Distributed Power, Energy Storage Planning, and Power Tracking Studies for Distribution Networks

Abstract

In recent years, global energy transition has pushed distributed generation (DG) to the forefront in relation to new energy development. Most existing studies focus on DG or energy storage planning but lack co-optimization and power tracking analysis. To address this problem, a multi-objective genetic algorithm-based collaborative planning method for photovoltaic (PV) and energy storage is proposed. On this basis, power flow tracking technology is further introduced to conduct a detailed analysis of distributed energy power allocation, providing support for system operation optimization and responsibility sharing. To verify the validity of the model, a 14-node distribution network is used as an example. Voltage stability, PV consumption rate, and economy are taken as objective functions. By solving the three scenarios, it is determined that the introduction of energy storage increases the PV consumption rate from 85.6% to 96.3%; the average network loss for the whole day increases from 1.81 MW to 2.40 MW. Utilizing power tracking techniques, various causes were analyzed; it was found that the placement of energy storage leads to a multidirectional and repetitive flow of power.

1. Introduction

In recent years, as the global energy transition and sustainable development calls continue to rise, low-carbon and high-efficiency processes have become the direction of future energy development. In order to further increase the speed of new energy development, distributed energy has received widespread attention. Distributed energy (DG) refers to the construction of wind and photovoltaic power generation sites, as well as other forms of energy supply. Distributed energy sources have become one of the most important ways to develop new energy sources in China because of the local access method, thus avoiding the line losses and the impacts caused by extreme environments of the power system’s long-distance transmission.

In the application of distributed energy technology, the rational selection of distributed power source locations and capacity settings not only significantly improves power quality and reduces the system’s active power losses, but also enhances the economic efficiency and reliability of grid operation, making it a topic of great interest to many scholars. When solving this typical nonlinear problem of distributed power sources, intelligent optimization algorithms can be employed. Odyuo et al. [1] proposed four simple machine learning algorithms for evaluating the optimization scale and location performance of distributed power sources in test systems. Furthermore, Li et al. [2] proposed an improved gray wolf optimization algorithm to determine the location and capacity of distributed power sources, thereby reducing active power losses in distribution grids. Moreover, Zhang et al. [3] introduced a new fractional-order particle swarm optimization algorithm for optimizing the location and capacity of distributed power sources connected to the grid. Raja Lakshmi et al. [4] proposed a multi-objective differential evolution algorithm for determining the placements and capacity of distributed power sources to address the challenges posed by the highly nonlinear interactions among numerous variables. Additionally, Han et al. [5] proposed a squirrel search algorithm to solve the model for determining optimal placement and capacity for distributed photovoltaic grid connections, while Yu et al. [6] proposed a method for the optimizing the placement and capacity of distributed photovoltaic grid connections to distribution grids based on improved particle swarm optimization.

Intelligent optimization algorithms have excellent problem-solving capabilities for discrete, combinatorial optimization problems and have been widely used in recent years in fields such as distribution network planning. Among these, the objective function is a core component of intelligent optimization algorithms. Ahmadi et al. [7] proposed a multi-objective sine-cosine algorithm using objective functions such as annual energy loss, annual installation and operating costs of distributed energy resources (DERs), and average unsupplied energy (AENS) to determine planning strategies. Geng et al. [8] carried out capacity planning for energy storage systems with the objective of minimizing distribution networks’ operational costs. Adetunji et al. [9] further developed a category-based multi-objective framework to optimize multiple objective functions—power losses, voltage stability, voltage deviation, installation and operational costs, and emission costs. Morillo et al. [10] proposed two objective functions—the cost of energy transmission and network reliability—to address dynamic planning in distributed generation distribution systems.

Distributed new-energy power generation systems are generally small in size and have limited access to the distribution network; therefore, it is necessary to use an appropriate power management method to ensure its orderly operation [11]. In order to solve these problems, the introduction of energy storage in the distribution network not only suppresses power fluctuations to improve the reliability of new energy generation [12], but also achieves the timely transfer of new energy power through peak shaving and valley filling strategies to improve the level of new energy consumption and energy utilization efficiency.

For the planning of energy storage systems in distribution grids containing new energy sources, Zhou et al. [13] proposed an optimal design method for energy storage and capacity in distribution grids using the typical daily all-network loss as an objective function for placement and capacity planning. Feifei et al. [14] proposed a process for the joint planning of energy storage placement and line capacity increase in distribution networks considering the volatility of new energy sources by utilizing actual large-scale new energy operation data. Azibek et al. [15] proposed a genetic algorithm approach for the optimal allocation of energy storage capacity for the problem of voltage fluctuation and power perturbation in distribution networks under the influence of renewable energy discontinuity. Wang et al. [16] proposed an improved multi-objective particle swarm optimization algorithm to determine the optimal capacity and location of charging stations for the problem of the optimal allocation of distribution networks containing a high percentage of new energy and electric vehicles.

