Integrated Active and Reactive Power Control Methods for Distributed Energy Resources in Distribution Systems for Enhancing Hosting Capacity

Abstract

Recently, there has been a significant increase in the integration of distributed energy resources (DERs) such as small-scale photovoltaic systems and wind turbines in power distribution systems. When the aggregated outputs of DERs are combined, excessive reverse current may occur in distribution lines, leading to overvoltage issues and exceeding thermal limits of the distribution lines. To address these issues, it is necessary to limit the output of DERs to a certain level, which results in constraining the hosting capacity of DERs in the distribution system. In this paper, coordination control methodologies of DERs are developed and executed to mitigate the overvoltage and overcurrent induced by DERs, thereby increasing the hosting capacity for DERs of the distribution system. This paper proposes three coordinated approaches of active and reactive power control of DERs, namely Var Precedence, Watt Precedence, and Integrated Watt and Var Control. The Var and Watt Precedence prioritizes reactive power for voltage (Q–V) and active power for current (P–I) to address network congestion, thereby enhancing hosting capacity. Conversely, the Integrated Var and Watt Precedence propose a novel algorithm that combines four control indices (Q–V, P–V, Q–I, and P–I) to solve network problems while maximizing hosting capacity. The three proposed methods are based on the sensitivity analysis of voltage and current to the active and reactive power outputs at the DER installation locations on the distribution lines, aiming to minimize DER active power curtailment. Each sensitivity is derived from linearized power equations at the operating points of the distribution system. To minimize the computation burden of iterative computation, each proposed method decouples active and reactive power and proceeds with sequential control in its own unique way, iteratively determining the precise output control of distributed power sources to reduce linearization errors. The three proposed algorithms are verified via case studies, evaluating their performance compared to conventional approaches. The case studies exhibit superior control effectiveness of the proposed DER power control methods compared to conventional methods when issues such as overvoltage and overcurrent occur simultaneously in the distribution line so that the DER hosting capacity of the system can be improved.

1. Introduction

The increasing integration of renewable energy resources (RERs), particularly solar photovoltaics (PVs) and wind turbines (WTs), into distribution feeders has marked a transformative shift in the way electricity is generated and distributed [1,2,3]. These technologies have become outstanding owing to their environmental benefits and decreasing costs, making them more accessible to both residential and commercial users [4,5,6]. By leveraging solar and wind energy within distribution grids, we are not only diversifying our energy sources but also reducing our dependence on fossil fuels. However, this transition comes with its own set of challenges, including intermittent generation, grid stability issues, and hosting capacity [7,8,9]. The integration of RERs into distribution feeders presents significant potential issues related to voltage and thermal current. One key concern is voltage fluctuation, which can occur because of the intermittent nature of renewable energy sources such as solar and wind energy. Another critical issue is the potential for overvoltage problems in the distribution system due to reverse power flow in distribution lines, particularly with high RER penetration [10,11,12]. Regarding the thermal current limit, the distribution equipment and power lines must be capable of handling the increased current flow when RERs are generating at their peak. Overloading of transformers, lines, and other components can lead to overheating, reduced equipment lifespan, and even outages [13,14]. These voltage and thermal current issues can ultimately limit the integration of RERs into the distribution system, thereby reducing the hosting capacity of RERs within the grid [15,16].

Hosting capacity (HC) is a critical concept in the context of distributed energy resource (DER) integration into distribution systems. It refers to the maximum amount of DERs, such as solar PV plants, WTs, and battery systems, that can be accommodated by the grid without causing distribution network congestions, particularly in terms of voltage and thermal current limits. Hosting capacity analysis in the context of DER integration involves three key approaches: (1) snapshot hosting capacity relies on static snapshots, often failing to capture evolving DER behaviors or unlikely scenarios, making it relatively limited in its assessment; (2) uncoordinated dynamic hosting capacity considers DER and grid device behaviors over time without communication, accommodating short-term overvoltage and thermal overload, offering a more flexible analysis; and (3) coordinated dynamic hosting capacity, which is the most comprehensive approach involving communication-based coordinated control to optimize DER output. It adapts to various levels of control within the distribution system and maximizes the integration of DERs. In this paper, the term HC is approached based on the key (3) which represents the most comprehensive approach involving communication-based coordinated control to optimize DER output.

Figure 1 illustrates the concept of hosting capacity with and without DER coordination power control. The solid line represents the original performance curve of the hosting capacity, while the dashed line indicates the performance curve after implementing hosting capacity enhancement measures. An index limit defines the acceptable operation and unacceptable operation of the hosting capacity. Through the utilization of DER coordination power control algorithms such as Var Precedence, Watt Precedence, or the Integrated Var/Watt Precedence, the additional DER penetration is significantly enhanced compared to the original capacity without employing these controls.

Technical virtual power plants (VPPs) and the DER aggregator (DERA) have emerged as a potential solution in improving hosting capacity by coordinating and optimizing the contributions of DERs to the grid [17]. The authors of [18] proposed a power aggregation method to quantify the aggregate flexibility from different types of DERs in an unbalanced distribution system to improve DER integration. A two-stage adaptive robust optimization for power flexibility aggregation is proposed in [19]. DERAs coordinate the operation of various DERs and optimize the utilization of these resources to ensure that the available capacity is utilized effectively without exceeding the network’s constraints.

However, there are notable gaps in these approaches in terms of maximizing hosting capacity efficiently. One critical gap is the need for more precise forecasting and real-time adaptability within VPPs and DERA. These systems often rely on simplified forecasting models, which may not capture the dynamic nature of DER behavior accurately. Additionally, interoperability challenges between various DER types and communication protocols can limit the scalability and effectiveness of VPPs and aggregators [20]. To address these gaps, a sophisticated DER management system (DERMS) can be proposed, which places a strong emphasis on enhancing hosting capacity. DERMSs should incorporate advanced forecasting techniques, such as machine learning and real-time data analysis, to provide accurate predictions of DER behavior and grid conditions. This enables better estimation of hosting capacity limits and enhances grid stability. Furthermore, a DERMS plays a pivotal role in optimizing the distribution network by providing control and coordination of various DERs [21,22]. By integrating advanced monitoring and control functionalities, a DERMS can help mitigate voltage fluctuations and thermal line current limit issues. It enables operators to manage the generation and distribution of energy more efficiently, balancing supply and demand while reducing the risk of equipment overloads. Additionally, a DERMS supports grid stability by demand response, grid voltage regulation, and the integration of RERs, ultimately maximizing the hosting capacity of renewable energy sources within the distribution network.

