control systems amalgamate the benefits of cloud computing technology, advanced theory of networked control system, and other recent developed wireless and communication-based approaches. Figure 21 represents the cloud computing-based NCS. This system consists of plants to be controlled, a gateway computer, the cloud, and the network. The cloud is equipped with a large quantity of computational and storage resources; however, the plants have restricted resources. The plants send the sensor data to the cloud through the available network, so that the The cloud and networked control systems amalgamate the benefits of cloud computing technology, advanced theory of networked control system, and other recent developed wireless and communication-based approaches. Figure 21 represents the cloud computingbased NCS. This system consists of plants to be controlled, a gateway computer, the cloud, and the network. The cloud is equipped with a large quantity of computational and storage resources; however, the plants have restricted resources. The plants send the sensor data to the cloud through the available network, so that the desired control signals can be evaluated by the cloud. These control signals are then sent back to the plants as the input of the actuator.

desired control signals can be evaluated by the cloud. These control signals are then sent back to the plants as the input of the actuator. In a large-scale networked control system, the bagged information consists of information captured by universal information-sensing mobile devices, sensory technologies related to aerials, such as remote sensing, cameras, microphones, RFIDs, and WSNs [164].

**Figure 21.** Cloud computing-based NCS. **Figure 21.** Cloud computing-based NCS.

#### **8. Concluding Remarks and Future Potentials**

In a large-scale networked control system, the bagged information consists of information captured by universal information-sensing mobile devices, sensory technologies related to aerials, such as remote sensing, cameras, microphones, RFIDs, and WSNs [164]. **8. Concluding Remarks and Future Potentials** The progress of NCSs can be termed as the steady progress which was based on evolution of computation and communication technology. The research of NCSs started with decentralized control systems, which later converged to several theories related to the stability analysis of NCSs. Then, many research papers discussed issues, such as sampling, quantization, and time delays. In a recent phase of NCSs development, some new topics, such as controller design for NCSs with event-triggered sampling and cyberattacks, have received a lot of attention. NCSs have also been implemented for many practical systems, like UAVs, power systems and smart grids, robots, missiles, and manufacturing systems. At present, the components are distributed over long distances, such as in a smart grid, teleoperation control system, etc. Conventional control cannot satisfy the latest challenges, so novel control structures are needed to resolve the newly-The progress of NCSs can be termed as the steady progress which was based on evolution of computation and communication technology. The research of NCSs started with decentralized control systems, which later converged to several theories related to the stability analysis of NCSs. Then, many research papers discussed issues, such as sampling, quantization, and time delays. In a recent phase of NCSs development, some new topics, such as controller design for NCSs with event-triggered sampling and cyber-attacks, have received a lot of attention. NCSs have also been implemented for many practical systems, like UAVs, power systems and smart grids, robots, missiles, and manufacturing systems. At present, the components are distributed over long distances, such as in a smart grid, teleoperation control system, etc. Conventional control cannot satisfy the latest challenges, so novel control structures are needed to resolve the newly-presented complex control systems. Even though a lot of advancement has been made in NCSs, their practical applications are very limited. Most of the research works dealt with simple-nodes and simple-system. Multi-sensors (or multi-nodes) and multi-system, in addition to coupling of numerous nodes or subsystems, should be considered in the future research. In accordance with the undeniable fact that the complex NCSs have characteristics of wide area, wide selection, and big data, we ought to combine the network control technology with the computer technology, the cloud storage technology, the data mining technology, and the

presented complex control systems. Even though a lot of advancement has been made in

wide-area measurement techniques in such a way that more effective control algorithms are developed. The research in NCSs has come a long way since its inception, but, in terms of real-time implementation, there is still a lot of scope. This is definitely going to be taken into account in further research problems.

**Author Contributions:** Research methodology, M.K.G., A.P., S.K.M., and B.A.; writing—original draft preparation, M.K.G., A.P., and S.K.M.; supervision, E.K., P.T., and N.B.; validation, B.A. and N.B.; writing—review and editing, M.K.G., B.A., N.B., P.T., and E.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was partially supported by the International Research Partnerships: Electrical Engineering Thai-French Research Center (EE-TFRC) between King Mongkut's University of Technology North Bangkok and University of Lorraine under Grant KMUTNB−BasicR−64−17.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**


## **References**


## *Article* **Unification of Edge Energy Grids for Empowering Small Energy Producers**

**Evangelos K. Markakis <sup>1</sup> , Yannis Nikoloudakis <sup>1</sup> , Kalliopi Lapidaki <sup>2</sup> , Konstantinos Fiorentzis <sup>1</sup> and Emmanuel Karapidakis 1,\***


**Abstract:** The current energy landscape is largely comprised of big stakeholders, who are often the monopolistic drivers of their local market. This fact does not leave any room for smaller players to participate in this procedure by contributing their part in the energy pool. Moreover, the dynamic demand for power along with the current power production rate are not corelated, rendering the power distribution grid, a best effort network, prone to power failures, due to the inevitable irregularities in demand. This paper introduces a novel concept that allows small energy producers, such as solar panel grids, to offer their production excess through an intelligent energy brokerage blockchainbased framework. The proposed framework ingests the vast amounts of bigdata stemming from the distributed smart energy grids smart metering and allows for automatic commercial transactions of power between the participants of a dedicated marketplace. Values dynamically fluctuate depending on the real-time offer and demand and the grid's state. Thus, all partaking stakeholders are able to take the most out of their product by leveraging the intelligence provided by the energy marketplace, and contribute to the overall stabilization of the energy grid.

**Keywords:** energy grids; energy producers; cold spinning reserve; DLT; brokerage; SMEs; energy optimisation

#### **1. Introduction**

The way we interact with our world around us in almost every aspect of our lives, from how we monitor our environment to how we power our homes and communities is revolutionized, through the collection of vast amounts of information, from a variety of heterogeneous Internet of Things (IoT) devices [1] and Energy net metering [2], which can help to evolve and transform the electric Grid optimization [3]. This information can have an immediate impact towards the improvement of our wellbeing, by providing unprecedented insights on the intelligent and proactive control [4] and monitoring of how power is delivered from a powerplant and used throughout our communities. In this respect, existing energy grids are tightly coupled with a vast network of smart devices and sensors, capable of generating enormous volumes of heterogenous data [5] (bigdata), daily. These data flows, which are difficult to manage and control, can be either dropped, or dismissed, or in some cases underutilized, thus minimizing their impact on benefiting energy grids' optimization. The processing of the collected data, due to its wide diversity, requires intelligent decision-support systems that must utilize current market trends, while also empowering energy distributors to optimize their grids. It is reported by the world economic forum that the deployment and installation of smart meters could generate between 30€ to 60€ [6] in annual savings per customer, raising this number to billions of Euros in total savings.

**Citation:** Markakis, E.K..; Nikoloudakis, Y.; Lapidaki, K.; Fiorentzis, K.; Karapidakis, E. Unification of Edge Energy Grids for Empowering Small Energy Producers. *Sustainability* **2021**, *13*, 8487. https:// doi.org/10.3390/su13158487

Academic Editor: Tomonobu Senjyu

Received: 27 May 2021 Accepted: 26 July 2021 Published: 29 July 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Current power systems consist of several Gensets (Electricity generators) for cold spinning reserve (ancillary services) [7,8], which are activated trough industrial networks [8] (Scada, PLCs, etc), in case of unexpected events (i.e., power disturbances or total failures) in the distribution grid. These units, along with Power Factor Correctors are capable of correcting reactive power (Q) in addition to active power production, both for on-premises issues, and even more for Neighbor or Total Line issues. Currently these gensets are off-line during any disturbance of the grid, thus not contributing to the system's stability optimal performance. This modus operandi leaves a huge room for improvement, through which both the owner/consumers of the units as well as the whole nearby distribution network can benefit, resulting to the overall enhancement of the power network, and reaching the required power quality.

Currently, the peak-load demand distribution [9] is never a straight line. This fact, apart from the disastrous results it can bring within the distribution lines, can also significantly raise the running costs of electric grids, and also impose. Being aware of this uneven distribution can help identify "cheaper" time-periods [10] of electricity production lifecycle the current energy market is not exploiting. Furthermore, the energy market is primarily comprised of large Power providers, who are leaving no room for Small and Medium-sized Enterprises (SMEs) [11], who are usually based on renewable energy sources, to take part in the power-production market. These small players are mostly "forced" to sell their produced energy to the large power distributors; thus, are abolishing any leverage they could have to influence the energy market. An optimized distributed ledger powered energy market where energy producers and distributors can buy and sell energy automatically, according to a set of criteria, defined by the stakeholders and influenced by the demand, or unexpected events (i.e., power failures in large geographical areas, or big sports events that increase the demand), could mitigate this imbalance. Utilizing public blockchain networks optimized for smart contracts (e.g., Ethereum blockchain [12]), will empower small power suppliers (i.e., solar panels) to securely record the excess power output on the block chain and sell it to large power distributors, or allow themselves to become large power distributors, while at the same time increase their revenue by omitting intermediaries.

In addition, the revolutionization of the smart cities and smart communities, integral part of which are the smart power grids, stems from the immerging ICT era, empowered by the 5G and the distributed Edge Computing paradigms. These immersive technologies introduce the concept of network technology "recycling" and unification [13] for creating a common access playground that can provide a variety of services to the end-users/clients or edge Supervisors (Neighbor based). The advancements of 5G and Edge Computing provide a "fertile" environment for enabling intelligent decision-making, where and when they are needed the most, at the source where the data flows of heterogeneous source are generated. At the same time, the combination of Edge Computing with energy in Hybrid approaches can enable total management in numerous fields. In this paper we present a novel unification of the edge that can be used for the optimization and the empowerment of small energy producers and the utilization of the data stemming from all energy producers and energy sensors of the network.

#### **2. System Description**

The system is based on the well-known three-layered architectural [14–16] approach, able to work cooperatively in every part of the grid Network. Starting from the "extreme edge" layer we have the data and energy generating layer that consists of all near-the-edge devices. These devices can be probes, sensors, smart meters, and monitoring devices that are creating an interconnected heterogeneous network of things, in a unified community. This enhancement is supported by an edge layer, which is able to interconnect communities in larger groups, creating clusters called "suburbs" that are able to monitor the power consumption of a specific area in real-time, and enable the smooth out-of-the-peak loaddemand distribution by enabling, in an automated manner, the cold spinning reserve (ancillary services) by the use of industrial networks (Scada, PLCs, etc). Finally, an energy

layer is introduced, which can unify and support "suburbs" to provide common energy resource-utilization and at the same time help in the necessary resource supplement management. The key idea is to partition the three-layer infrastructure, consisting of the extreme edge, the edge, and the energy layers into logical virtual networks whose membership can partially overlap with that of other Fog grids and to dynamically reshape this segmentation to ensure fine-grained management of the available resources. agement. The key idea is to partition the three-layer infrastructure, consisting of the extreme edge, the edge, and the energy layers into logical virtual networks whose membership can partially overlap with that of other Fog grids and to dynamically reshape this segmentation to ensure fine-grained management of the available resources. To achieve the above, we are borrowing the successful model of Distributed networks in a hybrid form, where a peer can be "primus inter pares". In this context we ena-

(ancillary services) by the use of industrial networks (Scada, PLCs, etc). Finally, an energy layer is introduced, which can unify and support "suburbs" to provide common energy resource-utilization and at the same time help in the necessary resource supplement man-

*Sustainability* **2021**, *13*, x FOR PEER REVIEW 3 of 9

To achieve the above, we are borrowing the successful model of Distributed networks in a hybrid form, where a peer can be "primus inter pares". In this context we enable two types of interconnected elements (Figure 1). The first type work as regular objects, named Edge Nodes (EN) and the latter are Enablers Edge Nodes (EEN). The achieved unification creates a community playground, SMEs can provide their produced power and translate into a digital energy unit, though a novel element named EnergyStore, which takes under consideration the power consumption and the market requests in power in real-time. Though the proposed system we bypass the "obligation" of small energy producers [17] to sell their produced energy to the large power distributors; thus, they partake in the common energy market as equals, directly competing with large power producers. Secondly, we introduce the dynamic cold spinning reserve in the total "suburb" peak load equation, which can efficiently support power-offloading and improve the peak load graph. Finally, we present a distributer ledger powered energy market, where energy producers and distributors can buy and sell energy automatically, according to a set of criteria defined by the stakeholders and influenced by the current market demand, and unexpected events throughout the grid (i.e., power failures in large geographical areas, or big sports events that increase the demand). An EN can be any end-device having at least some processing and communication capabilities that will allow us to deploy our solution on it and thus transform the device into a fully operational edge node. An EN interacts with its corresponding EEN, firstly to inform it about the device's available resources, and secondly to receive and carry out the assigned computational or/and networking tasks. ble two types of interconnected elements (Figure 1). The first type work as regular objects, named Edge Nodes (EN) and the latter are Enablers Edge Nodes (EEN). The achieved unification creates a community playground, SMEs can provide their produced power and translate into a digital energy unit, though a novel element named EnergyStore, which takes under consideration the power consumption and the market requests in power in real-time. Though the proposed system we bypass the "obligation" of small energy producers [17] to sell their produced energy to the large power distributors; thus, they partake in the common energy market as equals, directly competing with large power producers. Secondly, we introduce the dynamic cold spinning reserve in the total "suburb" peak load equation, which can efficiently support power-offloading and improve the peak load graph. Finally, we present a distributer ledger powered energy market, where energy producers and distributors can buy and sell energy automatically, according to a set of criteria defined by the stakeholders and influenced by the current market demand, and unexpected events throughout the grid (i.e., power failures in large geographical areas, or big sports events that increase the demand). An EN can be any enddevice having at least some processing and communication capabilities that will allow us to deploy our solution on it and thus transform the device into a fully operational edge node. An EN interacts with its corresponding EEN, firstly to inform it about the device's available resources, and secondly to receive and carry out the assigned computational or/and networking tasks.

**Figure 1.** High level architecture of the Energy Store. **Figure 1.** High level architecture of the Energy Store.

An EEN plays two roles within the proposed ecosystem, namely the role of the edge intra-supervisor and the role of the edge's envoy to the edge orchestrator. As an intrasupervisor, an EEN: (a) Oversees the formation of the extreme edge network by performing operations such as the (de)registering of extreme nodes; (b) queries the registered edge nodes about their state and their available resources; and (c) creates a logical topology of

the extreme and edge network along with a virtual pool of the ENs available resources. As an envoy, an EEN interacts with the edge orchestrator towards (a) (de)registering an extreme edge network to the edge overlay; (b) providing a "copy" of the EEN's virtual pool of resources and energy, therefore enabling edge orchestrator to have a clear image for the available energy resources across the whole ecosystem; and (c) mediating between orchestrator and ENs for reserving resources, assigning energy tasks or even deploying cold-spinning elements. Following hybrid Peer to Peer (P2P) paradigm, an EEN is selected from the currently running ENs taking into account several attributes like energy production, energy consumption element, computation processing and power level/type, etc. Recognizing that the unrestrained membership of Edge nodes in the selection process could pose security threats, we are providing a Security as a Service (SaaS) tool that can provide the means for "screening" the candidates list based on the stakeholder's policies. The EEN is elected from the existing ENs; it manages ENs and it is the point of contact to the orchestrator.

#### **3. Energy Store**

Energy Store is itself a distributed system following the decentralization and digitalization trends [18]. This toolset will deal with energy monitoring of the edge deployment including sensors, actuators, devices, gateways, and the software deployed at the edge. Additionally, it will provide the needed services to provide updates triggered by the system administrator or by the users using the Service Store. The Store subsystem of the proposed platform allows for optional or third-party software installation to the edge system, in a plug-n-play manner.

The edge layer will facilitate the software components and PaaS capabilities that will allow third-party systems to safely integrate into the platform. The toolset provides a set of services that enable the energy monitoring of legacy subsystems as well as the integration of services that connect the legacy systems to the rest of the platform. This toolset will leverage existing services to facilitate the deployment of new services and updates.

#### **4. Brokering Ability**

In this section we introduce the brokerage module that lives inside the Energy Store that acquires all energy sources and brokers them focusing on achieving revenue for all energy producers. The ability to interconnect and unify the production of multiple energy producers provides multiple new revenue streams with the ability to create tailored products (e.g.," green contracts" from only "green" energy producers). The brokerage system performs various functionalities, namely discovery, integration, aggregation, customization, quality assurance and optimization.

Discovery deals with the identification and selection of existing energy services to allow the creation of user-tailored contracts. This functionality allows the Energy Store to list all energy offerings from different providers, where end-users can directly compare similar energy services, their ratings, and other relevant features.

Integration is related to the provision of energy-based environment in order to integrate separate energy systems. The integration aims at either facilitating power exchange between separate systems or realizing collaborative business processes within the existing energy systems.

Aggregation concerns the provision of energy services that comprise multiple thirdparty energy producers. An aggregated energy service may allow users to interact with the interfaces of the third-party services directly (for instance, through a smart-meter interface), or indirectly, through a common interface that encapsulates the individual services and possibly add common functionality such as cold-spinning reserve, coupling capacitors and capacitor dividers.

Customization enables the implementation of new functionalities to enrich the offered energy services, by means of extension rather than modification of that services' implementation e.g., include only "green" energy sources.

Quality assurance ensures that one or more energy services achieve specific quality expectations. This can be performed by service testing, policy enforcement, SLA monitoring, and possibly by self-management mechanisms triggered, to restore service quality. Quality assurance ensures that one or more energy services achieve specific quality expectations. This can be performed by service testing, policy enforcement, SLA monitoring, and possibly by self-management mechanisms triggered, to restore service quality.

interface), or indirectly, through a common interface that encapsulates the individual services and possibly add common functionality such as cold-spinning reserve, coupling ca-

Customization enables the implementation of new functionalities to enrich the offered energy services, by means of extension rather than modification of that services'

Optimization enables the opportunistic improvement of the consumption or provisioning of an energy service with respect to various criteria, such as cost, functionality, or performance. Optimization enables the opportunistic improvement of the consumption or provisioning of an energy service with respect to various criteria, such as cost, functionality, or performance.

The overall architecture of the brokerage module is depicted in Figure 2. The overall architecture of the brokerage module is depicted in Figure 2.

*Sustainability* **2021**, *13*, x FOR PEER REVIEW 5 of 9

implementation e.g., include only "green" energy sources.

pacitors and capacitor dividers.

**Figure 2.** Brokerage module internal architecture. **Figure 2.** Brokerage module internal architecture.

It consists of five main modules that are used in various interactions, as shown in the Figure above: It consists of five main modules that are used in various interactions, as shown in the Figure above:

• Energy Discovery Module • Energy Discovery Module

This module retrieves all the available and tradable energy units from the small energy grids. This module retrieves all the available and tradable energy units from the small energy grids.

• Smart Filtering Module • Smart Filtering Module

This module applies a smart filtering to the list of the available energy services, based on the users' preferences and the SLA parameters. This module applies a smart filtering to the list of the available energy services, based on the users' preferences and the SLA parameters.

• Trading Module • Trading Module

This module provides all the interaction between the service provider and the function providers. The Trading module is used for requesting a new trade/offer from the Energy Providers (EP). This module provides all the interaction between the service provider and the function providers. The Trading module is used for requesting a new trade/offer from the Energy Providers (EP).

• Energy Contract Advertise Module • Energy Contract Advertise Module

This module is responsible for the advertisement/return of all tradable Energy Services to the EPs.

• Accepted Offers DLT

This module is responsible for updating the distributed Ledger for the accepted offers in order to be available for the accounting module for billing purposes and provide transparent transactions to all involved parties.

According to the proposed mechanism, the EP browse the offerings from the energy contracts' catalogue that match its requirements. If the requested function supports Brokering/Trading, the internal modules will try to fulfil the criteria set by the EP. Furthermore, the brokerage module initiates the appropriate bid/trading policies according to the EP's request in collaboration with the Energy Discovery module.

The high-level architecture of the brokerage module along with the interaction inside the Marketplace is described below and depicted above in the high-level architecture of the brokerage module along with the interaction inside the Marketplace.


According to the trading process (i.e., auction-based algorithm in XX), the Energy brokerage module determines the optimal allocation solution, considering the maximization of Energy Provider's income. Consequently, the brokerage module undertakes the trading procedure that collects bids from Energy Producers (EPRs), in order to lease the produced power to the energy customers, through the EP. The brokerage module computes the assigning solution through this mechanism together with price and SLA per service.