A few scholars have also studied methods for coordinating distributed photovoltaic power generation with energy storage. Luo et al. [17] investigated the conflict characteristics between different planning stages and proposed an incremental planning method, thereby establishing a progressive planning model for coordinating distributed photovoltaic power generation with energy storage. Zhu et al. [18] proposed a quantitative evaluation method for DG-FL balance based on IET to find a method for the coordinated optimization of DG, FL, and ES. Most scholars have only employed intelligent algorithms to solve planning problems and optimize objective functions, without further analyzing power flows in distribution grids. Some scholars have also studied power tracking, with Chen et al. [19] developing an analytical method for power tracking using basic circuit laws. Wang et al. [20] addressed how to calculate grid prices through proportional power flow tracking, thereby enhancing the accuracy and scientific rigor of transmission and distribution calculations. Jodeiri-Seyedian [21] introduced a market clearing framework based on power tracking and loss allocation. Power flow tracking calculates the proportion of power emitted by the generators that each load consumes. Any power consumed by a load is transmitted from multiple power sources at a specific proportion. Most scholars use power tracking to calculate power markets, but they have not linked joint photovoltaic–storage placement with power tracking. To further analyze power flow in distribution grids under photovoltaic storage coordinated planning, a power tracking method based on the proportional allocation principle is required. Through this analysis, a deeper understanding of the operational mechanisms of distribution grids can be achieved.

The aforementioned research provides a theoretical basis and foundation for addressing application issues in distributed power supply systems. However, several unresolved challenges remain. First, the integration of distributed energy resources (DERs) and energy storage is a key approach to addressing network losses and voltage stability issues in distribution grids incorporating distributed renewable energy sources. Yet, most scholars have focused solely on the planning of either DERs or energy storage as individual components, neglecting the need for coordinated planning between the two. This approach risks yielding planning outcomes that deviate from optimal solutions. Additionally, traditional single genetic algorithms have limitations when addressing multi-objective problems, necessitating an algorithm that is capable of handling multiple objectives, such as MOGA. Second, the integration of distributed energy and energy storage will have a greater impact on power distribution in distribution grids. Understanding their power distribution characteristics can guide their rational allocation and operation, yet the current literature on this topic remains insufficient.

Therefore, starting from the planning of distributed energy and energy storage, this paper proposes a method based on a multi-objective genetic algorithm for the placement and sizing of distributed photovoltaic energy and energy storage in distribution networks; using power flow tracking technology, it carefully analyzes the impact of distributed energy and energy storage access on the power allocation of the distribution network, which provides support for the subsequent operation optimization and responsibility apportionment.

The remainder of the paper is organized as follows: Section 2 introduces the optimal model and model solving methods. Section 3 introduces the power system power flow tracking principle. Section 4 presents a case study of the optimization model to validate the model and further analyze the power flow tracking results. Finally, Section 5 summarizes the research results and discusses the limitations and future research directions.

2. Optimization Modeling of Distributed Energy and Energy Storage

2.1. Photovoltaic-Storage Placement and Capacity Sizing with Optimization Models

A description of the overall structure of the PV placement and capacity model is shown in Figure 1. The model takes the distribution network equipment parameters, as well as the load and network parameters, as inputs; constructs a multi-objective function containing voltage stability, PV consumption rate, and economic efficiency; incorporates the distribution network current, node voltage, and physical characteristics of the energy storage constraints; relies on the multi-objective genetic algorithm (MOGA) to solve the problem; and outputs a multi-objective Pareto optimal solution set, which provides decision support for the determining the placement and capacity of distributed energy and energy storage.

2.2. Objective Function

Genetic algorithms for multi-objective optimization problems, i.e., for determining the optimal value of the objective function [22], can be described using the following mathematical planning model:

$$\min F(X)={\left[f_1(X),f_2(X),\dots ,f_p(X)\right]}^T$$

(1)

where $F(X)$ is the total optimal value of the system and $f_1(X),f_2(X),\dots ,f_p(X)$ is the objective function.

2.2.1. Average Voltage Stability

The impact of the grid integration of PV power on the stability and volatility of the distribution network in the case of distributed energy-containing distribution networks is significant [23]. The average voltage stability index is based on the reactive power deviation and the eigenvalues of the Jacobi matrix, which can determine the evaluation of the voltage stability state in each time period, as well as being able to identify the voltage weak time period, which can provide support for planning the placement of distributed energy. This index can effectively deal with the volatility of distributed photovoltaic energy, as well as the intermittency brought about by the impact of voltage fluctuations, thereby enhancing the stability of the distribution network, effectively reducing the phenomenon of abandoned light and enhancing the utilization rate of renewable energy. This objective function can be expressed as follows:

$$f_1(X)={\displaystyle \frac{1}{\mathrm{T}}}{\displaystyle \sum _{t=1}^{\mathrm{T}}\left[\max \left(\frac{1}{{\lambda }_i^{(t)}}\right)\cdot \max \left(|\Delta Q^{(t)}|\right)\right]}$$

(2)

where T denotes that there are T time periods in the evaluation cycle, ${\lambda }_i^{(t)}$ denotes the eigenvalue of the sub-matrix of the Jacobi matrix at hour t, and $\Delta Q^{(t)}$ denotes the amount of reactive power at hour t. The smaller this indicator is, the better the voltage stability of the distribution network system.

