Multi-Objective Optimization and Reconstruction of Distribution Networks with Distributed Power Sources Based on an Improved BPSO Algorithm

Abstract

The continuous integration of distributed power into the distribution network has increased the complexity of the distribution network and created challenges in distribution-network reconfiguration. In order to make the distribution network operate in the optimal mode, this paper establishes a multi-objective reconfiguration-optimization model that takes into account active network loss, voltage offset, number of switching actions and distributed power output. For a distribution network with a distributed power supply, it is easy for the traditional binary particle swarm optimization algorithm to fall into a local optimum. In order to improve the convergence speed of the algorithm and avoid premature convergence, this paper adopts an improved binary particle swarm optimization algorithm to solve the problem. The IEEE33 node system is used as an example for simulation verification. The experimental results show that the algorithm improves the convergence speed and global search ability, effectively reduces the system network loss, and greatly improves the voltage level of each node. It improves the stability and economy of distribution-network operation and can effectively solve the problem of multi-objective reconfiguration.

1. Introduction

The power system is a complex system. In the process of power transmission, the distribution network plays a vital role as a network for carrying and distributing power [1]. Therefore, its quality and efficiency are crucial to the entire power system. Through reconfiguration of the distribution network, the potential of the distribution system can be brought into play without increasing investment in equipment and the performance index of the system can be improved, with improvements including reduced active power loss in the system, reduced voltage difference, and increased output of distributed power. Therefore, distribution-network reconfiguration has good economic benefits for the operation and management of modern power systems, and it is also an important means by which to realize the intelligent and sustainable development of power systems [2].

In recent years, with the development of distributed power sources, more and more distributed power sources have been connected to the distribution network, leading to significant changes in the magnitude and direction of power flow in the distribution network [3]. In addition, node voltage and network loss will also be greatly affected. Therefore, the question of how to reconstruct a distribution network containing distributed power sources has become a hot topic in current smart-grid research [4].

To date, scholars both domestically and internationally have conducted extensive research on reconstruction methods for the integration of distributed power sources into distribution networks. The main methods used include traditional algorithms and artificial intelligence algorithms [5]. Due to the unsatisfactory nature of the results from the use of traditional algorithms in large-scale distribution networks, intelligent algorithms including the ant colony algorithm [6], genetic algorithm [7], and particle swarm algorithm [8], as well as various combinations of and improvements on these algorithms are currently commonly used. In reference [9], minimizing network loss is taken as the objective function and the distribution network is reconstructed by improving the quantum particle swarm optimization algorithm. Reference [10] takes active power loss as the objective function and incorporates fuzzy theory into the group search algorithm to solve the optimization and reconstruction model of photovoltaic distribution networks. Reference [11] addresses the problem of slow convergence speed in the cuckoo algorithm by introducing a simulated annealing operation. Simulation results show that this method can effectively improve convergence speed and reduce network loss. In Reference [12], a multi-objective mathematical model of distribution-network reconfiguration that considers the network loss, average safety factor, and minimum safety factor was established. Through improvements to the traditional mouse swarm optimization algorithm, the global search efficiency of the algorithm was improved. In Reference [13], an optimal method of distribution-network reconfiguration based on hybrid simulated annealing and the cuckoo search algorithm is proposed; this method effectively reduced the active power loss of a distribution network with distributed generation and improves the voltage quality. The stability and universality of the algorithm were verified, so the algorithm provides a reference for the safe and economic operation of smart grid. In Reference [14], an optimal reconfiguration model of a distribution network with distributed energy based on an improved wolf pack algorithm is proposed. Through the introduction of Levy flight and adaptive step-size strategy, the convergence performance of the algorithm was improved. This paper analyzes and verifies the effectiveness and superiority of this method for reducing network loss and improving node voltage. In Reference [15], through the establishment of a distribution-network reconfiguration model considering demand response and ‘source-storage-load’ structure, the second-order cone optimization method was used to deal with uncertain factors, which effectively improved the voltage quality and operational efficiency of the distribution system over different time periods. These studies provide a theoretical basis for the reconstruction of distributed power generation integration into distribution networks.

However, most of the above studies in the literature aim at minimizing the network loss, and there is a problem in that the objective function is relatively simple and the above heuristic algorithms risk falling into a local optimal solution. In this context, for distribution-network reconfiguration, this paper proposes an improved algorithm that combines the dual advantages of the binary particle swarm optimization algorithm and the genetic algorithm. By introducing the strategy of the genetic algorithm, the improved binary particle swarm optimization algorithm can better deal with the constraints in distribution-network reconfiguration. This approach effectively avoids the generation of invalid solutions and improves search efficiency. This paper not only considers the traditional minimization of active network loss, but also includes various factors such as reducing network loss, reducing voltage offset, reducing the number of switching actions, and increasing the output of distributed power in the objective function. This approach not only considers the economy of the system but also considers improvements in the stability of the distribution network’s operation. In this paper, the effectiveness of the method in different scenarios is verified by simulation.