There have been several approaches for managing and controlling DERs, including the development of DERMSs. A DERMS offers utilities and grid operators advanced tools to effectively integrate and manage DERs. By leveraging real-time data analysis, sophisticated control algorithms, and demand response capabilities, a DERMS enables improved grid flexibility, enhanced hosting capacity, and better integration of RESs. Petrovich et al. [23] gave an overview of state-of-the-art DERMS technologies. VPP, DER aggregators, and DERMSs are considered intelligent systems that can forecast, monitor, and control DER behavior. Wang [24] developed a DERMS to manage voltage regulation, where overvoltage regulation mitigation using the DERMS was introduced using distributed reactive power management and optimization algorithms. However, in the literature, the coordination approach of the active power curtailment and reactive power compensation using a DERMS for commercial DERs has not been discussed. Coordination approaches can be helpful in mitigating voltage and thermal current violations to a considerable extent.

On the other hand, several studies have focused on active and reactive power management to enhance DER hosting capacity in distribution networks [25]. Research has shown that utilizing reactive power control positively impacts the enhancement of DER hosting capacity while reducing power flow constraint violations. In [26], a coordinated approach is presented based on reactive power control devices such as on-load tap changers (OLTCs) and Var sources to maximize the HC of PV resources, considering uncertainties in PV generation. This research employs probability functions for the probabilistic operation of reactive control devices under various operational conditions. Additionally, a two-stage stochastic operational planning model for enhancing the hosting capacity of PV systems has been proposed in [27], considering uncertainties in both load and PV generation, as well as the installation of a static Var compensator (SVC). However, the approach presented in this study did not account for the effects of active power control on the hosting capacity of PV systems.

This paper focuses on active and reactive power control algorithms of DERs to address power network congestion issues such as overvoltage and thermal limit violations in distribution systems. Herein, we propose three types of active and reactive power control algorithms of DERs, which are named as Var Precedence, Watt Precedence, and Integrated Watt and Var Control, and compare them with the conventional algorithms.

Three proposed algorithms aim to effectively deal with network congestion problems with the objective of minimizing DER power curtailment and maximizing DER hosting capacity. To achieve this goal, sensitivity analysis is conducted to evaluate the impact of DER active and reactive power output on the magnitude of voltage and current in the distribution system. We obtain four sensitivity factors representing the correlation between reactive power–voltage (Q–V), active power–voltage (P–V), reactive power–current (Q–I), and active power–current (P–I). The Q–V and P–V functions control voltage by adjusting reactive and active power, respectively. The commands for active and reactive power are determined through power flow analysis and voltage sensitivity analysis. Conversely, the Q–I and P–I functions regulate line thermal current, using active and reactive power correspondingly. These functions employ current sensitivity analysis and iterative searching algorithms to calculate power control commands. The main idea of the proposed DER control algorithms is to prioritize the control of DERs with high-sensitivity factors.

Var Precedence and Watt Precedence utilize the relatively high sensitivities of Q–V and P–I sensitivity factors and decouple active power control (for current control) and reactive power control (for voltage control). Var Precedence prioritizes reactive power control first and then performs active power control, while Watt Precedence prioritizes active power control and performs reactive power control subsequently, which is designed as a two-step control process. If the first round of the two-step control cannot reach the accurate control commands of DERs, both methods can use iterative calculation by going back to the first step to obtain a more relevant solution.

Var Precedence and Watt Precedence have relative strengths and weaknesses depending on whether overvoltage or overcurrent in the distribution line is more dominant. In cases where both voltage and current issues arise because of excessive surplus generation from DERs, Var Precedence and Watt Precedence require multiple iterative operations. In such cases, Integrated Watt and Var Control, which simultaneously calculates DER active and reactive power output commands by considering the four sensitivity indices (Q–V, P–V, Q–I, and P–I) simultaneously, is proposed. The control process of the integrated algorithm includes two main stages: (1) power flow analysis identifies voltage profiles and line currents, and system detection flags any issues. The Q–V function rectifies voltage problems, followed by Q–I for thermal current issues. The P–V function is applied if voltage issues reoccur. (2) Q–I and P–I functions optimize hosting capacity by adjusting active and reactive power control values. Incrementing reactive power increases maximum current towards the threshold, while reducing maximum bus voltage. This discrepancy is used to enhance hosting capacity by controlling active power injection with the P–I function. Further details about the algorithm are provided in Section 3.2.4. From various case studies, it is confirmed that the proposed Integrated Watt and Var Control is the most efficient solution among the three proposed methods.

These control functions are applied within the framework of power load flow analysis and the voltage sensitivity factor concept as discussed in [28,29,30]. The proposed algorithms are implemented in a DERMS simulator, which can manage multiple DERs in the distribution system using a centralized control concept. The results are evaluated and compared with those obtained using conventional methods such as last-in first-out (LIFO), Pro-Rata algorithms, and the linear programming (LP)-based optimization method proposed by Abad et al. [31].

This paper is organized as follows: Section 2 describes the design of the DERMS encompassing multiple functions. The details of the algorithms integrated into the DERMS are presented in Section 3. In Section 4, we verify the effectiveness of the proposed coordination control methods by comparing them with conventional methods by various simulation studies. Finally, Section 5 concludes the paper.