2.2.2. Photovoltaic Consumption Rate

In relation to distributed photovoltaic grid access, there is a difference between the actual and theoretical power generation. This exists in order to determine the energy utilization of the distributed photovoltaic power generation. To improve power generation efficiency, which is an important guarantee to reduce the abandonment rate, through the calculation of photovoltaic consumption rate, you can quantify the distribution grid in different time periods of the photovoltaic consumption capacity. At the same time, it provides a basis for the installation location of distributed PV energy; through the PV consumption rate seeking optimization, the system can be partitioned and the high-consumption-rate area can appropriately increase the PV capacity to improve the economy and reliability of the distribution network operation. Its objective function can be expressed as follows:

$$f_2(X)={\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T\left(\frac{Q_t}{P_t}\right)}\times 100\%$$

(3)

where T denotes that there are T time periods in the assessment cycle; $Q_t$ denotes the amount of electricity consumed by PV in the tth time period; and $P_t$ denotes the amount of electricity generated by PV in the tth time period. The formula reacts to the degree of PV power consumption in the assessment cycle, whereby the higher the value, the stronger the consumption capacity and the higher the utilization of the selected distributed PV energy.

2.2.3. Economics

For the economic optimization of distribution grids, in this paper, economic factors such as the power generation costs; investment, operation, and maintenance costs of photovoltaics and energy storage; photovoltaic curtailment costs; and grid loss costs are considered with the goal of minimizing these costs. The objective function can be expressed as follows:

$$f_3\left(X\right)=C_{\mathrm{elec}}+F_{cut}^{PV}+F_{loss}+C_{inv}$$

(4)

$$C_{\mathrm{elec}}={\displaystyle \frac{P_{\mathrm{coal}}\times {10}^6}{LHV\times \eta \times 3.6}}$$

(5)

$$F_{\mathrm{cut}}^{\mathrm{PV}}=C_{\mathrm{cut}}{\displaystyle \sum _{i=1}^N{\displaystyle \sum _{t=1}^{N_{\mathrm{T}}}\left(P_{i,t}^{\mathrm{cap}}{\beta }_t-P_{i,t}^{\mathrm{PV}}\right)}}$$

(6)

$$F_{\mathrm{Loss}}={\displaystyle \sum _{t=1}^{N_{\mathrm{T}}}{\displaystyle \sum _{ij\in {\Omega }^{\mathrm{L}}}{C}_{\mathrm{Loss},t}}}{I}_t^2{R}_{ij}$$

(7)

$$C_{\mathrm{inv}}={\displaystyle \sum _{i=1}^N\left({\eta }_{\mathrm{P}}{P}_{\max ,i}+{\eta }_{\mathrm{S}}{E}_{\max ,i}\right)}/T_{\mathrm{s}}+M$$

(8)

where $C_{\mathrm{elec}}$ represents the cost of thermal power generation; $F_{cut}^{PV}$ represents the cost of curtailed solar power in the distribution grid; $F_{loss}$ represents the network loss cost of distribution grid operation; $C_{inv}$ represents the average daily investment and maintenance cost of photovoltaic storage; $LHV$ represents the lower calorific value of coal; $C_{\mathrm{cut}}$ and $C_{\mathrm{Loss},t}$ represent the cost per unit of curtailed solar power and network loss power, respectively; ${\eta }_{\mathrm{P}}$ and ${\eta }_{\mathrm{S}}$ represent the power cost and capacity cost of energy storage, respectively; $P_{\max ,i}$ and $E_{\max ,i}$ represent the maximum charging/discharging power and maximum capacity of energy storage, respectively; $T_s$ represents the expected number of days of use for energy storage; and $M$ represents the operation and maintenance costs of photovoltaic and energy storage systems.

2.3. Restrictive Condition

2.3.1. Distribution Network Current Constraints

$$\left\{\begin{array}{l}{P}_i=U_i{\displaystyle \sum _{j\in i}{U}_j}(G_{ij}\cos {\theta }_{ij}+B_{ij}\sin {\theta }_{ij})\hfill \\ Q_i=U_i{\displaystyle \sum _{j\in i}{U}_j}(G_{ij}\sin {\theta }_{ij}-B_{ij}\cos {\theta }_{ij})\hfill \end{array}\right.$$

(9)

Here, $P_i$ denotes the active power at node i; $Q_i$ denotes the reactive power at node i; $U_i$ and $U_j$ denote the voltage magnitude at nodes i and j, respectively; $G_{ij}$ and $B_{ij}$ denote the conductance and the conductance between nodes i and j of the conductance matrix, respectively; and ${\theta }_{ij}$ denotes the phase angle of the line.

2.3.2. Node Voltage Constraints

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

(10)

Here, $U_i^{\min }$ and $U_i^{\max }$ denote the minimum and maximum values of voltage allowed at node i.

2.3.3. Energy Storage Constraints

$$\left\{\begin{array}{l}{P}_{\mathrm{ESS},i}^{\min }\le P_{\mathrm{ESS},i}(t)\le P_{\mathrm{ESS},i}^{\max }\hfill \\ \mathrm{if}{P}_{\mathrm{ESS},i}(t)\le 0,\hfill \\ S_{\mathrm{ESS},i}(t+1)=S_{\mathrm{ESS},i}(t)-P_{\mathrm{ESS},i}(t)\Delta t\cdot {\eta }_{\mathrm{ch},i}\hfill \\ \mathrm{if}{P}_{\mathrm{ESS},i}(t)>0,\hfill \\ S_{\mathrm{ESS},i}(t+1)=S_{\mathrm{ESS},i}(t)-P_{\mathrm{ESS},i}(t)\Delta t/{\eta }_{\mathrm{dis},i}\hfill \\ S_{\mathrm{ESS},i}^{\max }\times 20\%\le S_{\mathrm{ESS},i}(t+1)\le S_{\mathrm{ESS},i}^{\max }\times 90\%\hfill \end{array}\right.$$

