Review of Voltage Control Strategies for DC Microgrids

Abstract

With the continuous development of the global economic level, global energy consumption is also on the rise, and the global power industry is faced with a number of formidable challenges including load growth, low energy efficiency, high power quality, and environmental protection. Despite the fact that distributed energy cannot be directly connected to the power grid, the concept of the microgrid (MG) is proposed to make better use of distributed energy and reduce its effect on the power grid. The low cost and high controllability of DC MGs have piqued the interest of academicians both at home and abroad. If DC MGs are to be implemented in real-world engineering, a stability control strategy is required; therefore, research on voltage stability and coordinated control of DC MGs is extremely important and promising. This paper summarizes the current research on the voltage control strategy of the DC MG from the perspective of the voltage control strategy of the DC MG. Lastly, it is proposed that the future development of DC MGs will be more focused on intelligence and control precision and that the consistency algorithm combined with the benefits of centralized control and distributed control can effectively aid the future development of DC MGs, taking into account the grid’s dependability and control precision.

1. Introduction

The form of the DC microgrid (MG) tends to become more adaptable and intelligent as time and society progress. The energy supply is transitioning to environmentally friendly new energy, the control mode is evolving to readily expandable distributed control, and the power grid model is modernizing. When an algorithm for machine learning is combined with the development strategy of DC MGs, two distinct modes of operation exist: island mode and grid-connected mode. MGs can effectively utilize renewable resources under normal, grid-connected conditions. When a large-scale power grid experiences faults or severe weather, the MG can disconnect an isolated island’s operation from the large-scale power grid, achieving localization and enhancing the reliability of the power grid. The administration of MGs represents the greatest difficulty in the advancement of MG technology. This paper provides a summary and analysis of the DC side control system of MGs based on an adaptive algorithm.

2. Basic Structure and Operation Control of MGs

2.1. Basic Structure of MGs

MGs incorporate various forms of decentralized energy generation such as photovoltaic cell fans. Multiple distributed power sources, including compact gas turbines, fuel cells, fuel cells, and energy storage, utilize electronic power converters as interfaces to connect the MGs of power systems. MGs can be divided into the following three subtypes and hybrid subtypes. Figure 1 depicts the structural schematic diagram of MGs utilizing different power supply systems.

An AC MG is based on the connection between AC and distributed generator sets. The most basic load unit MG has the advantage of not having to change the original grid structure, and the control and protection technology of the AC system is relatively mature. However, the distributed energy storage and DC load in an AC MG must be connected to the system via multi-stage AC/DC converters, resulting in low system efficiency [1]. PCC point control can be used to transition between grid-connected and isolated networks, as shown in [2].

A DC MG is able to utilize DC power and distributed generators. In the process of energy conversion between MG and DC load, the issues of low efficiency, high loss, and phase frequency conversion control do not exist, and flexibility can be matched with high power quality [3,4]. DC MGs are being extensively researched for application in areas such as large data centers, commercial structures, and electric ships [5]. The DC MG demonstration project of the CERTS Experimental Base in the United States is a typical demonstration project. An AC/DC MG is a hybrid MG system comprised of DC MG and AC MG. Each of the distributed energy storage devices and charging devices can be linked to their respective carriers. The MG can meet the power requirements of a variety of charging methods, and the process of power conversion has been streamlined. Functionally, it has high operational efficiency, strong controllability, and strong network capacity [6]. Examples include the Anamon MG Demonstration Project in California, Resia, and the Ythnos Slands MG Demonstration Project. An AC/DC MG can be regarded as the interconnection of AC MGs and DC MGs [7] based on the structural characteristics of numerous MGs. If a DC MG corresponds to a DC power input, an AC/DC MG can still be considered as an AC MG. As shown in Figure 2, the current research on independent MG operation control focuses primarily on independent AC MGs and independent DC MGs.

2.2. Operation Control of MGs

There are two modes of operation for microgrids: grid-connected operation and island operation. When the MG is connected to the grid, it can dispatch power output flexibly, actively respond to the power demand of the main grid, and serve as reserve power for the black start. Utilizing energy storage devices and corresponding control and protection connections, the power balance can be maintained during the independent and stable operation of the MG. An isolated island microgrid is typically employed in remote mountainous regions or islands, or in the event of a major power grid failure or other emergencies, and is temporarily disconnected from the external grid to ensure the reliability of the power supply within the MG.

There are two categories [8] of MG operation control: cell-level control and system-level control. Cell-level distributed power generation control is primarily comprised of droop control, PQ control, and Vf control, which refer to the particular control strategy employed by a single distributed power generation in the MG. Master–slave control and peer-to-peer control refer to the control relationship between multiple distributed generators in an MG. Unit-level and system-level control modes can be adapted by the MG’s various operational modes. Currently, the most prevalent method is droop control. The particular procedure is depicted in Figure 3 and Figure 4.