#### *4.1. Infrastructure Cost of Brokering*

Infrastructure costs are calculated with the use of the algorithm described below Algorithm 1. The overhead lines cost OL\_cost, underground and subsea cables (US\_Cost), onshore AC substation Cost (OAS\_Cost) and the HVDC converter stations and Transformer's cost (HVDCCT\_COST) are calculated based on the prices stemming from various Energy Infrastructure providers on the internet [18]. Furthermore, when the auction-based algorithm is followed, the sellers (i.e., EPRs) that are denoted as S = {1, 2, . . . , s}, lease the Energy Services, denoted as V = {1, 2, . . . , v}, to b = 1 buyers (EPs). The EP is able to buy/lease Energy Services, denoted as xv for a specific time period ti, by reporting a price P(b) = {xv, ti} (i.e., bid price of Energy Services considering specific requirements), while the EPRs lease Energy Services yv, providing a function cost fv, for a specific time ti and with a specific SLA Lv, by reporting a price P(S) = {fv, yv, ti, Lv} (i.e., asking price of Energy Services considering specific requirements). Finally, the pair (b,v) in the pseudo-code bellow represents possible combinations of solutions, regarding "v" Energy Service to EP. In case EP benefit must be maximized, an optimization problem is formulated as follows, based on linear programming, i.e., the following equation:

$$\max \text{ : } \sum\_{s=1}^{s} (|P(b) - P(S)|) \tag{1}$$


In this respect and to facilitate competition among Function Providers (EPRs) a novel brokerage platform is designed that will allow (i) the customers to search for available offerings, (ii) auctioning between the third-party function developers (EPRs) and the EP, in order to find the best price for the Energy Services that will be part of each Energy Contract.

Furthermore, while the provision of Energy Services encompasses several system functionalities, Energy Service trading can be regarded as one part of the process that deals with the economic aspects. The trading process determines all the issues related with Energy Services selling and buying (e.g., direct trading between service provider and function provider or via a brokerage module), while pricing is a major issue that determines the value (or worth) of the Energy Services to the service provider and the function provider.

Another issue is the competition/cooperation among function and service providers, as well as customers involved in Energy Services trading. Depending on the Energy Services trading model, the Energy Service access may require permission through the cooperation of service provider and function provider, through a payment process. To determine the optimal network function provision during the trading process, optimization and decision theory techniques can be used.

#### *4.2. Brokering with an Energy Blockchain*

The blockchain is a distributed ledger recording the events of all Power producers that generate data, processing and sharing. It is composed of a growing number of blocks. In our Broker, each block contains one or more events identified by event hash. An event hash is computed by hashing the event content, as the event fingerprint. A block also has a block header, which contains (shown in figure down):


The cascaded hash computing at the event level (event hash), the block level (root), and the chain level (block hash) ensures the content immutability of a blockchain. If someone wants to modify the block information, he/she has to modify the entire chain. Yet, any tampering with the content can be easily detected by re-generating the hash codes and comparing them with the original ones.

In our Brokerage model, the blockchain service manages the immutable information of energy data. Two types of events are recorded on a blockchain: Energy generation event and session creation event.

Energy Generation Event. An energy generation event is created when an energy record file or a cold spinning reserve is requested to be started. It contains overhead lines cost OL\_cost, underground and subsea cables (US\_Cost), onshore AC substation Cost (OAS\_Cost) and the HVDC converter stations and Transformers cost (HVDCCT\_COST), signature, event type, last chunk location in chain, etc.

Session Creation Event. A session creation event is created when a Energy consumer takes an action in the system. It contains the start time, end time, public key of the provider and the requester for identifying the session participants, as well as the signature.

The operation of the proposed engine will be based on pioneering mathematical models (e.g., game theory) for analyzing, compiling, combining, and correlating all related information and data from different levels patterns and contexts in a privacy-aware manner. These techniques will provide the basis required for supporting the processing and storage of Energy contracts gathered from various sources in a unified structure in order to discover the relationships between Energy producers and Energy consumers along with the timeline of the contract, including a map of affected power producers and a set of meaningful chain of contract.

#### **5. Conclusions**

This paper introduces a novel concept that allows small energy producers, such as solar panel grids, to offer their production excess through an intelligent energy brokerage blockchain-based framework. These units, along with Power Factor Correctors (ancillary services) are capable of correcting reactive power (Q) in addition to active power production, both for on-premises issues, and even more for Neighbor or Total Line issues. Currently these gensets are off-line during any disturbance of the grid, thus not contributing to the system's stability optimal performance. This modus operandi leaves a huge room for improvement, through which both the owner/consumers of the units as well as the whole nearby distribution network can benefit, resulting to the overall enhancement of the power network, and reaching the required power quality. Additionally, the utilization of the small energy producers in the optimization equation along with the ability to commonly contribute to the energy grid provides a new approach of operation. In this paper we describe a novel framework that ingests the vast amounts of bigdata stemming from the distributed smart energy grids though the net metering and allows for automatic commercial transactions of power between the participants of a dedicated marketplace. Values dynamically fluctuate depending on the real-time offer and demand and the grid's state. Thus, all partaking stakeholders are able to take the most out of their product, by leveraging the intelligence provided by the energy marketplace, and contribute to the overall stabilization of the energy grid.

**Author Contributions:** Conceptualization, E.K.M.; methodology, E.K.M.; validation, K.L., Y.N., K.F.; formal analysis, E.K.M.; writing—original draft preparation, E.K.M., Y.N., K.L.; writing—review and editing, E.K.M., Y.N., K.L., K.F. and E.K.; supervision, E.K.M. and E.K.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


## *Article* **New Decentralized Control of Mesh AC Microgrids: Study, Stability, and Robustness Analysis**

**Youssef Hennane 1,2,\*, Abdelmajid Berdai <sup>2</sup> , Jean-Philippe Martin <sup>1</sup> , Serge Pierfederici <sup>1</sup> and Farid Meibody-Tabar <sup>1</sup>**


**Abstract:** In this paper, we investigated the power sharing issues in mesh islanded microgrids that contain several distributed generators (DGs) and loads connected to different points of common coupling (PCC). Firstly, an improved decentralized droop control algorithm is proposed to achieve the active and reactive power sharing of different DGs in reconfigurable mesh islanded microgrids. Accurate power sharing was obtained even though line parameters or the mesh microgrid configuration were unknown. Secondly a state-space model of the whole mesh microgrid was developed, considering several generators with their decentralized controllers, line feeders, and dynamic loads. This model was used to design parameters of droop controllers, to study the asymptotic stability and the robustness properties of the system. All strategies and analyses were validated by simulation based on the generic microgrid detailed in the standard IEEE 9bus test feeder.

**Keywords:** droop control; mesh microgrids; power sharing; synchronization; system stability; robustness analysis; constant power load; reconfiguration

#### **1. Introduction**

Microgrids are able to integrate different distributed generator (DG) systems converting different types of renewable energy and to supply different types of loads. This gives a certain level of independence, allowing them to be connected or disconnected from the main grid. One of the challenges is to synchronize and connect all the distributed generators to an islanded microgrid, while providing the "plug and play" functionality and respecting the active and reactive power sharing between the different distributed generation units (DGs) [1,2]. Currently, the most used methods for power sharing and synchronization in literature are based on the droop control strategy [3–8]. However, most of the microgrids considered in these research works have only a single point of common coupling (PCC), which are connected to all DGs through converters and the loads like in Figure 1. In order to level up the independence of microgrids from the main grid by increasing the penetration rate of distributed generators in microgrids, the choice of mesh multi-PCC microgrids seems to be a good solution. However, the intermittency of renewable energy may cause more instability problems in mesh microgrids due to their higher level of complexity compared to microgrids with single points of common coupling.

**Citation:** Hennane, Y.; Berdai, A.; Martin, J.-P.; Pierfederici, S.; Meibody-Tabar, F. New Decentralized Control of Mesh AC Microgrids: Study, Stability, and Robustness Analysis. *Sustainability* **2021**, *13*, 2243. https://doi.org/10.3390/su13042243

Academic Editors: Tomonobu Senjyu and Mousa Marzband

Received: 30 December 2020 Accepted: 14 February 2021 Published: 19 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

different frequency components by observing the dynamic behavior of different state variables. The analysis of the system stability was then performed by observing the evolution of the system eigenvalues with respect to droop parameters and different load power variations. It will be shown that the system stability may be affected due to unadapted droop

The established state-model was also used to verify the robustness of the considered mesh microgrid, including the new droop-control that ensured active and reactive power sharing to the modifications caused by the connection of DGs and large load variations

To summarize, the main points of this paper are, firstly, the development of a new droop control strategy for power sharing especially reactive power in mesh islanded microgrids. Unlike in the solutions mostly used by authors for power sharing in reconfigurable mesh microgrids, this modified droop control strategy is decentralized, which means that it does not require any sort of communication between the DGs connected to the microgrids. Thanks to the non-linear term added to the classical droop control, the power coupling phenomenon created by the line impedances and the change in the microgrid configuration is removed. The modified droop control strategy was proven efficient for active and reactive power sharing in different microgrid structures. Additionally, a fast and efficient synchronization strategy did not affect the power sharing. The second major point is the development and validation of a state-space model describing the mesh microgrid and its control. This state-space model was used to study the microgrid stability especially in the presence of active loads such as CPLs. The state model was also used to test the robustness of the modified droop control under different microgrid configurations and different states of charge. The validated state-space model made the manipulation of the system so much easier and allowed many more studies to be carried out on the meshed microgrid. For example, one of many scenarios where the state-space model can be useful is when the CPL-injected power in the microgrid increases, and the state model can easily predict the right value of the capacitor that should be added to the PCC where the CPL is

control parameters and/or CPL levels.

(changes in network configuration).

veloped and validated state-space model.

**Figure 1.** Microgrid with one point of common coupling (PCC). **Figure 1.** Microgrid with one point of common coupling (PCC).

**2. Power Sharing and Synchronization Strategies in Mesh Microgrids** *2.1. Power Sharing Using Droop Control Strategies* The traditional droop strategy imposing the electrical pulsation and the RMS voltage of a distributed generator via Equations (1) and (2) is efficient in microgrids with a single PCC shown in Figure 1, only if the effect of power line impedance is ignored [4]. ω = ω − m(P − P), (1) In mesh multi-PCC reconfigurable microgrids, with many distributed generation sources (DGs) and loads randomly connected to different PCCs, classical synchronization methods and power sharing strategies based on droop control and used in mono-PCC microgrids are less efficient. Indeed, most droop methods assume that the transmission lines are purely inductive or resistive in nature which leads to a linear droop characteristic where active power sharing depends on either frequency or voltage magnitude. However, in microgrids with reconfigurable structure, the sources as well as the networks may become redundant. The changes in the network impedance whenever a branch or source is disconnected in a microgrid means that the active and reactive power cannot be totally decoupled. These changes affect the power sharing among the sources and reduce the stability of the microgrid for any disturbance [9,10].

> Much research has focused on solutions that concern the active and reactive power sharing in droop-controlled mesh microgrids [11,12] either by using virtual impedance correction loop and a convergence acceleration strategy to compensate the offset created by the power line impedances and improve the reactive power sharing such as in ref [11], or by adopting a voltage compensation strategy to keep the bus voltage stable at the rated value and improve the reactive power sharing such as in ref [12]. However, only a few studies have focused on active and reactive power sharing in reconfigurable mesh microgrids such as in ref [10], where the authors propose the use of L1 adaptive methods for stable operation of a microgrid with wide range of R/X ratios.

> Another problem is the possible unstable behavior of the microgrid caused by the interaction between the DGs and loads as well as the changes in the network configuration. The system stability depends on the type of loads being connected to the microgrid, especially the ones supplied through tightly regulated power converters. These loads behave as constant power loads (CPL) and may cause system instability [13–15]. In the literature, the main studies are based on linearization techniques [16]. The non-linear models of the considered power systems are linearized around an operating point and then studied using linear analysis tools. Moreover, linearization tools only predict the stability of the system for small perturbations [17,18] and cannot guarantee the system stability for large perturbations.

> In this paper, a mesh microgrid constituting several PCCs connected to two DGs (DG1 with a nominal power of three megawatts and DG2 with a nominal power of two megawatts) through two transformers (6 kV/20 kV) as well as three loads (LOAD1 with a nominal power of one megawatt, LOAD2 with a nominal power of 1.2 megawatts, and LOAD3 with a nominal power of 1.5 megawatts) are considered. The different PCCs are interconnected with power supply lines, modeled by resistance, inductance and capacitance (RLC) circuits inspired by an IEEE 9-bus test feeder (Figure 2). All the microgrid data are presented in Tables 1 and 2.

With: m =

classical droop.

∆<sup>ഘ</sup> 

, n =

∆ಶ ொ

and ൝

In the absence of information on E the coefficient *J* is set to 0 and we return to the

**Figure 2.** IEEE 9 bus test feeder **Figure 2.** IEEE 9 bus test feeder. .

**Table 1.** Parameters of the considered microgrid power lines.


ω = ω<sup>୬</sup> − m(P −P), (6)

ܧ = ܧ<sup>୬</sup> − n൫Q − Q൯ − J(P −P), (7)

ݐ݀ߝ ∫ Kூ = J

 ா

− 1ቁ −ቀ

୕ ୕

− 1ቁ]

, (8)

ቀ− = [ߝ

**Table 2.** Sources and load powers.


In order to ensure an accurate power sharing and to provide the "plug and play" function adapted to the considered multi-PCC mesh microgrid, a new droop control and synchronization strategies is applied, such as the one demonstrated in ref [19]. This new droop control in islanded mode consists of removing the decoupling between the

active and reactive power caused by the line impedances and the change in the microgrid configuration. The first DG connected to the microgrid imposes its voltage and frequency. For other DGs, an adapted synchronization strategy is proposed and applied before their interconnection to the microgrid. The simulation results using a model developed in the Simscape feature of MATLAB/Simulink environment enabled the validation of the efficiency of this new droop control.

To study the stability of the microgrid, a state model of the entire meshed microgrid was developed considering its power lines and loads including a CPL as well as its generators, with their decentralized controllers integrating modified droop algorithms. The comparison of the results obtained from the stablished state model and the developed model in Simscape environment confirm the validity of the proposed microgrid state model. This validated state model was then used to study the microgrid stability by calculating its Jacobean matrix and its eigenvalues at each operating point. Based on these results, the root locus, and eigenvalues sensitivity analysis, depending on the parameters of the established model, were performed. The latter made it possible to find the origin of different frequency components by observing the dynamic behavior of different state variables. The analysis of the system stability was then performed by observing the evolution of the system eigenvalues with respect to droop parameters and different load power variations. It will be shown that the system stability may be affected due to unadapted droop control parameters and/or CPL levels.

The established state-model was also used to verify the robustness of the considered mesh microgrid, including the new droop-control that ensured active and reactive power sharing to the modifications caused by the connection of DGs and large load variations (changes in network configuration).

To summarize, the main points of this paper are, firstly, the development of a new droop control strategy for power sharing especially reactive power in mesh islanded microgrids. Unlike in the solutions mostly used by authors for power sharing in reconfigurable mesh microgrids, this modified droop control strategy is decentralized, which means that it does not require any sort of communication between the DGs connected to the microgrids. Thanks to the non-linear term added to the classical droop control, the power coupling phenomenon created by the line impedances and the change in the microgrid configuration is removed. The modified droop control strategy was proven efficient for active and reactive power sharing in different microgrid structures. Additionally, a fast and efficient synchronization strategy did not affect the power sharing. The second major point is the development and validation of a state-space model describing the mesh microgrid and its control. This state-space model was used to study the microgrid stability especially in the presence of active loads such as CPLs. The state model was also used to test the robustness of the modified droop control under different microgrid configurations and different states of charge. The validated state-space model made the manipulation of the system so much easier and allowed many more studies to be carried out on the meshed microgrid. For example, one of many scenarios where the state-space model can be useful is when the CPL-injected power in the microgrid increases, and the state model can easily predict the right value of the capacitor that should be added to the PCC where the CPL is also connected. This means that many future studies can be conducted based on this developed and validated state-space model.

#### **2. Power Sharing and Synchronization Strategies in Mesh Microgrids**

#### *2.1. Power Sharing Using Droop Control Strategies*

The traditional droop strategy imposing the electrical pulsation and the RMS voltage of a distributed generator via Equations (1) and (2) is efficient in microgrids with a single PCC shown in Figure 1, only if the effect of power line impedance is ignored [4].

$$
\omega\_{\rm i} = \omega\_{\rm n} - m\_{\rm i}(P\_{\rm i} - P\_{\rm in}),
\tag{1}
$$

$$E\_i = \ \ E\_n - \ n\_i (Q\_i - Q\_{in}) \tag{2}$$

$$\text{With}:\ m\_{l} = \left. \frac{\Delta\_{\omega}}{P\_{\text{in}}} \right. \left. n\_{l} = \frac{\Delta\_{E}}{Q\_{\text{in}}} \right.$$

where *P<sup>i</sup>* and *Q<sup>i</sup>* are the measured values of the active and reactive power of the *i*th DG, *Pin* and *Qin* are their nominal values, *ω<sup>n</sup>* and *E<sup>n</sup>* are the nominal values of the pulsation and voltage of the *i*th DG, ∆*<sup>ω</sup>* and ∆*<sup>E</sup>* are the permissible variations of pulsation and voltage, and *m<sup>i</sup>* and *n<sup>i</sup>* are the droop control coefficients. The active and reactive power sharing method is based on a droop control algorithm that sets the frequency and voltage amplitude at the associated PCC for each DG according to Equations (1) and (2).

This droop control does not ensure efficient reactive power sharing even in single PCC micro-grids due to the line impedances. A droop control strategy that has been proven effective for active and reactive power sharing in mono-PCC microgrids (3) and (4) was applied to the complex mesh microgrid in Figure 2, and considering one of the PCC voltages as reference potential of the studied microgrid. The simulation results are presented in Figures 3 and 4.

$$\delta\_{\dot{i}} = \int \left( \mathcal{K}\_a (\delta\_{\dot{m}} - \delta\_{\mathcal{L}}) - m\_{\dot{i}} (P\_{\dot{i}} - P\_{\dot{m}}) \right) dt,\tag{3}$$

$$\mathbf{E}\_{i} = \int \left( \mathbf{K}\_{\mathbf{e}} (\mathbf{E}\_{\text{int}} - \mathbf{E}\_{L}) - n\_{i} (\mathbf{Q}\_{i} - \mathbf{Q}\_{\text{int}}) \right) dt,\tag{4}$$

**Figure 3.** Evolution of the distributed generator (DG) active (**a**) and reactive (**b**) powers (first DG supplies the microgrid up to 5 s, the second DG is connected to the microgrid at 5 s). **Figure 3.** Evolution of the distributed generator (DG) active (**a**) and reactive (**b**) powers (first DG supplies the microgrid up to 5 s, the second DG is connected to the microgrid at 5 s).

To prove the efficiency of the proposed synchronization and power sharing strategies, the mesh microgrid in Figure 2 is modeled using the Simscape toolbox of Matlab/Simulink. Source 1 and Source 2 of Figure 2 are modeled by two controllable voltage sources shown in Figure 4, connected to two different PCCs and controlled by ܧ, which was generated using the modified droop strategy described by Equations (9) and (10), a power calculation bloc, a power filter, park transform and inverse park transform, as explained in the equivalent synoptic diagram describing a droop-controlled DGi in Figure 5. The main microgrid parameters are listed in Table 1. The powers of sources and

ܤ൧)ܧ − ீܧ)∫ ܭൣ − ൯P − ൫P

, (9)

, (10)

age droop control, Equation (10). **Figure 4.** Scheme of the controllable voltage sources DG1 and DG2.

**Figure 4.** Scheme of the controllable voltage sources DG1 and DG2.

**Figure 5.** Equivalent synoptic diagram describing a droop-controlled DGi.

**Lines Resistance (Ω) Inductance (mH) capacitance (µF) Points of connections** Line 1 0.63 7.14 205 Bus 8–Bus 7 Line 2 2.55 11.4 230 Bus 5–Bus 7 Line 3 0.63 7.14 205 Bus 8–Bus 9 Line 4 2 7 180 Bus 9–Bus 6 Line 5 1.7 7.6 153.4 Bus 4–Bus 5 Line 6 1.7 7.6 153.4 Bus 4–Bus 6

**Table 1.** Parameters of the considered microgrid power lines.

ܧ = ܧ<sup>୬</sup> − n ቀQ − Qቁ− J

loads are listed in Table 2.