(11)

Here, $P_{\mathrm{ESS},i}^{\min }$ and $P_{\mathrm{ESS},i}^{\max }$ denote the minimum and maximum values of the charging and discharging power of the ith energy storage system, respectively; $P_{\mathrm{ESS},i}(t)$ denotes the actual power of the ith energy storage system at the moment t; $\Delta t$ denotes the time step of the charging and discharging of the energy storage system; ${\eta }_{\mathrm{ch},i}$ and ${\eta }_{\mathrm{dis},i}$ denote the efficiencies in the charging and discharging process of the energy storage system, respectively; and $S_{\mathrm{ESS},i}^{\max }$ denotes the maximum state of charge of the ith energy storage system.

2.4. Model Solving Methods

The genetic algorithm is an adaptive optimization search algorithm based on the inheritance and evolution of organisms in the natural environment, which draws on Darwin’s theory of evolution and Mendel’s genetic theory. After repeated adaptive searches, the adaptive ability of the population is becoming stronger and stronger, and decoding the optimal individuals in the last generation of the population can lead to the determination of the near-optimal solution of the mathematical planning model [24].

In this study, the generation of the Pareto front is based on an improved non-dominated sorting genetic algorithm. First, the three objective functions—voltage stability, photovoltaic absorption efficiency, and economic efficiency—are evaluated in parallel for each individual. Then, using a fast non-dominated sorting algorithm, non-dominated solutions are screened by determining the dominance relationships between individuals and performing hierarchical classification. Simultaneously, the crowding distance is calculated for solutions within the same hierarchy. Finally, a hybrid elite strategy is adopted, whereby after merging the parent and offspring generations, solutions are prioritized based on the frontier level and crowding degree, with non-dominated solutions from the first frontier being retained first. Through multiple iterations, the final Pareto frontier is gradually converged.

Additionally, the information entropy method is used to determine the weights of the objective values [25] by assessing the differences between them within the Pareto solution set. If the differences between the m-th objective values of each solution in the Pareto solution set are small, it indicates that this objective value has a smaller influence on the final decision and should therefore have a smaller weight. The calculation process is shown in Figure 2, and the optimization process is as follows:

(1)

Step 1: Input and initialize the parameters according to the original parameters.

(2)

Step 2: Generate the initial population and set the population size. In this paper, the initial population size is 60, the number of iterations is 500, the crossover probability is 0.7, and the mutation probability is 0.3.

(3)

Step 3: Calculate the fitness of the population. For individuals that do not satisfy the flow constraints, node voltage constraints, and energy storage constraints in this paper, the constraint violation degree is converted into a penalty term in the objective function through a penalty function and a new population is generated through selection, crossover, and mutation operations.

(4)

Step 4: Generate the Pareto frontier based on the weights of the information entropy method target values.

(5)

Step 5: Calculate the new Pareto optimal solution and update it to the population.

(6)

Step 6: Site the individual with the highest fitness during the calculation process, obtain the optimal solution, and save it.

(7)

Step 7: Perform 24 h power flow tracking on the saved distribution network model and output the results.

3. Power System Power Flow Tracking Based on the Proportional Sharing Principle

3.1. Basic Principles of the Power Flow Tracking Method

3.1.1. Principle of Proportional Sharing

In power flow tracking, the principle of proportional power allocation is considered important. This principle was first proposed by J. Bialek in 1996 [26]. It explains how power is allocated at a node and embodies the principles of equal opportunity and fairness. Many power flow tracking algorithms are based on this principle. As shown in Figure 3, it is assumed that lines 1 and 2 are connected to the generator, while node m is connected to four lines, where lines 1 and 2 are incoming lines and lines 3 and 4 are outgoing lines.

The power injected into the incoming lines 1 and 2 is depicted as $P_{g1}^{\mathrm{inj},\mathrm{corr}}$ and $P_{g2}^{\mathrm{inj},\mathrm{corr}}$, respectively, while the power flowing out of the outgoing lines 3 and 4 is depicted as $P_j^{\mathrm{out},\mathrm{fw}}$ and $P_i^{\mathrm{out},\mathrm{fw}}$, respectively, i.e., for the outgoing power $P_j^{\mathrm{out},\mathrm{fw}}$ of line 3, the power supplied by the incoming line 1 can be expressed as follows:

$$P_{3,1}={\displaystyle \frac{P_{g1}^{\mathrm{inj},\mathrm{corr}}}{P_{g1}^{\mathrm{inj},\mathrm{corr}}+P_{g2}^{\mathrm{inj},\mathrm{corr}}}}{P}_j^{\mathrm{out},\mathrm{fw}}$$

(12)

The incoming power $P_{g1}^{\mathrm{inj},\mathrm{corr}}$ can be expressed as the power distributed in output line 3, as follows:

$$P_{1,3}={\displaystyle \frac{P_j^{\mathrm{out},\mathrm{fw}}}{P_j^{\mathrm{out},\mathrm{fw}}+P_i^{\mathrm{out},\mathrm{fw}}}}{P}_{g1}^{\mathrm{inj},\mathrm{corr}}$$

(13)

3.1.2. Average Network Loss Method

The average network loss method is a simplified network loss sharing method, whereby the loss of the line is evenly distributed to the nodes at both ends of the branch. At this time, the first end of the line power for the original power minus half of the line loss is equal to the end of the line power for the original power plus half of the line loss; this method transforms a complex loss network into a lossless network, thus determining the generator power to the load node tracking [27].

