Optimal Configuration for Photovoltaic and Energy Storage in Distribution Network Using Comprehensive Evaluation Model

Abstract

To enhance the efficiency of renewable energy consumption and reduce reliance on fossil fuels, the study addresses the challenges of distributed photovoltaic and energy storage integration in distribution networks, such as voltage fluctuations, safety risks, and insufficient converter considerations to the distribution network. Through a four-dimensional comprehensive evaluation system including grid-strength quantification indicators like the generalized short-circuit ratio, a multi-objective mathematical model-based performance evaluation system using an analytic hierarchy process and criteria importance through the intercriteria correlation method has been established, and an optimization model for the configuration of photovoltaic and energy storage equipment is optimized. The study innovatively proposes a multi-type synchronous control framework enabling dynamic GFL/GFM converter selection at different nodes, overcoming traditional single-control limitations. The simulation results show that the proposed optimal configuration scheme can effectively improve the operating states and reduce the energy consumption of the distribution network.

1. Introduction

To achieve the goal of “carbon neutrality” in China, promoting the development of new energy and transforming the energy structure in the power industry has become an important issue. The distribution network is responsible for converting high-voltage electric energy into voltage suitable for users and distributing it safely and reliably to households, enterprises, and public facilities, and it is a key link in the power system connecting the transmission network and end users [1,2].

Optimal configuration of the distribution network is one of the important research fields regarding distribution networks, and it is directly related to the economy, security, and power supply reliability in future operational processes. Due to the random, intermittent, and fluctuating characteristics of photovoltaic (PV) power generation [3], a large amount of PV equipment connected to the grid is accompanied by extensive access to energy storage (ES), and the dynamic interaction between power supply, ES, and load in the distribution network is more complex, with new changes in operation characteristics [4]. Therefore, it is necessary to formulate a reasonable control strategy for the PV-ES system and the location and capacity-determination scheme in the optimal configuration of the distribution network, which also promotes the process of enhancing the efficiency of renewable energy consumption and reducing reliance on fossil fuels [5,6].

The optimization configuration problem of distribution networks can generally be divided into three categories: siting and sizing, topology optimization, and operational strategy optimization [7]. Siting and sizing are the core problems in the planning and operation of the distribution network, which aims to achieve the optimal balance of economy, reliability, and power quality through the reasonable selection of an equipment installation location and capacity [8,9]. Literature [10] demonstrates the optimization of solar-assisted heat pump systems by integrating thermal (TES) and electrical energy storage (EES). Through an innovative co-control strategy (e.g., utilizing surplus PV electricity to drive heat pumps for thermal storage), a configuration with 1000 L TES and 5 kWh EES achieves an 80% self-consumption rate and self-sufficiency degree—tripling the performance of non-storage systems. Literature [11] proposes a master–slave methodology combining the Multiverse Optimizer (MVO) algorithm and a matrix-based power flow method (MAX) to optimally integrate PV generators and distributed static compensators (D-STATCOMs) in electrical distribution systems, minimizing annual investment and operational costs, with the approach demonstrating superior performance over the VSA, CSA, GA, and PSO methods in statistical analyses. Topology optimization involves improving and optimizing the connection structure of the distribution network to achieve load balance, reduce losses, and improve system reliability [12,13]. Literature [14] proposes a convex mixed-integer quadratic programming-based integrated optimization approach to optimize the network topology and the outputs of distributed generations together for reduced network power losses. Operation strategy optimization is of great significance in improving the anti-interference ability of the power grid, enhancing the utilization rate of renewable energy and improving user satisfaction, which ensures the reliability and security of the power supply [15,16]. Literature [17] proposes a population-based genetic algorithm (PGA) framework for microgrid energy management, which minimizes operational costs in both grid-connected and isolated modes by optimizing the active power dispatch of distributed wind turbines. Rigorous statistical validation shows that in the grid-connected mode of a 33-node microgrid, the PGA achieves the lowest daily cost of 3837.22 (SD = 0.80), reducing baseline costs (9931.64) by 61.35%, demonstrating the PGA’s superior cost efficiency and solution stability. Literature [18] proposes a Gray Wolf Optimizer (GWO)-based master–slave methodology to minimize operational costs in AC microgrids by optimally managing wind generators, battery storage (BESS), and D-STATCOMs across grid-connected and islanded modes, validated via statistical analysis against PSO and GA on a 33-node test system.

The grid-following (GFL) converter achieves more efficient resource allocation and interaction through network technology during power generation and consumption, which relies on grid voltage and frequency signals and is used in grid-connected PV systems and ES systems. It simplifies the control design and is suitable for small-scale distributed power generation [19]. Grid-forming (GFM) converters can independently establish voltage and frequency, simulate the characteristics of synchronous generators, and maintain grid stability by controlling the amplitude and frequency of output voltage. With the increasing penetration rate of renewable energy, GFM technology becomes a key support for the stability of future power grids [20]. At present, multi-type synchronous control strategies based on GFL and GFM devices have been carried out, which can combine the advantages of both devices and take cost and stability into account [21].

The security guarantee of the existing distribution network with a high proportion of new energy access mainly starts with optimizing the control strategy. Literature [22] proposes a mathematical model that minimizes the absolute change in line power flows to maintain post-contingency grid operation close to the pre-fault state, reduce the risk of power flow exceeding the limit in lines, and enhance the transient safety after power grid failures. Literature [23] resolves consistency deviations in HVAC systems by weighted-mean state representation and control-variable weighted-sum relationships, showing a 1400% deviation in empirical models (a = 0.75, n = 60), while the new method achieves zero-error consistency and reduces user temperature deviation to 0.6% (a = 0.99, n = 6). However, existing research [24,25,26] fails to address the safety implications of hybrid GFL/GFM control, particularly the following aspects:

• Studies on PV-ES configuration often neglect voltage stability under hybrid GFL/GFM operations.
• Grid-strength degradation due to high-penetration converters is rarely quantified in planning models.
• There is a lack of frameworks evaluating converter-induced voltage fluctuations.

To bridge these gaps, the optimal configuration of PV and ES devices in these distribution networks is studied to improve their operating status and to provide a theoretical reference and practical basis for improving the safety and reliability of PV and ES in the distribution network. This study considers the use of the analytic hierarchy process (AHP) and criteria importance through the intercriteria correlation (CRITIC) method to comprehensively assign weights to indicators and establish a comprehensive evaluation system of distribution network operation status under the grid-connected condition of distributed renewable energy. It is the first unified metric embedding the generalized short-circuit ratio (gSCR) for grid resilience quantification. In addition, through the improved beetle antenna search algorithm (BAS) and particle swarm optimization (PSO), a method for the location and size planning of PV and ES devices under dynamic converter selection technology, allowing adaptive GFL (efficiency)/GFM (stability) operation, is proposed to improve the operating state of the distribution network. The study compares current research and its own results across many areas, as shown in

Table 1. Comparisons of the paper and other articles.