2. Structural and Functional Design of DERMS

2.1. Design of DERMS Structure

This work aimed to develop a DERMS application with DER control algorithms to enhance the integration capacity of DERs into the distribution system. Typically, the power generated by DERs and injected into the distribution feeder is constrained by various limiting factors. Two critical factors that determine normal system operation include the following: (1) maintaining voltage profiles within the acceptable ranges according to national standards, and (2) ensuring that line currents remain below the thermal limit of the distribution lines.

DERMS functions are delineated in two operation modes: normal and abnormal. The normal operation mode encompasses several functions, such as DER grouping, DER forecasting, DER capability and availability, and DER power dispatch, as illustrated in Figure 2.

The DER grouping function categorizes individual DERs into distinct groups according to various criteria such as type, location, feeders, phases, or other pertinent factors. This enables the effective management of various DERs scattered throughout the distribution system, grouping them together for better management.

The DER forecasting function performs predictions of renewable energy generation output and power demand in the distribution system. With such predictions, it enables the analysis of potential issues in distribution system operation caused by overgeneration or overload in advance. In this work, we effectively forecast DER and load consumption using a deep learning algorithm based on long short-term memory recurrent neural networks (LSTM-RNNs) introduced in [32,33]. This forecasting function additionally assesses the capability and availability of power within the DER group.

The DER power dispatch function aims to effectively control the active and reactive power output of DERs when necessary to ensure the stable management of the distribution system within normal operating ranges. We implemented various algorithms in the DERMS such as LIFO and Pro-Rata algorithms; an LP-based optimization algorithm; and proposed active and reactive power control methods such as Var Precedence, Watt Precedence, and Integrated Watt and Var Control algorithms. The DER power dispatch function is the primary focus of this paper.

During the abnormal operation mode, the application of network reconfiguration is employed to either eliminate or isolate faults, thereby sustaining the DER interconnection to comply with voltage and thermal limits within the reconfigured distribution network. This mode is beyond the scope of this paper.

2.2. Functions of DERMS

We introduce a comprehensive control framework in the DERMS aimed at effectively regulating the active and reactive power of DERs. The primary goal of this framework is to mitigate overvoltage and thermal current violations within normal operating ranges of the distribution system, thereby enhancing the hosting capacity of the distribution system. Figure 3 provides a schematic representation of the control framework, while its details are elaborated in three distinct stages as outlined below:

• Stage 1: The establishment of forecasting models for load and PV generation is imperative for predicting key parameters such as maximum PV power generation, power availability, power capability, and minimum loading conditions within the distribution system. The methodology employed in this forecasting stage is the LSTM-RNN as proposed in [32,33].
• Stage 2: Using the input data obtained from stage 1, including maximum load, maximum PV group power, and network data, power flow analysis is performed to analyze the states of system operation such as voltage profiles and line currents throughout the entire distribution system. By sophisticated power flow analysis, it is possible to anticipate overvoltage and overcurrent issues occurring in the distribution system.
• Stage 3: On the basis of the results in stages 1 and 2, the DERMS is responsible for minimizing reactive power compensation and active power curtailment of DERs. This optimization is achieved by employing control algorithms, encompassing conventional methods, Var Precedence, Watt Precedence, and the proposed advanced algorithms. The dispatched commands are meticulously determined, considering overvoltage and thermal current constraints within acceptable ranges, thereby enhancing the DER hosting capacity. Further elaboration on the intricacies of these algorithms is provided in the subsequent subsection.

2.3. Development of a DERMS Simulator

Figure 2 illustrates the DERMS simulator implemented in MATLAB and distribution system models in OpenDSS. The DERMS is designed to perform all the functions related to the management and control of DERs. The distribution management system (DMS) serves as the upper-level control system of the DERMS, managing operations across the entire distribution system. When the management of DERs is required, the DMS can request the DERMS to group the local DERs and execute necessary controls.

The power flow analysis function is integrated into both the DMS and DERMS modules. To execute this function, power system data such as network topology, line parameters, forecasted DER generation, and load consumption are necessary. From power flow analysis, the DMS identifies potential challenges in the distribution system and subsequently issues control commands to other control systems. For issues such as DER control, the DMS can request power dispatch from the DERMS, and the DERMS takes charge of controlling DERs in response to such requests. This integrated process significantly contributes to the effective management and maintenance of the operational integrity of the distribution system.

3. Active and Reactive Power Control Algorithms of DERs for DERMS

3.1. Conventional P/Q Dispatch Algorithms

3.1.1. LIFO and Pro-Rata Algorithms

LIFO and Pro-Rata algorithms represent widely employed methods for power curtailment of DERs [34]. The LIFO algorithm adheres to the straightforward principle of “last-in first-out”, curtailing power of DERs in a sequential manner until the total required power curtailment is achieved. If multiple DERs are installed on a distribution system, the active power curtailment proceeds in reverse order of the installation sequence of the DERs. The purpose of LIFO is to ensure generation from the initially installed DERs, and the active power curtailment is conducted starting from the DERs installed later.

The Pro-Rata algorithm distributes power curtailment uniformly among all operating DERs in the distribution system according to the same ratio. The calculation of power curtailment for each DER using the Pro-Rata approach is expressed as Equation (1):

$$\Delta P_k^{curt}=\frac{P_{total}^{curt}}{{\displaystyle \sum _{j=1}^{N_{DER}}{P}_j}}\cdot P_k$$

(1)

where $\Delta P_k^{curt}$ is the power curtailment of the k-th DER, $P_k$ is the power generation of the k-th DER, $N_{DER}$ is the number of DERs, and $P_{total}^{curt}$ is the total power curtailment.

The total power curtailment of DERs is calculated for purposes such as line congestion prevention, voltage regulation, and power system stability management. This calculation is based on the results of load flow calculations performed by upper-level management systems such as energy management systems or DMS, or DERMS can independently calculate it based on local information.

