Multi-Time Scale Energy Storage Optimization of DC Microgrid Source-Load Storage Based on Virtual Bus Voltage Control

Abstract

The energy storage adjustment strategy of source and load storage in a DC microgrid is very important to the economic benefits of a power grid. Therefore, a multi-timescale energy storage optimization method for direct current (DC) microgrid source-load storage based on a virtual bus voltage control is studied. It uses a virtual damping compensation strategy to control the stability of virtual bus voltage and establishes a virtual energy storage model by combining different types of distributed capability units. The design of an optimization process for upper-level daily energy storage has the objective function of maximizing the economic benefits of microgrids to cope with unplanned fluctuations in power. A real-time energy-adjustment scheme for the lower level is introduced, and a real-time energy-adjustment scheme based on virtual energy storage for the short-term partition of the source-load storage is designed to improve the reliability of microgrid operations. The experiment shows that, in response to the constant amplitude oscillation of the power grid after a sudden increase in power, this method introduces a virtual damping compensation strategy at 20 s, which can stabilize the virtual bus voltage. From 00:00 to 09:00, the battery power remains at around 4 MW, and from 12:00 to 21:00, the battery exits the discharge state. The economic benefits from applying this method are significantly higher than before. This method can effectively adjust the source-load energy storage in real time. During peak electricity price periods, the SOC value of supercapacitors is below 0.4, and during normal electricity price periods, the SOC value of supercapacitors can reach up to 1.0, which can make the state of the charge value of supercapacitors meet economic requirements.

1. Introduction

As a new type of distributed energy system, the DC microgrid shows significant advantages in renewable energy access, energy management, and optimal utilization [1]. The DC microgrid is composed of a variety of distributed power sources, energy storage devices, loads, and the corresponding control and protection equipment. Its core goal is to ensure the safe and stable operation of the system while [2] realizing the efficient use of energy and economic operation. In a DC microgrid, distributed generation, controllable load, and energy storage all have the control potential to participate in system power regulation [3]. During the operation of a DC microgrid, the energy flow and balance between source, load, and storage are crucial [4]. Among them, “source” refers to distributed power sources, such as photovoltaic, wind power, and other renewable energy. “Load” refers to the load in the system, including the constant load and the interrupted load. “Storage” refers to energy storage devices, such as virtual energy storage systems, supercapacitors, etc., which can stabilize the power fluctuation in the system and improve the stability and reliability of the system [5]. However, due to the intermittency and uncertainty of renewable energy, as well as the diversity and time variability of the load, the energy management of DC microgrids is facing enormous challenges. In order to realize the efficient utilization of energy and the stable operation of the system [6], it is necessary to optimize the energy flow between the source, load, and storage in multiple timescales. This includes energy planning in the future to ensure the economy and sustainability of the system and the optimization of energy storage to cope with the rapid fluctuations in renewable energy and load [7]. At present, the microgrid focuses on the reasonable allocation and full utilization of the adjustable resources at the source-load storage side to improve the operational flexibility of the system. For example, Boqtob, O. et al. first outlined the application background and importance of incentive demand–response schemes in microgrids and, then, introduced different types of incentive demand–response schemes in detail, including price incentives, direct load control, and interruptible loads. By modeling and analyzing the energy system of the microgrid, this study evaluates the effect of the incentive demand–response scheme on the energy optimization of the microgrid and discusses the key factors and challenges in its implementation. The research results show that the incentive demand–response scheme can significantly reduce the energy cost of the microgrid, improve energy utilization efficiency, and enhance the stability of the system [8]. However, although this method introduces incentive-based demand response, the operating modes of controllable energy are independent of each other, lacking unified scheduling measures and failing to comprehensively evaluate the collaborative optimization benefits of multiple types of controllable energy, which affects the effectiveness of energy storage optimization. Ebrahimi, M.R., et al. captured the uncertainty of photovoltaic output through a two-way stochastic model to deal with transient stability constraints. The objective of optimization is to minimize the operation cost of the microgrid and ensure the transient stability of the system. The effectiveness of the proposed strategy in dealing with uncertainties and transient stability constraints is verified through case analysis, and its advantages in reducing operating costs and improving system stability are demonstrated [9]. However, the introduction of bidirectional random models and adaptive robust optimization techniques will increase the complexity of the model, making it difficult for this method to achieve rapid response and optimization in practical applications. Gassi, K.B. et al. introduced the application of linear programming in the energy optimization of a renewable energy microgrid and elaborated on how to optimize the energy distribution, energy storage management, and interaction with other grids by building a linear programming model. This method aims to minimize the operation cost and ensure the maximum utilization of renewable energy while meeting the system requirements and constraints. Through example analysis and simulation experiments, the effectiveness of the optimization method based on linear programming for improving the energy utilization efficiency of microgrids, reducing carbon emissions, and enhancing system stability is verified [10]. However, due to the lack of controllable parameters suitable for sensing the power supply and operation status of controllable devices in real time when dealing with sudden disturbances, Kavitha, V. et al. used the Mimosa optimization algorithm to solve the energy management model with multiple constraints and multi-objective optimization problems. By simulating the biological behavior of Mimosa, the algorithm can effectively search for the global optimal solution in the solution space to achieve the cost-effectiveness, environmental protection, and stability of the microgrid. Simulation experiments show that this method can significantly improve energy utilization efficiency, reduce operating costs, and optimize access to renewable energy [11]. However, this method cannot achieve a continuous dynamic response, and it is difficult to complete the global energy optimization management on a long timescale.

Optimal energy management has become a challenging task to accomplish in today’s advanced energy systems. If energy is managed in the most optimal manner, tremendous societal benefits can be achieved [12]. Therefore, based on the above analysis, this article proposes a multi-timescale energy storage optimization method for DC microgrids based on virtual bus voltage control, in order to provide theoretical support and practical guidance for the efficient operation and sustainable development of DC microgrids. The virtual bus voltage control here maintains voltage stability in DC microgrids by simulating the bus voltage control mechanism in traditional AC power grids. In the AC power grid, bus voltage is one of the key parameters for the stable operation of the power grid, and controlling the bus voltage can ensure the stability and reliability of the power grid. In DC microgrids, due to the lack of frequency and phase concepts in AC power grids, voltage control becomes the main means of maintaining system stability [13].