Ref. No.	Method	Optimization Type			Advantages and Disadvantages Compared with the Study
		Siting and Sizing	Topology Optimization	Operational Strategy Optimization	Advantage	Disadvantage
[5]	Cheetah–Grey Wolf Optimizer			√	Good convergence speed and solution quality	Lacking stochastic modeling for renewable/load uncertainties
[6]	Mixed-Integer Second-Order Cone Programming	√	√		Modifying energy router topology to enhance practicality	Ignoring renewable generation uncertainty
[7,14]	MILP	√	√		Good solving efficiency	Ignoring terrain constraints
[9]	Hybrid Synchronous Control			√	Primary frequency regulation with <20 ms response	Limited to lab-scale validation, untested in large-scale grids.
[11]	Multiverse Optimizer	√		√	Incorporating real-world demand/PV profiles	/
[12]	Perturbation Heuristic, GA		√		Algebraic connectivity and reliability optimization	Excluding dynamic traffic variations or co-optimization with routing algorithms
[15]	GA, BDD, MILP			√	A low-cost alternative to adaptive protection	Challenging for large-scale networks, ignoring cybersecurity
[16]	MILP, GA			√	A DA-ID-simulation three-level framework, combining optimization with high-resolution	Long time for simulation, unsuitable for real-time use
[18]	Modified GWO			√	Superior cost efficiency and high solution stability	Higher computation time
[22]	GWO with Logarithmic Convergence	√		√	Logarithmic convergence and strong robustness	Empirical parameter tuning required
[23]	Multi-Objective GA			√	Flexible constraint handling and hierarchical control	High forecast dependency
The study	BAS-PSO	√	√	√	/	/

.

The main contribution and novelty of this study are as follows:

• First unified evaluation framework incorporating gSCR for grid-strength quantification, addressing safety, power quality, renewable utilization, and flexibility under hybrid GFL/GFM control.
• Hybrid GFL/GFM control strategy enables dynamic converter mode selection during PV-ES planning, enabling PV/ES to switch between GFL (efficient operation) and GFM (voltage support) based on node requirements.
• An evaluation model of multiple indicators with mixed weight methods enables a multi-dimensional assessment of distribution network operation status under high-penetration distributed PV and ES integration.
• Enhanced BAS-PSO algorithm with adaptive inertia weights overcomes local optima traps and premature convergence in nonlinear constraint solving.

The rest of this article is organized as follows. Section 2 presents the comprehensive evaluation system for distribution network operation status and the optimal configuration model for PV and ES equipment. Section 3 provides a case study validating the proposed methodology through simulation analysis. Finally, Section 4 draws conclusions from the results.

2. Comprehensive Evaluation of Distribution Network Operation Status

2.1. Comprehensive Evaluation System

The existing assessment indicator system for distribution network operational states mainly evaluates aspects such as power quality, voltage limits, and system overload [27]. However, these indicators do not reflect the impacts of factors such as power electronic devices and PV grid integration, resulting in a lack of consideration for the complex power flows and safety associated with a high proportion of electronic devices in current distribution network systems. To comprehensively analyze the characteristics of the distribution network under the integration of distributed renewable energy, this study establishes a comprehensive assessment system for operational states from four perspectives: safety, power quality, characteristics of renewable energy generation, and flexibility.

Figure 1 illustrates the framework of the comprehensive assessment system for the distribution network operational state.

Safety is closely related to the stable operation of the distribution network. Due to the randomness and volatility of distributed new energy, its access to the distribution network may lead to greater fluctuations in node voltage, and some fluctuations may exceed the limit. The wide access of distributed devices will also make the distribution network show a high degree of power electronic characteristics, affecting the safety of the distribution network operation. This study selects two key indicators—generalized gSCR and the voltage compliance rate—to reflect safety.

In the distribution network, with the increase of the grid-connected capacity of the distributed power supply, the problem of the load-bearing limit also exists. When the access capacity is large enough, the converter may reach a critical value, affecting the stability and security of operation. The study introduces the gSCR to measure the stability of the power system under the access of power electronic devices, which can be used to reflect the grid-connected strength of multiple power electronic devices and characterize the load-bearing limit of the power electronic multi-feed system [28].

The closed-loop characteristic equation for the MIMO feedback control system of the distribution network in Figure 2 can be expressed as follows:

$$det(Y_{Gm}(s)+Y_{netm}(s))=0$$

(1)

$$det(Y_{Gm}(s)Y_{net}^{-1}(s)+I_n)=0$$

(2)

where $Y_{netm}$ and $Y_{Gm}$ respectively represent the frequency-domain admittance matrix of the network and PV.

When analyzing the gSCR, the following two assumptions are generally made:

(1)

The effect of AC equivalent network capacitance is ignored.

(2)

The power electronic devices in the multi-feed system are isomorphic, i.e., all PVs have the same control configuration and control parameters at their own rated capacity, while the device capacity of each PV can be different.

For the network side impedance modeling, there are the following derivation formulas:

$$Y_{netm}(s)=B_{red}\otimes \gamma (s)$$

(3)

$$Y_{Gm}(s)=diag(S_{Bi}{G}_{ixy}(s))$$

(4)

$$B=\left[\begin{array}{cc}{B}_{\mathrm{nn}}& B_{\mathrm{nm}}\\ B_{\mathrm{mn}}& B_{\mathrm{mm}}\end{array}\right]={\left[b_{\mathrm{ij}}\right]}_{(\mathrm{n}+\mathrm{m})\times (\mathrm{n}+\mathrm{m})}$$

(5)

$$B_{\mathrm{red}}=B_{\mathrm{nn}}-B_{\mathrm{nm}}{B}_{\mathrm{mm}}^{-1}{B}_{\mathrm{mn}}$$

(6)

$$\gamma (s)={\displaystyle \frac{1}{{(s+\tau )}^2/{\omega }_0+{\omega }_0}}\left[\begin{array}{cc}(s+\tau )& {\omega }_0\\ -{\omega }_0& (s+\tau )\end{array}\right]$$