The proposed angular droop aims to indirectly control the voltage at the PCC and its phase to be equal to the nominal values (i.e., *Ein* and *δin*). The added integrators can minimize the static error between the feedback signal and the corresponding nominal values. By choosing identical *K<sup>a</sup>* and *K<sup>e</sup>* for each generator, an accurate active and reactive power sharing is achieved which no longer depends on the system impedance and is unaffected by the digital errors and disturbances [9].

In practice, real microgrids can have several PCCs, interconnected by several supply lines with non-negligible impedances. In order to study such a microgrid, a slightly modified IEEE 9bus test feeder is considered, composed of two DGs and three loads, interconnected by RLC lines (Figure 2). It can be noticed that the application of the droop method, based on Equations (3) and (4), on the multi-PCC microgrid of Figure 2 leads to a perfect active power sharing when the second DG is connected at 5 s (Figure 3a). However, the reactive power sharing when the second DG is connected is not achieved (Figure 3b). It can also be remarked that unacceptable disturbing active and reactive power peaks occur due to the lack of synchronization (Figure 3a,b at 5 s).

In mesh microgrids, each line, connecting the *i*th PCC to the *j*th, has a non-negligible inductance (*λi*,*<sup>j</sup>* ) and resistance (*ρi*,*<sup>j</sup>* ), leading to a line voltage drop between these two PCCs that creates a coupling between the active power (*Pi*,*<sup>j</sup>* ) and reactive power (*Qi*,*<sup>j</sup>* ) exchanged between *i*th and *j*th PCCs, according to Equation (5):

$$
\Delta E = \rho\_{i,j} I\_{i,j} \cos \varphi + j \lambda\_{i,j} \omega I\_{i,j} \sin \varphi = \frac{\rho\_{i,j} P\_{i,j} + j \lambda\_{i,j} Q\_{i,j}}{E\_i} \tag{5}
$$

where *ϕ* is the phase shift between the phase voltage *E<sup>j</sup>* and the phase current *Ii*,*<sup>j</sup>* .

To achieve an efficient reactive power sharing in this type of mesh microgrids, the voltage equation in (2) is modified by adding a decoupling term (see Equation (7)) removing the coupling phenomenon between active and reactive power [12]. This coefficient, called *Ji* , is estimated using a PI controller, forcing the suppression of the error *ε<sup>i</sup>* defined in Equation (8). In steady state, when the error *ε<sup>i</sup>* tends to zero, the reactive power sharing is well ensured between the DGs. This approach allows the primary control of the voltage of the *i*th DG, regardless of the operating point of the loads. It should be noted that *Ere f* in Equation (8) is the measured value of one of the PCC voltages of the studied mesh microgrid acting as the pilot node and considered as its reference potential. The rated voltage of this pilot node is called *En*.

$$
\omega\_{\rm i} = \omega\_n - m\_{\rm i} \left( P\_{f\rm i} - P\_{\rm in} \right) \tag{6}
$$

$$E\_i = \ E\_n - n\_i \left( Q\_{fi} - Q\_{in} \right) - f\_i \left( P\_{fi} - P\_{in} \right) \tag{7}$$

$$\text{With}: \ m\_{i} = \frac{\Delta\_{\omega}}{P\_{in}}, \ n\_{i} = \frac{\Delta\_{E}}{Q\_{in}} \text{ and } \left\{ \begin{array}{c} \mathbf{J}\_{i} = \mathbf{K}\_{I} \int \varepsilon\_{i} dt \\\ \varepsilon\_{i} = \left[ -\left(\frac{\mathbf{E}\_{\text{ref}}}{\mathbf{E}\_{\text{n}}} - 1\right) - \left(\frac{\mathbf{Q}\_{i}}{\mathbf{Q}\_{\text{in}}} - 1\right) \right] \end{array} \right. \tag{8}$$

In the absence of information on *Ere f* the coefficient *J* is set to 0 and we return to the classical droop.

#### *2.2. Synchronization Strategy in Mesh Islanded Microgrid*

Due to the complexity of the mesh microgrids and the intermittency of renewable energies, DGs frequently connect to and disconnect from the microgrid, so a fast and efficient synchronization method is required. To achieve the synchronization of the *i*th DG to the *i*th PCC before their interconnection, the voltage amplitude *Epcci*, the pulsation *ωpcci* and the phase θ*pcci* of the *i*th PCC must be approximately equal to those of the *i*th DG (*EDGi*, *ωDGi*, θ*DGi*) [2]. To achieve this objective, the errors between the amplitudes, pulsations, and phases of both sides (the *i*th DG and the *i*th PCC) are forced to zero by adding pure integral controllers to the *i*th DG droop control, as shown in Equations (9) and (10) [19]. It should be noted that the binary coefficient *B<sup>i</sup>* in these equations is equal

to one only during the synchronization interval, and equal to zero otherwise. For the pulsation and phase synchronization, the pure integrators are added to the pulsation droop control, Equation (9), and for the voltage synchronization, the pure integrator is added to the voltage droop control, Equation (10).

$$
\omega\_{\rm i} = \omega\_{\rm n} - m\_{\rm i} \left( \mathbf{P}\_{\rm f\bar{i}} - \mathbf{P}\_{\rm in} \right) - \left[ \mathbf{K}\_{\rm ii} \int \left( \omega\_{\rm DGi} - \omega\_{\rm pcci} \right) + \mathbf{K}\_{\rm bi} \int \left( \mathbf{\Theta}\_{\rm DGi} - \mathbf{\Theta}\_{\rm pcci} \right) \right] \mathbf{B}\_{\rm i} \tag{9}
$$

$$E\_i = E\_n - n\_i \left( Q\_{fi} - Q\_{in} \right) - f\_i \left( P\_{fi} - P\_{in} \right) - \left[ K\_{ei} \int \left( E\_{DGi} - E\_{pci} \right) \right] B\_{i\nu} \tag{10}$$

To prove the efficiency of the proposed synchronization and power sharing strategies, the mesh microgrid in Figure 2 is modeled using the Simscape toolbox of Matlab/Simulink. Source 1 and Source 2 of Figure 2 are modeled by two controllable voltage sources shown in Figure 4, connected to two different PCCs and controlled by *Eabcre f i* , which was generated using the modified droop strategy described by Equations (9) and (10), a power calculation bloc, a power filter, park transform and inverse park transform, as explained in the equivalent synoptic diagram describing a droop-controlled DGi in Figure 5. The main microgrid parameters are listed in Table 1. The powers of sources and loads are listed in Table 2. **Figure 4.** Scheme of the controllable voltage sources DG1 and DG2.

**Figure 5.** Equivalent synoptic diagram describing a droop-controlled DGi. **Figure 5.** Equivalent synoptic diagram describing a droop-controlled DGi.

**Table 1.** Parameters of the considered microgrid power lines. **Lines Resistance (Ω) Inductance (mH) capacitance (µF) Points of connections** Line 1 0.63 7.14 205 Bus 8–Bus 7 Line 2 2.55 11.4 230 Bus 5–Bus 7 Line 3 0.63 7.14 205 Bus 8–Bus 9 Line 4 2 7 180 Bus 9–Bus 6 Line 5 1.7 7.6 153.4 Bus 4–Bus 5 Line 6 1.7 7.6 153.4 Bus 4–Bus 6 Based on this Simscape model, the efficiency of the proposed synchronization and power sharing strategies assumed in Equations (9) and (10) is evaluated. Figure 6a and 6b show the evolution of the active and reactive powers delivered by DG1 and DG2. In the beginning, the first DG (DG1) imposes the frequency of the microgrid as well as the voltages of each PCC; up to t = 5 s, DG1 supplies the loads connected to the microgrid. The second generator (DG2) is synchronized during the interval 1–5, and then it is connected to the microgrid at t = 5 s. The power-sharing of the active and reactive powers are ensured in steady state without being affected by the synchronization procedure. In addition, compared to the previous results shown in Figure 3a,b, the power peaks appearing after the connection of DG2 to the microgrid are considerably attenuated. It should be noted that these performances are maintained with a higher number of DGs connected to the microgrid, even though the results are not presented in this paper.

crogrid, even though the results are not presented in this paper.

**Table 2.** Sources and load powers.

**Active Power (Mw)**

**Reactive Power (Mvar)**

Source 1 3 0.9 6 Bus 7 Source 2 2 0.9 6 Bus 9 Load 1 1.5 0.35 20 Bus 5 Load 2 1.2 0.25 20 Bus 6 Load 3 1 0.25 20 Bus 8

Based on this Simscape model, the efficiency of the proposed synchronization and power sharing strategies assumed in Equations (9) and (10) is evaluated. Figure 6a and 6b show the evolution of the active and reactive powers delivered by DG1 and DG2. In the beginning, the first DG (DG1) imposes the frequency of the microgrid as well as the voltages of each PCC; up to t = 5 s, DG1 supplies the loads connected to the microgrid. The second generator (DG2) is synchronized during the interval 1–5, and then it is connected to the microgrid at t = 5 s. The power-sharing of the active and reactive powers are ensured in steady state without being affected by the synchronization procedure. In addition, compared to the previous results shown in Figure 3a,b, the power peaks appearing after the connection of DG2 to the microgrid are considerably attenuated. It should be noted that these performances are maintained with a higher number of DGs connected to the mi-

**Phase to Phase Voltage (kV)**

**Point of Connection**

**Sources and Loads**

**Figure 6.** Evolution of the DG active (**a**) and reactive (**b**) powers (first DG supplies the microgrid up to 5 s, the second DG is connected to the microgrid at 5 s). **Figure 6.** Evolution of the DG active (**a**) and reactive (**b**) powers (first DG supplies the microgrid up to 5 s, the second DG is connected to the microgrid at 5 s).

In order to highlight the effect of the loss of the information on ܧ, a simulation test was made using the developed model in Simscape environment, and the results are shown in Figure 5. It consists of connecting both DGs to the microgrid at 0 s using the control strategy defined in Equations (6) and (7). The information on ܧ is lost at 4 s and becomes available again at 8 s, and in this scenario Figure 7a,b show the evolution of the active and reactive powers, respectively. The active power sharing is not affected by the loss of information on ܧ୰ୣ because it only depends on the frequency, being the same in all the microgrid PCCs. However, the reactive power sharing is totally lost when the information on ܧ୰ୣ is absent, but it is easily regained when the information on ܧ୰ୣ becomes available again. In order to highlight the effect of the loss of the information on *Ere f* , a simulation test was made using the developed model in Simscape environment, and the results are shown in Figure 5. It consists of connecting both DGs to the microgrid at 0 s using the control strategy defined in Equations (6) and (7). The information on *Ere f* is lost at 4 s and becomes available again at 8 s, and in this scenario Figure 7a,b show the evolution of the active and reactive powers, respectively. The active power sharing is not affected by the loss of information on *E*ref because it only depends on the frequency, being the same in all the microgrid PCCs. However, the reactive power sharing is totally lost when the information on *E*ref is absent, but it is easily regained when the information on *E*ref becomes available again. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 9 of 27

**Figure 7.** Evolution of the DG active (**a**) and reactive (**b**) powers (both DGs are connected at 0 s). **Figure 7.** Evolution of the DG active (**a**) and reactive (**b**) powers (both DGs are connected at 0 s).

Even though the considered microgrid including its loads and DGs are well controlled, the synthesis of the droop control parameters is not based on a methodical ap-

This method cannot guarantee the system stability when the parameters of the load change or additional dynamical constant power loads (CPL) are connected to the microgrid. For example, when a CPL is added to the microgrid it is not evident to foresee the system stability with the variation of its absorbed active power. Figure 8 shows that, as previously, the first DG1 imposes the frequency of the microgrid as well as each PCC voltage of up to t = 5s and supplies the R–L loads connected to the microgrid. The second generator (DG2) is synchronized and connected to the microgrid at t = 5 s. A dynamic CPL is connected parallel to load 1 (see Figure 2) at t = 7 s, absorbing an active power of 120 kW and zero reactive power. The active power absorbed by this CPL is increased to 500 kW at t = 8 s. It can be remarked that the connection of the CPL absorbing 120 kW does not impact the stability, but when its absorbed power increases to 500 kW the system becomes unstable. Hence, for each modification, the trial-and-error method should be applied again in order to find the eventual new values of the microgrid control parameters which may ensure its stability. In order to overcome this constraint, one solution consists of establishing the state-model that represents the microgrid including its control and studying the microgrid stability by calculating its Jacobean matrix and its eigenvalues at

each operating point, as is detailed in the next section.

Even though the considered microgrid including its loads and DGs are well controlled, the synthesis of the droop control parameters is not based on a methodical approach; they are tuned by trial-and-error method using Simscape.

This method cannot guarantee the system stability when the parameters of the load change or additional dynamical constant power loads (CPL) are connected to the microgrid. For example, when a CPL is added to the microgrid it is not evident to foresee the system stability with the variation of its absorbed active power. Figure 8 shows that, as previously, the first DG1 imposes the frequency of the microgrid as well as each PCC voltage of up to t = 5 s and supplies the R–L loads connected to the microgrid. The second generator (DG2) is synchronized and connected to the microgrid at t = 5 s. A dynamic CPL is connected parallel to load 1 (see Figure 2) at t = 7 s, absorbing an active power of 120 kW and zero reactive power. The active power absorbed by this CPL is increased to 500 kW at t = 8 s. It can be remarked that the connection of the CPL absorbing 120 kW does not impact the stability, but when its absorbed power increases to 500 kW the system becomes unstable. Hence, for each modification, the trial-and-error method should be applied again in order to find the eventual new values of the microgrid control parameters which may ensure its stability. In order to overcome this constraint, one solution consists of establishing the state-model that represents the microgrid including its control and studying the microgrid stability by calculating its Jacobean matrix and its eigenvalues at each operating point, as is detailed in the next section. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 10 of 27

**Figure 8.** Evolution of the DG active power under different state of charge (first DG supplies the microgrid up to 5 s, the second DG is connected to the microgrid at 5 s). **Figure 8.** Evolution of the DG active power under different state of charge (first DG supplies the microgrid up to 5 s, the second DG is connected to the microgrid at 5 s).

#### **3. System Modeling for its Stability Analysis 3. System Modeling for Its Stability Analysis**

ship between their outputs and inputs are presented in the following.

**Figure 9.** Equivalent synoptic diagram describing a droop-controlled DGi.

In the first bloc (Figure 9), the *i*th DG measured voltages (ܧ

݅) are used to calculate the instantaneous active and reactive powers using classical equa-

*3.1. State-Space Model of a Distributed Generator (DG)*

lished in this section.

tions (11) and (12).

Due to the interaction between the DGs and the loads, the stability of the microgrids is strongly influenced. Therefore, to study the stability and robustness of the droop-con-Due to the interaction between the DGs and the loads, the stability of the microgrids is strongly influenced. Therefore, to study the stability and robustness of the droop-controlled

ܧ ,

) and currents (݅ௗ,

trolled microgrid, a complete mathematical dynamic model of the whole system is estab-

The equations describing the behavior of the *i*th DG are presented on the equivalent synoptic diagram of Figure 9. It is composed of four cascaded blocs for which the relationmicrogrid, a complete mathematical dynamic model of the whole system is established in this section. is strongly influenced. Therefore, to study the stability and robustness of the droop-controlled microgrid, a complete mathematical dynamic model of the whole system is established in this section.

Due to the interaction between the DGs and the loads, the stability of the microgrids

**Figure 8.** Evolution of the DG active power under different state of charge (first DG supplies the

#### *3.1. State-Space Model of a Distributed Generator (DG) 3.1. State-Space Model of a Distributed Generator (DG)*

**3. System Modeling for its Stability Analysis** 

microgrid up to 5 s, the second DG is connected to the microgrid at 5 s).

*Sustainability* **2021**, *13*, x FOR PEER REVIEW 10 of 27

The equations describing the behavior of the *i*th DG are presented on the equivalent synoptic diagram of Figure 9. It is composed of four cascaded blocs for which the relationship between their outputs and inputs are presented in the following. The equations describing the behavior of the *i*th DG are presented on the equivalent synoptic diagram of Figure 9. It is composed of four cascaded blocs for which the relationship between their outputs and inputs are presented in the following.

$$\begin{array}{|c||c|c|c|c|}\hline \mathcal{E}\_{\mathsf{d}} & \mathsf{e}\_{\mathsf{d}} & \mathsf{h} & \mathsf{h} & \mathsf{h} & \mathsf{h} & \mathsf{h} & \mathsf{h} \\ \hline \mathcal{E}\_{\mathsf{d}} & \mathsf{h} & & & & & & & & & & \\ \hline \mathcal{E}\_{\mathsf{d}} & \mathsf{h} & & & & & & & & & & & \\ \hline \mathcal{E}\_{\mathsf{d}} & \mathsf{h} & & & & & & & & & & & & \\ \hline \mathcal{E}\_{\mathsf{d}} & \mathsf{h} & & & & & & & & & & & & \\ \hline \mathcal{E}\_{\mathsf{d}} & \mathsf{h} & & & & & & & & & & & & & \\ \hline \mathcal{E}\_{\mathsf{d}} & \mathsf{h} & & & & & & & & & & & & & \\ \hline \mathcal{E}\_{\mathsf{d}} & \mathsf{h} & & & & & & & & & & & & & \\ \hline \mathcal{E}\_{\mathsf{d}} & \mathsf{h} & & & & & & & & & & & & & \\ \hline \end{array}$$

**Figure 9.** Equivalent synoptic diagram describing a droop-controlled DGi.

**Figure 9.** Equivalent synoptic diagram describing a droop-controlled DGi. In the first bloc (Figure 9), the *i*th DG measured voltages (*Ei<sup>d</sup>* , *Ei<sup>q</sup>* ) and currents (*idi*, *iqi*) are used to calculate the instantaneous active and reactive powers using classical Equations (11) and (12).

$$P\_{\mathbf{i}} = E\_{\mathbf{i}\_d} \cdot \mathbf{i}\_{\mathbf{i}\_d} + E\_{\mathbf{i}\_q} \cdot \mathbf{i}\_{\mathbf{i}\_q} \tag{11}$$

$$\dot{\mathbf{Q}}\_{i} = \mathbf{E}\_{i\_{\rm q}} \, \dot{\mathbf{i}}\_{i\_{\rm d}} - \mathbf{E}\_{i\_{\rm d}} \, \dot{\mathbf{i}}\_{i\_{\rm q}} \tag{12}$$

tions (11) and (12). In the second bloc, the instantaneous active and reactive powers (*P<sup>i</sup>* and *Q<sup>i</sup>* ) are filtered using a first-order low-pass filter to obtain the average (filtered) values *Pf i* and *Qf i* using Equations (13) and (14). It should be emphasized that the cut-off frequency *ω<sup>f</sup>* of the filter is related to the dynamics of the droop control-loop.

$$\frac{d}{dt}P\_{fi} = \omega\_f \left(P\_i - P\_{fi}\right) = \omega\_f \left(P\_i - P\_{fi}\right) \tag{13}$$

$$\frac{d}{dt}Q\_{fi} = \omega\_f \left(Q\_i - Q\_{fi}\right) = \omega\_f \left(Q\_i - Q\_{fi}\right) \tag{14}$$

The third bloc applies the modified droop control in Equations (6)–(8), using *Pf i* and *Qf i* to achieve the active and reactive power sharing.