(1)

Control under the grid-connected operation mode

Grid-connected MGs are sustained by large grids to stabilize the frequency and voltage of the system; consequently, distributed generation in grid-connected MGs is typically managed by PQ. For controllable units in MGs, such as energy storage and micro gas turbines, PQ control can enable the storage of energy to output active and reactive power in accordance with the dispatching power instruction; for photovoltaic, wind power, and other new energy generating units, maximum power point tracking (MPPT) technology can be used to maximize output power and increase the utilization rate of renewable energy. PQ control is used for AC MG control, whereas there is no concept of reactive power for DC MG control, which instead uses constant power control or constant current control and requires only voltage stability.

(2)

Control under the island-like mode of operation

Isolated MG lacks the power support of a large power grid and must rely on distributed generation to maintain the system’s frequency and voltage stability. In this instance, either master–slave control mode or peer control mode may be implemented. A microgrid with master–slave control mode requires distributed generation as the primary controller and utilizes Vf to control the system’s frequency and voltage. For a DC MG, the control paradigm is comparable, with the primary controller employing constant voltage control and the slave controller employing constant power or constant current control. In master–slave control mode, the master controller corresponds to the current source and the subordinate controller corresponds to the voltage source. All distributed generators use sag control in the point-to-point control mode to maintain the frequency and voltage of the system by simulating the sag characteristics of the generator set. All distributed generators are equivalent to voltage sources in peer-to-peer control mode. For AC microgrids, droop control is typically based on the power-frequency active power (f-P) droop characteristic and the voltage and reactive power (V-Q) droop characteristic, whereas for DC microgrids, droop control is typically based on the voltage-current (V-I) or voltage-power (V-P) droop characteristic.

3. Research Status of Stability Control of DC MGs

3.1. Research on Transient Control Strategy of DC MGs

In 2004, Tokyo University of Technology, Osaka University, and other institutions introduced the concept of a DC MG distribution system and built a series of 10 kW DC distribution system prototypes; in 2006, Osaka University of Japan proposed a bipolar structure of a DC microgrid system [8], a 6.6-kV distribution network, through a step down and rectifier using DC power and connected to a 170 V DC earth bus. The other side of the structure was a gas turbine. The specific DC MG microsource parameters are listed in the

Table 1. Parameters of DC micromesh microsource.

Microsource	Output Voltage/V	Line Impedance/Ω
MGH1	400	0.3 + j3
MGH2	400	0.2 + j2
MGH3	400	0.1 + j1
MGL1	48	0.3 + j3
MGL2	48	0.2 + j2
MGL3	48	0.1 + j1

.

In 2007, the Virginia Polytechnic Institute and State University proposed the Sustainable Building Initiative [9] to provide electricity for smart buildings; in 2010, it proposed the SBNC Sustainable Building and Nanogrids project, setting 380 V and 48 V DC bus voltage levels (to match the power needs of industrial standards and communication standards) to power electrical equipment; in 2011, the University of North Carolina, United States of America, based on the SBN, proposed the Smart Building Network. Eventually, the AC and DC networks will connect to the grid via the energy management device IEM [10]. Figure 5 illustrates the DC MG’s fundamental structure.

The Italian University of Technology in Milan proposed a system architecture of DC MGs with distributed generation as the power supply [11] in 2004.

In 2007, the Polytechnic University of Bucharest, Romania, proposed a DC MG system structure powered by bioenergy such as methane [12]; since 2008, several countries in Europe have simultaneously carried out a research project called “UNIFLEX” [9]. This project is a power electronics-based power conversion technology to address the management of power flows caused by a large number of distributed power connections; in January 2010, some countries in Europe jointly proposed the “SUPER GRID” project [13], which mainly uses DC MG technology to integrate wind power, photovoltaic power, and hydropower generation from some countries on the north coast and connect them to a super-large grid based on renewable energy; in 2012, some universities and enterprises in Europe jointly launched a project called “DCC + G” to design and develop a future residential project for a 380 V DC distribution system.

Stability is the central issue in MG operation control. Since there is no regenerative power flow in a DC MG, the DC bus voltage is the only indicator of a DC MG’s safety and stability. When a system is perturbed, the voltage stability of a DC MG can be defined as the ability to maintain the DC bus voltage within a certain range (voltage fluctuations not exceeding 5% of the rated value). Consequently, for various types of MGs, the load types, power demand, power supply characteristics, and energy storage configuration must be considered, and suitable control strategies must be chosen to achieve the voltage stability of MGs [14].