(7)

where $B$ represents the admittance matrix of the system; $B_{red}$ is the admittance matrix retaining only distributed power source nodes; $\mathrm{n}$ is the number of PV nodes; $\mathrm{m}$ is the number of passive nodes; $G_{ixy}$ is the impedance matrix of distributed power supply under rated power; τ is the ratio of resistance to inductance. The grid-connected converter in the study is an isomorphic system, in which the $Y_i\left(s\right)$ distributed power sources are the same. With simultaneous equations, the closed-loop eigenvalue equation can be written as

$$det[I_{\mathrm{n}}\otimes Y_{\mathrm{i}}(s)+(S_{\mathrm{B}}^{-1}{B}_{\mathrm{red}})\otimes I_2]=0$$

(8)

$$Y(s)=G_{\mathrm{xy}}(s){\gamma }^{-1}(s)$$

(9)

After the matrix change, it can be written as

$${\displaystyle \prod _{\mathrm{i}=1,2,\dots ,\mathrm{n}}det(Y(s)+{\lambda }_{\mathrm{i}}{I}_2)=0}$$

(10)

where ${\mathsf{\lambda }}_i$ is the eigenvalue of the weighted Laplacian matrix, which is $S_B^{-1}{B}_{red}$. The stability of each fed system depends on the eigenvalue ${\mathsf{\lambda }}_i$, that is, the minimum network eigenvalue. The larger ${\mathsf{\lambda }}_i$ is, the higher the strength of the distribution network at the receiving end. Lower values will increase the risk of the unstable operation of power electronic equipment connected to the grid.

The extended admittance matrix of a distributed power supply is defined as follows:

$$J_{\mathrm{eq}}=-diag(U_{\mathrm{i}}^2)S_{\mathrm{B}}^{-1}\approx -S_{\mathrm{B}}^{-1}{B}_{\mathrm{red}}$$

(11)

$$gSCR=min({\lambda }_{\mathrm{i}})=min(\lambda (-S_{\mathrm{B}}^{-1}{B}_{\mathrm{red}}))$$

(12)

where $S_B$ is a diagonal matrix of the rated capacities of the feeding PV–ES equipment. From the above formulas, it can be seen that the access position and capacity of distributed power sources affect the gSCR of the distribution networks. The larger the capacity of PV integration, the smaller S_B⁻¹ becomes, leading to a smaller gSCR for the distribution networks. The access position of distributed power sources influences the matrix Bred, thereby affecting the gSCR of the distribution networks.

Since the external characteristics of grid-connected converters manifest as current source features, for PV-ES devices connected to the distribution network through GFL converters using the DC voltage–current dual vector control strategy based on phase-locked loops, their connection does not affect the dynamic characteristics on the equipment side of the system. The external characteristics of the GFM converter can be regarded as a voltage source with internal reactance, where the internal reactance is inversely proportional to its capacity. Therefore, the PV-ES devices connected to the distribution network through GFM converters will change the network topology of the power grid and the admittance matrix on the network side, which can be expressed as follows:

$$B_{prime}=B_{red}+\left[\begin{array}{cccc}0& 0& \dots & 0\\ 0& 0& \dots & 0\\ ⋮& ⋮& & ⋮\\ 0& 0& \dots & S_{GFM}^{-1}{B}_p\end{array}\right]$$

(13)

where $S_{GFM}$ is the capacity of the connected PV–ES device, $B_P$ is the equivalent electrical admittance per unit capacity, and $B_{prime}$ is the corrected admittance matrix after installing the PV–ES device connected to the power grid through a GFM converter. The study proposes a multi-type synchronous control architecture that contains GFL/GFM converters, breaking through the limitations of the traditional single-control mode. The GFL device tracks the grid frequency through a phase-locked loop, while the GFM device independently builds voltage support. The two achieve coordination through power-voltage sag control.

The voltage compliance rate (VCR) refers to the ratio of the number of nodes with compliant voltages to the total number of nodes in the network at a specific moment, expressed as follows:

$$VCR={\displaystyle \frac{N_{\mathrm{RQV},\mathrm{t}}}{N}}\times 100\%$$

(14)

where $N_{RQV,t}$ represents the number of nodes with compliant voltages in the network at time t.

Power quality is a property used to measure the voltage quality at nodes within the distribution network. The integration of distributed power sources and ES alters the voltage distribution at the nodes. In this study, the voltage deviation coefficient and voltage fluctuation are adopted to reflect the power quality.

The voltage deviation coefficient represents the degree to which the actual voltage value of a network node deviates from the rated value at a certain time. The expression is as follows:

$$\Delta U={\displaystyle \frac{U_{\mathrm{i},t}-U_{i,rated}}{U_{\mathrm{i},\mathrm{rated}}}}\times 100\%$$

(15)

where $U_{i,t}$ is the actual voltage value of node i at time t, and $U_{i,rated}$ is the voltage rating of node i.

Voltage fluctuation represents a series of voltage changes or continuous voltage deviations, expressed as follows:

$$\Delta d={\displaystyle \frac{U_{i,t}-U_{i,t-1}}{U_{\mathrm{N}}}}\times 100\%$$

(16)

where $U_{i,t}$ and $U_{i,t-1}$, respectively, represent the voltage at node i at time t and t − 1.

Configuration should actively respond to China’s carbon peaking and carbon neutrality goals under the new development philosophy, making the operation of the distribution network greener and more economical. Therefore, it is necessary to incorporate renewable energy generation characteristics into the indicators. Two key indicators—the proportion of the renewable energy generation and the renewable energy generation capacity—are selected in this study to reflect the new energy generation characteristics.

The proportion of renewable energy generation represents the penetration rate of renewable energy within the distribution networks, expressed as the ratio of total renewable generation to total load in a region:

$${\lambda }_{\mathrm{jt}}={\displaystyle \frac{{\displaystyle \int P_{\mathrm{ne}}\mathrm{d}t}}{{\displaystyle \int P_{\mathrm{L}}\mathrm{d}t}}}\times 100\%$$

(17)

where $P_{ne}$ is the power generated by renewable energy sources within the distribution network, and $P_L$ is the load power of the distribution network.

The renewable energy generation capacity (REGC) represents the PV access capacity in the distribution network, expressed as

$$REGC={\displaystyle \int P_{ne}dt}$$

(18)

Flexibility reflects the ability of the distribution network to meet the output changes required for balancing load fluctuations. This study selects two key indicators: the fluctuation rate of net load (FENL) and the interactive power between synchronous control devices.