The fourth bloc models the delay imposed by the voltage source inverter (VSI), controlling the *i*th DG output voltages by means of a second-order filter. This filter has a faster dynamic compared to the external droop control loop *ω<sup>c</sup> ω<sup>f</sup>* . The relationship between the output voltage of the *i*th DG and its voltage reference is expressed by the transfer function defined in Equation (15):

$$\frac{E\_{i\_{dq}}}{E\_{i\_{dq}}^{\*}} = \frac{\omega\_{\text{c}}^{2}}{s^{2} + 2\xi\omega\_{\text{c}}s + \omega\_{\text{c}}^{2}},\tag{15}$$

#### *3.2. Microgrid Structure and Modeling*

Figure 10 shows a microgrid inspired from the IEEE 9bus test feeder that differs slightly from the microgrid of Figure 2 and contains an additional CPL. In fact, this type of load is increasingly present in microgrids and imposes more severe constraints to the system stability. The considered microgrid is composed of two DGs powering three classical inductive loads, modeled by serial R–L circuits, and a CPL load. They are interconnected by RLC power lines to represent a mesh multi-PCC microgrid. The line connecting the *PCC<sup>i</sup>* and *PCC<sup>j</sup>* have a resistance *rij*, an inductance *lij*, and a capacitance of *cij*. Their values are determined knowing the distance between the considered PCCs. The capacitance *cij* is connected to the *PCC<sup>j</sup>* .

where: ܶଷଶ

the voltage vectors at PCC<sup>1</sup> and PCC<sup>2</sup> and their ߙ −ߚ components.

). ቆ ഀ<sup>ଵ</sup>ܧ ഁ<sup>ଵ</sup>ܧ

). ቆ ഀ<sup>ଶ</sup>ܧ ഁ<sup>ଶ</sup>ܧ

ቇ = ቆ

−ܧ∆

−ܧ∆

ೕ ೕ

ೕ ೕ

൫E −E

ቇ = ܲ(−ߜ<sup>ଵ</sup>

ቇ = ܲ(−ߜ<sup>ଵ</sup>

ቆ <sup>ଶ</sup>ܧ <sup>ଶ</sup>ܧ

where: ∆ܧ =

DG1:

DG2:

connecting its ܲܥܥ and ܲܥܥ

⎩ ⎪ ⎨ ⎪ ⎧ቆ <sup>ଵ</sup>ܧ <sup>ଵ</sup>ܧ

⎩ ⎪ ⎨ ⎪ ⎧ቆ <sup>ଶ</sup>ܧ <sup>ଶ</sup>ܧ

> ⎩ ⎪ ⎨ ⎪ ⎧ ௗ ௗ௧ ݅ = ଵ ೕ

ௗ ௗ௧ ݅ = ଵ ೕ <sup>௧</sup> = ට ଶ ଷ ∙ 1 − ଵ ଶ − ଵ ଶ

ቇ = ൬

ቆ <sup>ଵ</sup>ܧ <sup>ଵ</sup>ܧ

ቇ = ൬

<sup>ଶ</sup>ܧ 3.√

<sup>ଶ</sup>ܧ 3.√

Then, Equations (18) and (19) give the relationship between the d–q components of

ቇ = ൬

. cos(δ)

. sin(δ)

Equation (20) presents a network model of N power lines of a mesh microgrid, inter-

݅ + ߱݅

݅ −߱݅

0

√ଷ ଶ

cos ߜ<sup>ଵ</sup> sin ߜ<sup>ଵ</sup> −sin ߜ<sup>ଵ</sup> cos ߜ<sup>ଵ</sup>

> <sup>ଵ</sup>ܧ 3.√ 0 ൰

cos ߜ<sup>ଵ</sup> sin ߜ<sup>ଵ</sup> −sin ߜ<sup>ଵ</sup> cos ߜ<sup>ଵ</sup>

, where ݅ and ݆ ∈ [1, 2, … , ܰ] and ݅ ≠ ݆ (Figure 10).

൯ ∆ܧ =

− √ଷ ଶ

൰ . ቆ

൰ . ቆ

ቀE − E

ቁ

ቇ with: δ = ߜ<sup>ଶ</sup> −ߜ<sup>ଵ</sup>

<sup>ଵ</sup>ܧ 3.√

<sup>ଵ</sup>ܧ 3.√

<sup>ଶ</sup>ܧ 3.√

<sup>ଶ</sup>ܧ 3.√

, (17)

. cos ߜ<sup>ଵ</sup>

. sin ߜ<sup>ଵ</sup> ቇ

. cos ߜ<sup>ଶ</sup>

. sin ߜ<sup>ଶ</sup> ቇ , (18)

, (19)

, (20)

**Figure 10. Figure 10.**  IEEE 9bus test feeder. IEEE 9bus test feeder.

In order to study the considered microgrid having two DGs, the state equations are given using a common reference frame for expressing the different variables. The used d–q reference frame is defined in a way that its d-axis is oriented toward the first DG voltage vector (*E*<sup>1</sup> Figure 11). Then, the d-axis is shifted by *δ*<sup>1</sup> with respect to the *α*-axis, where *δ*<sup>1</sup> is the argument of the DG1 voltage vector (*E*<sup>1</sup> = *E*1*e <sup>j</sup>δ*<sup>1</sup> = *<sup>E</sup>*1*<sup>α</sup>* + *jE*1*<sup>β</sup>* ). The rotating d–q reference frame turns with an electrical speed of *ω*<sup>1</sup> = *dδ*<sup>1</sup> *dt* with respect to the fixed reference frame *α* − *β*. When the different DGs are synchronized and connected to the microgrid, their pulsations vary simultaneously. Then, the pulsations of the DG1 and DG2 voltages (*ω*<sup>1</sup> = *dδ*<sup>1</sup> *dt* and *ω*<sup>2</sup> = *dδ*<sup>2</sup> *dt* ) are the same (i.e., *ω*<sup>1</sup> = *ω*<sup>2</sup> = *ωcom*)). Knowing that the phase voltages of DG1 and DG2 (connected to PCC1 and PCC2) have the RMS values of *E*<sup>1</sup> and *E*2, the *α* − *β* components of *E*<sup>1</sup> and *E*<sup>2</sup> are obtained using the Concordia transformation *T t* <sup>32</sup> in (16) and (17):

$$\begin{pmatrix} E\_{1\_a} \\ E\_{1\_\beta} \end{pmatrix} = T\_{32}^t \begin{bmatrix} E\_{1\_a} \\ E\_{1\_b} \\ E\_{1\_c} \end{bmatrix} = \begin{pmatrix} \sqrt{3}.E\_1.\cos\delta\_1 \\ \sqrt{3}.E\_1.\sin\delta\_1 \end{pmatrix} \text{ and } \begin{pmatrix} E\_{2\_x} \\ E\_{2\_\beta} \end{pmatrix} = T\_{32}^t \begin{bmatrix} E\_{2\_x} \\ E\_{2\_\delta} \\ E\_{2\_\epsilon} \end{bmatrix} = \begin{pmatrix} \sqrt{3}.E\_2.\cos\delta\_2 \\ \sqrt{3}.E\_2.\sin\delta\_2 \end{pmatrix} \tag{16}$$

$$\text{where: } T\_{32}^t = \sqrt{\frac{2}{3}} \cdot \begin{bmatrix} 1 & -\frac{1}{2} & -\frac{1}{2} \\ 0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2} \end{bmatrix} . \tag{17}$$

**Figure 11.** Reference frames ߙ − ߚ and d−q. **Figure 11.** Reference frames *α* − *β* and d − q.

=ܧ

=ܧ

ଵ 

ଵ 

൰ = ቆ

The d–q components of the R–L load current connected to ܲܥܥ

ଵ ಽೌ ൫ܧ

ଵ ಽೌ ቀܧ

ቐ ௗ ௗ௧

ௗ ௗ௧

> ⎩ ⎪ ⎨ ⎪ ⎧൬ ܲ ܳ

can be determined using Equation (23):

ቐ ௗ ௗ௧

ௗ ௗ௧

݅ௗସ

൬ ݅ௗ ݅<sup>൰</sup> <sup>=</sup>

݅ௗ =

݅ௗ =

the state vector ݔ, described in the following (24):

݅ௗହ

ܧ

[ݔ]

் = [݅ଵଷ

ܧ ܧ <sup>ହ</sup>ܧ

݅ଵଷ ݅ଶଷ ݅ଶଷ ݅ଶହ ݅ଶହ ݅ଵସ ݅ଵସ ݅ହ ݅ହ ݅ସ

݅ௗଷ

݅ௗଷ

݅ௗସ

droop controllers.

ܧ and

lines connected to ܲܥܥ

sorbed by the active ܥܲܮ

work were serial passive R–L loads and an active CPL (Figure 10). With the sum of the current connected to ܲܥܥ being zero (Kirchhoff current law), Equation (21) relates to all PCCs except the ones connected to the DGs for which the voltages are imposed by their

൫−݅ௗ − ݅ + ∑ ݅

ቀ−݅ௗ − ݅ + ∑ ݅

components knowing the active and reactive powers ܲ and ܳ absorbed by ܥܲܮ

ܧ ܧ ܧ− ܧ

ଵ ா <sup>మ</sup>ାா మ . ቆ

where ܴௗ and ܮௗ represent the resistance and inductance of the RL load.

crogrid model is non-linear and can be finally put into the following form:

It should be noted that ∑ ݅ in Equation (17) is the sum of the currents of the power

ቇ . ൬ ݅ௗ ݅<sup>൰</sup>

− ܴௗ . ݅ௗ

− ܴௗ . ݅ௗ

The overall model of the microgrid presented in Figure 10 including its control, defined by the previous equations, has 40 state variables which constitute the elements of

݅ௗହ ܲଵ ܳଵ ܲଶ ܳଶ <sup>ߜ</sup> ܧ̇

Considering the non-linear Equations (7), (11), (12), (19) and (21), the overall mi-

ܧ ܧ ܧ− ܧ ܧ . ߱ + ൯

, (21)

, (22)

ܽ݊݀ ݅ௗ

, (23)

(݅ௗ

.

)

(24)

ܧ . −߱ ቁ

. ݅ௗ and ݅ are the d–q components of the current ab-

. The non-linear Equation (22) allows the determination of these

ቇ . ൬ ܲ ܳ ൰

൯+ ߱ . ݅ௗ

ቁ− ߱ . ݅ௗ

݅ସ ܧ<sup>ଵ</sup> ܧ<sup>ଵ</sup> ܧ<sup>ଶ</sup> ܧ<sup>ଶ</sup> ܧ<sup>ଷ</sup> ܧ<sup>ଷ</sup> ܧ<sup>ସ</sup> ܧ<sup>ସ</sup> ܧ<sup>ହ</sup>

̇ܧଵ

̇ܧଵ

̇ܧ ଶ ଶ ,[ܬ

Then, Equations (18) and (19) give the relationship between the d–q components of the voltage vectors at PCC<sup>1</sup> and PCC<sup>2</sup> and their *α* − *β* components.

$$\mathbf{DG1}: \begin{cases} \begin{pmatrix} E\_{1\_d} \\ E\_{1\_q} \end{pmatrix} = P(-\delta\_1) \cdot \begin{pmatrix} E\_{1\_d} \\ E\_{1\_\beta} \end{pmatrix} = \begin{pmatrix} \cos \delta\_1 & \sin \delta\_1 \\ -\sin \delta\_1 & \cos \delta\_1 \end{pmatrix} \cdot \begin{pmatrix} \sqrt{3}.E\_1, \cos \delta\_1 \\ \sqrt{3}.E\_1, \sin \delta\_1 \end{pmatrix} \\\ \cdot \quad \begin{pmatrix} E\_{1\_d} \\ E\_{1\_q} \end{pmatrix} = \begin{pmatrix} \sqrt{3}.E\_1 \\ 0 \end{pmatrix} \end{cases} , \tag{18}$$

$$\text{DG2: } \begin{cases} \begin{pmatrix} E\_{2\_d} \\ E\_{2\_q} \end{pmatrix} = P(-\delta\_1) \cdot \begin{pmatrix} E\_{2\_d} \\ E\_{2\_\beta} \end{pmatrix} = \begin{pmatrix} \cos\delta\_1 & \sin\delta\_1 \\ -\sin\delta\_1 & \cos\delta\_1 \end{pmatrix} \cdot \begin{pmatrix} \sqrt{3}.E\_2, \cos\delta\_2 \\ \sqrt{3}.E\_2, \sin\delta\_2 \end{pmatrix} \\\ \begin{pmatrix} E\_{2\_d} \\ E\_{2\_\theta} \end{pmatrix} = \begin{pmatrix} \sqrt{3}.E\_2.\cos(\delta) \\ \sqrt{3}.E\_2.\sin(\delta) \end{pmatrix} \text{with}: \ \delta = \delta\_2 - \delta\_1$$

Equation (20) presents a network model of N power lines of a mesh microgrid, interconnecting its *PCC<sup>i</sup>* and *PCC<sup>j</sup>* , where *i* and *j* ∈ [1, 2, . . . , *N*] and *i* 6= *j* (Figure 10).

$$\begin{cases} \frac{d}{dt}\dot{\mathbf{i}}\_{\text{ij}d} = \frac{1}{l\_{\text{ij}}}\Delta \mathbf{E}\_{\text{ij}d} - \frac{r\_{\text{ij}}}{l\_{\text{ij}}}\dot{\mathbf{i}}\_{\text{ij}d} + \omega\_{com}\dot{\mathbf{i}}\_{\text{ij}q} \\\ \frac{d}{dt}\dot{\mathbf{i}}\_{\text{ij}q} = \frac{1}{l\_{\text{ij}}}\Delta \mathbf{E}\_{\text{ij}q} - \frac{r\_{\text{ij}}}{l\_{\text{ij}}}\dot{\mathbf{i}}\_{\text{ij}q} + \omega\_{com}\dot{\mathbf{i}}\_{\text{ij}d} \\\ \text{where} \quad \Delta E \dot{\mathbf{j}}\_{\text{j}d} = \left(\mathbf{E}\_{\text{i}\_{\text{d}}} - \mathbf{E}\_{\text{j}\_{\text{d}}}\right) & \Delta E \dot{\mathbf{i}}\_{\text{j}q} = \left(\mathbf{E}\_{\text{i}\_{q}} - \mathbf{E}\_{\text{j}\_{q}}\right) \end{cases} \tag{20}$$

*Eid* and *Ei<sup>q</sup>* are the d–q components of *PCC<sup>i</sup>* voltage. The loads considered in this work were serial passive R–L loads and an active CPL (Figure 10). With the sum of the current connected to *PCC<sup>i</sup>* being zero (Kirchhoff current law), Equation (21) relates to all PCCs except the ones connected to the DGs for which the voltages are imposed by their droop controllers.

$$\begin{cases} \frac{d}{d\mathbf{I}} \mathbf{E}\_{\mathbf{i}\_{d}} = \frac{1}{\mathbf{C}\_{i}} \Big( -\mathbf{i}\_{\mathrm{Loadi}\_{d}} - \mathbf{i}\_{\mathrm{CPL}\mathbf{i}\_{d}} + \sum\_{j} \mathbf{i}\_{j\mathbf{i}\_{d}} \Big) + \boldsymbol{\omega}\_{\mathrm{com}} \, . \, \mathbf{E}\_{\mathbf{i}\_{q}}\\ \frac{d}{d\mathbf{I}} \mathbf{E}\_{\mathbf{i}\_{q}} = \frac{1}{\mathbf{C}\_{i}} \Big( -\mathbf{i}\_{\mathrm{Loadi}\_{q}} - \mathbf{i}\_{\mathrm{CPL}\mathbf{i}\_{q}} + \sum\_{j} \mathbf{i}\_{j\mathbf{i}\_{q}} \Big) - \boldsymbol{\omega}\_{\mathrm{com}} \, . \, \mathbf{E}\_{\mathbf{i}\_{d}} \end{cases} \tag{21}$$

It should be noted that ∑*<sup>j</sup> iji* in Equation (17) is the sum of the currents of the power lines connected to *PCC<sup>i</sup>* . *iCPLid* and *iCPLiq* are the d–q components of the current absorbed by the active *CPL<sup>i</sup>* . The non-linear Equation (22) allows the determination of these components knowing the active and reactive powers *PCPLi* and *QCPLi* absorbed by *CPL<sup>i</sup>* .

$$\begin{cases} \begin{pmatrix} P\_{\text{CPLi}} \\ Q\_{\text{CPLi}} \end{pmatrix} = \begin{pmatrix} E\_{i\_d} & E\_{i\_q} \\ E\_{i\_q} & -E\_{i\_d} \end{pmatrix} \cdot \begin{pmatrix} i\_{\text{CPLi}} \\ i\_{\text{CPLi}\dot{q}} \end{pmatrix} \\\ \begin{pmatrix} i\_{\text{CPLi}\dot{d}} \\ i\_{\text{CPLi}\dot{q}} \end{pmatrix} = \frac{1}{E\_{i\_d}\,^2 + E\_{i\_q}} \cdot \begin{pmatrix} E\_{i\_d} & E\_{i\_q} \\ E\_{i\_q} & -E\_{i\_d} \end{pmatrix} \cdot \begin{pmatrix} P\_{\text{CPLi}} \\ Q\_{\text{CPLi}} \end{pmatrix} \end{cases} \tag{22}$$

The d–q components of the R–L load current connected to *PCC<sup>i</sup>* (*iLoadi<sup>d</sup> and iLoadi<sup>q</sup>* ) can be determined using Equation (23):

$$\begin{cases} \frac{d}{dt}\dot{\mathbf{i}}\_{\text{Loadi}\_{d}} = \frac{1}{\mathbf{L}\_{\text{Lodi}}} \left( \mathbf{E}\_{\text{i}\_{d}} - \mathbf{R}\_{\text{Loadi}} \cdot \mathbf{i}\_{\text{Loadi}\_{d}} \right) + \boldsymbol{\omega}\_{\text{com}} \cdot \dot{\mathbf{i}}\_{\text{Loadi}\_{q}}\\ \frac{d}{dt}\dot{\mathbf{i}}\_{\text{Loadi}\_{q}} = \frac{1}{\mathbf{L}\_{\text{Lodi}}} \left( \mathbf{E}\_{\text{i}\_{q}} - \mathbf{R}\_{\text{Lodi}} \cdot \dot{\mathbf{i}}\_{\text{Lodi}\_{q}} \right) - \boldsymbol{\omega}\_{\text{com}} \cdot \dot{\mathbf{i}}\_{\text{Loadi}\_{d}} \end{cases} \tag{23}$$

where *RLoadi* and *LLoadi* represent the resistance and inductance of the RL load.

The overall model of the microgrid presented in Figure 10 including its control, defined by the previous equations, has 40 state variables which constitute the elements of the state vector *x*, described in the following (24):

$$\begin{aligned} \mathbf{[x]}^T &= [\mathbf{i}\_{13\_d} \ i\_{13\_q} i\_{23\_d} i\_{23\_q} i\_{25\_d} i\_{25\_q} i\_{14\_d} \ i\_{14\_q} i\_{56\_d} i\_{56\_q} i\_{46\_d} i\_{46\_q} E\_{1\_d} E\_{1\_q} E\_{2\_d} E\_{2\_q} E\_{3\_d} E\_{3\_q} E\_{4\_d} E\_{5\_d} E\_{5\_q} \\ \mathbf{E}\_{\mathbf{6}\_d} & \mathbf{E}\_{\mathbf{6}\_q} i\_{1 \text{and} \mathbf{3}\_q} i\_{1 \text{and} \mathbf{4}\_d} \ i\_{1 \text{and} \mathbf{4}\_q} i\_{1 \text{and} \mathbf{5}\_d} \ \mathbf{P}\_{f1} \ \mathbf{Q}\_{f1} \ \mathbf{P}\_{f2} \ \mathbf{Q}\_{f2} \ \delta & \mathbf{E}\_{\mathbf{1}\_d} \ \mathbf{E}\_{\mathbf{1}\_q} \ \mathbf{E}\_{\mathbf{2}\_d} \ \mathbf{E}\_{\mathbf{2}\_q} \ \mathbf{I}\_{\mathbf{i}}] \end{aligned} \tag{24}$$

Considering the non-linear Equations (7), (11), (12), (19) and (21), the overall microgrid model is non-linear and can be finally put into the following form:

$$\dot{\mathfrak{x}} = f(\mathfrak{x}) \text{ with } f: \mathbb{R}^n \to \mathbb{R}^n, \ n = 40,\tag{25}$$

#### *3.3. Validation of the State Model 3.3. Validation of the State Model:*

*Sustainability* **2021**, *13*, x FOR PEER REVIEW 14 of 27

The results concerning the evolution of the microgrid active and reactive powers, obtained under the same conditions using the Simscape model and the established state model, were used to validate the established state model. The same simulation scenario was considered for obtaining the simulation results using both models. Both DGs were connected to the microgrid at 0 s. The simulation results of both considered models are presented in Figure 12a,b, illustrating the evolution of the active and reactive powers of DG1 and DG2. Both models led to similar results; therefore, the established state model is considered validated. Thus, it can be used for studying the microgrid stability, integrating its control. To further confirm the validity of the developed model, Figure 12c shows a zoomed-in view of the transitory state after the connection of both DGs at 0 s. The results concerning the evolution of the microgrid active and reactive powers, obtained under the same conditions using the Simscape model and the established state model, were used to validate the established state model. The same simulation scenario was considered for obtaining the simulation results using both models. Both DGs were connected to the microgrid at 0 s. The simulation results of both considered models are presented in Figure 12a,b, illustrating the evolution of the active and reactive powers of DG1 and DG2. Both models led to similar results; therefore, the established state model is considered validated. Thus, it can be used for studying the microgrid stability, integrating its control. To further confirm the validity of the developed model, Figure 12c shows a zoomed-in view of the transitory state after the connection of both DGs at 0 s.