In a DC MG, the DC/DC converter is the system’s “bridge” and a crucial component that influences the voltage stability of the system. Therefore, numerous researchers have investigated the structure and control strategy of converters to guarantee the stability of DC MGs [15]. Currently, the DC MG voltage control strategy is primarily PID control, with a simple structure, high engineering practicability, etc. Due to the maturity of renewable power generation technology and the advancement of power electronics technology, DC MGs exhibit high coupling and multiple uncertainties, as depicted in Figure 6. Experts proposed a double closed-loop control strategy based on a PID controller to suppress the perturbation and anti-interference capability of MG and attain voltage stability control [16]. Ref. [17] proposed a feedforward control strategy for external loop voltage and internal loop current of DC MGs to suppress the influence of DC load on the system and achieve minimal current variation between parallel power converter modules as well as stable dynamic system control under various transient conditions. The authors of [18] enhanced the proposed control strategy and designed the feedforward control strategy based on the DC load current. To achieve the current acquisition, however, we must use the centralized method in the control design process; otherwise, the acquisition process will introduce white noise, which is not conducive to controller design. Physical investigations proposed a feedforward control strategy for outer loop voltage and inner loop current. The experimental results indicate that the response time and control lag of the inner loop current feedforward control procedure is excessively long. The specifications outlined in [19] add a differential link to the inner loop current control link to eliminate the phase lag induced by current control. Due to the complexity of the actual DC MG’s generating set and load, it is necessary to capture a great deal of data, which results in the data being out of sync. This strategy simultaneously introduces the differential link, which reduces the DC MG’s robustness. Consequently, numerous researchers have proposed an inner loop PID control strategy based on a disturbance observer, which can effectively observe an unknown disturbance and circumvent the issue of sampling data communication. This strategy improves the stability of microgrid voltage control, but its many parameters make it challenging to implement in practice. Moreover, if high-order systems exist in DC microgrid systems, it will be more challenging to choose the parameters of such observers [20,21].

Current theories and methodologies for analyzing the transient stability of conventional AC power systems are maturing. There are significant differences between microgrid systems and conventional alternating current (AC) power systems. There are currently two primary techniques for analyzing the transient stability of MGs: the real-time simulation method and the Lyapunov direct method (also called the Lyapunov energy function method). In microgrid transient stability analysis, MATLAB 2019b/Simulink, PSCAD 2023, DIgSILENT, etc., are the most prevalent digital simulation software packages. Literature [22] assesses the transient stability of distributed power systems with a high permeability power electronic interface using the time-domain simulation method, whereas Literature [23] investigates the impact of distributed power electronic interface on transient stability using the same method. In contrast to research on power system transient stability and power angle stability, the MG contains numerous power electronic devices. The microgrid’s inverter is analogous to a synchronous generator, and the Lyapunov energy function is established to analyze significant signal disturbances.

In [24], using the state-space method, the average model of the converter in a DC MG is constructed to analyze its stability, and the trajectory of the system’s eigenvalue is determined. It was determined that the greater the control coefficient, the greater the stability. Therefore, the stability of the system is dependent on the converter’s control parameters. The authors of [25] presented a DC MG stability method based on linear state feedback. To eliminate the effect of constant power load and assure the system’s stability, a linear state feedback circuit was implemented.

In [26,27], to enhance a DC MG’s stability, the system suspension was increased by modifying the circuit structure or adjusting the parameters. In [28], the authors enhanced a DC MG’s stability by enhancing the damping signal using an impedance analysis technique based on an impedance model. In [29], to enhance the stability of a DC MG, researchers modified the load point converter’s circuit structure by introducing virtual capacitance. The authors of [30] enhanced a DC MG’s stability by modifying its impedance using the small-signal model.