In order to provide a more efficient and economical solution for energy storage and management of DC microgrids, especially in improving the stability and economic benefits of microgrids, this study makes the following contributions:

• This study improves the flexibility and response speed of microgrids based on energy storage requirements at different timescales.
• Virtual damping compensation strategy: This study introduces a virtual damping compensation strategy for virtual bus voltage control, ensuring the stability of virtual bus voltage, which is crucial for maintaining the stable operation of microgrids.
• Constructing a virtual energy storage model: This study combines wind power and controllable loads to simulate the charging and discharging characteristics of capacitive energy storage and constructs a virtual energy storage model with multiple flexible resources. Through this model, various energy storage resources in microgrids can be more effectively integrated and utilized.
• Economic benefit optimization: At the upper management level, a daily energy storage optimization process has been established with the objective function of maximizing the economic benefits of the microgrid. This process is based on the charging and discharging management of virtual energy storage systems, considering the operational and power generation characteristics of each power generation unit in the microgrid. By adjusting the power output to ensure power balance, the economic optimization of the microgrid has been achieved. At the lower management level, in order to cope with unplanned fluctuations in power, this study also introduced a real-time energy-adjustment scheme for the short-term zoning of source load storage based on virtual energy storage. It is based on the upper-level model and optimizes the stability of microgrid operation by adjusting the energy allocation of source-load storage in real time.

2. DC Microgrid Source-Load Storage Multi-Timescale Energy Storage Optimization

2.1. Virtual Bus Voltage Control of DC Microgrid Based on Virtual Damping Compensation

Through the virtual damping compensation strategy, the virtual bus voltage oscillation control of the DC microgrid is realized [14], and the virtual bus voltage running smoothly is obtained. The calculation formula of virtual bus voltage is as follows:

$$u_v=u_t+[\beta +\left(-L_v\right)s{\displaystyle \frac{{\omega }_0}{s+{\omega }_0}}]i_0$$

(1)

Among them, $u_t$ is the terminal voltage of the parallel node; $\beta$ is the compensation coefficient; $s$ is a complex frequency variable; ${\omega }_0$ is the cutoff frequency of the low-pass filter; $-L_v$ is the virtual negative inductance value; $\beta +\left(-L_v\right)s{\displaystyle \frac{{\omega }_0}{s+{\omega }_0}}$ is a modified virtual damping compensation term, which can suppress high-frequency noise interference; $i_0$ is the output current for DC bus.

The average mathematical model of the DC microgrid is as follows:

$$\left\{\begin{array}{l}L{\displaystyle \frac{\mathrm{d}{i}_d}{\mathrm{d}t}}=-R{i}_d+\omega L{i}_q+u_d-u_{dc}\\ L{\displaystyle \frac{\mathrm{d}{i}_q}{\mathrm{d}t}}=-R{i}_q-\omega L{i}_q+u_q-u_{dc}\\ Ch{\displaystyle \frac{\mathrm{d}{u}_{dc}}{\mathrm{d}t}}={\displaystyle \frac{3i_d+3i_q}{2}}-i_0\end{array}\right.$$

(2)

Among them, $u_d$, $u_q$ and $i_d$, $i_q$ are the component of the input voltage and current of the DC microgrid of the $d$ axis and $q$ axis; $u_{dc}$ is the DC side bus voltage; $t$ is time; $\omega$ is the angular frequency of the DC microgrid; $h$ is the damping coefficient; $L$, $R$ and $C$ are DC microgrid filter inductor, resistor and DC side voltage stabilizing capacitor.

Considering the power balance of the DC microgrid, the following equation can be obtained:

$${\displaystyle \frac{3u_d{i}_d}{2}}=u_{dc}\left(Ch{\displaystyle \frac{\mathrm{d}{u}_{dc}}{\mathrm{d}t}}+i_0\right)$$

(3)

According to Equations (2) and (3), the second-order system equation can be derived, which takes the following form:

$$\left\{\begin{array}{l}{\displaystyle \frac{\mathrm{d}{u}_{dc}}{\mathrm{d}t}}={\displaystyle \frac{i_0}{Ch}}-{\displaystyle \frac{3u_d{i}_d}{2u_{dc}}}\\ {\displaystyle \frac{\mathrm{d}{i}_d}{\mathrm{d}t}}=-{\displaystyle \frac{R{i}_d+\left(u_d-u_t\right)}{L}}+\omega i_q\end{array}\right.$$

(4)

In order to obtain the standard nonlinear form of NDO (National Deming Office), the following definitions are made:

$$\left\{\begin{array}{l}x=y\left[x_1\hspace{1em}{x}_2\right]=\left[u_{dc}\hspace{1em}{i}_d\right]\\ f\left(x\right)=\left[-{\displaystyle \frac{3u_d{x}_2}{2Ch{x}_1}}\hspace{1em}-{\displaystyle \frac{R{i}_d+\omega i_q+u_d}{L}}\right]\\ z_1\left(x\right)=\left[0\hspace{1em}-{\displaystyle \frac{1}{L}}\right]\\ z_2\left(x\right)=\left[-{\displaystyle \frac{1}{Ch}}\hspace{1em}0\right]\\ u=u_t,g\left(t\right)=i_0\\ y=x_1\end{array}\right.$$

(5)

Among them, $x_1$ and $x_2$ are a state variable; $u$ is the control input; $g\left(t\right)$ is the amount of perturbation; $y$ is the control output. Equation (4) can be rewritten as follows:

$$\left\{\begin{array}{l}\dot{x}=f\left(x\right)+z_1\left(x\right)u+z_2\left(x\right)g\left(t\right)\\ y=x_1\end{array}\right.$$

(6)

According to Equation (6), a nonlinear perturbation observer can be designed for observing the $i_0$, so the functional expression of the observer is:

$$\left\{\begin{array}{l}\widehat{g}\left(t\right)=\delta k+p\left(x\right)\\ {\displaystyle \frac{\mathrm{d}\delta }{\mathrm{d}t}}=-\psi \left(x\right)z_2\left(x\right)\beta -\psi \left(x\right)\left[z_2\left(x\right)p\left(x\right)+f\left(x\right)+z_1\left(x\right)u\right]\end{array}\right.$$

(7)

Among them, $\widehat{g}\left(t\right)$ is the observed value of the disturbance in the output current of the DC microgrid; $\delta$ is the observer internal state variables; $p\left(x\right)$ is the observation function to be designed; $\psi \left(x\right)$ is the observer gain.