**Figure 12.** *Cont.*

**Figure 12.** Simulation results obtained using Simscape and the mathematical state-model. Both DGs were connected to the microgrid at 0 s. (**a**) Evolution of the DGs per unit active powers. (**b**) Evolution of the DGs per unit reactive powers. (**c**) Zoomed-in view of the per unit reactive powers around 0 s. **Figure 12.** Simulation results obtained using Simscape and the mathematical state-model. Both DGs were connected to the microgrid at 0 s. (**a**) Evolution of the DGs per unit active powers. (**b**) Evolution of the DGs per unit reactive powers. (**c**) Zoomed-in view of the per unit reactive powers around 0 s.

#### **4. Mesh Microgrid Stability and Robustness of its Control**

#### **4. Mesh Microgrid Stability and Robustness of its Control** *4.1. Jacobian Matrix Eigenvalues*

*4.1. Jacobian Matrix Eigenvalues*  In order to study the stability of the microgrid, defined by the continuous nonlinear differential system (24), and to analyze its dynamic behavior, which is affected by several control parameters, an eigenvalue sensibility analysis was performed by means of the calculation of the eigenvalues of the Jacobian matrix ቀ ப ப୶ ቁ ୶బ at the operating point ݂(x ) = 0. The system, i.e., the microgrid, will be asymptotically stable around the operating point In order to study the stability of the microgrid, defined by the continuous nonlinear differential system (24), and to analyze its dynamic behavior, which is affected by several control parameters, an eigenvalue sensibility analysis was performed by means of the calculation of the eigenvalues of the Jacobian matrix *∂ f ∂x x*0 at the operating point *f*(*x*0) = 0. The system, i.e., the microgrid, will be asymptotically stable around the operating point *x*<sup>0</sup> if the real parts of all eigenvalues are strictly negative.

x if the real parts of all eigenvalues are strictly negative. The system parameters are given in Tables 3–5. The classical loads were modelled by serial R–L loads. The values of R and L were chosen depending on the operating point of these loads. The CPL was defined by constant values of its absorbed active and reactive powers, which may vary depending on its chosen operating point. The parameters of the DGs corresponded to their rated powers (available powers) and the parameters imposing the dynamic behavior of their control (߱, ߱ , ߦ, permissible variations of pulsation ∆<sup>ఠ</sup> The system parameters are given in Tables 3–5. The classical loads were modelled by serial R–L loads. The values of R and L were chosen depending on the operating point of these loads. The CPL was defined by constant values of its absorbed active and reactive powers, which may vary depending on its chosen operating point. The parameters of the DGs corresponded to their rated powers (available powers) and the parameters imposing the dynamic behavior of their control (*ω<sup>f</sup>* , *ωc*, *ξ*, permissible variations of pulsation ∆*<sup>ω</sup>* and voltage ∆*E*).


**Lines Resistance (Ω) Inductance (mH) Capacitance (µF) Points of Connection** Line 13 0.63 7.14 205 PCC1–PCC3 line 23 0.63 7.14 205 PCC2–PCC3 line 14 2.55 11.4 230 PCC1–PCC4

and voltage ∆ா). The eigenvalues of the system at the considered operating point, corresponding to **Table 3.** Parameters of the considered microgrid power lines.

**Table 3.** Parameters of the considered microgrid power lines.


**Table 4.** Parameters of the considered microgrid power loads.

**Table 5.** Parameters of the considered DGs.


The eigenvalues of the system at the considered operating point, corresponding to the parameters of the loads and DGs given in Tables 4 and 5, are shown in Table 6. It can be observed that four of the Jacobian matrix eigenvalues are the negative real numbers, and that the other 36 eigenvalues are two by two the complex conjugate numbers, having negative real parts.

**Table 6.** Eigenvalues under nominal operating condition.


All of the Jacobian matrix eigenvalues have negative real parts, therefore the microgrid including its DG's control and loads can be considered as a stable system around the considered operating point. The study of the considered mesh microgrid stability around other operating points can also be conducted based on the established state model.

In order to perform the sensitivity analysis and find the origin of different frequency components, depending on the parameters of the established model, the parameters of the different constituents of the microgrid, including its control parameters were modified separately. In the following sections, the evolution of eigenvalue trajectories with variation

of the parameters of each microgrid constituent is discussed to verify their impact on the system stability. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 17 of 27

#### *4.2. Eigenvalue Trajectory and Sensibility Analysis for Different Values of Power Line Parameters*

To vary the parameters of the 6 power lines of the microgrid, the values of the lengths of all of these power lines are modified by 10 steps of 10% (for each line, from its initial length to two times this length), the Jacobean matrix eigenvalues are determined, and their evolution shown on Figure 13. The variation of the parameters of the power lines only impacts the eigenvalues *λ*<sup>1</sup> to *λ*12, which are two by two complex conjugate numbers; the other eigenvalues *λ*<sup>13</sup> to *λ*<sup>40</sup> do not vary significantly with the evolution of the power line parameters. The real parts of the impacted eigenvalues (*λ*<sup>1</sup> to *λ*12) become closer to zero but remain sufficiently negative to not impact system stability when the line parameters are increased within the considered interval. However, if the lengths of the power lines become excessively long, the real parts of the impacted eigenvalues may become positives and cause system instability. To vary the parameters of the 6 power lines of the microgrid, the values of the lengths of all of these power lines are modified by 10 steps of 10% (for each line, from its initial length to two times this length), the Jacobean matrix eigenvalues are determined, and their evolution shown on Figure 13. The variation of the parameters of the power lines only impacts the eigenvalues ߣ<sup>ଵ</sup> to ߣଵଶ, which are two by two complex conjugate numbers; the other eigenvalues ߣଵଷ to ߣସ do not vary significantly with the evolution of the power line parameters. The real parts of the impacted eigenvalues (ߣ<sup>ଵ</sup> to ߣଵଶ) become closer to zero but remain sufficiently negative to not impact system stability when the line parameters are increased within the considered interval. However, if the lengths of the power lines become excessively long, the real parts of the impacted eigenvalues may become positives and cause system instability.

**Figure 13.** Evolution of eigenvalues corresponding to the change in line parameters. **Figure 13.** Evolution of eigenvalues corresponding to the change in line parameters.

#### *4.3. Eigenvalue Trajectory and Sensibility Analysis for Different Values of DG Parameters 4.3. Eigenvalue Trajectory and Sensibility Analysis for Different Values of DG Parameters*

The same approach as in Section 4.2. is used to study the impact of other parameters that may contribute to the instability of the system. For the considered DGs, the parameters which may impact the system stability are the cut-off frequency ݂߱ for power calculation (Equation (13) and (14)), the value of the filter's cut-off frequency ߱ of the second order filter (Equation (15)), as well as the frequency drop ∆<sup>ఠ</sup> and the voltage drop ∆ா in The same approach as in Section 4.2. is used to study the impact of other parameters that may contribute to the instability of the system. For the considered DGs, the parameters which may impact the system stability are the cut-off frequency *ω<sup>f</sup>* for power calculation (Equations (13) and (14)), the value of the filter's cut-off frequency *ω<sup>c</sup>* of the second order filter (Equation (15)), as well as the frequency drop ∆*<sup>ω</sup>* and the voltage drop ∆*<sup>E</sup>* in Equations (6)–(8).

Equations (6)–(8). First, the cut-off frequency ݂߱ is modified in 10 steps (from its initial value to 10 times this value), the Jacobean matrix eigenvalues are determined, and their evolutions are illustrated in Figure 14. The variation of ݂߱ impacts the real negative eigenvalues ߣଷହ, ߣଷ, ߣଷ and ߣଷ଼ as well as the eigenvalues ߣଷଷ, ߣଷସ which are two complex conjugate numbers. The other eigenvalues do not vary significantly with the evolution of ݂߱ . It can be seen that when ݂߱ increases, the eigenvalues ߣ33, ߣ34, ߣ36, ߣ<sup>37</sup> and ߣ<sup>38</sup> are shifted to the left while ߣ<sup>35</sup> moves very slightly toward zero, but its value does not change considerably and stays largely negative (from −4 to −3.6). The system always remains stable First, the cut-off frequency *ω<sup>f</sup>* is modified in 10 steps (from its initial value to 10 times this value), the Jacobean matrix eigenvalues are determined, and their evolutions are illustrated in Figure 14. The variation of *ω<sup>f</sup>* impacts the real negative eigenvalues *λ*35, *λ*36, *λ*<sup>37</sup> and *λ*<sup>38</sup> as well as the eigenvalues *λ*33, *λ*<sup>34</sup> which are two complex conjugate numbers. The other eigenvalues do not vary significantly with the evolution of *ω<sup>f</sup>* . It can be seen that when *ω<sup>f</sup>* increases, the eigenvalues *λ*33, *λ*34, *λ*36, *λ*<sup>37</sup> and *λ*<sup>38</sup> are shifted to the left while *λ*<sup>35</sup> moves very slightly toward zero, but its value does not change considerably and stays largely negative (from −4 to −3.6). The system always remains stable when *ω<sup>f</sup>* increases, but the system dynamics become increasingly faster.

increases, but the system dynamics become increasingly faster.

the voltage source inverter (VSI) controlling the DG, on the system stability, its value is largely decreased (from its initial value 1000 rad/s to 50 rad/s). The eigenvalues most sen-

eigenvalues move to the right when ߱ decreases and tend to be positive when ߱ be-

in Equation (13), representing the delay imposed by

comes inferior to 50 rad/s, which causes the system instability.

To examine the impact of ߱

when ݂߱

*Sustainability* **2021**, *13*, x FOR PEER REVIEW 18 of 27

**Figure 14.** Evolution of eigenvalues corresponding to the change in ߱ (20 < ߱ < 200(rad/s) with ߱ increasing). **Figure 14.** Evolution of eigenvalues corresponding to the change in *ω<sup>f</sup>* (20 <*ω<sup>f</sup>* < 200(rad/*s*) with *ωf* increasing). **Figure 14.** Evolution of eigenvalues corresponding to the change in ߱ (20 < ߱ < 200(rad/s)

To validate these results, the Simscape simulations were made to verify that any value of ߱ inferior to 50 rad/s can cause system instability. The results of the first simulation, made using the Simscape model with ߱ = 50 rad/s, are illustrated on Figure 16a, and those of the second simulation with ߱ = 45 rad/s are shown on Figure 16b. These results confirm the system stability for ߱ > 50 rad/s, as predicted by the stability analysis based on the established state model. To examine the impact of *ω<sup>c</sup>* in Equation (13), representing the delay imposed by the voltage source inverter (VSI) controlling the DG, on the system stability, its value is largely decreased (from its initial value 1000 rad/s to 50 rad/s). The eigenvalues most sensitive to the variation of *ω<sup>c</sup>* are *λ*<sup>27</sup> to *λ*<sup>32</sup> as well as *λ*<sup>39</sup> and *λ*40, which are two by two of the complex conjugate numbers. As shown in Figure 15, the real parts of the impacted eigenvalues move to the right when *ω<sup>c</sup>* decreases and tend to be positive when *ω<sup>c</sup>* becomes inferior to 50 rad/s, which causes the system instability. To validate these results, the Simscape simulations were made to verify that any value of ߱ inferior to 50 rad/s can cause system instability. The results of the first simulation, made using the Simscape model with ߱ = 50 rad/s, are illustrated on Figure 16a, and those of the second simulation with ߱ = 45 rad/s are shown on Figure 16b. These results confirm the system stability for ߱ > 50 rad/s, as predicted by the stability analysis based on the established state model.

with ߱ increasing).

**Figure 15.** Evolution of eigenvalues corresponding to the change in ߱ (50 < ߱ < 1000 (rad/s) with ߱ decreasing). (a) **Figure 15.** Evolution of eigenvalues corresponding to the change in ߱ (50 < ߱ < 1000 (rad/s) **Figure 15.** Evolution of eigenvalues corresponding to the change in *ω<sup>c</sup>* (50 < *ω<sup>c</sup>* < 1000 (rad/*s*) with *ωc* decreasing).

with ߱ decreasing). To validate these results, the Simscape simulations were made to verify that any value of *ω<sup>c</sup>* inferior to 50 rad/s can cause system instability. The results of the first simulation, made using the Simscape model with *ω<sup>c</sup>* = 50 rad/s, are illustrated on Figure 16a, and those of the second simulation with *ω<sup>c</sup>* = 45 rad/*s* are shown on Figure 16b. These results confirm the system stability for *ω<sup>c</sup>* > 50 rad/s, as predicted by the stability analysis based on the established state model.

4.5.

**Figure 16.** Evolution of the DG active power (Simscape model (both DGs are connected at 0 s)): (**a**) with ߱ = 50 rad/s. (**b**) with ߱ = 45 rad/s. **Figure 16.** Evolution of the DG active power (Simscape model (both DGs are connected at 0 s)): (**a**) with *ω<sup>c</sup>* = 50 rad/*s*. (**b**) with *ω<sup>c</sup>* = 45 rad/*s*.

To evaluate the impact of droop control parameters on the system stability, the frequency drop ∆<sup>ఠ</sup> is increased in 10 steps (from its initial value to 10 times this value). The eigenvalues mostly impacted by this variation are ߣଶଷ to ߣଶ as well as ߣଷଷ and ߣଷସ which are two by two complex conjugate numbers. As shown in Figure 17 when ∆<sup>ఠ</sup> increases the eigenvalues ߣଶଷ to ߣଶ move toward the left, while ߣଷଷ and ߣଷସ move toward the right side of the real axis and become positive for ∆<sup>ఠ</sup> ≥ 5 rad/s. By following the same approach as Simscape, simulations were made to verify that any value of ∆<sup>ఠ</sup> superior or equal to 5 rad/s can cause the system instability. The results of the first simulation, made using the Simscape model with ∆<sup>ఠ</sup> = 4.5 rad/s, are illustrated In Figure 18a, and those of the second simulation with ∆<sup>ఠ</sup> = 5 rad/s are shown In Figure 18b. These results confirm the system instability for ∆<sup>ఠ</sup> ≥ 5 rad/s, as predicted by the stability analysis based on the established state model. To evaluate the impact of droop control parameters on the system stability, the frequency drop ∆*<sup>ω</sup>* is increased in 10 steps (from its initial value to 10 times this value). The eigenvalues mostly impacted by this variation are *λ*<sup>23</sup> to *λ*<sup>26</sup> as well as *λ*<sup>33</sup> and *λ*<sup>34</sup> which are two by two complex conjugate numbers. As shown in Figure 17 when ∆*<sup>ω</sup>* increases the eigenvalues *λ*<sup>23</sup> to *λ*<sup>26</sup> move toward the left, while *λ*<sup>33</sup> and *λ*<sup>34</sup> move toward the right side of the real axis and become positive for ∆*<sup>ω</sup>* ≥ 5 rad/s. By following the same approach as Simscape, simulations were made to verify that any value of ∆*<sup>ω</sup>* superior or equal to 5 rad/s can cause the system instability. The results of the first simulation, made using the Simscape model with ∆*<sup>ω</sup>* = 4.5 rad/s, are illustrated In Figure 18a, and those of the second simulation with ∆*<sup>ω</sup>* = 5 rad/s are shown In Figure 18b. These results confirm the system instability for ∆*<sup>ω</sup>* ≥ 5 rad/s, as predicted by the stability analysis based on the established state model. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 20 of 27

**Figure 17.** Evolution of eigenvalues corresponding to the change in ∆<sup>ఠ</sup> (0.5 < ∆<sup>ఠ</sup> < 5.5 (rad/s)) with ∆<sup>ఠ</sup> increasing. **Figure 17.** Evolution of eigenvalues corresponding to the change in ∆*<sup>ω</sup>* (0.5 < ∆*<sup>ω</sup>* < 5.5 (rad/*s*) ) with ∆*<sup>ω</sup>* increasing.

(**a**) (**b**) **Figure 18.** Evolution of the DGs active power (Simscape model, both DGs connected at 0 s): (**a**) ∆<sup>ఠ</sup> = 4.5 rad/s and (b) ∆<sup>ఠ</sup> = 4.5.

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with ∆<sup>ఠ</sup> increasing.

**Figure 18.** Evolution of the DGs active power (Simscape model, both DGs connected at 0 s): (**a**) ∆<sup>ఠ</sup> = 4.5 rad/s and (b) ∆<sup>ఠ</sup> = 4.5. **Figure 18.** Evolution of the DGs active power (Simscape model, both DGs connected at 0 s): (**a**) ∆*<sup>ω</sup>* = 4.5 rad/s and (b) ∆*<sup>ω</sup>* = 4.5.

The voltage drop ∆*<sup>E</sup>* is the last parameter of the DGs for which its impact on the system stability is studied. This has been done by varying ∆*<sup>E</sup>* from its initial value to 10 times this value. The eigenvalues mostly impacted by this variation are *λ*<sup>23</sup> and *λ*24, which are the complex conjugate numbers with a negative real part as well as *λ*<sup>36</sup> which is a real negative number. When the voltage drop increases, Figure 19 shows that *λ*<sup>36</sup> moves to the left while *λ*<sup>23</sup> and *λ*<sup>24</sup> move slightly to the right but remain negative. Thus, contrary to ∆*ω*, the voltage drop ∆*<sup>E</sup>* has a negligible impact on the system stability. (**a**) (**b**) **Figure 18.** Evolution of the DGs active power (Simscape model, both DGs connected at 0 s): (**a**) ∆<sup>ఠ</sup> = 4.5 rad/s and (b) ∆<sup>ఠ</sup> =

**Figure 17.** Evolution of eigenvalues corresponding to the change in ∆<sup>ఠ</sup> (0.5 < ∆<sup>ఠ</sup> < 5.5 (rad/s))

**Figure 19.** Evolution of Eigenvalues with the change in voltage drop 6 < ∆*<sup>E</sup>* < 70(*V*) with ∆*<sup>V</sup>* increasing.