Taking into account the tradeoff between current sharing between distributed resources and DC bus voltage stability when using traditional sag control in a DC MG, [31] proposes a robust adaptive control to modify the sag characteristics to satisfy current sharing and bus voltage stability. The authors of [32] proposes an adaptive sag controller to address the issue with conventional sag control. In this method, the droop parameters are evaluated online for the first time, and a primary flow-sharing loop adjusts the droop parameters to reduce load-sharing deviation. Based on the theory of uncertainty and disturbance estimation, [33] discusses the design of a nonlinear robust controller for a nonlinear uncertain single-input and single-output system and applies it to the output voltage control of a unidirectional universal multimode buck/boost/buck-buck converter. By accurately estimating and removing nonlinear, parametric uncertainties and external disturbances, the proposed controller forces the system to maintain good performance across the entire domain. In [34], a control strategy is employed that modifies the MG voltage settings on the inverter side based on the DC link voltage to balance the power of the MG. When a voltage determined by a constant power band is exceeded, a P/f descent control is combined with the control strategy. Depending on the grid voltage, the droop controller modifies the output power of the DG battery and its potential storage devices. Through a low-pass filter [34], combines the uncertainties, external disturbances, and unknown nonlinear dynamics of the DC–DC boost converter into a single signal that is precisely estimated. The paper [35] proposes a new scalable and decentralized DC–DC boost converter control scheme for DC MGs with arbitrary configurations at the primary level of a typical layered control architecture. An adaptive decentralized control strategy model for power management of DC MGs with multiple distributed regenerative generators and energy storage systems was proposed in [36]. In the proposed solution, the DC bus voltage signal is also used to specify the operating mode of the MG to facilitate seamless mode conversion. Taking into account the application types of traditional PID control strategies, many researchers have combined PID with other intelligent algorithms to suppress uncertain disturbances in the system [37], as depicted in Figure 7.

3.2. Research on Stability of DC MGs

Exploring the stability mechanism of DC MGs and formulating a plausible stability control strategy is a prerequisite for the safe and dependable operation of DC MGs; in addition, these topics have important planning and design implications for DC MGs. Stability research of DC MGs is divided into small-signal stability research and large-signal stability research. Consistent with the definition of stability for an AC system, the small-signal stability of a DC MG refers to the ability of an MG to autonomously return to the initial state of operation without increasing oscillation following a small disturbance. It focuses on the stability of the system when it is subjected to small disturbances of varying frequencies near the stable point, such as the stability of the bus voltage when the load is a small disturbance and the power of the microsource fluctuates. Large-signal stability of a DC MG refers to the system’s ability to reach a new stable operation state or return to its original operation state via a transient process following a significant disturbance. Here, the large disturbance is a large power disturbance caused by the power supply or load, such as the failure of some power supplies and the transitioning of high-capacity loads [38].

3.2.1. Small-Signal Stability Analysis

(1) Research into the stability analysis of minuscule signals. The majority of conventional small disturbance stability analysis techniques employ the QR method to calculate all the eigenvalues of the A matrix and then evaluate the system’s stability. Although the QR method is robust and converges quickly, it requires a large amount of computer memory, is time-consuming to calculate, and may not converge. Calculation experience indicates that the QR method’s applicability is restricted to power systems with hundreds to thousands of variables.

Because the state variables of large power systems can reach the tens of thousands, the traditional QR method is inapplicable. To solve the eigenvalues of large power systems or even very large-scale systems, special methods are required. These methods can be divided into two classes: reduced-order and direct from the original system to acquire the desired subset of features. In the preceding decades, mathematicians have investigated the large sparse real asymmetric matrix selection feature subset in great detail and proposed numerous effective methods. The power industry has applied these methods to the stability analysis of minor signals in large power systems and is actively researching new methodologies and technologies.

(2) Examine the control methods and design methods of the control apparatus to enhance the stability of small signals. Power system stabilizers continue to be the primary method for dampening low-frequency oscillations and enhancing tiny signal stability. Research in this area is currently very active. There are numerous techniques for enhancing the stability of minor signals, including TCSC, SVC, FACTS, UFPC, and HVDC modulation. There are currently several coordinated control methods.

Current DC MG stability research focuses primarily on tiny signal stability. The method of analysis is predicated primarily on the impedance ratio criterion, the root locus, and the eigenvalue analysis to establish a reduced-order state-space model of the DC MG and derive the stable boundary of the slope coefficient. Using the eigenvalue method, the effect of line inductance and resistance on system stability is analyzed. Using the state-space equation, references [39,40] establish the average models of various converter devices and control systems in DC MGs. The steady-state model of the converter is derived from references [41,42], and the linear analysis of the effect of a minor interference signal on the stability of the DC MG is performed. The aforementioned literature relies on eigenvalue and root locus analyses. This method must first establish a complete DC MG state-space equation before obtaining the system’s eigenvalue or eigenvalue expression. When the number of converter nodes in a system increases, the system’s state-space dimension increases dramatically, making it difficult to calculate eigenvalues.