According to Equation (7), the error equation of NDO can be deduced as follows:

$${\displaystyle \frac{\mathrm{d}\left[g\left(t\right)-\widehat{g}\left(t\right)\right]}{\mathrm{d}t}}+\psi \left(x\right)z_2\left(x\right)+\dot{g}\left(t\right)=0$$

(8)

Among them, $\dot{g}\left(t\right)$ is the first-order equations of $g\left(t\right)$.

From Equation (8), in order to ensure the convergence of the observer, the following conditions need to be satisfied:

$$\left\{\begin{array}{l}\psi \left(x\right)z_2\left(x\right)>0\\ \lim {\displaystyle \frac{\mathrm{d}g\left(t\right)}{\mathrm{d}t}}\end{array}\right.$$

(9)

Accordingly, the simplified NDO model of the output current is obtained for the DC bus $i_0$:

$$\left\{\begin{array}{l}{\widehat{i}}_0=\delta \beta +l{u}_{dc}\\ {\displaystyle \frac{\mathrm{d}\delta }{\mathrm{d}t}}=-{\displaystyle \frac{\psi }{Ch}}\delta \beta -{\displaystyle \frac{{\psi }^2{u}_{dc}}{Ch}}+{\displaystyle \frac{3\psi u_d{i}_d}{2Ch{u}_{dc}}}\end{array}\right.$$

(10)

Among them, ${\widehat{i}}_0$ is the observed values of the output current $i_0$ on the DC side.

The smooth virtual bus voltage $u_v$ after oscillation control can be obtained by substituting ${\widehat{i}}_0$ into Formula (1).

2.2. Virtual Energy Storage Modeling of the DC Microgrid Source-Load Storage Based on Virtual Bus Voltage Control

In Section 2.1, a stable virtual bus voltage was obtained using a virtual damping compensation strategy. In this section, a virtual energy storage model will be constructed based on a stable bus voltage.

The capacitance value and state of charge of the virtual energy storage model can not only be used for constraining the operating status of controllable devices but, more importantly, it can be applied to the optimization of multi-timescale energy storage in DC microgrids. Through unified monitoring of virtual energy storage parameters, the overall planning, economic and safety evaluation of the DC microgrid operation can be significantly simplified.

Microgrid (MG) systems combine different types of distributed power generation units [15]. Therefore, when establishing a virtual energy storage model for DC microgrid source load storage, this study mainly considers three aspects: load characteristics of seawater desalination units, virtual energy storage of wind turbines, and load of electric vehicles. By considering the maximum power demand and current power demand of the load through the virtual capacitance value and virtual state of charge of the variable load, the energy demand changes of the load were simulated. The relevant variables are given below:

(a)

Load characteristics of seawater desalination unit: By introducing virtual capacitor $A_1$ and virtual capacitor energy state $SO{C}_1$, the load characteristics and energy storage charging and discharging regulation capabilities of seawater desalination units are simulated.

Seawater desalination units are usually driven by asynchronous motors, and their speed changes can simulate the charging and discharging process of energy storage. By calculating the virtual capacitance value, the energy storage capacity of the unit under different operating states can be quantified. The state of charge reflects the current energy storage level of the unit. By monitoring the virtual state of charge, the energy status of the unit can be understood in real time, enabling effective energy scheduling and management.

In order to construct the virtual capacitance model, the virtual capacitance $A_1$, the parameters of the energy state of the virtual capacitor $SO{C}_1$, which represents the controllable load of desalination, is introduced, with the following formula:

$$\begin{array}{l}{A}_1={\displaystyle \frac{Q_s}{{\rho }_n^2}}{\displaystyle \frac{\raisebox{1ex}{$\mathrm{d}{w}_r^2$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}t$}\right.}{\raisebox{1ex}{$\mathrm{d}{u}_v^2$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}t$}\right.}}\approx {\displaystyle \frac{Q_s}{{\rho }_n^2}}{\displaystyle \frac{w_r^{*2}-w_r^2}{\mathrm{\Delta }{u}_v}}\\ SO{C}_1={\displaystyle \raisebox{1ex}{$\frac{Q_s{w}_r^2}{2{\rho }_n^2}$}\!\left/ \!\raisebox{-1ex}{$\frac{Q_s{w}_{rn}^2}{2{\rho }_n^2}$}\right.}={\displaystyle \frac{w_r^2}{w_{rn}^2}}\end{array}$$

(11)

Among them, $Q_s$, $w_r$, ${\rho }_n$ are the rotor moment of inertia, the electrical angular velocity, and the pole pair number of the motor, respectively. $w_{rn}$ is the rated electrical angular velocity of the asynchronous motor. $w_r^{*}$ is the reference value of the angular velocity of the asynchronous motor. $\mathrm{\Delta }{u}_v$ is the amount of change in the quadratic of the virtual bus voltage.

For $A_1$, it is a continuous variable whose value can vary within a specific range, usually starting from 0, depending on the design and performance of the seawater desalination unit. For $SO{C}_1$, it is also a continuous variable, with values typically ranging from 0 to 1. Further, 0 indicates that the energy storage system is fully discharged, and 1 indicates that the energy storage system is fully charged.

(b)

Virtual energy storage of wind turbines: Simulate the energy capture and storage characteristics of the wind turbine by using the virtual capacitance value $A_g$ and virtual state of charge $SO{C}_g$.

Wind turbines capture wind energy and convert it into electrical energy, and their output power varies with wind speed, which can be seen as a process of energy storage and release. The calculation of virtual capacitance value helps to evaluate the energy capture capacity of wind turbines at different wind speeds. The virtual state of charge of wind turbines reflects their current energy output level, which is crucial for the energy balance and optimization of microgrids. By monitoring this state, the operation of the fan can be better controlled to achieve maximum energy utilization.

In order to ensure the level of energy management, real-time observation of the virtual energy storage input capacity, operating status, and safe operating range of wind turbines is carried out, and virtual energy storage is used as one of the reference conditions for joint management of the source-load energy storage [16,17]. The virtual capacitance value $A_g$ of the wind turbine and its virtual state of charge $SO{C}_g$ can be obtained:

$$\begin{array}{l}{A}_g={\beta }_o{\displaystyle \frac{\raisebox{1ex}{$\mathrm{d}{w}_g^2$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}t$}\right.}{\raisebox{1ex}{$\mathrm{d}{u}_v^2$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}t$}\right.}}\approx 2{\beta }_o{\displaystyle \frac{w_g^{*3}-w_g^3}{\mathrm{\Delta }{u}_v}}\\ SO{C}_g={\displaystyle \raisebox{1ex}{$\frac{Q_s{w}_g^2}{2{\rho }_n^2}$}\!\left/ \!\raisebox{-1ex}{$\frac{Q_s{w}_{gn}^2}{2{\rho }_n^2}$}\right.}={\displaystyle \frac{w_g^2}{w_{gn}^2}}\end{array}$$

(12)

Among them, $w_g$ is the electrical angular velocity of the generator. ${\beta }_o$ is the coefficient of the maximum power curve of the unit (at this time, the unit is running at the maximum power point under the wind speed to realize the capture of the maximum wind energy at that moment); $Q_s$ is the reference value of the angular velocity of the rotor of the wind turbine; $w_g^{*}$ is the angular velocity rating of the fan rotor.