#### *4.4. Eigenvalue Trajectory and Sensibility Analysis for Different Values of Load Parameters*

In order to explain the effect of load variation on system stability, a study of the variation of dominant eigenvalue trajectories under different load conditions is established. Starting with the CPL type, Figure 20a,b show the trajectory of the eigenvalues under the effect of the change in active *P<sup>c</sup>* and reactive *Q<sup>c</sup>* powers absorbed by the CPL. As the active power or the reactive power absorbed by the CPL increases up to 120 kW (with fixed *Q<sup>c</sup>* = 0) and 72 kVAr (with fixed *P<sup>c</sup>* = 100 kW), respectively, the eigenvalues *λ*<sup>5</sup> to *λ*<sup>8</sup> are the most sensitive to the change of *P<sup>c</sup>* or *Q<sup>c</sup>* of the CPL. The other eigenvalues do not vary

125 kW.

model.

kW when the capacitor ܿ<sup>ଷ</sup>

part of the eigenvalues ߣ<sup>ହ</sup> and ߣ

with the evolution of *P<sup>c</sup>* or *Qc*. When the active power (*Pc*) absorbed by the CPL increases from 100 kW up to 120 kW (with fixed *Q<sup>c</sup>* = 0), the eigenvalues *λ*<sup>7</sup> and *λ*<sup>8</sup> move to the left far away from zero while *λ*<sup>5</sup> and *λ*<sup>6</sup> move toward the right but remain sufficiently negative. In the same manner, when the reactive power (*Qc*) absorbed by the CPL increases from zero up to 72 kVAr (with fixed *P<sup>c</sup>* = 100 kW), the eigenvalues *λ*<sup>7</sup> and *λ*<sup>8</sup> move to the left while *λ*<sup>5</sup> and *λ*<sup>6</sup> move toward the right. For the considered intervals of the active power and reactive power, the real part of *λ*<sup>5</sup> and *λ*<sup>6</sup> remains sufficiently negative and the system stability is not affected. However, when the active power *P<sup>c</sup>* or the reactive power *Q<sup>c</sup>* become greater than certain limits, the real parts of the eigenvalues *λ*<sup>5</sup> and *λ*<sup>6</sup> become positive which causes system instability. For example, when *Q<sup>c</sup>* is fixed to zero, the limit value of active power *P<sup>c</sup>* absorbed by the CPL is 124.5 kW, beyond this value, the real part of the eigenvalues *λ*<sup>5</sup> and *λ*<sup>6</sup> becomes positive (Figure 21a for *P<sup>c</sup>* = 124kW and *P<sup>c</sup>* = 126kW) and the system cannot be considered asymptotically stable around the considered operating point. In the same manner, when *P<sup>c</sup>* is fixed to 100 kW, the limit value of reactive power *Q<sup>c</sup>* absorbed by the CPL is 74.3 kVAr; beyond this value, the real part of the eigenvalues *λ*<sup>5</sup> and *λ*<sup>6</sup> becomes positive (Figure 21b for *Q<sup>c</sup>* = 73 kVAr and *Q<sup>c</sup>* = 74 kVAr). CPL increases from zero up to 72 kVAr (with fixed ܲ = 100 kW), the eigenvalues ߣ and ߣ଼ move to the left while ߣ<sup>ହ</sup> and ߣ move toward the right. For the considered intervals of the active power and reactive power, the real part of ߣ<sup>ହ</sup> and ߣ remains sufficiently negative and the system stability is not affected. However, when the active power ܲ or the reactive power ܳ become greater than certain limits, the real parts of the eigenvalues ߣ<sup>ହ</sup> and ߣ become positive which causes system instability. For example, when ܳ is fixed to zero, the limit value of active power ܲ absorbed by the CPL is 124.5 kW, beyond this value, the real part of the eigenvalues ߣ<sup>ହ</sup> and ߣ becomes positive (Figure 21a for ܲ = 124kW and ܲ = 126kW) and the system cannot be considered asymptotically stable around the considered operating point. In the same manner, when ܲ is fixed to 100 kW, the limit value of reactive power ܳ absorbed by the CPL is 74.3 kVAr; beyond this value, the real part of the eigenvalues ߣ<sup>ହ</sup> and ߣ becomes positive (Figure 21b for ܳ = 73 kVAr and ܳ = 74 kVAr). To confirm the results concerning the stability limits imposed by the CPL, the Simscape simulations were made for two values of the CPL active power, one less than the active power limit (ܲ = 124 kW) and another one higher than this limit (ܲ = 125kW) and the results are shown in Figure 22a,b. These results are in perfect accordance with the conclusions drawn from the established state model relating to the impact of the CPL on the stability of the considered system.

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not vary with the evolution of ܲ or ܳ

increasing.

**Figure 19.** Evolution of Eigenvalues with the change in voltage drop 6 < ∆ா < 70(V) with ∆

*4.4. Eigenvalue Trajectory and Sensibility Analysis for Different Values of Load Parameters*

In order to explain the effect of load variation on system stability, a study of the variation of dominant eigenvalue trajectories under different load conditions is established. Starting with the CPL type, Figure 20a,b show the trajectory of the eigenvalues under the effect of the change in active ܲ and reactive ܳ powers absorbed by the CPL. As the active power or the reactive power absorbed by the CPL increases up to 120 kW (with fixed ܳ = 0) and 72 kVAr(with fixed ܲ = 100 kW), respectively, the eigenvalues ߣ<sup>ହ</sup>

ߣ଼ are the most sensitive to the change of ܲ or ܳ of the CPL. The other eigenvalues do

increases from 100 kW up to 120 kW (with fixed ܳ = 0), the eigenvalues ߣ and ߣ଼ move to the left far away from zero while ߣ<sup>ହ</sup> and ߣ move toward the right but remain

sufficiently negative. In the same manner, when the reactive power (ܳ

. When the active power (ܲ

to

) absorbed by the CPL

) absorbed by the

**Figure 20.** Evolution of eigenvalues with the change of the CPL active and reactive power: (**a**) ܲ increasing 100(kW) < ܲ < 120(kW) and ܳ = 0; (**b**) ܳ increasing 0 < ܳ < 72(kVAr) and ܲ = 100 kW. **Figure 20.** Evolution of eigenvalues with the change of the CPL active and reactive power: (**a**) *P<sup>c</sup>* increasing 100(kW) < *P<sup>c</sup>* < 120(kW) and *Q<sup>c</sup>* = 0; (**b**) *Q<sup>c</sup>* increasing 0 < *Q<sup>c</sup>* < 72(kVAr) and *P<sup>c</sup>* = 100 kW. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 22 of 27

**Figure 21.** Evolution of the eigenvalues with the change of the CPL active or reactive power around their limited values: (**a**) active power variation from ܲ = 124 kW to ܲ = 126 kW when ܳ = 0; (**b**) reactive power variation from ܳ = 73 kVAr to ܳ = 74 kVAr when ܲ = 100 kW. **Figure 21.** Evolution of the eigenvalues with the change of the CPL active or reactive power around their limited values: (**a**) active power variation from *P<sup>c</sup>* = 124 kW to *P <sup>c</sup>* = 126 kW when *Q<sup>c</sup>* = 0; (**b**) reactive power variation from *Q<sup>c</sup>* = 73 kVAr to *Q<sup>c</sup>* = 74 kVAr when *P<sup>c</sup>* = 100 kW.

(**a**) (**b**) **Figure 22.** Evolution of the DGs active power (Simscape model with both DGs connected at 0 s): (**a**) ܲ = 124 kW. (**b**) ܲ =

> In order to maintain the microgrid stability for higher values of active power absorbed by the CPL, one solution consists of adding a capacitor to the PCC to which the CPL is connected. Then, the established state model can be used to dimension the necessary capacitor value for the required CPL active power. For the considered microgrid, the CPL is connected to PCC3, and based on the above analysis, the system stability is affected when the CPL active power becomes higher than 124 kW. The latter active power limit can be augmented; for example, to ܲ = 620 kW by imposing an adapted value to the capacitor connected to PCC3. This value can be determined using the established state

When ܳ = 0, the limit value of active power ܲ absorbed by the CPL becomes 620

625 kW. Then the microgrid stability is ensured up to ܲ = 620 kW. This result is in perfect accordance with the Simscape simulation results shown in Figure 24a,b. Hence, the stability analysis based on the established state model can be used as a powerful tool to

is modified from 0.4 µF to 2 µF. Figure 23 shows that the real

is negative for ܲ = 620 kW and positive for ܲ =

To confirm the results concerning the stability limits imposed by the CPL, the Simscape simulations were made for two values of the CPL active power, one less than the active power limit (*P<sup>c</sup>* = 124 kW) and another one higher than this limit (*P<sup>c</sup>* = 125kW) and the results are shown in Figure 22a,b. These results are in perfect accordance with the conclusions drawn from the established state model relating to the impact of the CPL on the stability of the considered system. (**a**) (**b**) **Figure 21.** Evolution of the eigenvalues with the change of the CPL active or reactive power around their limited values: (**a**) active power variation from ܲ = 124 kW to ܲ = 126 kW when ܳ = 0; (**b**) reactive power variation from ܳ = 73 kVAr to ܳ = 74 kVAr when ܲ = 100 kW.

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**Figure 22.** Evolution of the DGs active power (Simscape model with both DGs connected at 0 s): (**a**) ܲ = 124 kW. (**b**) ܲ = 125 kW. **Figure 22.** Evolution of the DGs active power (Simscape model with both DGs connected at 0 s): (**a**) *P<sup>c</sup>* = 124 kW. (**b**) *Pc* = 125 kW.

In order to maintain the microgrid stability for higher values of active power absorbed by the CPL, one solution consists of adding a capacitor to the PCC to which the CPL is connected. Then, the established state model can be used to dimension the necessary capacitor value for the required CPL active power. For the considered microgrid, the CPL is connected to PCC3, and based on the above analysis, the system stability is affected when the CPL active power becomes higher than 124 kW. The latter active power limit can be augmented; for example, to ܲ = 620 kW by imposing an adapted value to the capacitor connected to PCC3. This value can be determined using the established state In order to maintain the microgrid stability for higher values of active power absorbed by the CPL, one solution consists of adding a capacitor to the PCC to which the CPL is connected. Then, the established state model can be used to dimension the necessary capacitor value for the required CPL active power. For the considered microgrid, the CPL is connected to PCC3, and based on the above analysis, the system stability is affected when the CPL active power becomes higher than 124 kW. The latter active power limit can be augmented; for example, to *P<sup>c</sup>* = 620 kW by imposing an adapted value to the capacitor connected to PCC3. This value can be determined using the established state model.

model. When ܳ = 0, the limit value of active power ܲ absorbed by the CPL becomes 620 kW when the capacitor ܿ<sup>ଷ</sup> is modified from 0.4 µF to 2 µF. Figure 23 shows that the real part of the eigenvalues ߣ<sup>ହ</sup> and ߣ is negative for ܲ = 620 kW and positive for ܲ = 625 kW. Then the microgrid stability is ensured up to ܲ = 620 kW. This result is in perfect accordance with the Simscape simulation results shown in Figure 24a,b. Hence, the stability analysis based on the established state model can be used as a powerful tool to When *Q<sup>c</sup>* = 0, the limit value of active power *P<sup>c</sup>* absorbed by the CPL becomes 620 kW when the capacitor *c*<sup>3</sup> is modified from 0.4 µF to 2 µF. Figure 23 shows that the real part of the eigenvalues *λ*<sup>5</sup> and *λ*<sup>6</sup> is negative for *P<sup>c</sup>* = 620 kW and positive for *P<sup>c</sup>* = 625 kW. Then the microgrid stability is ensured up to *P<sup>c</sup>* = 620 kW. This result is in perfect accordance with the Simscape simulation results shown in Figure 24a,b. Hence, the stability analysis based on the established state model can be used as a powerful tool to adjust mesh microgrids to guarantee their stability when their loads or even their architectures change.

Concerning the serial R–L loads in the microgrid, the impact of their variations on the system stability is studied by analyzing the evolution of the eigenvalues mostly impacted by the change under constant power factor of each RL-load connected to a given PCC. In fact, the power factor of classical loads is usually higher than 0.92 and its variation can be neglected. For the three serial RL-loads of the considered microgrid shown in Figures 10 and 25–27 show the evolution of the eigenvalues mostly impacted by varying (from initial value to 50% of this value) the impedances of RL-load3, RL-load4 and RL-load5 under constant power factor, respectively. The most impacted eigenvalues in this case are *λ*<sup>1</sup> to *λ*12, which correspond to line current equations and *λ*<sup>13</sup> to *λ*<sup>20</sup> as well as *λ*<sup>25</sup> and *λ*26, which correspond to the PCC voltage equations. It can be noticed that when the value of each RL-load decreases under constant power factor, the eigenvalues mostly impacted move to the right but remain sufficiently negative and do not impact the system stability as long as the load variation is within the indicated power range.

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tectures change.

**Figure 23.** Evolution of the eigenvalues with the change of the CPL active power around its limited value from ܲ = 620 kW to ܲ = 625 kW when ܳ = 0. **Figure 23.** Evolution of the eigenvalues with the change of the CPL active power around its limited value from *P<sup>c</sup>* = 620 kW to *P<sup>c</sup>* = 625 kW when *Q<sup>c</sup>* = 0. **Figure 23.** Evolution of the eigenvalues with the change of the CPL active power around its limited value from ܲ = 620 kW to ܲ = 625 kW when ܳ = 0.

adjust mesh microgrids to guarantee their stability when their loads or even their archi-

adjust mesh microgrids to guarantee their stability when their loads or even their archi-

625 kW. Concerning the serial R–L loads in the microgrid, the impact of their variations on **Figure 24.** Evolution of the DGs active power (Simscape model with both DGs connected at 0 s): (**a**) ܲ = 620 kW. (**b**) ܲ = 625 kW. **Figure 24.** Evolution of the DGs active power (Simscape model with both DGs connected at 0 s): (**a**) *P<sup>c</sup>* = 620 kW. (**b**) *Pc* = 625 kW. *Sustainability* **2021**, *13*, x FOR PEER REVIEW 24 of 27

the system stability is studied by analyzing the evolution of the eigenvalues mostly im-

Concerning the serial R–L loads in the microgrid, the impact of their variations on

**Figure 25.** Evolution of eigenvalues corresponding to the decrease in RL-load3 under constant power factor: 175 < R୭ୟୢଷ < 376(Ω) and 0.13 < L୭ୟୢଷ < 0.25(H). **Figure 25.** Evolution of eigenvalues corresponding to the decrease in RL-load3 under constant power factor: 175 < RLoad3 < 376(Ω) and 0.13 < LLoad3 < 0.25(H).

**Figure 26.** Evolution of eigenvalues corresponding to the decrease in RL-load4 under constant

power factor: 155 < R୭ୟୢସ < 319(Ω) and 0.085 < L୭ୟୢସ < 0.17(H).

**Figure 26.** Evolution of eigenvalues corresponding to the decrease in RL-load4 under constant power factor: 155 < R୭ୟୢସ < 319(Ω) and 0.085 < L୭ୟୢସ < 0.17(H). **Figure 26.** Evolution of eigenvalues corresponding to the decrease in RL-load4 under constant power factor: 155 < RLoad4 < 319(Ω)and 0.085 < LLoad4 < 0.17(H). **Figure 26.** Evolution of eigenvalues corresponding to the decrease in RL-load4 under constant power factor: 155 < R୭ୟୢସ < 319(Ω) and 0.085 < L୭ୟୢସ < 0.17(H).

**Figure 25.** Evolution of eigenvalues corresponding to the decrease in RL-load3 under constant

**Figure 25.** Evolution of eigenvalues corresponding to the decrease in RL-load3 under constant

power factor: 175 < R୭ୟୢଷ < 376(Ω) and 0.13 < L୭ୟୢଷ < 0.25(H).

power factor: 175 < R୭ୟୢଷ < 376(Ω) and 0.13 < L୭ୟୢଷ < 0.25(H).

*Sustainability* **2021**, *13*, x FOR PEER REVIEW 24 of 27

**Figure 27.** Evolution of eigenvalues corresponding to the decrease in RL-load5 under constant power factor: 126 < RLoad5 < 252(Ω) and 0.077 < LLoad5 < 0.1564(H).

#### *4.5. Mesh Microgrid Control Robustness*

Based on the established and validated state-model, including the modified droopcontrol that ensures active and reactive power sharing, the considered mesh microgrid control robustness with respect to the modifications caused by the connection of DGs and large load variations is studied. In this simulation, at 0 s, the first DG sets the frequency of the microgrid and the voltages of the PCCs while only the first RL load is connected. Then, the second DG is interconnected to the microgrid at 5 s after being synchronized from 1 s to 5 s. At 8 s, the second RL load is also connected, applying a high positive load step to the microgrid. Finally, at 11 s, the CPL load absorbing an active power of 100 kW is also connected to the microgrid to verify its effect on the active and reactive power sharing.

Due to the modified droop control strategy given by Equations (9) and (10), the active and reactive power sharing is ensured (Figure 28a,b). The convergence of the reactive power of the two DGs under different load conditions is convincingly verified in Figure 28b. In addition, and as foreseen by the stability analysis based on the state-model, the microgrid stability is ensured in different microgrid structure configuration when the CPL active power load does not exceed 124 kW.

**Figure 28.** Evolution of the DG active (**a**) and reactive (**b**) powers under different states of charge. **Figure 28.** Evolution of the DG active (**a**) and reactive (**b**) powers under different states of charge.

#### **5. Discussion** An improved droop control strategy for synchronization and power sharing was ap-**5. Discussion**

sharing.

plied on a mesh multi-PCC islanded microgrid. With only the information on the measured RMS voltage value at a pilot node, this strategy has proven its efficiency for fast synchronization as well as active and reactive power sharing between all microgrid DGs. This makes the mesh multi-PCC microgrid eligible to the "plug and play" feature. In order to study the microgrid stability and its droop control robustness, a state An improved droop control strategy for synchronization and power sharing was applied on a mesh multi-PCC islanded microgrid. With only the information on the measured RMS voltage value at a pilot node, this strategy has proven its efficiency for fast synchronization as well as active and reactive power sharing between all microgrid DGs. This makes the mesh multi-PCC microgrid eligible to the "plug and play" feature.

**Figure 27.** Evolution of eigenvalues corresponding to the decrease in RL-load5 under constant

Based on the established and validated state-model, including the modified droopcontrol that ensures active and reactive power sharing, the considered mesh microgrid control robustness with respect to the modifications caused by the connection of DGs and large load variations is studied. In this simulation, at 0 s, the first DG sets the frequency of the microgrid and the voltages of the PCCs while only the first RL load is connected. Then, the second DG is interconnected to the microgrid at 5 s after being synchronized from 1 s to 5 s. At 8 s, the second RL load is also connected, applying a high positive load step to the microgrid. Finally, at 11 s, the CPL load absorbing an active power of 100 kW is also connected to the microgrid to verify its effect on the active and reactive power

Due to the modified droop control strategy given by Equations (9) and (10), the active and reactive power sharing is ensured (Figure 28a,b). The convergence of the reactive power of the two DGs under different load conditions is convincingly verified in Figure 28b. In addition, and as foreseen by the stability analysis based on the state-model, the microgrid stability is ensured in different microgrid structure configuration when the CPL

power factor: 126 < R୭ୟୢହ < 252(Ω) and 0.077 < L୭ୟୢହ < 0.1564(H).

*4.5. Mesh Microgrid Control Robustness*

active power load does not exceed 124 kW.

model of the complete system has been proposed and validated based on simulation results achieved using both the Simscape model and proposed state-model. Then, the stability analysis of the considered non-linear system at each operating point was performed using the Jacobean matrix of the state model. In practice, the dynamic behavior of different state variables and the origin of different frequency components were found by studying the evolution of the system eigenvalues with respect to the parameters of the power lines, DGs and different loads. It was found that the most influent system parameters on its stability were the DGs control parameters and the CPL active power level. In order to study the microgrid stability and its droop control robustness, a state model of the complete system has been proposed and validated based on simulation results achieved using both the Simscape model and proposed state-model. Then, the stability analysis of the considered non-linear system at each operating point was performed using the Jacobean matrix of the state model. In practice, the dynamic behavior of different state variables and the origin of different frequency components were found by studying the evolution of the system eigenvalues with respect to the parameters of the power lines, DGs and different loads. It was found that the most influent system parameters on its stability were the DGs control parameters and the CPL active power level.

In addition, it has been shown through an example that the established state model, which allows the study of system stability, can be used as a powerful tool to adjust certain mesh microgrid parameters to guarantee its stability when the absorbed active power level of its CPLs becomes too high. Finally, the validated microgrid state-model, including the modified droop-control that ensures active and reactive power sharing, also achieved mesh microgrid control robustness with respect to the modifications caused by the connection of DGs and large load variations, which means that the new droop control is always effective under different network configurations.

The developed modified droop control strategy can be adapted and used for power sharing in grid-connected mesh microgrids, and the synchronization strategy can also be adapted for a seamless transfer from an islanded microgrid to a grid-connected microgrid. As mentioned in the Introduction, the developed and validated state-space model can be the base for many future studies in mesh microgrids.