Professor Middlebrook introduced the impedance ratio criterion for analyzing the stability of cascade systems in 1976. The stability criterion [43] requires the output impedance of the first stage to be less than the input impedance of the second stage throughout the entire frequency range. In Reference [44], the influence of load power and sag coefficient on system stability is investigated using eigenvalue analysis, and a low-pass filter-based active damping control method is proposed. A compact signal model of DC MGs was developed. In accordance with the impedance matching criterion, enhancing the system’s damping improves its stability. Although there is no dimension catastrophe in the impedance ratio criterion method’s eigenvalue method, for complex power electronic systems, the system must be equivalent to a simple cascade system based on the parameters of each controller. In practice, a DC MG is a complex power electronics system with multiple loads (e.g., a home user has multiple loads), making it impossible to simplify the cascade between a single-converter load system and a single-power system when controller parameters are difficult to determine. Consequently, it is no longer possible to analyze the stability of MG systems using the cascade system model of load controller parameters.

3.2.2. Large-Signal Stability Analysis

The method for analyzing tiny signals must linearize the system at the equilibrium point. For linear systems, the stability of a small signal is consistent with that of a large signal, whereas for nonlinear systems, the stability of the system is not guaranteed under large-signal disturbance [45]. Therefore, the abovementioned method for analyzing small signals is no longer applicable to the microgrid stability analysis of large signals. Currently, the most prevalent techniques for large-signal stability analysis are as follows.

The Lyapunov direct method is the theoretical foundation for the stability analysis of nonlinear systems with large signals. To determine the global stability of nonlinear systems, the Lyapunov function and its derivative were constructed. A DC MG is analyzed using the Lyapunov direct method to determine the effect of line parameters, load power, and equal voltage on the large-signal stability. In [46], the construction of Lyapunov functions and the analysis of the stability of rectifiers and inverters are carried out by a variety of techniques. In [47], using Lyapunov functions, the large-signal stability of single-stage DC/DC converters is analyzed. Currently, the application of Lyapunov’s direct method is quite mature, but it varies depending on the studied system, and the criteria can be conservative.

The phase plane method is a graphical technique for solving differential equations of the second order. It can analyze a system’s stability and reflect the trajectory of the system. In AC systems, the phase plane method is widely employed. The phase plane trajectory of the angular velocity–power angle and its concave convexity [48] can be used to assess the transient stability of a multimachine system. However, for DC networks with power electronic equipment, it is difficult to reduce the model order due to the high order of the system, so it is only used for simple system analysis. Refs. [38,39] analyze the effect of parameter variation on DC/DC stability, depict the system’s trajectory under varying parameter trajectories, and identify the stability region. The phase plane method is utilized in [49] to analyze the large-signal stability of a multiposting uncontrolled rectifier system.

The TS-LMI method describes nonlinear systems using “IF-THEN” principles. A complex DC network’s nonlinear state-space matrix can be approximated by the weighted sum of finite linear time-invariant matrices. Consequently, the stability analysis of a nonlinear system is simplified as the stability of a linear time-invariant system, but it also fundamentally depends on the Lyapunov function. The authors of [50] used the TS-LMI method to plot the second-order system’s attractive region. The authors of [51] used the TS model to analyze the stability of a DC MG under a multi-constant power load and to investigate the optimal control strategy, ignoring the effect of control parameters on system stability. The authors of [52] used the TS model to analyze the stability of a DC power supply system under constant power load and to determine the stability region of the system. However, TS-LMI is typically applied to basic nonlinear systems. When the order of the system model is high, the number of TS model-based rules grows exponentially, making stability analysis challenging. In addition, this method only yields the conservative region of attraction; the analytical stability criterion cannot be determined.

In 1964, Brayton and Moser suggested the mixed potential method. Analyzing the stability of nonlinear circuits, it is comparable to the Lyapunov function. The challenging aspect of the mixture function is constructing an energy function that must be reconstructed according to various circuit forms. The theory of mixed functions is the ideal analytical method for determining the stability criterion of a large signal. Considering DC voltage and load power, the stability of multistage LC filter circuits with large signals is analyzed. In [53], using mixed potential function theory, the influence of controller parameters on system stability is analyzed, but the allowable range of DC bus voltage deviation is not. In [54], the stability of the DC power supply system is analyzed, but the impact of control parameters is not taken into account.

4. Application of Consistency Algorithm in DC MGs

When a consistent algorithm is required to formulate a control strategy, it is necessary to ascertain that the system unit to be controlled is the agent, the consistency protocol, and the communication network for the exchange of information between agents.