The FENL indicates the rate of change of net load in the power network per-unit time, reflecting the degree of fluctuation of net load. The expression is as follows:

$$FRNL={\displaystyle \frac{\left|P_t^{\mathrm{NL}}-P_{t-1}^{\mathrm{NL}}\right|}{P_t^{\mathrm{NL}}}}\times 100\%$$

(19)

where $P_t^{NL}$ and $P_{t -1}^{NL}$ represent the net load values of the power network at the current time t and the previous time t − 1.

Interactive power is used to measure the power flow situation between the distribution networks and the power grid:

$$P_{\mathrm{E}}={\displaystyle \sum _{t=1,2,\dots ,24}{P}_{\mathrm{e}t}}$$

(20)

where $P_{et}$ represents the generated output of the distribution networks at time t, with inflow into the distribution networks considered as the positive direction.

2.2. Objective Function

Due to a large number of PV devices connected to the grid, the safety and power quality of the distribution network’s operation are affected, and the operation status is challenged. ES can improve the stability and reliability of PV grid connection, improve power quality, and solve the mismatch between energy supply and demand. In this study, the optimal operating state of the distribution network is taken as the objective function. Therefore, the comprehensive evaluation of the operation status of the distribution network under the access of PV and ES equipment can be evaluated by the following indicators:

(1) Generalized Short Circuit Ratio ($\mathrm{g}\mathrm{S}\mathrm{C}\mathrm{R}$):

$$F_1(X)=gSCR=\min (\lambda (-S_{\mathrm{B}}^{-1}{B}_{\mathrm{red}}))$$

(21)

(2) Voltage Compliance Rate (VCR): The study selects the minimum voltage compliance rate of 24 h as the criterion of voltage qualification rate.

$$F_2(X)=VCR=\min ({\displaystyle \frac{N_{RQV,t}}{N}}\times 100\%)$$

(22)

(3) Average Voltage Deviation Rate (ΔU):

$$F_3(X)=\Delta U=({\displaystyle \sum _{t=1}^{24}{\displaystyle \sum _{n\in N}\frac{U_{\mathrm{n},t}-U_{\mathrm{n},\mathrm{rated}}}{U_{\mathrm{n},\mathrm{rated}}}}/N})/24$$

(23)

(4) Maximum Voltage Fluctuation (Δd):

$$F_4(X)=\Delta d=\max ({\displaystyle \frac{U_{n,t}-U_{n,t-1}}{U_N}}\times 100\%)$$

(24)

(5) Renewable Energy Generation Capacity (REGC):

$$F_5(X)=REGC={\displaystyle \int P_{ne}dt}$$

(25)

(6) Average Interactive Power (P_E):

$$F_6(X)=P_E={\displaystyle \frac{1}{24}}{\displaystyle \sum _{t=1}^{24}{P}_{et}}$$

(26)

Due to the large number of evaluation indicators, this study cannot accurately compare the advantages and disadvantages of each scheme when selecting the optimal optimization scheme. In order to select the optimal optimization scheme more intuitively, this study introduces a scoring system that can reasonably allocate the weights of each index, calculate the scores of each index, and obtain a comprehensive score. This comprehensive score will be used to assist in selecting the optimal solution.

In order to eliminate the influence of dimension, the above indicators are divided into positive indicators and negative indicators. The gSCR, VCR, and REGC are set as positive indicators, and the ΔU, Δd, and PE are set as negative indicators. This study standardizes the data obtained from the experiment.

The positive indicators can be expressed as follows:

$$F_j^{\ast }={\displaystyle \frac{F_j-\min (F_j)}{\max (F_j)-\min (F_j)}} (j=1,2,5)$$

(27)

The negative indicators can be expressed as follows:

$$F_j^{\ast }={\displaystyle \frac{\max (F_j)-F_j}{\max (F_j)-\min (F_j)}} (j=3,4,6)$$

(28)

where $F_j$ represents actual data obtained from the simulation, and max($F_j$) and min($F_j$) represent the maximum and minimum values of the above data. By integrating the above data and conducting normalization processing, the standardized data ${F }_j^{\ast }$ is calculated, which ranges from 0 to 1.

To take into account the relative importance among the index data and the inherent statistical laws of the index data, combined with the evaluation index system of the operation status of the distributed new energy access to distribution networks, this study adopts a comprehensive evaluation method based on the AHP-CRITIC rule. This method can take into account the advantages of both subjective and objective empowerment methods. The weighting flowchart of the comprehensive evaluation method is shown in Figure 3.

The AHP [29] is a relatively common subjective weighting method that regards a single multi-objective decision problem as a system, divides the objective into multiple levels such as objective, criterion, and scheme, and calculates the hierarchical single ranking through qualitative and quantitative analyses and which is used as the weight of optimal decision. The AHP employs the Saaty scale method, namely the 1–9 scale method, to represent the importance of different indicators. Here, 1 indicates equal importance, and as the number increases, the importance gradually increases, while 9 indicates absolute importance. This method can transform fuzzy qualitative comparisons into precise values. A value of 1 means the lowest importance, and a value of 9 means the highest importance. After assigning values to each indicator, the judgment matrix of the AHP can be built, and it must meet positive reciprocity and consistency. In order for the obtained optimal configuration scheme to achieve the rational allocation of resources and meet some special requirements for the optimization strategy, like more photovoltaic equipment connected when ensuring the safety of the power system, the judgment matrix of the AHP can be as follows:

$$A=\left[\begin{array}{cccccc}1& {\displaystyle \frac{3}{4}}& 1& {\displaystyle \frac{3}{2}}& {\displaystyle \frac{3}{7}}& 3\\ {\displaystyle \frac{4}{3}}& 1& {\displaystyle \frac{4}{3}}& 2& {\displaystyle \frac{4}{7}}& 4\\ 1& {\displaystyle \frac{3}{4}}& 1& {\displaystyle \frac{3}{5}}& {\displaystyle \frac{3}{7}}& 3\\ {\displaystyle \frac{2}{3}}& {\displaystyle \frac{1}{2}}& {\displaystyle \frac{1}{2}}& 1& {\displaystyle \frac{2}{7}}& 2\\ {\displaystyle \frac{7}{3}}& {\displaystyle \frac{7}{4}}& {\displaystyle \frac{7}{3}}& {\displaystyle \frac{7}{2}}& 1& 7\\ {\displaystyle \frac{1}{3}}& {\displaystyle \frac{1}{4}}& {\displaystyle \frac{1}{3}}& {\displaystyle \frac{1}{2}}& {\displaystyle \frac{1}{7}}& 1\end{array}\right]$$

(29)

where the subjective weight matrix $W_a$ can be expressed as follows:

$$\begin{array}{cc}{W}_a\hfill & =[a_1 a_2 a_3 a_4 a_5 a_6]\hfill \\ & =\left[\begin{array}{cccccc}0.15& 0.2& 0.15& 0.1& 0.35& 0.05\end{array}\right]\hfill \end{array}$$

(30)

The CRITIC [30] method is an objective weighting method based on data volatility. The data weights are mainly weighted by two indicators of volatility and conflict, and then the final weights are obtained by the normalization of the volatility and conflict indicators. The CRITIC method is applicable to data in which the indicators for analysis are interrelated and the data consistency is regarded as important information. In the distribution network, there is a certain relationship between different indicators, so using the CRITIC weight method to dynamically assign the final data can better avoid the subjective defects of the AHP method.