For $A_g$, it is a continuous variable whose value can vary within a specific range, with a minimum value of 0 and a maximum value depending on the design and performance of the fan. The larger the value of $A_g$, the stronger the equivalent capacitance effect that the wind turbine can provide, thereby playing a better stabilizing role in the power system. For $SO{C}_g$, its value is usually between 0 and 1, where 0 indicates that the virtual energy storage of the wind turbine is fully discharged and 1 indicates that the virtual energy storage of the wind turbine is fully charged.

(c)

Electric vehicle load: Based on the virtual capacitance value $A_e$ and virtual state of charge $SO{C}_e$ of electric vehicles, the charging and discharging behavior and energy storage of electric vehicles were simulated.

The power battery of an electric vehicle can be regarded as a mobile energy storage unit, and its capacity determines the amount of energy that can be stored. On one hand, a battery can both purchase and sell electricity with a practically instant change in its output power. On the other hand, a battery is energy-limited, which makes its profit very sensitive to optimal scheduling [18]. The calculation of the virtual capacitance value helps to evaluate the energy storage potential of electric vehicles in microgrids. The state of charge of electric vehicles reflects the current charging level of the battery, which is of great significance for scheduling the charging and discharging behavior of electric vehicles to balance the grid load. By monitoring the virtual state of charge, the charging strategy of electric vehicles can be optimized, reducing the impact on the power grid.

Virtual capacitance values for electric vehicle loads $A_e$ and virtual state of charge $SO{C}_e$ can be expressed as follows:

$$\begin{array}{l}{A}_e={\displaystyle \frac{P_e}{u_v}}\\ SO{C}_e=SO{C}_0+{\displaystyle \frac{E_e\eta }{A}}\end{array}$$

(13)

Among them, $A$ is the total capacity of power batteries for electric vehicles. $SO{C}_0$ is the initial state of charge of the electric vehicle. $P_e$ is the total charging and discharging power of the electric vehicle. $\eta$ is the charging and discharging efficiency for electric vehicle batteries. $E_e$ is orderly charging and discharging loads for electric vehicles.

For $A_e$, its specific range depends on factors, such as the model of the electric vehicle, battery capacity, charging technology, etc., generally ranging from 0 (inability to charge and discharge) to the maximum value (maximum charge and discharge rate). For $SO{C}_e$, its feasible range is usually [0, 1], where 0 indicates the battery is completely depleted and 1 indicates the battery is fully charged.

In summary, a simplified energy balance equation $M={\displaystyle \sum _i\left(\mathrm{\Delta }{A}_i\times SO{C}_i\right)}$ can be obtained, which is the constructed virtual energy storage model, where $i=1,2,3$.

2.3. Multi-Timescale Energy Storage Optimization for DC Microgrid Source-Load Storage Based on Virtual Energy Storage

Based on the virtual energy storage model constructed above and its charging and discharging management characteristics, we developed an optimized energy storage strategy. The goal of this strategy is to maximize the economic benefits of microgrids. Therefore, this study aims to optimize energy storage at multiple timescales from the perspectives of both upper and lower layers as follows.

In the upper-level model, a day-ahead energy storage optimization process was established with the objective function of maximizing the economic benefits of the microgrid. This process is based on the charge and discharge management of the virtual energy storage system, considering the operational characteristics of each power generation unit in the microgrid. By adjusting the power output to ensure power balance, the economic optimization of the microgrid was achieved.

In the lower-level model, in order to cope with unplanned power fluctuations, this study also introduces a real-time energy-adjustment scheme for short-term zoning of source-load storage based on virtual energy storage. Based on the upper-level model, it optimizes the stability of microgrid operation by adjusting the energy allocation of source-load storage in real time.

2.3.1. Optimization of Energy Storage Before the Upper Day of the DC Microgrid Source-Load Storage

The upper-level day-ahead energy storage optimization model aims to simulate the joint virtual energy storage energy management model established by the multi-type flexibility resource regulation process through the transmission and interaction of the energy management system and energy storage information, in order to achieve the optimal allocation of the energy supply and use equipment of each subject. Considering the technical characteristics of the controllable equipment, the current market price, and other information, the global energy storage optimization scheme under a long timescale is obtained with the goal of maximizing the economic benefits of the DC microgrid.

In the day-ahead energy storage optimization process, 1 day is divided into 24 periods by hourly segments, and the day-ahead energy storage optimization objective function is as follows:

$$\max F={\displaystyle \sum _{t=1}^T(B_a^t+B_r^t-B_g^t-B_{g,om}^t-B_1^t-B_{ev}^t-B_m^t)}$$

(14)

Among them, $T$ is the total optimization time of energy storage before the DC microgrid day; $B_a^t$ and $B_r^t$ are battery and virtual energy storage benefits at time $t$; and $B_g^t$ is the cost of wind turbine power generation at time $t$. $B_{g,om}^t$ is turbine operation and maintenance costs. $B_1^t$ is the operating costs of desalination of controllable loads at time $t$. $B_{ev}^t$ is the hourly peaking costs paid to electric vehicle users at time $t$; $B_m^t$ is the operating costs of energy storage operators at time $t$.

The formula for $B_a^t$ is as follows:

$$B_a^t=R_a^t{P}_{a,dis}^t-R_a^t{P}_{a,ch}^t$$

(15)

Among them, $R_a^t$ is the purchase price of electricity at the time $t$. $P_{a,dis}^t$ and $P_{a,ch}^t$ are the amount of discharging and charging of the battery at time $t$.