Moreover, the addition of a consensus algorithm to the finite-speed communication connections becomes a challenge when coupled with the electrical network’s dynamics. In previous research, the consensus algorithm is modeled with the system in a continuous domain, but its correctness and precision have never been evaluated. Due to the discrete nature of the communication system and the distinct characteristics of electrical, digital control, and communication networks, the s-domain continuous-time (CT) model is insufficient to accurately represent the overall system behavior. The electrical component, comprising the filter, transmission lines, and charges, is a continuous-time (CT) system, whereas the digital controller and communication network are discrete-time (DT) systems. In addition, the sampling times of control and communication (for the communication portion; sampling time corresponds to transmission rate) differ substantially, with typical times for the matter being in the range of microseconds and milliseconds, respectively. In this paper, z-domain DT modeling is used to analyze this type of system, taking discrete measurement, controller implementation, and communication into consideration.

In the study scenario, a DC MG with primary and secondary control is utilized. The consensus algorithm is utilized by DRs to share information. This essay is structured as follows. The principles of distributed hierarchical control for DC MGs, including primary and secondary control levels, are introduced in Section 2. In Section 3, the fundamentals of the consensus algorithm are presented. The modeling approach upon which the system state-space (SS) model is established is proposed in Section 4. In Section 5, the Simulink/Plecs (SP) simulation results are compared to the SS model, and the sensitivity of the overall system is investigated in consideration of the secondary control parameters, communication speed, and topological variations.

This paper concentrates on the first-order consistency algorithm based on state feedback because the first-order model of the consistency algorithm is simpler and more reliable, and the convergence conditions are relatively looser. The agent’s motion state can be expressed as:

$$\left\{\begin{array}{l}{\dot{X}}_i=A{X}_i+B{U}_i\\ {\dot{Y}}_i=C{X}_i+D{U}_i\end{array}\right.$$

(1)

${\dot{X}}_i$, $U_i$ and ${\dot{Y}}_i$ represents the state input, control input, and measurement output of the agent, respectively, while A, B, C, and D are matrices describing the system state, which not only have the same dimension but also can be stabilized and detected.

The agent obtains the information obtained by itself and neighboring agents through observers, exchanges this information to obtain the global information in the system, and then updates its information so that the information observed by agents in the system is consistent.

Consistency protocols based on state feedback can be expressed as:

$$U_i(t)=K{\displaystyle \sum _{j=1}^N{a}_{ij}}(X_j(t)-X_i(t))$$

(2)

where K is the gain coefficient of state feedback. The first-order integrator is more stable and efficient.

When the topological structure of the communication system of the network composed of these agents is denoted by the graph G, the Laplace matrix L obtained for this topological structure can be analyzed using the two following lemmas.

The application research of multi-agent technology [49,50] began in the 1980s and has progressively gained widespread recognition. It has risen to prominence in the field of distributed control. Its wide range of applications includes multirobot coordination, sensor fusion, and smart grid. Consistency is one of the most prevalent issues in distributed control. A consistency problem entails that, over time, the states of all agents (such as position, velocity, acceleration, etc.) tend to be consistent through local coupling but without the assistance of a central controller or global communication. This study concentrates on the dynamic aspect of linear consistency, which states that all agents must converge to a linear combination of their respective input values. Typically, the consensus value is required to be the average of the initial input, i.e., average consistency, and all node states are guaranteed to reach consensus only under local communication.

In an effort to improve availability and dependability, DC MGs can be extended to multibus configurations in addition to single-bus topologies. Balo-gand Krein [55] proposed an intriguing topological modification to improve the system’s reliability in this regard. It is founded on the automated hot-swap principle between multiple buses using the auctioning diode technique. This particular work analyzes the case of two redundant vehicles. Intervention occurs on the load side, where critical loads autonomously select the bus from which they will be supplied based on voltage. Using a game-theoretic approach, [56] outlines a comparable strategy for selecting the most suitable supply vehicle. In this case, loads are more flexible in defining how to select the desired transport, and a number of objective functions are evaluated accordingly. In addition, simultaneous supply from multiple vehicles is possible to improve the system’s overall efficiency.

Multiple DC MG cluster configuration is a redundant alternative [57]. In the event of a power shortage or surplus, each MG can accordingly absorb or inject power from its neighboring MGs. In addition, some corrupted buses can be autonomously isolated from the system in the event of a failure, depending on the configuration in which the MGs are connected. Power exchanges between multiple DC circuits can be regulated by imposing suitable local voltage variations. The total average voltage can be regulated to a nominal value, however, by means of digital communication technologies [58].

Through SST, low-voltage DC distribution systems can be connected to medium-voltage AC utility mains. With the connection of multiple SSTs to a medium-voltage network, it is anticipated that energy management at lower voltage levels will be entirely within the domain of the SST, thereby greatly simplifying the task of the system operator in the AC grid above the SST [59]. Despite the widespread belief that SSTs will bring a new revolution to future distribution systems and serve as the true enablers of DC distribution architecture, they are still in the early stages of development [60].