The weight coefficients of the CRITIC method are obtained through the following process:

Firstly, calculate the comparison intensity of the indicators $m_j$ and the conflict of the indicators $c_j$, which can be expressed as follows:

$$m_j=\sqrt{{\displaystyle \frac{1}{6}}{\displaystyle \sum _{j=1}^6{(F_j^{\ast }-{\overline{F}}_j)}^2}} (\mathrm{j}=1,2,3,4,5,6)$$

(31)

$$c_j={\displaystyle \sum _{k=1}^6(1-\left|{\rho }_{jk}\right|}) (\mathrm{j}=1,2,3,4,5,6)$$

(32)

where F_j represents the average value of $F_j$, and ${\rho }_{jk}$ represents the correlation coefficient between the JTH and KTH indicators.

Secondly, calculate the amount of information $A_j$ and obtain the heaviest weight $b_j$, which can be expressed as

$$A_j=m_j\times c_j (\mathrm{j}=1,2,3,4,5,6)$$

(33)

$$b_j={\displaystyle \frac{A_j}{{\displaystyle \sum _{j=1}^6{A}_j}}} (\mathrm{j}=1,2,3,4,5,6)$$

(34)

Based on the above method, an objective weight matrix W_b is obtained, which can be expressed as follows:

$$W_b=\left[\begin{array}{cccccc}{b}_1& b_2& b_3& b_4& b_5& b_6\end{array}\right]$$

(35)

Therefore, the comprehensive weight matrix W can be expressed as follows:

$$W=\left[\begin{array}{cccccc}{\alpha }_1& {\alpha }_2& {\alpha }_3& {\alpha }_4& {\alpha }_5& {\alpha }_6\end{array}\right]$$

(36)

$${\alpha }_i={\displaystyle \frac{\sqrt{a_i\times b_i}}{{\displaystyle \sum _{i=1}^6\sqrt{a_i\times b_i}}}} (i=1,2,3,4,5,6)$$

(37)

where ${\mathsf{\alpha }}_1, {\mathsf{\alpha }}_2, {\mathsf{\alpha }}_3, {\mathsf{\alpha }}_4, {\mathsf{\alpha }}_5$, and ${\mathsf{\alpha }}_6$ represent the comprehensive weight of each indicator.

Based on the data standardization method introduced above and the comprehensive evaluation method of AHP-CRITIC, this study obtains the weight distribution and standardized scores corresponding to each indicator. The objective function can be expressed as follows:

$$\max F={\alpha }_1{F}_1^{\ast }(X)+{\alpha }_2{F}_2^{\ast }(X)+{\alpha }_3{F}_3^{\ast }(X)+{\alpha }_4{F}_4^{\ast }(X)+{\alpha }_5{F}_5^{\ast }(X)+{\alpha }_6{F}_6^{\ast }(X)$$

(38)

where ${ F}_1^{\ast }\left(X\right), F_2^{\ast }\left(X\right), F_3^{\ast }\left(X\right), F_4^{\ast }\left(X\right), F_5^{\ast }\left(X\right) \mathrm{a}\mathrm{n}\mathrm{d} F_6^{\ast }\left(X\right)$ represent the standardized scores of each index, and F represents the comprehensive assessment score under the evaluation system. When F reaches the maximum value, the distribution network has reached the optimal operation state.

2.3. Constraint Conditions

Constraints include power flow constraints, PV integration capacity constraints, node voltage constraints, location constraints, current constraints, and power factor constraints of the PV converters.

(1) Power Flow Constraints: In power flow calculations, the power flow constraints must be satisfied:

$$P_i(t)={\displaystyle \sum _{j\in N(i)}{U}_i(t)U_j(t)[G_{ij}\cos {\theta }_{ij}(t)+B_{ij}\sin {\theta }_{ij}(t)]}+G_{ii}{U}_i{(t)}^2=P_{\mathrm{LD}i}(t)+P_{\mathrm{DG}i}(t)$$

(39)

$$Q_i(t)={\displaystyle \sum _{j\in N(i)}{U}_i(t)U_j(t)[B_{ij}\cos {\theta }_{ij}(t)-G_{ij}\sin {\theta }_{ij}(t)]}-B_{ii}{U}_i{(t)}^2=Q_{\mathrm{LD}i}(t)+Q_{\mathrm{DG}i}(t)$$

(40)

where $G_{ij}$, $B_{ij}$, $G_{ii}$, and $B_{ii}$, respectively, represent the mutual conductance, mutual susceptance, self-conductance, and self-susceptance of the node admittance matrix. $P_{LDi}$ is the active power load, and $P_{LGi}$ is the distributed equipment output for node i. $Q_{LDi}$ and $Q_{LGi}$ are the reactive power load and the distributed equipment output for node i.

(2) PV Integration Capacity Constraint: In order to accelerate the development of renewable energy, a minimum integration capacity for PV capacity in distribution networks is set as follows:

$${\displaystyle \sum S_i\ge S_{\mathrm{sum}\_\min }}$$

(41)

where $S_{sum\_min}$ is the minimum PV integration capacity for the distribution network.

There is a maximum capacity limit for each PV connected to the distribution network, which must not exceed the stipulated maximum PV integration capacity:

$$S_i\le S_{\max }(i=1,\dots ,n)$$

(42)

where $S_{max}$ is the maximum PV integration capacity, as specified in the project.

(3) Node Voltage Constraints:

$$U_{\min }\le U_i\le U_{\max }$$

(43)

where $U_{max}$ and $U_{min}$ represent the maximum and minimum node voltages.

(4) Location Constraints: The number of integration locations for PV and ES must not exceed the planned maximum number of integration locations:

$$0<N_{\mathrm{pv}}\le N_{\mathrm{pv},\max }$$

(44)

$$0<N_{\mathrm{ES}}\le N_{\mathrm{ES},\max }$$

(45)

where $N_{PV}$ and $N_{ES}$ is the actual number of integration locations for PV and ES, and $N_{PV,max}$ and $N_{ES,max}$ is the maximum number of allowable integration locations for PV and ES.