Taking any line l in the distribution network as an example, its initial power is $P_{send}$, the line loss is $P_{\mathrm{loss}}$, the terminal power is $P_{receive}$, the power transmitted in the line is $P_l$, and $P_{send}=P_{receive}+P_{loss}$ is satisfied. Using the average network loss method, the initial power of line l becomes $P_{send}^{\prime }$, and the terminal power becomes $P_{receive}^{\prime }$, i.e., the initial and terminal powers of the line can be expressed as follows:

$$P_{send}^{\prime }=P_{send}-{\displaystyle \frac{P_{loss}}{2}}={\displaystyle \frac{P_{send}+P_{receive}}{2}}$$

(14)

$$P_{receive}^{\prime }=P_{receive}-{\displaystyle \frac{P_{loss}}{2}}={\displaystyle \frac{P_{send}+P_{receive}}{2}}$$

(15)

As shown in Equations (14) and (15), the power at the beginning of the line is equal to the power at the end of the line, and the loss network becomes lossless, i.e., the power transmitted in the line is $0.5(P_{send}+P_{receive})$.

3.2. Tidal Current Tracking Algorithm

3.2.1. Downstream Tracking

According to different tracking objects, the current tracking method can be categorized into downstream tracking and counter current tracking. The downstream tracking method is tracked in the direction of the current power flow to accurately identify the generator’s contribution to the distribution node; then, it can determine the percentage of a particular generator’s use in the corresponding line. The counter current tracking method tracks the direction of load power, i.e., along the opposite direction of the power flow, to determine which loads ultimately use the power in the line, thereby determining the share of line usage for a particular load.

In this paper, the downstream tracking method is used as an example, whereby a certain distribution network has n nodes with N generator nodes. Through the average network loss method, after obtaining a lossless network, there is $\left|P_{ij}\right|=\left|P_{ji}\right|$, i.e., the power flowing from node i to node j is equal in magnitude to the power flowing from node j to node i, which satisfies the following equation:

$$P_i-{\displaystyle \sum _{j\in {\alpha }_{\mathrm{i}}^{″}}\left|P_{ij}\right|}=P_{Gi}$$

(16)

where $P_i$ denotes the injected power flowing into node i; ${\alpha }_{\mathrm{i}}^{\prime \prime }$ denotes the set connected to node i; and $P_{Gi}$ denotes the injected power of the generator.

Introducing the matrix of power distribution coefficients $A_{\mathrm{u}}$ and substituting it in Equation (16), the following is obtained:

$$A_{\mathrm{u}}P=P_G$$

(17)

where $A_{\mathrm{u}}$ denotes the n × n order backtracking matrix; $P$ and $P_G$ denote the column vectors of injected power and generator power, respectively. The power allocation coefficient matrix $A_{\mathrm{u}}$ can be expressed as follows:

$${[A_u]}_{ij}=\left\{\begin{array}{ll}{\displaystyle \frac{\left|P_{PF}\right|}{P_j}}\hfill & j=i\hfill \\ {\displaystyle \frac{\left|P_{ji}\right|}{P_j}}\hfill & j\ne i\hfill \end{array}\right.$$

(18)

where ${[A_u]}_{ij}$ denotes the percentage of power flowing from node j to node i; ${[A_u]}_{ii}$ denotes the percentage of load power at node i; and $\left|P_{PF}\right|$ denotes the corrected power.

From the above analysis, the power $\left|P_{ij}\right|$ flowing out of the line connected to node i can be obtained as follows:

$$\left|P_{ij}\right|={\displaystyle \frac{\left|P_{ij}\right|}{P_i}}{P}_i={\displaystyle \frac{\left|P_{ij}\right|}{P_i}}{\displaystyle \sum _{k=1}^N{\left[A_u^{-1}\right]}_{ik}}{P}_{Gk}$$

(19)

From Equation (19), the downstream tracking method enables the precise identification of which generators, distributed energy sources, and energy storage contribute to any line power, which, in turn, enables further analysis of distributed energy placement.