The formula for $B_r^t$ is as follows:

$$B_r^t=\left(\gamma +R_a^t\right)\left(P_{r,dis}^t-P_{r,ch}^t\right)$$

(16)

Among them, $\gamma$ is the subsidized price per unit of power for virtual energy storage charging and discharging at time $t$; $P_{r,dis}^t$ and $P_{r,ch}^t$ are the virtual energy storage system discharges and charges at the time $t$.

The formula for $B_g^t$ is as follows:

$$B_g^t=K_g[P_{go}^t-P_g^t]$$

(17)

Among them, $K_g$ is the air conditioning coefficient of the fan; $P_{go}^t$ and $P_g^t$ are the virtual energy storage participation in wind power output before and after wind regulation at time $t$.

The formula for $B_{g,om}^t$ is as follows:

$$B_{g,om}^t=K_w{P}_{go}^t$$

(18)

Among them, $K_w$ is the turbine operation and maintenance cost factor.

The formula for $B_1^t$ is as follows:

$$B_1^t=K_1{D}^t$$

(19)

Among them, $K_1$ is the unit price per ton of freshwater. $D^t$ is the water production flow at the time $t$.

The formula for $B_{ev}^t$ is as follows:

$$B_{ev}^t=K_{ev}{P}_{ev}^t$$

(20)

Among them, $K_{ev}$ is the subsidized feed-in tariff for electric vehicles per unit of discharge. $P_{ev}^t$ is the total charging and discharging power of electric vehicles participating in virtual energy storage at the time $t$.

The formula for $B_m^t$ is as follows:

$$B_m^t=\xi \left(P_{a,dis}^t+P_{a,ch}^t\right)+P_{ev,ch}^t\left(1-{\eta }_{ev,ch}^t\right)+P_{ev,dis}^t\left({\displaystyle \frac{1}{{\eta }_{ev,dis}^t}}-{\eta }_{ev,dis}^t\right)$$

(21)

Among them, $\xi$ is the cost factor of the battery at the time $t$. $P_{ev,dis}^t$ and $P_{ev,ch}^t$ are the discharging power and charging power of the electric vehicle, respectively; ${\eta }_{ev,ch}^t$ and ${\eta }_{ev,dis}^t$ are the charging efficiency and discharging efficiency of electric vehicles, respectively.

Within the previous day’s energy storage optimization model, the power balance constraints are as follows:

$$(P_{a,dis}^t-P_{a,ch}^t)+P_g^t=P_1^t+{\displaystyle \sum _{t=1}^T{P}_{ev}^t}$$

(22)

The battery charging and discharging states are constrained to be:

$$\begin{array}{l}{X}_{a,ch}^t\cdot P_{a,ch\_\mathrm{m}\mathrm{i}\mathrm{n}}\le P_{a,ch}^t\le X_{a,ch}^t\cdot P_{a,ch\_\mathrm{m}\mathrm{a}\mathrm{x}}\\ X_{a,dis}^t\cdot P_{a,dis\_\mathrm{m}\mathrm{i}\mathrm{n}}\le P_{a,dis}^t\le X_{a,dis}^t\cdot P_{a,dis\_\mathrm{m}\mathrm{a}\mathrm{x}}\end{array}$$

(23)

Among them, $X_{a,ch}^t$ and $X_{a,dis}^t$ are the state of charge and discharge of the battery at the time $t$. $P_{a,ch\_\mathrm{m}\mathrm{a}\mathrm{x}}$ and $P_{a,ch\_\mathrm{m}\mathrm{i}\mathrm{n}}$ are the upper and lower limits of the charging power of the battery, respectively. $P_{a,dis\_\mathrm{m}\mathrm{a}\mathrm{x}}$ and $P_{a,dis\_\mathrm{m}\mathrm{i}\mathrm{n}}$ are the upper and lower limits of battery discharge power, respectively.

The battery state of charge is constrained to be:

$$SO{C}_{a,\mathrm{m}\mathrm{i}\mathrm{n}}^t\le SO{C}_a^t\le SO{C}_{a,\max }^t$$

(24)

Among them, $SO{C}_a^t$, $SO{C}_{a,\max }^t$, $SO{C}_{a,\mathrm{m}\mathrm{i}\mathrm{n}}^t$ are the state of charge of the battery at any time and the upper and lower limits of the state of charge of the battery at the time $t$.

The output power constraints for the desalination controllable load are as follows:

$$P_{1,\mathrm{m}\mathrm{i}\mathrm{n}}^t\le P_1^t\le P_{1,\max }^t$$

(25)

Among them, $P_{1,\mathrm{m}\mathrm{i}\mathrm{n}}^t$ is the minimum output power of the controllable load for desalination; $P_{1,\max }^t$ is the maximum output power of the desalination controllable load.

Desalination controlled load start/stop operation time constraints are as follows:

$$\begin{array}{l}\left(T_1^{on}-T_{1,\mathrm{m}\mathrm{i}\mathrm{n}}\right)\left(X_1^{t-1}-X_1^t\right)\ge 0\\ \left(T_1^{off}-T_{1s,\mathrm{m}\mathrm{i}\mathrm{n}}\right)\left(X_1^t-X_1^{t-1}\right)\ge 0\end{array}$$

(26)

Among them, $T_1^{on}$ is the duration of operation of the desalination controllable load before the end of the previous dispatch period. $T_1^{off}$ is the duration of the desalination controllable load outage before the end of the previous dispatch period. $T_{1,\mathrm{m}\mathrm{i}\mathrm{n}}$ is the minimum duration of operation. $T_{1s,\mathrm{m}\mathrm{i}\mathrm{n}}$ is the minimum continuous downtime. $X_1^{t-1}$ and $X_1^t$ are the switching state of the desalination controllable loads at the previous scheduling moment and the current scheduling moment.

The wind turbine energy storage constraints are as follows:

$$SO{C}_{g,\mathrm{m}\mathrm{i}\mathrm{n}}^t\le SO{C}_g^t\le 100\%$$

(27)

Among them, $SO{C}_g^t$ is the virtual state of charge of the turbine. $SO{C}_{g,\mathrm{m}\mathrm{i}\mathrm{n}}^t$ is the lower limits of the virtual charging state of the turbine, respectively.

The energy storage constraints for desalination controllable loads are as follows:

$$SO{C}_{1,\mathrm{m}\mathrm{i}\mathrm{n}}^t\le SO{C}_1^t\le 100\%$$

(28)

Among them, $SO{C}_1^t$ is the virtual state of charge of the desalination controllable load; $SO{C}_{1,\mathrm{m}\mathrm{i}\mathrm{n}}^t$ is the lower limit of the virtual charging state of the desalination controllable load.