**Author Contributions:** Conceptualization, Y.H., A.B., S.P. and F.M.-T.; methodology, S.P. and F.M.- T.; software, Y.H.; validation, A.B., J.-P.M., S.P. and F.M.-T.; formal analysis, Y.H.; investigation, Y.H.; resources, S.P., F.M.-T. and A.B.; data curation, Y.H.; writing—original draft preparation, Y.H.; writing—review and editing, F.M.-T. and S.P.; visualization, Y.H.; supervision, A.B., J.-P.M., S.P. and F.M.-T.; project administration, A.B., J.-P.M., S.P. and F.M.-T.; funding acquisition, A.B., J.-P.M., S.P. and F.M.-T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project was financially supported by Ministry of Europe and Foreign Affairs, Ministry of Higher Education, Research and Innovation and the French Institute of Rabat (PHC TOUBKAL 2019 (French–Morocco bilateral program) Grant Number: 12345AB).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** No suggested Data Availability Statements.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article*

## **Improving the E**ffi**ciency and Sustainability of Power Systems Using Distributed Power Factor Correction Methods**

## **Ciprian Mihai Coman 1,2,\*, Adriana Florescu <sup>3</sup> and Constantin Daniel Oancea <sup>4</sup>**


Received: 27 February 2020; Accepted: 8 April 2020; Published: 13 April 2020

**Abstract:** For the equipment connected to the three-phase or single-phase grid, the power factor represents an efficiency measure for the usage of electrical energy. The power factor improvement through correction methods reduces the load on the transformers and power conductors, leading to a reduction of losses in the mains power supply and a sustainable grid system. The implications at the financial level are also important. An example of load that generates a small power factor is represented by a motor without mechanical load or having a small mechanical load. Given the power factor correction (PFC), the costs are reduced through the elimination of penalties, applying only in the common coupling point (CCP). The advantages of using equipment for the power factor correction are related also to their long operation duration and the easiness of their installation. The device presented in this article takes advantage of the advances in information and communication technology (ICT) to create a new approach for telemetry and remote configuration of a PFC. This approach has flexibility and versatility, such that it can be adapted to many loads, easily changing the capacitance steps and settings of the power factor correction device.

**Keywords:** power factor; reactive power; capacitance; harmonics; telemetry; Industry 4.0

### **1. Introduction**

The power factor is a measure of the efficiency of the use of electricity. Improved power factor correction reduces the load of the transformers and conductors of electrical installations. The implications are also financial in nature, a low power factor increasing the cost of consumed electrical energy [1–4].

Reactive power is an important parameter of the electrical power that leads to a decreased power factor. It is generated by two main factors: reactive elements and unbalances in the three-phase systems [5]. For example, AC rotary machines will induce extra losses when unbalanced load current and reactive power are absorbed by a single-phase load. Sensitive electronic equipment is particularly disturbed by the low power factor generated by unbalanced current. There are many authors that explored ways to reduce the extra costs generated by reactive power [6–11].

The use of capacitors for the correction of the power factor is related to the long service life and the ease of installation. It should be kept in mind that the capacitor batteries introduce disturbances in the network when they are connected and disconnected. The maximum value of the voltage does not exceed (in the absence of harmonics) twice the maximum value of the rated voltage, when switching the discharged capacitors [12].

In the case of a capacitor already charged at the time of switching off, the overvoltage can reach a maximum value approaching three times the peak nominal value. When considering the automatic step change of capacitor batteries, care must be taken that the section of capacitors to be supplied is completely discharged [1,12].

An overexcited synchronous condenser is another option to correct the power factor. Basically, it is a synchronous electric drive/generator in the no load electric drive state, but with overexcited current. This is a much more expensive option because of the special design needed (e.g., oversized windings and special rotor shaft), which is the main disadvantage. An advantage is the missing disturbances in the power network.

Good management of an electrical energy consumer network includes the evaluation of the power factor and actions to improve it. For the reliable measurement of power, reactive power, the appearance of the resonance phenomenon needs to be taken into consideration and has been studied by various authors, with several approaches being published in various articles [13–15]. We use mathematical models to describe the performance of the power factor corrector, similar to the ones described in [16]. There are also principles for optimization of the power factor in a closed network, such as the proportional-integral-derivative (PID) algorithm [17].

In the context of increasing the penetration of the intermittent renewable energy sources, the concept of microgrids (MG) becomes more frequent as a solution to these issues. There are efforts being made to improve the solutions available to microgrid developers in order to compensate the power factor and the load asymmetries inside the microgrid by utilizing advanced functionalities enabled by grid tied inverters of photovoltaics and energy storage systems [18,19].

Advanced operational capabilities of power electronic based distributed energy resources (DERs) can be employed to compensate power quality phenomena such as harmonics, interharmonics, and current/voltage unbalances [15,19–22]. Hence, smart and multi-functional inverters are capable of providing multiple ancillary services to the MG, along with dedicated resources such as automatic power factor correction equipment.

The problems of degrading power factor and reactive power are mainly present in the industrial environment, where the frequency of inductive loads is significant, most commonly from electric motors. Due to rapid advances in ICT, the digital transformation is expanding across all domains. In the industrial environment, most often, it takes the form of Industry 4.0 ecosystems that integrate several technologies and concepts such as the Internet of Things (IOT), big data, cloud computing, and smart metering, in order to allow real-time monitoring and controlling of a complex industrial system using remote computers and mobile devices [23–27].

Similar applications are employed in ship main propulsion power monitoring systems. In the particular application explored in [28], wireless telemetry technology was used alongside the MODBUS communication protocol.

The topic of power factor correction has been previously explored and presented in the literature, using different approaches. In [29], a new digital power factor correction (PFC) control strategy was presented, based on digital signal processor speed to solve the problem of limited switching frequency. In [30], a programmable logic controller (PLC) was used to control switch capacitors for PFC near a three-phase electric induction motor. More complex PFC decision algorithms were analyzed in [31], and a new teaching learning based optimization (TLBO) approach was studied along with a cloud based data warehouse for electrical parameters. The power factor has different limits depending on the country. A value of about 0.8 is suitable for industrial loads. Under semi-industrial/mixed conditions, a value of 0.85 is a common value, while 0.9 is generally used/considered for residential areas.

In order to improve electrical energy efficiency through the current quality, this paper analyzes the performances of a proposed distributed power factor correction methodology. For this purpose, a new design and implementation of a PFC are performed. It uses an industrial decision device manufactured by Ducati Energia [32,33], five capacitor batteries that can be engaged incrementally, ICT in general, and IOT in particular. This approach has flexibility and versatility, such that it can be adapted to many loads, easily changing the capacitance steps and the settings of the power factor correction device. The switching overvoltage problem is solved using the decision software to prevent a switch from taking place before the capacitors are discharged. Tests are performed on a motor with no load, at initial PF of 0.64. Using the correction device, the PF is improved to 0.8. Our goal is to create a versatile solution that is easy to adapt and configure in industrial settings, not to push the PF to the ideal value of one.

The rest of the paper is organized as follows. Section 2 presents the general architecture of the PFC system, along with the materials and methods used. Details on the implementation of the experimental model are presented in Section 3, while Section 4 presents the measured results at the switching moment. The paper concludes in Section 5.

#### **2. Background, Materials, and Methods**

#### *2.1. Background*

In the sinusoidal regime, for single-phase or three-phase circuits symmetrically charged, for which the RMS values of the voltages and currents on the three phases (but also the phase differences between the corresponding phasors) are equal, the power factor is defined as the positive and subunit ratio between the active power P and the apparent power S [34]. Regarding the power factor notations, the PF notation is used in the U.S. regulations, while the λ notation is used in the European regulations.

$$1 \ge \lambda \equiv \text{PF} = \frac{\text{P}}{\text{S}} \ge 0 \tag{1}$$

For a linear and passive dipole, we have for the power factor the expression:

$$\lambda \equiv \text{PF} = \frac{\text{P}}{\text{S}} = \frac{\text{U} \cdot \text{I} \cdot \cos \varphi}{\text{U} \cdot \text{I}} = \cos \varphi, \ 0 \le \cos \varphi \le 1 \tag{2}$$

The PF is easily determined from the power triangle. Thus, the power factor is the ratio of active power to apparent power. If mathematically, this ratio is also described by the cosine of the angle between the two powers, in reality, the coincidence between the two sizes will exist only if the waveform of the current is sinusoidal (that is, if they are not harmonic):

$$\text{PF} = \frac{\text{P}}{\text{S}} \quad \cos(\varphi) = \frac{\text{P}\_1}{\text{S}\_1} \tag{3}$$

where P and S are the active, respectively the apparent, total power, and P<sup>1</sup> and S<sup>1</sup> are the active power, respectively the apparent, power given by the fundamental (1st order harmonic).

In the non-sinusoidal regime, the components that define the power factor (the active power P, respectively the apparent power S) are the same with the mention that the apparent power S is written according to the three orthogonal components: the active power P, the reactive power Q, and the deforming power D, so that Equation (2) changes into (4):

$$\lambda \equiv \text{PF} = \frac{\text{P}}{\text{S}} = \frac{\text{P}}{\sqrt{\text{P}^2 + \text{Q}^2 + \text{D}^2}} \tag{4}$$

Even if there is no reactive power, the power factor remains lower than 1, due to the deforming power specific to the non-sinusoidal regime. Generally, the cancellation of the reactive power does not improve the power factor as it does in the sinusoidal regime. It is possible that by reducing the reactive power, the deforming power increases even more. This means that in the non-sinusoidal mode, by adding capacitors, it is sometimes possible to even worsen the power factor.

The reactive factor and the deforming factor are defined. The reactive factor is defined as the ratio between the reactive power and the active power in the circuit, at one point [34]:

$$
\rho = \frac{\mathbf{Q}}{\mathbf{P}} \tag{5}
$$

while the deforming factor represents the ratio between the deforming power and the non-deforming power:

$$\pi = \frac{\mathbf{D}}{\sqrt{\mathbf{P}^2 + \mathbf{Q}^2}} \tag{6}$$

Relation (4) turns into Relation (7), where cos ξ is a notation given by (8):

$$\lambda \equiv \text{PF} = \frac{\text{P}}{\text{S}} = \frac{\text{P}}{\sqrt{\text{P}^2 + \text{Q}^2}} \cdot \frac{\sqrt{\text{P}^2 + \text{Q}^2}}{\sqrt{\text{P}^2 + \text{Q}^2 + \text{D}^2}} = \cos \varphi \cdot \cos \xi,\tag{7}$$

$$\cos \xi = \frac{\sqrt{\mathbf{P}^2 + \mathbf{Q}^2}}{\sqrt{\mathbf{P}^2 + \mathbf{Q}^2 + \mathbf{D}^2}} < 1 \tag{8}$$

The expression of the power factor can be rewritten as (9):

$$
\lambda = \text{PF} = \frac{1}{\sqrt{1+\rho^2}} \cdot \frac{1}{\sqrt{1+\tau^2}} \tag{9}
$$

In the non-sinusoidal regime, the definition of the power factor does not express the degree of use of the power available in the network, because the sources of harmonics are not the generators of the network, but actually the nonlinear receivers.

In the non-sinusoidal mode, two values for the power factor are defined and measured: the power factor for the fundamental component (fundamental 50/60 Hz power factor or displacement power factor (DPF)) and the total power factor (PF) (true/total power factor):

$$\lambda\_1 \equiv \text{DPF} = \cos \varphi\_1 = \frac{\mathbf{P}\_1}{\mathbf{S}\_1} \tag{10}$$

$$
\lambda \equiv \text{PF} = \frac{\text{P}}{\text{S}} = \frac{\text{P}}{\text{U} \cdot \text{I}} \tag{11}
$$

In the U.S., the penalties applied to industrial consumers are based on the value of the fundamental power factor given by Relation (10) above [34]. The total power factor includes the influence of the harmonics on the active power, and the apparent power provides information on the efficiency of the use of the active power at the consumer.

An expression can be established for the total power factor in the non-sinusoidal regime, depending on the current and voltage distortion factors. To do this, the expressions of active power and apparent power are written. The active power in the non-sinusoidal regime is given by the sum of the active powers corresponding to each harmonic in part, generating two components, the fundamental active power and the harmonic active power (the deforming residue of the active power):

$$\mathbf{P} = \sum\_{\mathbf{h}=1} \mathbf{U\_h} \cdot \mathbf{l\_h} \cdot \cos(\alpha\_\mathbf{h} - \beta\_\mathbf{h}) = \sum\_{\mathbf{h}=1} \mathbf{U\_h} \cdot \mathbf{l\_h} \cdot \cos \varphi\_\mathbf{h} = \mathbf{P}\_1 + \mathbf{P}\_\mathbf{H} \tag{12}$$

$$\mathbf{P}\_1 = \mathbf{U}\_1 \cdot \mathbf{I}\_1 \cdot \cos \varphi\_1 \tag{13}$$

$$\mathbf{P\_H} = \sum\_{\mathbf{h}=1} \mathbf{U\_h} \cdot \mathbf{l\_h} \cdot \cos \varphi\_{\mathbf{h}} \tag{14}$$

The apparent power of an electric dipole is defined by the product of the RMS values of the voltage and current, denoted by S in Relation (15). Similarly, the apparent power in the non-sinusoidal regime can be decomposed into the fundamental apparent power S1 given by Relation (16) and the harmonic apparent power (the residual apparent power) SN given by Relation (17). The fundamental apparent power, S1, and its components P1 and Q1 are of great interest because they intervene in the circulation of powers in the circuit. In the non-sinusoidal mode, the apparent power can be expressed according to the RMS value of the voltage and the RMS value of the current, according to (18):

$$\mathbf{S} = \mathbf{U} \cdot \mathbf{I} \tag{15}$$

$$\mathbf{S}\_1 = \mathbf{U}\_1 \cdot \mathbf{I}\_1 \tag{16}$$

$$\mathbf{S}\_1^2 = \mathbf{P}\_1^2 + \mathbf{Q}\_1^2 \tag{17}$$

$$\mathbf{S}^2 = (\mathbf{U} \cdot \mathbf{I})^2 = \left(\mathbf{U}\_1^2 + \mathbf{U}\_\mathbf{H}^2\right) \cdot \left(\mathbf{I}\_1^2 + \mathbf{I}\_\mathbf{H}^2\right) = \mathbf{S}\_1^2 + \mathbf{S}\_\mathbf{H}^2 \tag{18}$$

The power factor can be rewritten in a form that takes into account the Total Harmonic Distortion factor for the voltage (THDU) and the Total Harmonic Distortion factor for the current (THD<sup>I</sup> ) both defined below [34]:

$$\mathbf{k}\_{\rm dl} \equiv \mathbf{T} \mathbf{H} \mathbf{D}\_{\rm l} = \frac{\mathbf{I}\_{\rm H}}{\mathbf{I}\_{\rm l}} = \sqrt{\frac{\sum\_{\mathbf{h} \neq 1} \mathbf{I}\_{\mathbf{h}}^{2}}{\mathbf{I}\_{\rm l}^{2}}};\\\mathbf{k}\_{\rm dU} \equiv \mathbf{T} \mathbf{H} \mathbf{D}\_{\rm U} = \frac{\mathbf{U}\_{\rm H}}{\mathbf{U}\_{\rm l}} = \sqrt{\frac{\sum\_{\mathbf{h} \neq 1} \mathbf{U}\_{\rm h}^{2}}{\mathbf{U}\_{\rm l}^{2}}} \tag{19}$$

$$\lambda \equiv \text{PF} = \frac{\text{P}}{\text{S}} = \frac{\text{P}\_1 + \text{P}\_{\text{H}}}{\sqrt{\text{S}\_1^2 + \text{S}\_{\text{N}}^2}} = \frac{\frac{\text{P}\_1}{\text{S}\_1} \left(1 + \frac{\text{P}\_{\text{H}}}{\text{P}\_1}\right) \cdot \text{DPF}}{\sqrt{1 + \frac{\text{S}\_{\text{N}}}{\text{S}\_1}}^2} = \frac{\left(1 + \frac{\text{P}\_{\text{H}}}{\text{P}\_1}\right) \cdot \text{DPF}}{\sqrt{1 + \text{T}\text{HD}\_1^2 + \text{T}\text{HD}\_{\text{U}}^2 + \left(\text{THD}\_1 + \text{THD}\_{\text{U}}\right)^2}}\tag{20}$$

For THD<sup>U</sup> < 5% and for THD<sup>I</sup> > 40%, the relation between the total power factor and the fundamental power factor can be written with the approximate formula (21):

$$\lambda \equiv \text{PF} = \frac{1}{\sqrt{1 + \text{THD}\_{\text{I}}^2}} \cdot \text{DPF} = \frac{\text{I}\_{\text{I}}}{\text{I}} \cdot \cos \varphi\_{\text{I}} \tag{21}$$

The meanings of the quantities in (21) are: I<sup>1</sup> is the RMS value of the fundamental component of the current; I is the RMS value of the non-sine current; and ϕ<sup>1</sup> is the offset angle between the curves of the fundamental components of the voltage and the current.

Many modern equipment such as switching power supplies or speed adjustment equipment have the fundamental power factor close to 1, but the total power factor can be 0.5–0.6. In order to avoid non-compliant situations, it is necessary to measure both the fundamental power factor and the total power factor. The modern measuring devices (for example, the electric meters) can measure both DSP (PF1) and PF. For industrial consumers, PF is lower than DPF.

A special mention is that in the case of three-phase systems, in the sinusoidal and non-sinusoidal regime, the arithmetic power factor and the vector power factor are defined. In the case of the sinusoidal regime, these values are described below.

The arithmetic apparent power (A, B, C represent the three phases) in (22):

$$\mathbf{S\_{A}} = \sum\_{\mathbf{x} \in \mathbf{A}, \mathbf{B}, \mathbf{C}} \mathbf{S\_{x}} = \mathbf{S\_{A}} + \mathbf{S\_{B}} + \mathbf{S\_{C}} = \sum\_{\mathbf{x} \in \mathbf{A}, \mathbf{B}, \mathbf{C}} \sqrt{\mathbf{P\_{x}^{2}} + \mathbf{Q\_{x}^{2}}} \tag{22}$$

where SA,B,C, PA,B,C, and QA,B,C, represent the apparent power, the active power, and the reactive power on the phase.