3.1.2. Optimal DER Control Using LP

Abad et al. [31] introduced LP with a probabilistic-based framework aimed at ascertaining the maximum integration limits of DERs, taking into account voltage deviation constraints. The optimization model proposed by them employs a two-step algorithm designed to linearize the hosting capacity model as illustrated in Figure 4. They considered the linear optimization problem model, denoted as the linear DistFlow equation, to ascertain an approximation of the operating point. Subsequently, they tackled the complex linear optimization model, utilizing the operating point to ascertain optimal active power curtailment and reactive power compensation across the entire distribution system.

Whereas the methods such as LIFO or Pro-Rata are operated on simple rules to find the individual DER curtailment, this LP method can obtain the optimal DER curtailment by optimizing the objective functions designed by the operator. The power curtailment of individual DERs is calculated as per the DER location, network constraints, generation costs, etc.

However, the drawback of LP-based optimization lies in the possibility of errors occurring during the linearization process of nonlinear optimization problems. Additionally, as the size of the distribution system increases and the number of interconnected distributed power sources grows, the computational time required for optimization also increases. The details of the mathematical model analysis are extensively discussed in [31].

3.2. Proposed DER Active and Reactive Power Dispatch Algorithms

In this section, we propose three DER active and reactive power control algorithms, namely, Var Precedence, Watt Precedence, and Integrated Watt and Var Control. The main idea of the proposed approach is to control the minimum amount of active and reactive power of DERs to deal with overvoltage and overcurrent problems in the distribution system. This approach is based on the fact that the impact of power output of DERs on the voltage and current of distribution lines depends on the installation location of distributed power sources. The utilization of power flow analysis enables voltage and current sensitivity techniques to regulate the active and reactive power output of the DER, thereby enhancing the overall hosting capacity while ensuring compliance with the network constraints, such as maintaining voltage profiles and thermal currents within the normal ranges. Subsequent subsections provide detailed explanations of each algorithm.

3.2.1. Voltage Sensitivity Factor

To successfully implement the control algorithms outlined herein, it is essential to conduct a sensitivity factor analysis of active and reactive power for DERs. Voltage sensitivity factor (VSF) coefficients are employed to quantify the influence of alterations in active and reactive power at specific buses where DERs are connected on voltage changes at other buses. These VSF coefficients serve as a metric for assessing the magnitude of voltage variation resulting from changes in active and reactive power across each bus. The VSF is commonly computed by utilizing the Newton–Raphson (NR) method for power flow analysis, which a widely adopted technique in power system analysis. After computing the Jacobian matrix (J) using the NR method, the inverse of the Jacobian matrix serves as the sensitivity factor for active and reactive power:

$$\left[\begin{array}{c}\Delta \delta \\ \Delta V\end{array}\right]={\left[\begin{array}{cc}{J}_1& J_2\\ J_3& J_4\end{array}\right]}^{-1}\left[\begin{array}{c}\Delta P\\ \Delta Q\end{array}\right]=\left[\begin{array}{cc}{S}^{\delta P}& S^{\delta Q}\\ S^{VP}& S^{VQ}\end{array}\right]\left[\begin{array}{c}\Delta P\\ \Delta Q\end{array}\right],$$

(2)

where column vectors ∆P and ∆Q represent the changes in active and reactive power at the arbitrary buses, and the vectors ∆V and $\Delta \delta$ illustrate the changes in voltage magnitudes and phase angles at the target buses. The inverse of the Jacobian matrix comprises submatrices $S^{\delta P}$, $S^{\delta Q}$, $S^{VP}$, and $S^{VQ}$, which denote the phase angle and voltage sensitivity factors for active and reactive power.

From Equation (2), the voltage change at the target buses can be determined as follows:

$$\Delta V=\left[S^{VP}\right]\left[\Delta P\right]+\left[S^{VQ}\right]\left[\Delta Q\right].$$

(3)

The reactive power control command at bus k $\left(\Delta Q_k\right)$ to regulate the voltage at the target bus $i$ is subsequently determined by using Equation (4), assuming that the active power at the k-th bus is held constant $\left(\Delta P=0\right)$

$$\Delta Q_k=\frac{\Delta V_i}{S_{i,k}^{VQ}}=\frac{V_i-V_{threshold}}{S_{i,k}^{VQ}},$$

(4)

where $V_{threshold}$ represents the voltage threshold magnitude.

Similarly, the active power control command at bus k $\left(\Delta P_k\right)$ to regulate the voltage at the target bus i is derived as

$$\Delta P_k=\frac{\Delta V_i}{S_{i,k}^{VP}}=\frac{V_i-V_{threshold}}{S_{i,k}^{VP}}$$

(5)

3.2.2. Current Sensitivity Factor

The current sensitivity factor (CSF) is a coefficient that quantifies the impact of modification in active and reactive power of a DER at a particular bus on the current change on other sectional lines in the distribution system. The CSF is analyzed using the relationship between voltage and current [35].

The line current between buses i and j is derived as

$$I_{ij}=Y_{ij}\left(V_i-V_j\right),$$

(6)

where $Y_{ij}$ represents the admittance of the line between buses i and j.

The CSF of the sectional line currents between buses i and j $\left(I_{ij}\right)$ to the active and reactive power outputs of the DER connected to bus $k$ can be obtained by differentiating both sides of Equation (6) with respect to the active power $\left(P_k\right)$ and reactive power $\left(Q_k\right)$ of the DER, resulting in expressions (7) and (8):

$$S_{k\to ij}^{IP}=\frac{\partial I_{ij}}{\partial P_k}=Y_{ij}\left(S_{i,k}^{VP}-S_{j,k}^{VP}\right),$$

(7)

$$S_{k\to ij}^{IQ}=\frac{\partial I_{ij}}{\partial Q_k}=Y_{ij}\left(S_{i,k}^{VQ}-S_{j,k}^{VQ}\right),$$

(8)

where $S_{k\to ij}^{IP}$ and $S_{k\to ij}^{IQ}$ represent the CSF for active and reactive power, respectively, at bus k to the line current between buses i and j.