The energy storage constraints for the electric vehicles are as follows:

$$SO{C}_{e,\mathrm{m}\mathrm{i}\mathrm{n}}^t\le SO{C}_e^t\le SO{C}_{e,\max }^t$$

(29)

Among them, $SO{C}_e^t$ is the virtual state of charge of an electric vehicle; $SO{C}_{e,\max }^t$ and $SO{C}_{e,\mathrm{m}\mathrm{i}\mathrm{n}}^t$ are the upper and lower limits of the virtual state of charge of the electric vehicle.

2.3.2. Real-Time Adjustment of Lower-Tier Capacities of the DC Microgrid Source and Load Storage

Although the optimization of upper-level energy storage can provide long-term economic guidance, microgrids often face unplanned power fluctuations in actual operation. To address these challenges, this study designed a real-time energy-adjustment scheme for the lower layer based on the upper-layer model. This plan is based on the upper-layer optimization model and utilizes the flexibility of the virtual energy storage system to achieve real-time adjustment of the short-term energy partitioning for source-load storage. In this way, even in the face of unplanned fluctuations in power, microgrids can maintain high operational reliability and stability.

The lower-level capacity real-time adjustment system switches the control mode according to the charge state of each energy storage device, adjusts the deviation of the actual operation state from the ideal optimized operation state of the global optimization control [19], and realizes the real-time adjustment of the capacity in the neighborhood of the global optimized operation point. Thus, the benefits of microgrids are promoted through hierarchical optimization [19].

Repeated charging and discharging will affect the service life of the energy storage battery [20], and the composition of virtual energy storage can make up for the above shortcomings of the battery. Comprehensive virtual energy storage response speed, energy storage battery characteristics, and economic aspects, by setting the critical value of the charge state to develop various types of energy storage components input priority rules, the DC microgrid is divided into six different operation scheduling modes. They are economic dispatch, supercapacitor charging and discharging area, controllable load virtual energy storage charging and discharging area, electric vehicle charging and discharging area, wind turbine virtual energy storage charging and discharging area, and battery charging and discharging area.

After the introduction of virtual energy storage, the relationship between the supercapacitor terminal voltage and the virtual amplification is expressed as follows.

$$\kappa ={\displaystyle \frac{U_c^2\left(t\right)-U_c^2\left(t_1\right)}{U_c^2\left(t\right)-U_c^2\left(t_2\right)}}$$

(30)

Among them, $U_c$ is the supercapacitor terminal voltage; $U_c\left(t_1\right)$ is to reach the capacitor end voltage at the value of the set charge state $SO{C}_c$; setting $SO{C}_c$ reaches the limit at time $t_2$; the supercapacitor terminal voltage is $U_c\left(t_2\right)$.

Combining Equations (11) and (30) to obtain the reference value of the electrical angular velocity of the controllable seawater load lead to the following:

$$\left\{\begin{array}{ll}{w}_{r,\mathrm{m}\mathrm{i}\mathrm{n}}\hfill & w_r\le w_{r,\mathrm{m}\mathrm{i}\mathrm{n}}\hfill \\ w_{rn}{\left[K_1\left(SO{C}_c-SO{C}_{cres}\right)+SO{C}_1\right]}^{{\displaystyle \frac{1}{2}}}\hfill & w_{r,\mathrm{m}\mathrm{i}\mathrm{n}}\le w_r\le w_{rn}\hfill \\ w_{rn}\hfill & w_r\ge w_{rn}\hfill \end{array}\right.$$

(31)

Among them, $K_1=2{\rho }_n^2{U}_c{A}_1\left(U_{c,\max },-,U_{c,\mathrm{m}\mathrm{i}\mathrm{n}}\right)/Q_s{w}_{rn}^2$; $SO{C}_{cres}$ is the $SO{C}_c$ limit values for seawater controllable loads when putting in virtual energy storage. $w_{r,\mathrm{m}\mathrm{i}\mathrm{n}}$ is the minimum electrical angular velocity of the asynchronous motor.

Combining Equations (11) and (24) to obtain the reference value of the electrical angular velocity of the wind turbine leads to the following:

$$w_g^{*}=\left\{\begin{array}{ll}{w}_{g,\mathrm{m}\mathrm{i}\mathrm{n}}\hfill & w_g\le w_{g,\mathrm{m}\mathrm{i}\mathrm{n}}\hfill \\ w_{gn}{\left[K_2\left(SO{C}_c-SO{C}_{cges}\right)+SO{C}_g\right]}^{{\displaystyle \frac{3}{2}}}\hfill & w_{g,\mathrm{m}\mathrm{i}\mathrm{n}}\le w_g\le w_{gn}\hfill \\ w_{gn}\hfill & w_g\ge w_{gn}\hfill \end{array}\right.$$

(32)

Among them, $K_2=U_c{A}_g(U_{c,\max }-U_{c,\mathrm{m}\mathrm{i}\mathrm{n}})/{\beta }_o{w}_{gn}^3$; $SO{C}_{cges}$ is the $S$ limit value of adding virtual energy storage to the fan. $w_{g,\mathrm{m}\mathrm{i}\mathrm{n}}$ is the minimum electrical angular velocity of the fan.

$w_r^{*}$ and $w_g^{*}$ reference values can be obtained through Equations (25) and (26). The reference value can adjust the power of the asynchronous motor and wind turbine and complete the real-time adjustment of the DC microgrid source-load storage lower-layer capacity, so as to achieve the purpose of seawater load and wind turbine virtual energy storage to suppress power fluctuations.

Energy management within microgrids under the presence of a large number of renewables such as photovoltaics is complicated due to the uncertainties involved [21]. This study constructs a virtual energy storage model with multiple flexible resources through a virtual damping compensation strategy combined with virtual bus voltage, achieving optimized management of multi-timescale energy storage for source-load storage in DC microgrids. A structural diagram of this method is shown in Figure 1.

3. Experimental Analysis

3.1. Experimental Environment

A DC microgrid is used as an experimental object, and the relevant parameters of this DC microgrid are shown in

Table 1. Related parameters of the DC microgrid.