Geometrical apparent power can be written as:

$$\mathbf{S}\_{\mathbf{g}} = \sqrt{\mathbf{p}^2 + \mathbf{Q}^2} \tag{23}$$

$$\mathbf{P} = \sum\_{\mathbf{x} \in \mathbf{A}, \mathbf{B}, \mathbf{C}} \mathbf{P}\_{\mathbf{x}} = \mathbf{P}\_{\mathbf{A}} + \mathbf{P}\_{\mathbf{B}} + \mathbf{P}\_{\mathbf{C}} \tag{24}$$

$$\mathbf{Q} = \sum\_{\mathbf{x} \in \mathbf{A}, \mathbf{B}, \mathbf{C}} \mathbf{Q}\_{\mathbf{x}} = \mathbf{Q}\_{\mathbf{A}} + \mathbf{Q}\_{\mathbf{B}} + \mathbf{Q}\_{\mathbf{C}} \tag{25}$$

but can also be written in the form (26):

$$\mathbf{S}\_{\mathbf{S}} = \left| \mathbf{P}\_{\mathbf{A}} + \mathbf{P}\_{\mathbf{B}} + \mathbf{P}\_{\mathbf{C}} + \mathbf{j} \cdot (\mathbf{Q}\_{\mathbf{A}} + \mathbf{Q}\_{\mathbf{B}} + \mathbf{Q}\_{\mathbf{C}}) \right| = \left| \mathbf{P} + \mathbf{j} \cdot \mathbf{Q} \right| \tag{26}$$

Following the conference of the American Institute of Electrical Engineers in 1920, two definitions for the arithmetic power factor, respectively geometrical, were proposed:

$$\lambda\_{\mathbf{a}} \equiv \text{PF}\_{\mathbf{a}} = \frac{\mathbf{P}}{\mathbf{S}\_{\mathbf{a}}} = \frac{\mathbf{P}\_{\mathbf{A}} + \mathbf{P}\_{\mathbf{B}} + \mathbf{P}\_{\mathbf{C}}}{\mathbf{S}\_{\mathbf{A}} + \mathbf{S}\_{\mathbf{B}} + \mathbf{S}\_{\mathbf{C}}} \tag{27}$$

$$
\lambda\_{\mathbf{g}} \equiv \text{PF}\_{\mathbf{g}} = \frac{\mathbf{P}}{\mathbf{S}\_{\mathbf{g}}} = \frac{\mathbf{P}\_{\mathbf{A}} + \mathbf{P}\_{\mathbf{B}} + \mathbf{P}\_{\mathbf{C}}}{\left| \underline{\mathbf{S}\_{\mathbf{A}}} + \underline{\mathbf{S}\_{\mathbf{B}}} + \underline{\mathbf{S}\_{\mathbf{C}}} \right|} \tag{28}
$$

in which the apparent complex powers on the phases are given by:

$$\underline{\mathbf{S\_A}} = \mathbf{P\_A} + \mathbf{j} \cdot \mathbf{Q\_A}; \; \underline{\mathbf{S\_B}} = \mathbf{P\_B} + \mathbf{j} \cdot \mathbf{Q\_B}; \; \underline{\mathbf{S\_C}} = \mathbf{P\_C} + \mathbf{j} \cdot \mathbf{Q\_C} \tag{29}$$

If we have the case of the non-sinusoidal regime, the powers are described below. The apparent arithmetic power (A, B, C represent the three phases) is given in (30). In addition to the sinusoidal regime, it is the appearance of deforming power.

$$\mathbf{S}\_{\mathbf{A}} = \sqrt{\mathbf{P}\_{\mathbf{A}}^2 + \mathbf{Q}\_{\mathbf{A}}^2 + \mathbf{D}\_{\mathbf{A}}^2};\\\mathbf{S}\_{\mathbf{B}} = \sqrt{\mathbf{P}\_{\mathbf{B}}^2 + \mathbf{Q}\_{\mathbf{B}}^2 + \mathbf{D}\_{\mathbf{B}}^2};\\\mathbf{S}\_{\mathbf{C}} = \sqrt{\mathbf{P}\_{\mathbf{C}}^2 + \mathbf{Q}\_{\mathbf{C}}^2 + \mathbf{D}\_{\mathbf{C}}^2} \tag{30}$$

The apparent arithmetic power is:

$$\mathbf{S\_{A}} = \mathbf{S\_{A}} + \mathbf{S\_{B}} + \mathbf{S\_{C}} \tag{31}$$

while the geometrical apparent power is given in (30), and its components are given in (31):

$$\mathbf{S}\_{\mathbf{g}} = \sqrt{\mathbf{P}^2 + \mathbf{Q}^2 + \mathbf{D}^2} \tag{32}$$

$$\mathbf{P} = \mathbf{P}\_{\mathbf{A}} + \mathbf{P}\_{\mathbf{B}} + \mathbf{P}\_{\mathbf{C}} \mathbf{j} \cdot \mathbf{Q} = \mathbf{Q}\_{\mathbf{A}} + \mathbf{Q}\_{\mathbf{B}} + \mathbf{Q}\_{\mathbf{C}} \mathbf{j} \cdot \mathbf{D} = \mathbf{D}\_{\mathbf{A}} + \mathbf{D}\_{\mathbf{B}} + \mathbf{D}\_{\mathbf{C}} \tag{33}$$

In order to characterize the apparent power in the case of unbalanced loads, the term equivalent apparent power is introduced. This can be correlated with losses in power lines and in transformers, in the same way that we have an apparent power for balanced loads. Compared to (34), an equivalent current I<sup>e</sup> and an equivalent phase voltage U<sup>e</sup> can be defined in (35):

$$\mathbf{S} = \sqrt{\mathbf{3}} \cdot \mathbf{U} \cdot \mathbf{I} \tag{34}$$

$$\mathbf{S\_e = 3} \mathbf{\dot{U\_e}} \mathbf{\dot{I\_e}} \tag{35}$$

For a three-phase circuit with a neutral conductor, the equivalent voltage is given by (36):

$$\mathbf{U\_e} = \sqrt{\frac{\mathbf{U\_a^2} + \mathbf{U\_b^2} + \mathbf{U\_c^2}}{3}} \tag{36}$$

For a three-phase circuit without a neutral conductor, the equivalent voltage can be calculated with (37):

$$\mathbf{U\_e} = \sqrt{\frac{\mathbf{U\_{AB}^2} + \mathbf{U\_{BC}^2} + \mathbf{U\_{CA}^2}}{9}} \tag{37}$$

The RMS value of the equivalent current is evaluated according to the RMS values of the currents, IA, IB, and I<sup>C</sup> in (38):

$$\mathbf{I}\_{\mathbf{e}} = \sqrt{\frac{\mathbf{I}\_{\mathbf{A}}^2 + \mathbf{I}\_{\mathbf{B}}^2 + \mathbf{I}\_{\mathbf{C}}^2}{3}} \tag{38}$$

For the particular case of a balanced and linear load, we have U<sup>e</sup> = U, I<sup>A</sup> = I<sup>B</sup> = I<sup>C</sup> = I<sup>e</sup> = I, and the apparent power is written according to Relation (39):

$$\mathbf{S}\_{\mathbf{e}} = \mathbf{S} = \sqrt{3} \cdot \mathbf{U} \cdot \mathbf{I} \tag{39}$$

Finally, the equivalent power factor results in (40):

$$
\lambda\_{\mathbf{e}} \equiv \text{PF}\_{\mathbf{e}} = \frac{\mathbf{P}}{\mathbf{S}\_{\mathbf{e}}} \tag{40}
$$

#### *2.2. Materials and Methods*

For the equipment connected to the three-phase or single-phase network, the power factor is a measure of the efficiency of the use of electricity. Improved power factor correction reduces the load of transformers and conductors of electrical installations. In ideal conditions, the power factor would be 1. An example of a load that produces a low power factor is an engine without a mechanical load or a low mechanical load.

Correcting the power factor leads to increasing the capacity of the network infrastructure and reducing losses in transformers and cables. One method of reducing the power factor, considering that most loads are inductive, is the use of electric capacitor batteries.

The advantages of using electric capacitors for power factor correction are related to the long service life and ease of installation. It should be kept in mind that the capacitor batteries introduce disturbances in the network when they are connected and disconnected. The use of capacitor batteries in automated power factor correction equipment uses several steps, thus ensuring load flexibility.

Creating a database with information on the evolution of the power factor, but also of other current parameters, can only improve the decision of choosing the optimal method for the correction of the power factor, based on the statistical analysis.

There are a number of standards that a device used for power factor correction must meet. Voltages and currents are measured in TrueRMS value. The entire design of the R5 device from Ducati Energia meets the standards: IEC/EN 61010-1, IEC/EN 61000-6-2, IEC/EN 61000-6-4, IEC/EN 61326-1, EN 62311, EN 301-489-1, EN 301-489-3, EN 300-220-2, and EN 300-330.

The switches for connecting/disconnecting the capacitor batteries were specially designed for this operation, being provided with resistors for limiting the current. It was not necessary to use a possible fourth contact for neutral, as the capacitor batteries were connected in a delta configuration according to the manufacturer's recommendations for the power factor correction device. Their supply was through a general switch. The fuses for supplying the Ducati device and the control circuits were dimensioned at 2 A, and the power part was protected by a tripolar safety of 25 A.

The equipment was designed to be used for the 3 × 120 V three-phase network, but could also be used for the 3 × 230 V three-phase network, with minimal modifications.

The electrical diagram, according to the manufacturer's recommendations, is shown in Figure 1. The T1 transformer was only required if the capacitor battery contactor coils were operating at a voltage di *Sustainability*  fferent from that of the mains supply. **2019**, *11*, x FOR PEER REVIEW 8 of 20

**Figure 1.** Power factor correction (PFC) device power diagram for three-phase current. **Figure 1.** Power factor correction (PFC) device power diagram for three-phase current.

The power factor correction equipment was optimally positioned near the load (electric motor). The minimum costs were when the power factor correction equipment was installed in a central position, within the installation. Usually, the power factor correction equipment is installed near the consumption measurement point (meter). The relationships underlying the calculations for determining the power factor compensation capacity are contained in (41) and (42). If it is desired to obtain a certain power factor, not fully compensating it, we can use the relation obtained from the triangle of powers, which directly calculates the reactive power needed to be compensated by the capacitor (43). The initial angle between the voltage and current phases is 1, and the target phase shift is 2. The load was a serial network consisting of a resistor (R) and an inductance (L), which simulated a real inductive load. This was to be offset by a C<sup>C</sup> capacity. The reactive power to be compensated is denoted with Qc. The current transformer was Class 0.5 with the ratio of currents 10/1. It was considered that the equipment would be used for laboratory experiments, for loads up to 10kW. For each particular industrial implementation, the capacitors battery must be adapted to the load, and the decision system parameters must be configured for the algorithm to know the parameters of the system it controls. The components and devices used and the necessary conductors were installed in a box with dimensions of 500 × 400 × 250. The safety measures imposed by the use of dangerous voltages were respected. Thus, safety measures were taken against electrocution by using terminals according to the European standards (they did not have accessible metal elements), and for unauthorized access, an alarm was provided that triggered when the door of the panel was opened, when the panel was powered. The operation of the panel was started with a key, thus avoiding the unauthorized use of the equipment. For each step of the capacitor stack, a light was installed to signal the change. Light indicators were also used to signal the presence of voltage on each phase.

 = = √<sup>2</sup> + <sup>2</sup> = ∙ <sup>2</sup> = ∙ = ∙ <sup>2</sup> (41) = 2 = 1 (42) The power factor correction equipment was optimally positioned near the load (electric motor). The minimum costs were when the power factor correction equipment was installed in a central position, within the installation. Usually, the power factor correction equipment is installed near the consumption measurement point (meter).

 2 ∙ ∙ ∙ = ∙ ((<sup>1</sup> ) − (<sup>2</sup> )) (43) To make the calculations easier, one can imagine a simple application that can determine, for a particular consumer, the capacity needed to achieve full or partial compensation of the power factor. The relationships underlying the calculations for determining the power factor compensation capacity are contained in (41) and (42). If it is desired to obtain a certain power factor, not fully compensating it, we can use the relation obtained from the triangle of powers, which directly calculates the reactive power needed to be compensated by the capacitor (43). The initial angle between the voltage and current phases is ϕ1, and the target phase shift is ϕ2. The load was a serial network

for the compensation capacity using two different calculation methods.

consisting of a resistor (R) and an inductance (L), which simulated a real inductive load. This was to be offset by a C<sup>C</sup> capacity. The reactive power to be compensated is denoted with Qc.

$$\mathbf{I} = \frac{\mathbf{U}}{Z} \mathbf{Z} = \sqrt{\mathbf{R}^2 + \mathbf{X}\_{\mathbf{L}}^2} \mathbf{P} = \mathbf{R} \cdot \mathbf{I}^2 \mathbf{S} = \mathbf{U} \cdot \mathbf{I} \,\mathbf{Q} = \mathbf{X}\_{\mathbf{L}} \cdot \mathbf{I}^2 \tag{41}$$

$$\mathbb{X}\_{\mathbb{C}} = \frac{\mathbb{U}^2}{\mathbb{Q}\_{\mathbb{C}}} \mathbb{C}\_{\mathbb{C}} = \frac{1}{2 \cdot \pi \cdot \mathbb{f} \cdot \mathbb{X}\_{\mathbb{C}}} \tag{42}$$

$$\mathbf{Q}\_{\mathbb{C}} = \mathbf{P} \cdot \left( \tan(\varphi\_1) - \tan(\varphi\_2) \right) \tag{43}$$

To make the calculations easier, one can imagine a simple application that can determine, for a particular consumer, the capacity needed to achieve full or partial compensation of the power factor. Here, MS Excel was used for the calculation; see Figure 2. Yellow is the initial (primary) size and red the intermediate size. Green is the measurements in direct relation with the determination of the compensating capacity, partial or total, of the power factor. The application calculated the same value for the compensation capacity using two di *Sustainability* **2019** fferent calculation methods. , *11*, x FOR PEER REVIEW 9 of 20


**Figure 2.** Application for determining the capacity for power factor compensation. **Figure 2.** Application for determining the capacity for power factor compensation.

To verify the calculations, a simulation was performed in LTSpice; see Figure 3 and Figure 4. The circuit elements were chosen for a phase shift of approximately 45 degrees. The circuit resistance was chosen to be 50 ohms, and the inductance resulted from 150 mH, from the triangle of impedances. For the total compensation of the phase shift determined by the resistor-inductor (RL) circuit R1L1, a capacitor C<sup>1</sup> with a capacity of approximately 32 μF was obtained, connected in parallel with the RL circuit considered. The presented circuit was single-phase (chosen for simplicity and clarity), and for the three-phase circuits, the situation was similar. To verify the calculations, a simulation was performed in LTSpice; see Figures 3 and 4. The circuit elements were chosen for a phase shift of approximately 45 degrees. The circuit resistance was chosen to be 50 ohms, and the inductance resulted from 150 mH, from the triangle of impedances. For the total compensation of the phase shift determined by the resistor-inductor (RL) circuit R1L1, a capacitor C<sup>1</sup> with a capacity of approximately 32 µF was obtained, connected in parallel with the RL circuit considered. The presented circuit was single-phase (chosen for simplicity and clarity), and for the three-phase circuits, the situation was similar.

the three-phase circuits, the situation was similar.

**Figure 2.** Application for determining the capacity for power factor compensation.

To verify the calculations, a simulation was performed in LTSpice; see Figure 3 and Figure 4. The circuit elements were chosen for a phase shift of approximately 45 degrees. The circuit resistance was chosen to be 50 ohms, and the inductance resulted from 150 mH, from the triangle of impedances. For the total compensation of the phase shift determined by the resistor-inductor (RL) circuit R1L1, a capacitor C<sup>1</sup> with a capacity of approximately 32 μF was obtained, connected in parallel with the RL

**Figure 3.** Scheme for simulating the operation of an RL circuit. **Figure 3.** Scheme for simulating the operation of an RL circuit.

**Figure 4.** Scheme for simulating the phase compensation function using a capacitor. **Figure 4.** Scheme for simulating the phase compensation function using a capacitor.

#### **3. Results 3. Results**

#### *3.1. Power Factor Compensation Equipment*

phase and three-phase networks.

*3.1. Power Factor Compensation Equipment* For a power factor compensation circuit, equipment consisting of a Ducati Energia R5 485 device that controlled a five-step capacitor battery and a Raspberry Pi 3 IoT device with the corresponding For a power factor compensation circuit, equipment consisting of a Ducati Energia R5 485 device that controlled a five-step capacitor battery and a Raspberry Pi 3 IoT device with the corresponding program for greater functionality were developed, with more command and control possibilities

program for greater functionality were developed, with more command and control possibilities and a high degree of automation; see Figure 5. The R5 device could be configured to work on both single-

**Figure 5.** Schematic representation of the proposed assembly for power factor correction.

The Ducati Energia R5 device ensured quality analysis in the monitored electrical network, by calculating the cosine of the phase difference between the current and the voltage. Its configuration was achieved both from the buttons on the front panel, but especially by the much greater number

phase and three-phase networks.

*3.1. Power Factor Compensation Equipment*

**3. Results**

and a high degree of automation; see Figure 5. The R5 device could be configured to work on both single-phase and three-phase networks. program for greater functionality were developed, with more command and control possibilities and a high degree of automation; see Figure 5. The R5 device could be configured to work on both single-

that controlled a five-step capacitor battery and a Raspberry Pi 3 IoT device with the corresponding

**Figure 4.** Scheme for simulating the phase compensation function using a capacitor.

*Sustainability* **2019**, *11*, x FOR PEER REVIEW 10 of 20

**Figure 3.** Scheme for simulating the operation of an RL circuit.

**Figure 5.** Schematic representation of the proposed assembly for power factor correction.

**Figure 5.** Schematic representation of the proposed assembly for power factor correction. The Ducati Energia R5 device ensured quality analysis in the monitored electrical network, by calculating the cosine of the phase difference between the current and the voltage. Its configuration was achieved both from the buttons on the front panel, but especially by the much greater number The Ducati Energia R5 device ensured quality analysis in the monitored electrical network, by calculating the cosine of the phase difference between the current and the voltage. Its configuration was achieved both from the buttons on the front panel, but especially by the much greater number of possibilities, using the communication through the MODBUS/RS485 protocol. In addition, the MODBUS protocol could also read data on the network (voltages, currents, powers, phases, total harmonic distortion (THD), etc.). Starting from formula (19), the THD is here calculated based on another equivalent consecrated formula (44), where the current was measured and IRMS easily computed, and the fundamental harmonic was calculated using Fast Fourier Transform (FFT).

$$\text{THD} = \sqrt{\left(\frac{\text{I}\_{\text{RMS}}}{\text{I}\_{1}}\right)^{2} - 1} \tag{44}$$

The capacitor battery schematic is presented in Figure 1 and the implementation in Figure 6. There were five steps, the first two using three monophasic capacitors each and the next three using triphasic capacitors, as follows:

Step I: 3 × 9.6 µF, 0.83 kvar, 1.6 A, 525 V Step II: 3 × 11.6 µF, 0.83 kvar, 1.73 A, 480 V Step III: 6.6 µF, 1 kvar, 1.4 A, 400 V Step IV: 6.6 µF, 1 kvar, 1.4 A, 400 V Step V: 9.95 µF, 1.5 kvar, 2.2 A, 400 V

The implemented MODBUS protocol was based on six callable functions, two of which were of particular interest: Function 03: "READ HOLDING REGISTERS" and Function 06: "PRESET SINGLE REGISTER", the first one for reading data and the second one for configuring the device for correction of the fault power [9,10].

Function 03: "READ HOLDING REGISTERS" reads one or more memory adjacent locations, each one being one or two words in size. It is possible to read up to 12 or 24 consecutive measures. Table 1 describes the read request format (from master to slave) and Table 2 describes the reply format (from slave to master). The standard abbreviations are used in the tables below: address (Addr), function (Func), cyclic redundancy check (CRC), register (Reg), high (H), low (L), most significant word (MSW), least significant word (LSW), integer (Int), voltage transformer (VT), current transformer (CT). triphasic capacitors, as follows:

Step I: 3x 9.6μF, 0.83kvar, 1.6A, 525V Step II: 3x11.6μF, 0.83kvar, 1.73A, 480V

Step IV: 6.6μF, 1kvar, 1.4A, 400V Step V: 9.95μF, 1.5kvar, 2.2A, 400V

of possibilities, using the communication through the MODBUS/RS485 protocol. In addition, the MODBUS protocol could also read data on the network (voltages, currents, powers, phases, total harmonic distortion (THD), etc.). Starting from formula (19), the THD is here calculated based on another equivalent consecrated formula (44), where the current was measured and IRMS easily computed, and the fundamental harmonic was calculated using Fast Fourier Transform (FFT).

> IRMS I1 ) 2

The capacitor battery schematic is presented in Figure 1 and the implementation in Figure 6. There were five steps, the first two using three monophasic capacitors each and the next three using

− 1 (44)

THD = √(

**Figure 6.** Capacitor battery implementation. **Figure 6.** Capacitor battery implementation.




The interpretation of the reply is as follows:


The physical address is always obtained from the measured address reduced by one unit. Examples of addresses and what is read from them are given in Table 3. There are hundreds of addresses with possible readable values [9,10]. The device implementation monitors Line 1, but the commands are available for implementations with several devices. Here, in Table 3, we have some examples of functions. The schematic in Figure 1, which is recommended by the Ducati manufacturer [33], monitors only one line, but is able to work in three-phase systems as well. According to the references, R5 Ducati is a power factor automatic controller for single-phase and three-phase networks with or

without neutral connection. The only precaution is when using the R5 Ducati device in a one-phase power system to select working phases. Using numerical methods, because of the integrated controller, the R5 Ducati device computes additional necessary quantities.


**Table 3.** Examples of readable addresses and the results returned.

Function 06: "PRESET SINGLE REGISTER" lets the user set the setup parameters of the Ducati Energia device. Table 4 presents examples of the addresses of this function.


**Table 4.** Configuration function.


**Table 4.** *Cont*.

#### *3.2. Application Development*

The application was developed in Phyton, an interpreter programming environment, which is relatively easy to follow and also ensures the possibility of an adequate interface. In this case, the user interface is in the form of an HTML page, for maximum compatibility of the application.

Flask is a micro web framework written in Python. It is classified as a microframework because it does not require particular tools or libraries. It was chosen for this application due to its small footprint and easy to use features.

The accessible routes to the application were split into two categories: public and private. The public routes were index and login, which were accessible for everyone, while the private routes required identification with a username and password and included read, admin, and logout.

In order to establish a connection to the remote power factor correction device, the MODBUS protocol was used. The function is presented below:

#### *def get\_instrument():*

```