3.2.2. Power Distribution

From Section 3.1.2, it can be seen that the loss network is lossless according to the average network loss method and the corresponding line power changes. For any generator node, its power needs to be corrected, and the corrected generator injected power $P_{G,j}^{\prime }$ is the original injected power minus half of the network loss of the line connected to that node. The expression can be expressed as follows:

$$|P_{PF}|=P_{G,j}^{\prime }=P_{G,j}-{\displaystyle \sum _{k\in {\alpha }_i^{\prime }}\frac{P_{loss}}{2}}$$

(20)

For any load node, the power is also corrected by adding the original load power plus half of the network loss of the line connected to the node. The expression can be expressed as follows:

$$|P_{PF}|=P_{Li}^{\prime }=P_{Li,j}+{\displaystyle \sum _{k\in {\alpha }_i^{″}}\frac{P_{loss}}{2}}$$

(21)

From Equations (21) and (22), after power correction for generator and load nodes, the power allocation coefficient matrix $A_{\mathrm{u}}$ of Equation (11) can be further expressed as follows:

$${[A_u]}_{ij}=\left\{\begin{array}{ll}{\displaystyle \frac{\left|P_{PF}\right|}{P_j}}={\displaystyle \frac{P_{G,j}-{\displaystyle \sum _{k\in {\alpha }_i^{\prime }}\frac{P_{loss}}{2}}}{P_j}}\hfill & j\in N,j=i\hfill \\ {\displaystyle \frac{\left|P_{PF}\right|}{P_j}}={\displaystyle \frac{P_{Li,j}+{\displaystyle \sum _{k\in {\alpha }_i^{\prime \prime }}\frac{P_{loss}}{2}}}{P_j}}\hfill & j\notin N,j=i\hfill \\ {\displaystyle \frac{\left|P_{ji}\right|}{P_j}}\hfill & j\ne i\hfill \end{array}\right.$$

(22)

4. Case Study

In this section, based on a genetic algorithm, the average voltage stability, photovoltaic (PV) absorption rate, and economic efficiency are used as objective functions to plan the location and capacity of PV-storage coordination. Additionally, power tracking is used to further analyze the line conditions. To validate the feasibility and superiority of this model and algorithm, this paper analyzes a distribution network with 14 nodes as an example and introduces a storage system. Based on the proportional allocation principle derived from power flow tracking results, the energy utilization efficiency, voltage stability, and economic viability of the distribution network are compared and analyzed after the addition of the storage system.

Table 1. The basic parameters of the power distribution network.

Number	Initial Node	Final Node	R (ohm)	X (ohm)
1	1	2	0.01938	0.05280
2	1	5	0.05403	0.22304
3	2	3	0.04699	0.19797
4	2	4	0.05811	0.17632
5	2	5	0.05695	0.17388
6	3	4	0.06701	0.17103
7	4	5	0.01335	0.04211
8	4	7	0.00000	0.20912
9	4	9	0.00000	0.55618
10	5	6	0.00000	0.25202
11	6	11	0.09498	0.19890
12	6	12	0.12291	0.25581
13	6	13	0.06615	0.13027
14	7	8	0.00000	0.17615
15	7	9	0.00000	0.11001
16	9	10	0.03181	0.08450
17	9	14	0.12711	0.27038
18	10	11	0.08205	0.19207
19	12	13	0.22092	0.19988
20	13	14	0.17093	0.34802

lists the resistance and reactance values of the power subsystem lines in the distribution network, providing basic parameters for subsequent photovoltaic-storage coordination planning and power flow analysis.

The topology of the 14-node distribution system is shown in Figure 4, where nodes 1, 2, 3, and 8 are connected to thermal generating units G1, G2, G3, and G4, respectively, and the system simulation parameters and variables are set as shown in

Table 2. Simulation parameters and variable settings.

Parameter or Variable	Numerical Value
Generator G1 generating capacity/MW	25
Generator G2 generating capacity/MW	30
Generator G3 generating capacity/MW	35
Generator G4 generating capacity/MW	40
Photovoltaic power generation capacity/MW	25
Energy storage capacity/MW	10
Number of photovoltaic power sources/pc	4
Number of energy storage/pcs	2
Maximum number of iterations/times	500
Population size/population	60
Crossover probability	0.7
Mutation probability	0.3

. Typical daily load curves and photovoltaic power output curves are shown in Figure 5. Typical actual daily load curves are shown in Figure 6.

Based on the above simulation algorithms and parameter settings, this paper will verify and analyze the simulation algorithms through the following three Scenarios. Scenario 1: access to energy storage in the distribution grid, as well as the placement and capacity of distributed energy and energy storage; Scenario 2: no access to energy storage in the distribution grid, as well as the placement and capacity of distributed energy; Scenario 3: no access to distributed energy in the distribution grid, as well as the placement and capacity of energy storage. All three Scenarios take the optimal voltage stability, renewable energy consumption rate, and economy as the objectives, and the Pareto optimal solution is obtained using the multi-objective genetic algorithm for comparative analysis; the three objective functions are given weights, with a voltage stability of 0.3, an average consumption rate of 0.4, and an economy of 0.3. The optimization results are shown in

Table 3. Optimization results under different scenarios.

Scenario	1	2	3
DG location No.	Nodes 3, 8, 11, 13	Nodes 3, 8, 11, 13	/
DG capacity/(MW)	11.07, 7.91, 13.89, 2.65	14.45, 8.01, 6.97, 3.86	/
Energy storage location No.	Nodes 8, 11	/	Nodes 8, 11
Energy storage capacity/(MW)	6.03, 7.21	/	3.63, 5.36
Voltage stability	0.01	0.11	0.03
Average consumption rate	96.3%	85.6%	/
Power generation cost	USD 20,147	USD 24,973	USD 27,329

.

As shown in Table 3, after the introduction of energy storage, Scenario 1 has a voltage stability of 0.01, an average PV consumption rate of 96.3%, and a power generation cost of USD 20,147; without the addition of energy storage, Scenario 2 has a voltage stability of 0.11, an average PV consumption rate of 85.6%, and a power generation cost of USD 24,973. With the addition of energy storage and without the addition of the DG, Scenario 3 has a voltage stability of 0.03 and a power generation cost of USD 27,329.