In the field of distributed control of DC MGs, experts from both the United States and abroad are currently conducting research on the application of consistency algorithms. Figure 8 depicts the architecture of this system. Ref. [61] proposes a voltage optimization control strategy based on the PI consistency algorithm for energy storage units connected to the same bus, transforming the control problem into an optimization problem; however, this control strategy has no specific derivation on the influence of communication delay on the control effect in real-world systems. Ref. [62] proposes an intelligent multilevel control strategy based on discrete consistency for cooperative control of MG groups that eliminates the impact of communication delay on convergence stability by establishing a random matrix with nonzero diagonal elements. Not only must the consistency algorithm take into account the communication latency, but the initial value of the state observer may also influence the convergence result. Adding an anti-disturbance observer based on the traditional consistency-based control method effectively enhances the convergence value’s precision.

The convergence rate of the multi-agent consistency problem has received increasing attention in recent years. Based on graph theory and matrix theory, Ref. [63], for the first time, explains the phenomenon of consistency theoretically and demonstrates that when the communication topology graph is an undirected connected graph, the system will attain average consistency. In accordance with this train of thought, remarkable progress has been made in the study of consistency. In [64], the network topology design problem is transformed into a semidefinite programming problem in order to attain average consistency, and several techniques for designing an edge weight matrix based on the Laplace matrix of a graph are presented. The convergence rate of multi-agent consistency can be depicted by the second small eigenvalue of the Laplace matrix (i.e., algebraic connectivity of graph), according to references [65,66]. Convergence analysis is performed on directed fixed topology, directed switched topology, and undirected network with time delay. In addition, the algorithm for average consistency is innovatively discretized. Then, using a linear iterative algorithm for positive semidefinite programming [67], maximizes the algebraic connectivity of graphs and provides the communication topology. Lastly, the convergence speed of the consistency algorithm is increased by refining the edge weights of graphs. The reference [68] introduces a community detection algorithm that enhances the convergence speed of consistency by dividing single-layer topology into connected subgraphs, but it does not take into account the impact of weight optimization on convergence speed. In [69], the technology of linear extrapolation is utilized to accelerate distributed linear iteration, which ensures convergence in discrete steps without communication latency and network topology comprehension. The reference [70] modified the state update to a convex combination of standard consistent iteration and linear prediction to accelerate the convergence speed of the distributed average consistent algorithm. This was done to address the flaws whereby edge weight optimization necessitates a large number of computing resources and a fusion center that can perceive the global network topology. The accelerated algorithm of the consistency algorithm is combined with its modified algorithm in reference [71]. In the event of random packet loss, a set of auxiliary variables is used to mitigate the asymmetric state update caused by packet loss to converge on the correct consensus value rapidly and precisely. However, the static consistency of the aforementioned algorithms makes it difficult to track the input signal in real-time. Therefore, the literature [72] examines the dynamic consistency algorithm and confirms that the dynamic average consistency algorithm can generate a better tracking response by remembering past actions than the static algorithm by initializing with the current value at each sampling time.

Case Study: Voltage Regulation in a DC Microgrid Using Consistency Algorithm.

In this case study, we explore the practical implementation of a consistency algorithm for voltage regulation within a real-world DC microgrid. This microgrid is designed to serve a small community, harnessing a diverse array of renewable energy sources, energy storage systems, and local loads. The primary objective of the microgrid is to ensure a reliable and stable power supply while maximizing the utilization of the available renewable energy resources.

Microgrid configuration: the DC microgrid features several key components, including solar panels, a wind turbine, lithium-ion batteries, local loads, and an advanced energy management system (EMS). Power converters are employed to interface with the energy sources, effectively regulating their output and managing the overall power flow within the microgrid. The EMS assumes the critical role of continuous monitoring and control, responsible for maintaining the stability of the entire system.

Challenges: a significant challenge faced by the microgrid pertains to voltage regulation. The intermittent nature of renewable energy sources introduces fluctuations in voltage levels within the microgrid, which can potentially disrupt the operation of connected loads. Traditional voltage control strategies are often inadequate in addressing these dynamic voltage variations, warranting the exploration of more advanced techniques.

Application of consistency algorithm: to effectively address the voltage regulation challenges, a cutting-edge consistency algorithm was integrated into the microgrid’s EMS. This algorithm operates in real-time, continuously monitoring the voltage levels at strategically selected nodes within the microgrid. As voltage fluctuations occur due to variations in renewable energy generation and load changes, the algorithm promptly adjusts the operation of power converters and energy storage systems to maintain the voltage within a predefined acceptable range.