(5) Current Constraints:

$$(G_{ij}^2+B_{ij}^2)\left[U_i{(t)}^2+U_j{(t)}^2-2U_i(t)U_j(t)\cos {\theta }_{ij}(t)\right]=I_{ij}{(t)}^2\le I_{ij\max }^2$$

(46)

where $I_{ij}(t)$ is the current on branch ij.

(6) Power Factor Constraints of PV converters:

$${\theta }_{\min }\le {\theta }_{\mathrm{pv}}\le 1$$

(47)

2.4. Model Solving Method

According to the optimization objectives, in the optimization configuration model for PV-ES devices to improve the operational state of distribution networks, the integration capacity of PV-ES devices is a continuous variable, while the integration location is a discrete variable. The gSCR in the objective function is difficult to linearize; therefore, heuristic algorithms are suitable for solving this problem. This study proposes to use an improved beetle antennae search (BAS)–particle swarm optimization (PSO) algorithm for the solution.

The BAS algorithm is an efficient intelligent optimization algorithm that simulates the foraging behavior of beetles using their two antennae. It relies on the perception and decision-making of a single firefly individual. As a result, the algorithm’s code is simple, and its computational complexity is significantly lower than that of other algorithms, making it easy to implement. However, this also leads to a lack of diversity within the population, limiting the algorithm’s global optimization capabilities and making it prone to becoming stuck in local optima. This study proposed the BAS-PSO algorithm, which has a faster convergence rate and addresses the issue of a lack of reference for the inertia weights of traditional PSO, balancing the global and local search capabilities of the particle swarm while achieving efficient optimization and reducing the likelihood of local convergence issues. The study proposes a direction-oriented search strategy, adding gradient information in the BAS perception stage, which can be expressed as follows:

$$d_{new}=d+\eta \nabla F(X)$$

(48)

where d and $d_{new }$ represent the randomly generated original beetle antenna search direction vector and the corrected search direction vector, η represents the adaptive learning rate dynamically adjusted with iteration, and $\nabla F\left(x\right)$ represents the gradient of the comprehensive scoring function $F\left(x\right)$. After introducing gradient information, the algorithm enhances the global optimization capability. The proposed BAS-PSO algorithm also adopts the adaptive inertia weight ($w_k$), which can be expressed as follows:

$${\omega }_k={\omega }_{max}-{\displaystyle \frac{({\omega }_{max}-{\omega }_{\min })k}{k_{max}}}$$

(49)

where ${\omega }_{max}$ and ${\omega }_{min}$ represent the maximum and minimum values of the ${\omega }_k$, $k$ represents the number of iterations, and $k_{max}$ represents the maximum number of iterations.

The flowchart for solving the optimization configuration of PV-ES devices is shown in Figure 4.

The specific steps for solving the optimization are as follows:

(1)

Determine the access location of PV and ES devices.

(2)

Initialize the distribution network and parameters of the improved PSO algorithm.

(3)

Set the power factor to 1, and use the improved BAS-PSO algorithm with the optimal operational state of the distribution network as the objective to optimize the capacities of the PV and ES devices.

(4)

Adjust the capacities of the PV devices.

(5)

If the termination condition is met, end the program; otherwise, return to Step 2.

(6)

Output the optimized configuration scheme for the PV-ES system in the distribution network.

3. Simulation Results

The study uses an improved IEEE 33-node distribution system for effectiveness verification. The structure of the system is shown in Figure 5, with a base voltage of 12.66 kV and a base power of 10 MW. Bus 1 serves as the balanced node with a voltage of 1.0 p.u., and its maximum and minimum voltage levels are 1.05 p.u. and 0.90 p.u. The maximum current for all lines is 300 A. The numbers in Figure 5 indicate node identifiers, where nodes 7, 24, 25, and 30 are selected as feasible locations for PV devices based on practical considerations, and nodes 29 and 33 are chosen as feasible locations for ES devices, considering practical factors.

To verify that the proposed site selection and sizing model can enhance the operational safety of distribution networks, improve power quality, and increase economic benefits, optimizations for PV connection positions and capacities are performed under three conditions: “direct PV connection”, “PV planning”, and “PV-ES planning”. “Direct PV connection” refers to connecting PV systems from feasible connection locations based on the size of load power at nodes, prioritizing from high to low load, with equal PV capacity for each connected location. “PV planning” only considers the connections of PV devices, optimizing both their locations and capacities. “PV-ES planning” considers the connections of PV and ES devices, optimizing their positions and sizes. Only GFL inverters are used under the above conditions. The planning results under different planning methods are shown in Figure 6 and

Table 2. The results of the ES equipment for PV-ES planning.

Conditions	Access Nodes
	29	33
PV-ES Planning	0.482 MW	1.122 MW

.

Table 3. Different planning methods in IEEE 33-node distribution system.

Conditions	Operation Indicators of Distribution Networks
	gSCR	VCR/%	ΔU/%	Δd/%	REGC/MW	PE/MW	Score
Direct PV Connection	3.17	100	1.85	3.41	4.02	1.95	0.581
PV Planning	3.47	100	1.83	3.16	3.87	1.54	0.622
PV-ES Planning	3.59	100	1.57	7.74	4.09	1.12	0.713

shows the operational indicators of the distribution network system under different planning methods when the PV and ES connection nodes are the same. Both the “PV planning” and “PV-ES planning”, considering distribution network operational states, can improve operational safety compared to direct PV connection, with the gSCR increasing by 9.46% and 13.3%, respectively, ensuring the enhanced grid stability under high penetration of power electronic devices. The average voltage deviation rate is reduced to 1.57%, outperforming direct access (1.85%) and PV-only planning (1.83%), indicating that the “PV-ES planning” proposed in this study can effectively improve power quality. The average interactive power decreased to 1.12 MW in PV-ES planning, a 42.6% reduction compared to “direct PV connection” and a 27.3% reduction compared to “PV planning”, reducing grid dependency. The REGC increased from 4.02 MW to 4.09 MW, enhancing self-sufficiency. Compared with “PV planning”, although “PV-ES planning” is not superior to “PV planning” in all indicators like maximum voltage fluctuation, the final comprehensive score obtained by “PV-ES planning” is higher than that of “PV planning”, which proves the feasibility of the comprehensive evaluation model.