In contrast to the VSF, which utilizes first-order derivatives for linearization equations, the CSF relies on second-order derivatives, making it highly sensitive to changes in the operating point of the power distribution system. Therefore, an iterative approach was employed in this work to accurately calculate the active and reactive power control quantities of DERs using the CSF to reduce errors.

3.2.3. Var Precedence and Watt Precedence Algorithms

In this section, we propose active and reactive power control algorithms for DERs, named Var Precedence and Watt Precedence strategies, respectively. The primary objective of these algorithms is to optimize active power curtailment and reactive power compensation of DERs, thereby flexibly improving the overall hosting capacity of DERs in the distribution system. The Var Precedence and Watt Precedence strategies decouple the control of active and reactive power of DERs to manage voltages and currents in the distribution system. By active power control, current regulation is performed, while voltage regulation is achieved via reactive power control. The methods are categorized into Var Precedence and Watt Precedence depending on which control, active or reactive power, is executed first. By sensitivity analysis on voltage and current, the algorithms determine the requisite active and reactive power control necessary for DERs to effectively manage network congestions.

Figure 5 illustrates the flowchart of the voltage and current control process of Var Precedence and Watt Precedence. The overall control process comprises three steps.

In the first step for both Var Precedence and Watt Precedence, input data, including network topology, line and load data, and DER profiles, are collected and analyzed. On the basis of this input, power flow analysis is conducted to determine the voltage profiles and line currents of the entire distribution system. The central controllers will then assess whether there are any network congestions.

In Steps 2 and 3, the control of voltage and current in the distribution system is achieved by the active and reactive power control of DERs, with Var Precedence and Watt Precedence following different detailed sequences. Var Precedence prioritizes the voltage control by reactive power control (Step 2), followed by active power control to maintain line currents below thermal limits (Step 3). Watt Precedence follows the opposite sequence, first performing line current control via active power control (Step 2) and controlling bus voltages by reactive power control (Step 3). At each step, the active and reactive power output commands of DERs are calculated using VSF and CSF. If the voltage and current exceed overvoltage and overcurrent limits even after Step 3, iterative execution of Steps 2 and 3 can be selected until the voltage and current are maintained within certain tolerance ranges.

In Step 4, the outputs, including total reactive power compensation and total active power curtailment of DERs, are determined and total hosting capacity is calculated.

3.2.4. Integrated Watt and Var Control Algorithms

In this section, we present advanced Integrated Watt and Var Control algorithms designed to maximize the hosting capacity while addressing network congestions, specifically targeting voltage problems and thermal current issues.

In the Var Precedence algorithm, during Step 2, reactive power control of DERs is performed for voltage control using the VSF. In this process, increased inductive current can suppress voltage rise in the distribution line; however, the magnitude of current flowing through the line increases. If the increased line current causes overheating problems in distribution lines, additional active power curtailment of DERs needs to be performed in Step 3, leading to an excessive application of active power curtailment for voltage control. This suboptimal output hinders the maximization of total hosting capacity.

By contrast, in the Watt Precedence algorithm, current control is performed first during Step 2, offering the advantage of preventing excessive DER active power curtailment compared to Var Precedence. However, in cases of overvoltage, the reactive power control in Step 3 may lead to an increase in inductive current in the line, potentially exceeding the line thermal limits satisfied during Step 2. In such cases, the iterative execution of Step 2 may be necessary, potentially resulting in inefficiencies in the overall control process.

Integrated Watt and Var Control is proposed to address the aforementioned concerns. This method employs a combination of four control functions: voltage control using reactive power (Q–V), voltage control using active power (P–V), current control using reactive power (Q–I), and current control using active power (P–I) (Figure 6). The implementation of these control functions is based on voltage and current sensitivity analyses as depicted in Figure 6. Iterative search algorithms are also utilized in conjunction with these four control functions to determine optimal reactive power compensation and active power curtailment control commands for DERs. This comprehensive approach aims to effectively tackle network congestions such as voltage and current limits, thereby maximizing the hosting capacity.

Figure 7 depicts the overall control process of the Integrated Watt and Var Control algorithms. The control is delineated into two main stages:

• Stage 1: In this stage, the network congestions for voltage and current limits are addressed using three control functions: Q–V, Q–I, and P–V. Initially, the central controller runs the power flow analysis to determine network parameters such as voltage profiles and line current. Subsequently, the power system detection identifies any voltage or thermal current issues. The Q–V control function is applied to rectify the voltage problems, followed by the use of the Q–I control function to mitigate thermal current problems. However, the control of reactive power for thermal current may reintroduce voltage issues in the system, prompting the application of the P–V control function to resolve them. After stage 1, there are no network congestions in terms of voltage and thermal current. The output of stage 1 comprises an unoptimized list of reactive and active power commands.
• Stage 2: The control process in stage 1 solves the voltage and thermal current issues in the overall distribution system. However, the P–V control function not only maintains the maximum voltage at the threshold but also reduces the thermal current below the threshold. This may result in the hosting capacity not being optimized. In this stage, two control functions, namely, Q–I and P–I, are employed to tune the control values of active and reactive power to maximize the hosting capacity. By incrementing a small amount of reactive power, the maximum current is increased toward the threshold, while the maximum bus voltage decreases below the threshold values. This gap is utilized to control the active power injection to enhance the hosting capacity with the P–I control function. The active power injection may bring the voltage back to the threshold while increasing the maximum thermal current. This tuning process is repeated until the difference between the thresholds and measurements is less than a defined value of ε.

In comparison to the Var Precedence and Watt Precedence algorithms, the Integrated Var and Watt Control algorithm effectively addresses the drawbacks associated with the two preceding algorithms. By employing the tuning process utilizing Q-I and P-I control functions in stage 2, the integrated algorithm ensures that the maximum voltage and line current are accurately regulated within the limits.