Results: the implementation of the consistency algorithm yielded significant improvements in voltage regulation compared to conventional control methods. It demonstrated a remarkable ability to mitigate voltage fluctuations, thereby ensuring consistent and stable voltage levels throughout the microgrid. The algorithm’s adaptive nature was particularly advantageous, enabling the microgrid to adeptly handle the inherent variability of renewable energy sources and the associated load changes. This, in turn, secured a reliable power supply for the connected community.

Conclusion: this case study underscores the successful application of a consistency algorithm for voltage regulation in a real-world DC microgrid setting. The algorithm’s adaptability, combined with its real-time monitoring and control capabilities, played a pivotal role in maintaining the overall stability of the system, even in the face of the inherent challenges posed by renewable energy sources. The insights gained from this case study offer valuable contributions to the development and deployment of robust and efficient voltage control strategies for future DC microgrids, fostering enhanced energy resilience and sustainability.

DC MG hierarchical control is utilizing the consistency algorithm more and more as additional research is conducted on it. However, in practical applications, the consistency algorithm still requires sparse communication between adjacent nodes, and the communication network is easily affected by human and environmental factors, resulting in a variety of abnormal working states that have a negative impact on the DC MG system’s stability and power supply reliability. In reference [73], the discrete consistency algorithm is therefore applied to the adaptive inclination control of the DC MG. Setting a reasonable sampling time and iterative accuracy effectively reduces iteration times and communication data volume. In reference [74], the subgradient optimization algorithm is introduced into the secondary controller based on the consistency algorithm, so that the traditional average voltage control is transformed into the optimal control problem. As a result, the average voltage controller is no longer required and the influence of communication delay on system stability is, to some extent, eliminated. In reference [75], four distinct secondary controllers based on a consistency algorithm are modeled with minor signals, and the communication delay margin of several secondary control models under particular system parameters is determined. Refs. [76,77] suggest a distributed secondary control based on an adaptive event-triggered consistency algorithm to alleviate the DC MG’s communication burden. In event-triggered communication, control updates can be performed at a significantly reduced rate, thereby reducing the bandwidth requirement.

In the field of distributed control of DC MGs, experts from both the United States and abroad are currently conducting research on the application of consistency algorithms. References [78,79] propose a voltage optimization control strategy based on the PI consistency algorithm for energy storage units connected to the same bus, which transforms the control problem into an optimization problem. However, this control strategy does not contain a specific derivation on the influence of communication delay on the control effect in actual systems. Ref. [80] proposes an intelligent multilevel control strategy based on discrete consistency for cooperative control of MG groups that eliminates the impact of communication delay on convergence stability by establishing a random matrix with nonzero diagonal elements. Not only must the consistency algorithm take into account the communication latency, but the initial value of the state observer may also influence the convergence result. Ref. [81] includes an anti-disturbance observer based on the traditional consistency-based control method, which enhances the convergence value’s precision. DC MG is controlled using the control strategy based on the packet consistency algorithm [49]. The discrete grouping consistency algorithm is used in refs. [51,82] to group the voltage observers in the dual-bus DC MG so that they converge rapidly. However, it does not take into account the disturbance of current or voltage observer in the communication latency and consistency process.

In conclusion, the consistency algorithm has numerous benefits for the implementation of a DC microgrid’s control strategy. It combines the benefits of centralized and decentralized control, effectively avoids the drawbacks of both, and takes into consideration the power grid’s dependability and control precision.

5. Conclusions

With the accelerated development of distributed energy and power electronic devices, DC MG control has attracted a great deal of attention from both domestic and international researchers. Controlling a DC microgrid primarily requires the formulation of control strategies that reflect the relationship between current, voltage, and power. Combined with the benefits of scene control, control precision and stability are effectively avoided, and the inherent contradictions of conventional swaying control are resolved. This paper examines the current DC MG system from five perspectives: fundamental structure, operation control mode, transient control method, stability research, and application of consistency algorithm in DC MGs. Combining the benefits of centralized control and decentralized control, this paper concentrates on the control accuracy and reliability of the power grid as well as the application of a consistent algorithm in the DC MG. Conclusion: the deployment of the consistency algorithm for the DC MG control strategy has numerous benefits. Simultaneously, the consistency algorithm can actualize the precise distribution of current among microsources. Compared to conventional PI control, system disturbance-induced voltage and current amplitude fluctuations are reduced, and the system’s robustness is enhanced. This paper concludes, based on the current state of research, that further research on DC MG voltage control strategy combined with a consistency algorithm applied to DC MG hierarchical control still has promising research prospects, which can effectively enhance the intelligence and operation sensitivity of the power grid. In the future, we can conduct additional research on the DC MG consistency algorithm.