Equipment	Numerical Value
Rated power of fan	100 kW
Starting wind speed	3 m/s
Rated wind speed	12 m/s
Cut-in wind speed	20 m/s
Fan conversion efficiency	85%
Supercapacitor capacity	50 kWh
Supercapacitor charge time (to full charge)	10 min
Supercapacitor discharge time	20 min
Charge and discharge efficiency of supercapacitors	95%
Battery capacity	200 kWh
Battery charge time (to full charge)	4 h
Battery discharge time	8 h
Battery cycle life	2000 times
Charging and discharging efficiency of battery	90%
Maximum power requirement for seawater load	50 kW
Daily operating time of seawater load	8 h
Seawater load stability	high
Electric vehicle charging power	50 kW
Electric vehicle battery capacity	70 kWh
Ev charging time (to full charge)	1.5 h (Fast charge)
Electric vehicle range	300 km
Maximum load capacity	300 kW

Typical daily power prediction curves and daily time-of-day tariffs used in the experiment are shown in Figure 2 and Figure 3, respectively.

It can be seen from Figure 2 that the peak load and wind power of this typical day are about 9:00 and 21:00. It can be seen from Figure 3 that the electricity price includes three periods, of which 23:00~06:00 belongs to the valley period, where the electricity price is about 0.5 CNY/kW·h, 06:00~12:00; 18:00~23:00 belongs to the peak period, where the electricity price is about 1.2 CNY/kW·h; 12:00~18:00 belongs to the ordinary period, where the electricity price is about 0.7 CNY/kW·h.

3.2. Experimental Results

3.2.1. Control Effect of Virtual Bus Voltage

On the above typical days and hours, when the DC microgrid runs to 10 s, its power suddenly increases by 5 kW. In this method, a virtual damping compensation strategy is used to control the oscillation of the virtual bus voltage, thereby obtaining a stable virtual bus voltage. The change in the virtual bus voltage before and after the virtual damping compensation is analyzed. To compare this experiment, the method proposed in this paper was compared with the methods in Refs. [8,9], and the analysis results are shown in Figure 4.

According to Figure 4, when the power suddenly increased by 5 kW at 10 s, the virtual bus voltage of the DC microgrid experienced a transient drop, with an amplitude of about 10 V. This phenomenon indicates that a sudden increase in power has a significant impact on the stable operation of microgrids. In addition, the virtual bus voltage experienced a constant amplitude oscillation of about 5 V after a transient drop. This high-frequency oscillation not only increases the instability of the DC microgrid but may also cause damage to sensitive equipment in the DC microgrid.

In response to this situation, this method introduces a virtual damping compensation strategy at 20 s, which enables the virtual bus voltage to quickly recover and stabilize, effectively suppressing high-frequency oscillations and stabilizing the bus voltage at 690 V. After comparing the methods in Refs. [8] and [9], it was found that the virtual bus voltage cannot be quickly stabilized in a short period of time after applying these two traditional methods. After applying the method in Ref. [9], the virtual bus voltage stabilized after 35 s, while after applying the method in Ref. [8], the virtual bus voltage fluctuated. The above experimental results indicate that the method proposed in this paper can effectively control the vibration problem of virtual bus voltage and obtain stable virtual bus voltage.

3.2.2. Optimization Results of Energy Storage in Different Time Periods of Typical Days

When EVs participate in virtual energy storage, EVs are subject to the load-level scheduling strategy, and the target of scheduling at this time is the group of EVs. According to the user’s driving habits, the centralized and orderly management of electric vehicles, under the premise of ensuring the economic indicators of the DC microgrid, plays a role in “peak shaving and valley filling” of the original load. The results of energy storage optimization for each time period on a typical day are shown in Figure 4.

It can be seen from the analysis of Figure 5a that, without considering the virtual energy storage scenario, the load power is relatively stable from 00:00 to 6:00, with wind power and seawater loads as the main load, and the battery is assisted to adjust within a small range to ensure that the margin required by the energy storage device to balance power fluctuations is met. At 12:00~18:00, the wind power output decreases, and the battery output increases to supplement the power shortage; after 18:00, the increase in load power increased, and the disordered charging of electric vehicle users led to “peak to peak”, which increased the burden of DC microgrid regulation. The battery power always exceeded 0 MW, indicating that the battery was discharged frequently from 12:00 to 24:00, and the battery aging cost increased significantly. After implementing the optimization scheme of day-ahead energy storage without virtual energy storage, it will cause serious harm to battery health.

It can be seen from the analysis of Figure 5b that the above problems can be effectively solved by considering the participation of virtual energy storage in microgrid dispatching. The optimization results take the virtual energy storage capacitance value as the prediction reference value to regulate the virtual energy storage charging and discharging power. At 00:00~06:00, according to the electricity price incentive strategy, the virtual energy storage of electric vehicles with gradually increasing virtual capacitance value is put into use, and the night redundant wind power is reasonably consumed. At 06:00, the virtual state of charge of seawater load reached the upper limit, and the desalination unit exited the virtual energy storage control. The virtual energy storage of the fan reduced the absorbed wind power, and the virtual capacitance of the fan increased; from 09:00 to 18:00, the seawater desalination controllable load was put into operation with a high virtual capacitance value, which played a major role in regulation. At the same time, the change of its virtual state of charge was observed to be stable. From 00:00 to 09:00, the battery power was always maintained at about 4 MW. From 12:00 to 21:00, the battery exited the discharge state, significantly reducing the number of battery discharges and significantly reducing the battery life cost. After 18:00, the idle electric vehicle will be discharged to supply the load. The negative virtual capacitance value can directly offset part of the battery regulation capacity.

3.2.3. Economic Benefit Analysis of DC Microgrids

The economic benefits of this DC microgrid are analyzed before and after applying the method of energy storage optimization in this study at different DC microgrid power fluctuations, and the analysis results are shown in

Table 2. Economic benefits of the DC microgrid (CNY).

Volatility/%	Before Applying This Method	After Applying This Method
2	18,115	28,230
4	17,850	27,943
6	16,744	26,943
8	15,760	25,987
10	13,540	23,765

.

Analyzing Table 2, when the power fluctuation rate of the DC microgrid is 2%, the economic benefits of applying the method proposed in this article can reach CNY 28,230. As the power fluctuation rate of the DC microgrid increases, the economic benefits of the microgrid show a downward trend. However, under different power fluctuations, the economic benefits of applying the method proposed in this article are significantly higher than before.

3.2.4. Analysis of SOC Value Changes in Supercapacitors

After the DC microgrid source load storage energy is adjusted in real time using the method in this paper, the SOC value change curve of the supercapacitor is shown in Figure 6.