Figure 7 shows the voltage timing distribution of nodes in the distribution network under different conditions. It can be seen that in the case of direct PV connection, the voltages of multiple nodes in the distribution network have exceeded the reliable operating range of the voltage level. During period 11–13, the voltage near the PV access node exceeded the qualified voltage range, and the node voltage was greater than 1.05 p.u. PV planning can improve power quality and reduce the number of nodes and time periods with voltages exceeding the qualified voltage range. However, at PV access nodes, there will still be situations where the voltage level exceeds the qualified voltage range. The planning and configuration of PV and ES further improve the power quality and ensure that the voltages at all nodes are within the qualified voltage range.

In order to study the impact of multi-type synchronous control on the planning scheme, PV and ES equipment can be connected to the distribution network through GFL or GFM converters to optimize the storage access location and access capacity of the distribution network. This study sets up three groups of conditions: “GFL planning”, “GFM planning”, and “multi-type synchronous control (MSC) planning”. The last condition refers to the idea that PV and ES equipment in different nodes can choose to be connected to the distribution network through GFL or GFM converters. The maximum number of access nodes for PV equipment is four, and for ES equipment, it is two.

Figure 8 shows the planning results of PV under different operating conditions.

Table 4. The access capacity of ES in different nodes considering hybrid GFL/GFM planning.

Conditions	Access Nodes
	29	33
GFL Planning	0.482 MW	1.122 MW
GFM Planning	0.154 MW	0.388 MW
MSC Planning	0.751 MW	0.013 MW

and

Table 5. The operational status of the distribution network in different operating conditions considering hybrid GFL/GFM planning.

Conditions	Operation Indicators of Distribution Networks
	gSCR	VCR/%	ΔU/%	Δd/%	REGC/MW	PE/MW	Score
GFL Planning	3.59	100	1.57	7.74	4.09	1.12	0.689
GFM Planning	5.58	100	0.45	0.06	3.34	2.61	0.712
MSC Planning	4.65	100	1.38	1.75	4.04	1.05	0.823

, respectively, present the access capacity of ES at each node and the corresponding operational status of the distribution network in different conditions. By comparing the operation status of the distribution network under the two modes of the grid and constructing the grid, it can be found that in the areas of the gSCR, the average voltage deviation rate and maximum voltage fluctuation, “GFM planning” is absolutely superior to “GFL planning”, which means that PV and ES equipment connected to GFM converters demonstrates better security and power quality than that connected to GFL converters. At the same time, compared to “GFM planning”, the REGC of “GFL planning” increases by 22.5%, and the average interactive power of “GFL planning” decreases by 57.9%, which indicates that PV and ES equipment connected to GFL converters has better flexibility and new energy generation characteristics. “MSC planning” takes advantage of the above two planning methods. It can guarantee the safety and stability of the distribution network, and it can access more new energy capacity. Figure 9 shows the temporal distribution of nodes in the distribution network under different planning conditions. After the optimized configuration, there was no situation where the node voltage exceeded the limit, which proves the reliability of the MSC planning.

In order to verify the advancement of the multi-objective optimization method proposed in this paper under multi-type synchronous control compared to single-objective optimization, this paper establishes multiple groups: optimal optimization of security, power quality, new energy generation, and flexibility. Figure 10 shows the planning results of PV under different operating conditions.

Table 6. The access capacity of ES in different nodes considering single/multi-objective optimization method.

Control Experiments	Access Nodes
	29	33
Security	0.857 MW	0.099 MW
Power Quality	0.032 MW	0.198 MW
New Energy Generation	0.543 MW	0.045 MW
Flexibility	0.378 MW	0.532 MW
Multi-objective	0.751 MW	0.013 MW

and

Table 7. The operational status of the distribution network in the control experiments.

Control Experiments	Operation Indicators of Distribution Networks
	gSCR	VCR/%	ΔU/%	Δd/%	REGC/MW	PE/MW
Security	7.21	100	1.38	2.03	3.25	0.88
Power Quality	4.44	100	1.35	0.42	3.60	1.41
New Energy Generation	3.03	100	1.38	1.26	4.62	1.04
Flexibility	4.11	100	1.36	0.91	3.44	0.79
Multi-objective	4.65	100	1.38	1.75	4.04	1.05

, respectively, present the access capacity of ES at each node and the corresponding operational status of the distribution network in different control experiments.

The results show that the multi-objective optimization method has better comprehensiveness in each indicator, which takes advantage of the other four single-objective optimization methods. The multi-objective optimization method proposed in this study under multi-type synchronous control can meet all the requirements of the distribution network and is a new method for achieving the all-around development of the distribution network in the future.

In order to study the influence of different minimum total PV access capacities on the planning scheme, the optimization of the access locations and access capacities of PV and ES were assessed under the different minimum proportions of renewable energy generation (50%, 60%, 70%). The maximum number of access nodes for PV and ES equipment is four and two.

Figure 11 shows the planning results of PV under different minimum PV penetration rates in distribution networks.

Table 8. The access capacity of ES in different nodes under the different minimum proportions of PV.

The Minimum Proportion of PV	Access Nodes
	29	33
50%	0.014 MW	0.781 MW
60%	0.161 MW	0.867 MW
70%	0.801 MW	0.912 MW

and

Table 9. The operational status of the distribution network under different minimum proportions of PV.

The Minimum Proportion of PV	Operation Indicators of Distribution Networks
	gSCR	VCR/%	ΔU/%	Δd(/%	REGC/MW	PE/MW	Actual Proportion
50%	4.21	100	1.38	0.63	3.62	1.35	51.4%
60%	2.83	100	1.34	0.61	4.25	1.41	60.4%
70%	2.35	100	1.30	0.58	5.05	1.88	71.8%

, respectively, present the access capacity of ES equipment at each node and the corresponding operational status of the distribution network in different scenarios. When the total PV access capacity is low, the total access capacity of ES equipment is also low. As the minimum total PV access capacity increases, the total access capacity of ES also increases. When the gSCR decreases, the grid connection stability of PV equipment reduces, which proves that the gSCR of the distribution network has a strong correlation with its PV carrying rate.

Figure 12 shows the temporal distribution of nodes in the distribution network system. After the optimized configuration of the distribution network, there was no situation where the node voltage exceeded the limit. During a complete cycle, the average voltage deviation rates are 1.38%, 1.34%, and 1.30%, respectively, and the voltage fluctuation rates are 0.63%, 0.61%, and 0.58%, respectively. With the increase in the access capacity of PV and ES equipment, the power quality has been further improved. Meanwhile, the optimization model proposed in this study can well meet the requirements of the high PV penetration rate, effectively increase the PV rate, and reduce carbon emissions.