4. Case Studies

4.1. System Description

To evaluate the effectiveness of the proposed algorithms, we implemented a simulation model of the distribution system using MATLAB. The distribution system represents a typical radial configuration comprising 10 buses, operating at a rated line-to-line voltage of 22.9 kV. The typical voltage maintenance range for distribution system is ±5% of the rated voltage; however, Korea Electric Power Corporation usually strives to limit the voltage variations to ±2% of the rated voltage across the entire distribution system. The distribution line is modeled as one of the commonly used overhead lines in South Korea, specifically the ASCR 160 mm² type. The line parameters are set with an impedance of 0.1823 Ω/km and conductance of 0.391 Ω/km. The thermal line current is constrained to a maximum capacity of 0.395 kA as specified by the manufacturer’s description.

We assumed the connection of five DERs to the distribution system, each having a rated power of 4 MW. The location of the DERs varied in each case study as described in

Table 1. DER profiles of the test distribution system.

Bus No.	Loads		DER Capacity (MW)
	P (MW)	Q (MVar)	Case 1	Case 2	Case 3
1	-	-	-	-	-
2	0.03	0.05	4	-	4
3	-	-	4	-	-
4	0.03	0.02	4	-	4
5	-	-	4	-	-
6	0.05	0.02	4	4	4
7	0.04	0.05	-	4	-
8	0.03	0.05	-	4	4
9	0.06	0.03	-	4	-
10	0.07	0.04	-	4	4

. DERs are equipped with smart inverters that have active and reactive power control functions, and the reactive power compensation is normally limited to 44% of the rated apparent power [36]. To assess algorithm performance, we assumed a light-loading condition that could cause surplus DER generation conditions as listed in Table 1.

In this section, we evaluate three case studies to analyze the performance of the proposed method in comparison to conventional methods. For each case study, we considered three DER location conditions: near the substation (Case 1), at the end of the feeder (Case 2), and distributed equally throughout the distribution system (Case 3), as presented in Table 1.

4.2. Simulation Results and Discussion

4.2.1. Case 1: DERs Concentrated near Substation

In Case 1 (Figure 8), we consider the placement of five PV power generation units situated in close proximity to the substation, specifically at buses 2, 3, 4, 5, and 6. This spatial DER arrangement is anticipated to give rise to thermal current concerns while not posing voltage-related issues. The voltage profiles and line currents are illustrated in Figure 9a and 9b, respectively. The maximum voltage recorded was 1.0186 per unit (p.u.) at bus 6, which was below the upper limit of 1.02 p.u. Conversely, the maximum line current reached 489.72 A, surpassing the stipulated maximum line capacity of 395 A.

Six DER control algorithms were employed to address the challenges, thereby enhancing the DER hosting capacity. Following this, an installation order was assumed of PV#4->PV#5->PV#3->PV#1->PV#2, where PV#2 located at bus 3 would be curtailed for the first time. The power curtailment of PV#2 was computed at 3.904 MW to meet the maximum line thermal limit between bus 1 and bus 2 of less than 393 A and the maximum voltage of 1.0161 p.u. at bus 6. After 3.904 MW was curtailed in PV#2, the total hosting capacity was obtained as 16.096 MW (=20.0 − 3.904 MW).

The Pro-Rata algorithm distributed equal curtailment to all PV units, amounting to 0.785 MW each and 3.925 MW in total. This strategy maintained the maximum current from bus 1 to bus 2 at 393 A and the maximum voltage of 1.0149 p.u. at bus 6. Then, the total hosting capacity was 16.07 MW.

The LP optimization algorithm in reference [31] yields a curtailment result of 3.902 MW at PV#1. Because of the absence of voltage issues, the Var Precedence, Watt Precedence, and Integrated Watt and Var Control algorithms provided the same results, with a power curtailment of 3.801 MW at PV#1. This contributed to an improved DER hosting capacity of 16.199 MW compared to other algorithms. The control measures effectively reduced thermal current to 395 A and maintained voltage profiles below the specified threshold of 1.02 p.u. A detailed comparison of the results is presented in

Table 2. Comparison of active and reactive power control of DERs—Case 1.

	No. of PVs	PV#1 (Bus 2)	PV#2 (Bus 3)	PV#3 (Bus 4)	PV#4 (Bus 5)	PV#5 (Bus 6)	Total DER Control
Methods
LIFO	P (MW)	0.000	3.904	0.000	0.000	0.000	3.904
	Q (MVar)	0.000	0.000	0.000	0.000	0.000	0.000
Pro-Rata	P (MW)	0.785	0.785	0.785	0.785	0.785	3.925
	Q (MVar)	0.000	0.000	0.000	0.000	0.000	0.000
LP	P (MW)	3.902	0.000	0.000	0.000	0.000	0.000
	Q (MVar)	0.000	0.000	0.000	0.000	0.000	0.000
Var Pre.	P (MW)	3.801	0.000	0.000	0.000	0.000	3.801
	Q (MVar)	0.000	0.000	0.000	0.000	0.000	0.000
Watt Pre.	P (MW)	3.801	0.000	0.000	0.000	0.000	3.801
	Q (MVar)	0.000	0.000	0.000	0.000	0.000	0.000
Int. Watt/Var	P (MW)	3.801	0.000	0.000	0.000	0.00	3.801
	Q (MVar)	0.000	0.000	0.000	0.000	0.000	0.000

PV connection order: PV#4->PV#5->PV#3->PV#1->PV#2.

and

Table 3. Comparison of DER hosting capacity and constraint satisfaction (Case 1).

	Parameters	DER HC	Maximum Voltage and Current
Methods			Max V (p.u.)	Margin (%)	Max I (A)	Margin (%)
LIFO		16.096	1.0161	0.39%	393	0.50%
Pro-Rata		16.075	1.0149	0.51%	393	0.50%
LP		16.098	1.0160	0.40%	394	0.25%
Var Precedence		16.199	1.0174	0.26%	395	0.00%
Watt Precedence		16.199	1.0174	0.26%	395	0.00%
Int. Watt/Var		16.199	1.0174	0.26%	395	0.00%

.