According to the analysis of Figure 6, it can be seen that after real-time adjustment of the source-load energy storage in the DC microgrid using the method proposed in this article, the SOC value (state of charge) of the supercapacitor exhibits the following characteristics during different electricity price periods:

(a)

Peak electricity price period: The SOC value of supercapacitors is relatively low. During the peak period of load demand, the energy demand in microgrids is high, and supercapacitors supplement the energy deficit of the DC microgrids through discharge to meet the load demand. Therefore, the SOC value will decrease accordingly.

(b)

Flat-price period: The SOC value of supercapacitors is relatively high. The load demand is relatively stable, the electricity price is moderate, and supercapacitors store energy through charging for emergency use. Therefore, the SOC value will increase.

(c)

During the valley electricity price period, supercapacitors generally maintain their maximum SOC value. During the lowest electricity price period, supercapacitors maximize their energy storage capacity by charging, preparing for subsequent peak electricity price periods or sudden energy demands.

3.3. Discussion and Analysis

3.3.1. Discussion and Analysis of the Control Effect of Virtual Bus Voltage

In Figure 3, after a sudden increase in power, the virtual bus voltage of the DC microgrid experienced a transient drop. This phenomenon indicates that a sudden increase in power has a significant impact on the stable operation of microgrids. As an important indicator of power quality in microgrids, the transient drop of virtual bus voltage means that the response of the DC microgrids to power changes is not fast or stable enough, which may cause adverse effects on equipment in DC microgrids and even lead to more serious faults. In addition, the virtual bus voltage experienced a constant amplitude oscillation of about 5 V after a transient drop. This high-frequency oscillation not only increases the instability of the DC microgrid but may also cause damage to sensitive equipment in the DC microgrid. The existence of high-frequency oscillations indicates that microgrids have insufficient self-regulation ability after power changes, and corresponding measures need to be taken to suppress this oscillation.

In response to this situation, this method introduces a virtual damping compensation strategy at 20 s. By simulating the damping effect in physical systems, the microgrid’s ability to respond to power changes and self-regulate is enhanced, enabling the virtual bus voltage to quickly recover and stabilize and high-frequency oscillations to be effectively suppressed. Damping is a mechanism in physical systems that reduces oscillations and enhances stability. By simulating the damping effect, the responsiveness of microgrids to power changes is enhanced. When power changes occur, the system can respond more quickly by adjusting its internal parameters to balance this change. By introducing appropriate damping, DC microgrids can recover to a stable state faster and reduce or eliminate high-frequency oscillations.

3.3.2. Discussion and Analysis of Energy Storage Optimization in Different Time Periods of Typical Days

Without considering virtual energy storage, the power balance and regulation of microgrids face significant challenges, especially at different times of the day, where microgrids rely on frequent charging and discharging of batteries to balance the fluctuations in wind power output and load demand. At night and in the evening, due to the decrease in wind power output and the impact of disorderly charging of electric vehicles, the burden of microgrid regulation is increased, resulting in the continuous output of battery power, which exacerbates battery aging and increases maintenance costs.

However, the introduction of virtual energy storage in microgrid scheduling in this article can significantly improve this situation. By optimizing and regulating the charging and discharging power of virtual energy storage (including virtual energy storage for electric vehicles and virtual energy storage for controllable loads of seawater desalination), microgrids can more effectively balance power fluctuations and reduce dependence on batteries. Particularly, under the guidance of electricity price incentive strategies, the investment of virtual energy storage for electric vehicles and controllable load virtual energy storage for seawater desalination can reasonably absorb redundant wind power at night and provide regulation support during peak hours, significantly reducing the number of battery discharges, extending the battery life, and reducing maintenance costs.

From this, it can be seen that the application of virtual energy storage technology in microgrid scheduling has significant advantages, which can effectively improve the stability and economy of microgrids, reduce the burden of batteries, and reduce the cost of battery aging.

3.3.3. Discussion and Analysis of the Economic Benefits of DC Microgrids

As the power fluctuation rate of the DC microgrids increases, that is, when the system faces greater instability and challenges, the overall economic benefits of microgrids show a downward trend. However, under different power fluctuations, the economic benefits of applying the method proposed in this article are significantly higher than those before applying the method. This result fully demonstrates that the method proposed in this article can effectively optimize energy storage strategies and improve the economic benefits of microgrids when dealing with varying degrees of power fluctuations.

3.3.4. Discussion and Analysis of SOC Value Changes in Supercapacitors

During peak electricity prices, the strategy of utilizing the fast charging and discharging characteristics of supercapacitors to reduce or avoid purchasing electricity from high-priced grids effectively reduces the operating costs of the DC microgrids. This not only demonstrates the advantages of supercapacitors in quickly responding to load demands but also demonstrates the role of real-time energy management strategies in improving the system economy.

During the flat electricity price period, the charging behavior of supercapacitors not only provides energy reserves for the system but also prepares for potential energy demands in the future. This strategy not only ensures the stable operation of the system but also provides flexibility for the system to cope with uncertain factors.

During the valley electricity price period, supercapacitors maximize their SOC value to fully utilize low-cost electricity and provide sufficient energy support for the system. This not only reduces the cost of purchasing electricity during subsequent periods of high electricity prices but also enhances the system’s ability to respond to emergencies.

In summary, the method proposed in this paper not only optimizes the energy management of the DC microgrids (see Appendix A for details) but also improves the economic and operational efficiency of the system.

4. Conclusions

In this study, for the controllable source storage load within the DC microgrid, a two-layer multi-timescale energy storage optimization method is designed for the upper daytime energy storage optimization and the lower real-time adjustment, which can effectively reduce the number of discharging times of the battery, extend its service life, reduce the operating cost, and enhance the economic efficiency of the DC microgrid by reasonably deploying the virtual energy storage resources. Experiments proved that the method in this paper is capable of fine management and optimal scheduling of source-load storage units in DC microgrids on different timescales, so as to realize the economic, efficient, and stable operation of microgrids.

Although the method proposed in this article achieved some success, the parameter selection in the virtual damping compensation strategy has a significant impact on the stability of the virtual bus voltage and the performance of the system. However, determining the optimal values of these parameters may require extensive experimentation and simulation, and parameter adjustments may be necessary in different scenarios, which increases the difficulty in practical applications. Therefore, in future research, attention can be paid to how to adaptively adjust the parameters in the virtual damping compensation strategy based on the real-time operating status of the DC microgrid source-load storage system and external environmental changes, in order to improve the adaptability and robustness of the DC microgrid.