To ensure that the BAS-PSO algorithm obtains the global optimum, the study uses other methodologies to compare the solutions. According to the introduction in the previous text, literature [11] proposes a PGA method to minimize operational costs. In this study, the PGA was modified to a certain extent in accordance with the experimental requirements and compared with the BAS-PSO in many areas. The results are as follows.

Table 10. The operational status of the distribution network under different algorithms.

Algorithms	Operation Indicators of Distribution Networks
	gSCR	VCR/%	ΔU/%	Δd/%	REGC/MW	PE/MW	Score
BAS-PSO	4.65	100	1.38	1.75	4.04	1.05	0.823
PGA	4.51	100	1.37	1.63	4.45	1.78	0.821

shows the different operation indicators of distribution networks between the two algorithms. The results show that the operation indicators of distribution networks under the two algorithms, especially the comprehensive scores, are very close, which proves that the study using BAS-PSO has obtained the global optimum.

Table 11. The comparison of the optimization effects of different algorithms.

Algorithms	Comparison of Optimization Effects of Different Algorithms
	Min	Mean	Std	Degree of Convergence
BAS-PSO	0.0168	0.4806	0.2721	26
PGA	0.0029	0.5075	0.2812	30

shows the comparison of the optimization effects of different algorithms, which calculates statistical indicators of fitness values after multiple independent runs and simulations, such as the minimum value (Min), the mean value (Mean), the standard deviation (Std), and the degree of convergence. The Min and Mean under BAS-PSO are worse than the PGA, but the Std and the degree of convergence of the former are better. The two optimization methods are evenly matched in various indicators. Given that the PGA has been proven to be an effective algorithm, it can be considered that the improved BAS-PSO algorithm with adaptive inertia weights overcomes the local optimal trap in solving nonlinear constraints.

Based on a certain actual distribution network pilot project, the distribution network topology is selected, as shown in Figure 13, where the numbers represent the node numbers. Among them, nodes 7, 11, 14, 22, 23, and 31 are the PV equipment access locations selected by comprehensively considering the actual situation. Nodes 8, 12, 21, and 24 are the locations for the connection of ES devices selected by comprehensively considering the actual situation. To meet the engineering requirements, the maximum PV capacity that can be connected to multiple microgrid nodes is 60 kVA, the rated capacity of system nodes is 60 kW, the per-unit value range of node voltage is 0.92–1.08, and the rated voltage is 400 V.

Figure 14 shows the temporal distribution of nodes under PV-ES and MSC planning, where we can see that the optimized temporal distribution meets the requirements of the engineering.

Table 12. Different planning methods in an actual distribution network.

Conditions	Operation Indicators of Distribution Networks
	gSCR	VCR/%	ΔU/%	Δd/%	REGC/kW	PE/kW	Score
Direct PV Connection	3.17	93.75	3.46	4.31	192	195	0.575
PV Planning	5.27	100	2.88	3.75	202.8	109.6	0.655
PV-ES Planning	4.72	100	1.61	1.25	204.9	112.4	0.743

shows the different operation indicators of the distribution networks between different planning methods, and

Table 13. The operational status of the distribution network in different operating conditions in an actual distribution network.

Conditions	Operation Indicators of Distribution Networks
	gSCR	VCR/%	ΔU/%	Δd/%	REGC/MW	PE/kW	Score
GFL Planning	3.27	100	1.57	2.68	222.8	165.4	0.675
GFM Planning	5.58	100	1.45	1.43	184.6	104.6	0.743
MSC Planning	4.72	100	1.61	1.75	204.9	112.4	0.842

shows the different operation indicators of the distribution networks between different operating conditions. Like the above simulations, the results of PV-ES planning in the VCR, ΔU, Δd, and REGC are superior to the other conditions, and the score of PV-ES planning is the highest. Meanwhile, as shown in Table 13, MSC planning combines the advantages of GFL and GFM planning and achieves the best performance comprehensively. All of the above simulations and experiments prove the superiority and stability of the evaluation system and optimization planning.

4. Conclusions

This study focuses on the optimal configuration of PV-ES systems in distribution networks under high-penetration renewable energy integration. Based on the comprehensive evaluation model, which includes integrating safety, power quality, renewable utilization, and flexibility under multi-type synchronous control, the operation mode of the distribution network was analyzed, and a multi-objective optimization framework under multi-type synchronous control for improving the operation status of the distribution network was proposed. The coordinated configuration strategies, integrating site selection and capacity determination under the hybrid GFL/GFM control strategy, ensure stable operation and effective resource allocation. The enhanced BAS-PSO algorithm with adaptive inertia weights overcomes local optima traps in nonlinear constraint solving and improves the speed and accuracy of the calculation process. Simulation case studies and experimental tests are conducted, and the specific findings from the simulation and experimental results are as follows.

(1)

The proposed PV-ES planning achieves the best results for the evaluation indexes used, such as the gSCR, average voltage deviation rate, REGC, and P_E, and ultimately obtains the highest comprehensive score. Compared with the reference value, the gSCR increases by 13.3%, the average voltage deviation rate is reduced to 1.57%, and the voltage qualification rate has remained at 100%, which proves that the PV-ES planning can significantly improve the power quality of the system and ensure its safety.

(2)

MSC planning, a scheme that uses GFL and GFM converters at the same time, is able to maintain the value of the gSCR (4.65) compared with the GFM planning (5.58) and the capacity of new energy access at a relatively high level (4.04 MW) compared with the GFL planning (4.09 MW), proving that it combines the advantages of the above two schemes.

(3)

With the increase of the PV penetration rate (50%, 60%, 70%), the demand of the ES equipment is higher. During this period, the voltage qualification rate remained at 100%, which means that the optimization model proposed in this study can well meet the requirements of a high PV penetration rate, effectively increase the PV rate, and reduce carbon emissions.

The study addresses the dual challenges of renewable energy attainment (maximizing PV integration) and energy use optimization (enhancing operational efficiency via hybrid GFL/GFM control), directly aligning with the special issue’s focus. At the same time, the work highlights the advantages of the optimal PV-ES configuration scheme, such as enhanced system safety through gSCR optimization, adaptability to diverse distributed generation scenarios, and integration of renewable energy sources. By addressing critical challenges like voltage fluctuations and grid-strength degradation, the proposed approach significantly enhances the reliability and sustainability of modern distribution networks. These capabilities provide a robust solution for future low-carbon power systems.

Future work will incorporate detailed economic indicators like the payback period and explore collaborative energy management strategies for large-scale distributed PV-ES systems. These efforts will further advance the intelligence and sustainability of next-generation distribution networks.