The primary advantages of LIFO and Pro-Rata algorithms compared to other methods lie in their simplicity of implementation and real-time responsiveness. These algorithms are suitable for Case 1, where only thermal current issues occur, and the results of curtailment almost reach the optimal values compared to other algorithms.

4.2.2. Case 2: DERs Concentrated at the End of the Feeder

In Case 2, five PV installations were interconnected at the end of the feeder, specifically at buses 6, 7, 8, 9, and 10 as shown in Figure 10. This configuration induced both overvoltage and thermal current issues in the distribution system. The maximum voltage was observed at bus 10, reaching a value of 1.0412 per unit (p.u.), which exceeded the specified threshold of 1.02 p.u. Simultaneously, the maximum current was measured to be 479.23 A, surpassing the thermal threshold of 395 A. The voltage profiles and thermal currents across the entire distribution system are delineated in Figure 11.

Table 4. Comparisons of active and reactive power control of DERs (Case 2).

	No. of PVs	PV#1 (Bus 6)	PV#2 (Bus 7)	PV#3 (Bus 8)	PV#4 (Bus 9)	PV#5 (Bus 10)	Total DER Control
Methods
LIFO	P (MW)	4.000	4.000	4.000	0.000	0.100	12.10
	Q (MVar)	0.000	0.000	0.000	0.000	0.000	0.000
Pro-Rata	P (MW)	2.100	2.100	2.100	2.100	2.10	10.500
	Q (MVar)	0.000	0.000	0.000	0.000	0.000	0.000
LP	P (MW)	4.000	1.182	0.000	0.000	0.00	5.182
	Q (MVar)	0.000	0.000	0.000	−0.420	−1.760	−2.180
Var Pre.	P (MW)	4.000	0.304	0.000	0.000	0.000	4.304
	Q (MVar)	0.000	0.000	0.000	−1.625	−1.760	−3.385
Watt Pre.	P (MW)	3.968	0.054	0.000	0.000	0.000	4.022
	Q (MVar)	0.000	0.000	0.000	−0.763	−1.760	−2.523
Int. Watt/Var	P (MW)	0.000	0.000	0.000	1.350	2.577	3.927
	Q (MVar)	0.000	0.000	0.000	−0.250	−1.760	−2.010

PV connection order: PV#4->PV#5->PV#3->PV#1->PV#2.

and

Table 5. Comparison of DER hosting capacity and constraint satisfaction (Case 2).

	Parameters	DER HC	Maximum Voltage and Current
Methods			Max V (p.u)	Margin (%)	Max I (A)	Margin (%)
LIFO		7.900	1.0200	0.00%	187.89	52.43%
Pro-Rata		9.500	1.0200	0.00%	227.80	42.33%
LP		14.818	1.0196	0.04%	363.30	8.03%
Var Precedence		15.696	1.0139	0.61%	395.30	0.08%
Watt Precedence		15.978	1.0193	0.07%	395.10	0.03%
Int. Watt/Var		16.073	1.0200	0.00%	395.00	0.00%

provides a comparison of active power curtailment, reactive power compensation and DER hosting capacity using six different algorithms in Case 2. Similar to Case 1, the LIFO and Pro-Rata algorithms curtail active power to ensure that both voltage and thermal current remain within the normal range. In this case, where both voltage and thermal current issues are prevalent, active power must be curtailed by a total of 12.10 MW at buses 7, 6, 8, and 10 for the LIFO algorithm in accordance with the order of connection. This curtailment is instrumental in maintaining the voltage at 1.02 per unit (p.u.) and reducing the maximum current to 187.89A, which is 52.43% below the threshold. By contrast, the Pro-Rata algorithm necessitates a curtailment of 2.1 MW for each PV unit to uphold the maximum voltage at 1.02 p.u., resulting in a maximum current reduction of 227.80 A, representing a 42.33% reduction compared to the threshold. The hosting capacity was calculated to be 7.90 and 9.50 MW for the LIFO and Pro-Rata algorithms, respectively.

In contrast to the two conventional algorithms, the LP methodology outlined in reference [31] demonstrated better results as evident from a total active power curtailment of 5.182 MW at PV#1 and PV#2. Consequently, the augmentation in total hosting capacity reached 14.818 MW, marking a substantial improvement over the capacities achieved by the LIFO and Pro-Rata algorithms, which were 7.90 and 9.50 MW, respectively. This optimization effectively maintained the maximum voltage at 1.196 p.u., with a marginal deviation of 0.04% from the rated voltage. Furthermore, the maximum current was confined to 363.3 A, representing an 8.03% margin from the thermal line current maximum capacity. It is imperative to acknowledge the presence of error originating from the approximation in the linearization of the mathematical model derived from the nonlinear model in this work.

Table 4 lists the results of active power curtailment and reactive power compensation using the proposed algorithms: Var Precedence, Watt Precedence, and Integrated Watt and Var Control.

In Var Precedence algorithms, reactive power must be compensated to the distribution system, totaling 3.385 MVar at buses 10 and 9, to reduce the voltage from 1.0412 per unit (p.u.) to 1.0139 p.u. Simultaneously, PV units at buses 6 and 8 need to be curtailed by a total of 4.304 MW, as indicated in Table 4, to maintain the maximum thermal current at 395.3 A.

Similarly, in Watt Precedence algorithms, the total reactive power compensation required is 2.523 MVar at buses 9 and 10, accompanied by an active power curtailment of 4.022 MW at buses 6 and 7. This strategy maintains the maximum voltage at 1.0193 p.u., while the maximum current is held at 395.1 A. This results in DER hosting capacities of 15.696 and 15.978 MW for Var Precedence and Watt Precedence, respectively.

Compared to Var Precedence and Watt Precedence algorithms, the Integrated Watt and Var Control algorithm yielded superior results. It required a total active power curtailment of 3.927 MW and total reactive power compensation of 2.010 MVar for PV units at buses 9 and 10 as illustrated in Table 4. The hosting capacity is defined as 16.073 MW, which represents the highest value compared to other algorithms.