Through a comparison of the above data, Scenario 1 has a better voltage stability of the distribution network than Scenarios 2 and 3, while also having the lowest cost and the best economy. The average PV consumption rate of Scenario 1 is increased by 12.5% compared to Scenario 2, and the utilization of PV distributed energy is significantly improved. Scenario 1 is identified as the optimal configuration based on simulation results.

The impacts of Scenarios 1 and 2 on distribution network operation are further analyzed by taking them as an example, combining them with the typical load and PV output curves in Figure 4 and the 24 h analysis of DG output under different scenarios, as shown in Figure 7.

From the overall view of the power output to the distribution network, due to the charging and discharging strategy of the energy storage, the DG output is more stable in different time periods. The power output of Scenario 1 is significantly larger than that of Scenario 2 throughout the day. From the characteristics of the time period, at the 13th and 14th timepoints, the DG output of Scenario 2 is 18.94 MW and 22.25 MW, respectively, which is a significant increase in the power output; however, large fluctuations are observed, which is likely a result of the impact on the distribution network. In the case of Scenario 1, the DG output at the 13th and 14th timepoints is 30.26 MW and 29.28 MW, respectively, and this fluctuation is effectively suppressed by energy storage, and the output curve is smoother. Therefore, it can be obtained that energy storage can effectively optimize the DG output characteristics, and it balances the power fluctuations and enhances the adaptability of the grid to distributed energy sources in the distribution network operation.

Through the above analysis, it can be understood that Scenario 1 is better overall compared to Scenario 2 in terms of DG output. The following is a further analysis of the amount of output of different energy sources to the grid for each time period for Scenario 1, as shown in Figure 7 for the 24 h output of Scenario 1’s DG, generator, and energy storage.

It can be observed from Figure 8 that there is a significant difference in the power output of each power source in different time periods. In the 8th–20th time period, distributed PV energy is affected by light conditions. For example, at time 8, the entire distribution grid output 22.07 MW; at time 12, the entire distribution grid output is 32.75 MW. The output increases significantly and the overall efficiency of the distribution grid is good in this time period. Four generators, on the other hand, reduced the power generation during the 8th to 20th time periods when there was sufficient photovoltaic resources to meet the load requirements and economic efficiency, and provided relatively stable power generation during other time periods to maintain the basic power supply requirements of the system.

This distributed energy, energy storage, and generator cooperative distribution network operation mode intuitively reflects the important role of energy storage in suppressing power fluctuations, peak shaving, and valley filling strategies, as well as converting the abandoned power into usable energy to supply the key loads.

However, when energy storage is integrated into the distribution network, some of the operating parameters in the optimization process of the objective function will be affected, as shown in Figure 8 for the two Scenarios of the line network loss diagram.

The 24-h power consumption in different scenarios is shown in Figure 9. The average network loss of Scenario 1 is 2.40 MW, and the average network loss of Scenario 2 is 1.81 MW; the network loss of Scenario 1 is higher than that of Scenario 2. The introduction of energy storage increases the network loss of the distribution network, which indicates that the charging stage needs to supply power to the energy storage from the power source through the line, and the discharging stage needs to supply power to the load from the energy storage through the line, resulting in the repeated transmission of electricity on the same or multiple lines, which significantly increases the line losses.

Comparing the changes in the network loss of each of the two Scenarios, the characteristics of the network loss in the 8th–20th time period show significant differentiation, whereby Scenario 2 is obviously larger than the average network loss, due to its lack of energy storage regulation. Additionally, the PV transmission power needs to be delivered to the load through a number of distribution lines, resulting in the lengthening of the tidal current path and the elevation of the network loss. In Scenario 1, it is observed that the energy storage is smaller than the average network loss, as well as the time period of the distributed PV energy out of the power supply. Storage access nodes are close to the side of the PV power supply. By shortening the electrical distance between the PV power source and the energy storage device, the network loss is reduced in that time period.

To further elucidate the mechanisms by which the location of energy storage systems and power transmission paths influence network losses, this study employs power flow tracking. This method constructs a node power allocation coefficient matrix to quantify the contribution of different power sources to loads and their respective shares of transmission losses along each line. Compared to traditional power flow calculations, power flow tracking clearly illustrates the “source-load” transmission paths of energy, making it particularly suitable for analyzing the distribution characteristics of network losses in hybrid systems combining distributed power sources and energy storage. By tracking the power transmission paths of the two Scenarios during typical time periods, the reasons for increased network losses can be intuitively verified.

According to the basic principle of power flow tracking and the power flow tracking algorithm in this paper, power flow tracking is carried out for Scenarios 1 and 2 at the 12th hour. The 12 h power allocation coefficient matrix for Scenario 1 is shown in Figure 10, while the 12 h power allocation coefficient matrix for Scenario 2 is shown in Figure 11.

As shown in Figure 12 and Figure 13, at time 12, the distributed PV power supply provides energy for the entire distribution network, the generator sends out less power, the cost of power generation is reduced, and the overall economy of the distribution network is improved. It also shows the impact of energy storage system connection on distribution network losses. During charging, energy storage needs to draw power from the power source side through the line, while during discharging, it needs to release energy to the load through the line. This bidirectional power flow causes energy to be transmitted repeatedly in the same line or multiple lines, thereby significantly increasing line losses.