Compared to LIFO and Pro-Rata algorithms, which may lack consistent prioritization of proper DERs and cooperation between active and reactive power control, the Var Precedence, Watt Precedence, and Integrated Var/Watt Precedence algorithms offer decoupled approaches to active and reactive power control. While these algorithms involve greater complexity due to integrating power flow analysis with iterative methods, they yield better results, as demonstrated in simulations. Though implementing these algorithms may initially require a slightly more complex process, advancements in energy management systems have made their integration into distribution system control and operation increasingly feasible.

4.2.3. Case 3: DERs Distributed throughout the Distribution System

In Case 3, we consider the even distribution of five PV units across the entire distribution system, specifically at buses 2, 4, 6, 8, and 10 as illustrated in Figure 12. Figure 13 shows that both voltage and thermal current issues arise in the distribution system.

Table 6. Comparison of active and reactive power control of DERs (Case 3).

	No. of PVs	PV#1 (Bus 2)	PV#2 (Bus 4)	PV#3 (Bus 6)	PV#4 (Bus 8)	PV#5 (Bus 10)	Total DER Control
Methods
LIFO	P (MW)	4.000	4.000	3.500	0.000	0.000	11.50
	Q (MVar)	0.000	0.000	0.000	0.000	0.000	0.000
Pro-Rata	P (MW)	1.370	1.370	1.370	1.370	1.370	6.850
	Q (MVar)	0.000	0.000	0.000	0.000	0.000	0.000
LP	P (MW)	4.000	0.985	0.000	0.000	0.000	4.985
	Q (MVar)	0.000	0.000	0.000	0.000	−1.150	−1.150
Var Pre.	P (MW)	3.857	0.000	0.000	0.000	0.000	3.857
	Q (MVar)	0.000	0.000	0.000	0.000	−1.598	−1.598
Watt Pre.	P (MW)	3.827	0.000	0.000	0.000	0.000	3.827
	Q(MVar)	0.000	0.000	0.000	0.000	−1.412	−1.412
Int. Watt/Var	P(MW)	0.000	0.000	0.000	0.000	3.803	3.803
	Q(MVar)	0.000	0.000	0.000	0.000	−0.113	−0.113

PV connection order: PV#4->PV#5->PV#3->PV#1->PV#2.

and

Table 7. Comparison of DER hosting capacity and constraint satisfaction (Case 3).

	Parameters	DER HC (MW)	Maximum Voltage and Current
Methods			Max V (p.u)	Margin (%)	Max I (A)	Margin (%)
LIFO		8.5000	1.0200	0.00%	202.92	48.630%
Pro-Rata		13.150	1.0200	0.00%	319.44	19.130%
LP		15.015	1.0209	0.09%	365.60	7.440%
Var Precedence		16.143	1.0186	0.14%	395.10	0.025%
Watt Precedence		16.173	1.0199	0.01%	395.10	0.025%
Int. Watt/Var		16.197	1.0200	0.00%	395.00	0.000%

present the comparison results obtained by utilizing different algorithms for active and reactive power control in Case 3. Given the connection order of PV#4->PV#5->PV#3->PV#1->PV#2, the results obtained from the LIFO algorithm are significantly worse than those of the Pro-Rata algorithm. Specifically, the LIFO algorithm requires a curtailment of 11.50 MW for the PV unit at buses 4, 2, and 6, while the Pro-Rata algorithm necessitates a curtailment of 1.370 MW for each PV unit. This substantial difference leads to a more favorable DER hosting capacity of 13.150 MW for the Pro-Rata algorithm, compared to 8.50 MW for the LIFO algorithm.

Similar to Cases 1 and 2, the LP algorithm in reference [31] delivers a total curtailment of 4.985 MW and total reactive power compensation of 1.150 MVar, thereby augmenting the total hosting capacity to 15.015 MW. This performance surpasses that of the LIFO and Pro-Rata algorithms.

The proposed algorithms yielded superior results compared to conventional LIFO and Pro-Rata algorithms and the LP algorithm presented in reference [31]. Specifically, the Var Precedence algorithm required a curtailment of 3.857 MW at bus 2 and compensated for 1.598 MVar in reactive power at bus 10. In comparison, the Watt Precedence algorithm provided a curtailment of 3.827 MW at bus 2 and compensated for 1.412 MVar at bus 10. Consequently, this resulted in hosting capacities of 16.413 and 16.173 MW.

By contrast, the Integrated Watt and Var Control algorithm necessitated only 3.803 MW for active power curtailment and 0.113 MVar for reactive power compensation to sustain both voltage and thermal current at the specified thresholds. This approach achieved the highest DER hosting capacity of 16.197 MW among all algorithms.

From the simulation of three cases, it is evident that the proposed algorithms outperformed conventional LIFO and Pro-Rata methods and the LP algorithm.

5. Conclusions

This paper presents the design and implementation of a DERMS simulator using MATLAB. The simulator incorporates advanced DER power control algorithms, specifically the Var Precedence and Watt Precedence algorithms, as well as the Integrated Watt and Var Control algorithm. These coordinated control strategies for DERs optimize both active and reactive power compensation. The integration of various control functions, including Q–V, P–V, Q–I, and P–I, aims to ensure that voltage and thermal current levels remain within acceptable limits, thereby enhancing the hosting capacity of the overall distribution system. The design of these algorithms leverages sensitivity-based methods, power flow analysis, and an iterative approach, showcasing a comprehensive and sophisticated approach to DER management.

Simulation results revealed that the proposed algorithms outperformed conventional techniques. Among the three proposed algorithms, Var Precedence, Watt Precedence, and Integrated Var and Watt Precedence, simulation results indicate that the Integrated Var and Watt Precedence algorithm exhibits superior performance in maintaining system parameters within specified thresholds while maximizing hosting capacity. This research contributes to the advancement of DERMS capabilities, providing an effective and robust solution for maximizing the flexible DER integration in distribution systems.