For a node in the distribution network, e.g., node 5, at hour 12 of Scenario 1, node 5 receives 0.34 MW from the generator and PV power source at node 8, 4.40 MW from the PV power source at node 11, and 1.07 MW from the PV power source at node 13, and delivers power to node 1 and node 2 at 0.44 MW and 0.56 MW, respectively. In hour 12 of Scenario 2, node 5 receives 0.01 MW from generator G1, node 8 receives 0.45 MW from the generator and PV, node 11 receives 3.34 MW from the PV, and node 13 receives 0.99 MW from the PV. The amount of power transmitted by different Scenarios in the same time period is reduced by 75.76%, and the introduction of the energy storage system effectively reduces the burden on the generators.

During the same time period, the total power generation in scenario 2 was significantly higher than that in scenario 1. Energy storage reduces the role of generator output in the distributed PV distribution grid by optimizing the balance between power supply and demand. The energy storage system is connected to the distribution network, and the two storage systems assume the responsibility of supplying power to some nodes. The introduction of energy storage in the distributed PV distribution network reduces the dependence on thermal generators and improves the rate of elimination and economy.

Through the power flow tracking results and basic data, it can be concluded that in the 12th hour, the maximum output power of PV nodes 3, 8, 11, and 13 in Scenario 1 is 11.07 MW, 7.91 MW, 13.89 MW, and 2.65 MW, respectively, while the actual output power is 5.21 MW, 6.36 MW, 9.83 MW, and 2.64 MW, respectively, In Scenario 2, the maximum output power of PV nodes 3, 8, 11, and 13 is 14.45 MW, 8.01 MW, 6.97 MW, and 3.86 MW, while the actual output power is 2.71 MW, 2.52 MW, 4.11 MW, and 2.71 MW, respectively.

For Scenario 1, nodes 3, 8, 11, and 13 discard 5.86 MW, 1.55 MW, 4.06 MW, and 0.01 MW of power, accounting for 52.9%, 19.6%, 29.2%, and 0.4%, respectively, for a total loss of 11.48 MW of power. For Scenario 2, nodes 3, 8, 11, and 13 discarded 11.74 MW, 5.49 MW, 2.86 MW, and 0.15 MW, accounting for 81.2%, 68.5%, 41.0%, and 3.9%, respectively, with a total loss of 20.24 MW of electrical energy. In summary, the introduction of the energy storage system not only reduces the percentage of lost electrical energy to the PV electrical energy node but also reduces the total lost electrical energy by 43.3%.

5. Conclusions and Future Work

Containing distributed energy access to the distribution grid, as well as the placement and capacity of energy storage, is a complex and important issue. This paper focuses on a model of the distribution grid for distributed energy, as well as the placement and capacity of the energy storage system linked to the distribution grid, proposing an optimal allocation method of the distribution grid based on the multi-objective genetic algorithm and innovatively proposing a power tracking method based on the principle of proportional sharing. The distribution network voltage stability, PV consumption rate, and economy are taken as the objective functions and are analyzed as an example of a distribution network with 14 nodes. After the introduction of energy storage into the distributed PV-containing distribution network, the PV consumption rate increases from 85.6% to 96.3%, which is an improvement of 12.5%, and the cost is reduced from USD 24,973 to USD 20,147, which is a reduction of 19.3%. From the network loss point of view, the application of energy storage in the distribution network increases the network loss, leading the energy flow process to pass through a few more sections of the line, which is related to the node of the energy storage location. However, for the purpose of this paper, despite the incremental network losses associated with energy storage access, the enhancement effect on the stability of the distribution network and the optimization benefits in terms of economics dominate. This model provides a technical reference path for the optimization and analysis of distribution grids by combining methods such as the coordinated planning and power tracking analysis of distributed photovoltaics and energy storage. It has a certain application value in improving grid stability and economic efficiency.

However, when using multi-objective genetic algorithms for the coordinated configuration of photovoltaic and energy storage systems in distribution grids, certain limitations exist. The non-domination sorting in this algorithm requires a large number of pairwise comparisons between individuals, resulting in a high computational complexity. As the scale of distribution grids expands, this issue becomes increasingly prominent, significantly increasing computational time and resource consumption. Additionally, the average network loss method used in power tracking, while making network loss distribution more reasonable to some extent, still exhibits variations in its proportion across different times and locations in practical applications. Furthermore, distribution grids are inherently complex nonlinear network systems, and the distributed energy sources connected to them exhibit significant diversification, encompassing not only photovoltaic power sources but also various types of energy equipment. Therefore, future research could explore the following areas:

(1)

Combining other optimization algorithms to complement each other’s strengths and enhance the algorithm’s ability to optimize the coordinated configuration of photovoltaics and energy storage in complex distribution network environments.

(2)

Incorporating real-time data and dynamic parameters to improve the calculation model of the average network loss method by enhancing its adaptability to different times and locations.

(3)

Researching configuration issues in scenarios involving wind-storage integration and wind-solar-storage integration, as in the construction of new distribution grids, distributed resources include not only distributed photovoltaics but also wind power generation.