2. Mathematical Model for Distribution-Network Reconstruction

2.1. Objective Function

Distribution-network reconstruction is a typical nonlinear programming problem in power systems. Due to the constant changes in load, the distribution network needs to find the optimal structure to achieve the best solution for active power loss, node voltage offset, distributed power-generation active output, and switch-operation-frequency coordination. The main goal of reconstruction is to find the optimal network structure, which is of great significance for reducing distribution network losses and improving voltage quality and power-supply reliability.

(1) Considering the economic considerations of the system, this article will minimize the network loss of the system as one of the objectives, and its objective function expression is as follows:

$$P_{\mathrm{loss}}=\min \sum _{i=1}^m{k}_i{R}_i{\displaystyle \frac{P_i^2+Q_i^2}{U_i^2}}$$

(1)

Among these variables, $P_{loss}$ represents the total network loss of the system; m represents the total number of switch branches in the network; $k_i$ represents the switch status of the ith branch, with 0 and 1 representing on and off, respectively; $R_i$ represents the resistance value of the i-th branch; $P_i$ represents the active power of the i-th branch; $Q_i$ represents the reactive power of the ith branch; and $U_i$ represents the voltage value of the i-th node.

(2) Voltage deviation is an important indicator of power and voltage quality and is considered as one of the objective functions in this article. The objective function takes the deviation between the actual node voltage amplitude and the given voltage amplitude as the measurement standard, aiming to maintain the node voltage within the allowable range of the system and minimize voltage deviation. Its expression is as follows:

$$\Delta U=\min \sum _{i=1}^m\left|{\displaystyle \frac{U_i-U_{iN}}{U_{iN}}}\right|$$

(2)

Among these variables, $\Delta U$ represents the voltage deviation of node i, m is the total number of nodes in the network, and $U_{iN}$ represents the specified voltage amplitude at node i.

(3) The objective function for optimizing the total number of switch operations in the distribution network can be expressed as follows:

$$S=\min \sum _{i=1}^m\left|S_i-S_i^{\prime }\right|$$

(3)

In the formula, $S_i$ and $S_i^{\prime }$ represent the switch states of branch i before and after reconstruction, with 1 indicating that the switch is closed and 0 indicating that the switch is open.

(4) When restructuring the distribution network, it is necessary to optimize the use of distributed power sources in the system to maximize the utilization of these resources, thereby reducing the load and energy costs of the entire system and improving the reliability and efficiency of the system. Specifically, the objective function can be expressed as follows:

$$P_{\min }=-\min {\displaystyle \sum _{i=n_{DG}}{P}_{iDG}}$$

(4)

Among these variables, $P_{iDG}$ represents the active output of distributed power source i.

In order to reduce the subjectivity of artificially fixed weights, we use a random weight-allocation method to normalize the objective function. Through different weight ratios, different normalization formulas can be obtained; as a result, the final approximate solution set is also different. Through this method, the multi-objective function can be normalized simply and quickly, and for the convex Pareto optimal front-end problem, the optimal solution can be obtained so as to evaluate the performance of the algorithm more objectively and fairly. Therefore, the total objective function is expressed as follows:

$$\left\{\begin{array}{c}f(x)=\min [{\omega }_1{f}_1+{\omega }_2{f}_2+{\omega }_3{f}_3+{\omega }_4{f}_4]\\ {\omega }_i={\displaystyle \frac{{\lambda }_i}{{\displaystyle \sum _{i=1}^4{\lambda }_i}}}\\ {\lambda }_i=rando{m}_i\end{array}\right.$$

(5)

Because the dimensions of the four constraint conditions are different, the linear scaling method is used to normalize each objective function and obtain the normalized objective function $f_1,f_2,f_3,f_4$. The random weight normalization algorithm is used to normalize the objective function by using the randomly generated weights and the weighted summation method. On this basis, the multi-objective model is solved. $w_i$ is the random weight of the i-th variable, and ${\lambda }_i$ is the ith random number generated, resulting in a total of four random weights.

2.2. Constraint Condition

When optimizing and reconstructing a distributed power-distribution-network system, in addition to considering the optimization objectives, it is also necessary to consider whether the reconstructed system meets the specified operating conditions, which are listed below.

(1)

Node-voltage constraint:

$$U_{i,\min }⩽{\mathrm{U}}_i⩽U_{i,\max }$$

(6)

Here, $U_{i,\min }$ and $U_{i,\max }$ are the minimum and maximum effective voltage values corresponding to the ith node, respectively. The reconstructed distribution network needs to meet the requirements of stability and reasonable distribution of voltage to prevent equipment damage or power-quality problems caused by high or low voltage.

(2)

Power-flow-equation constraints:

$$\begin{array}{c}{P}_i+P_{DGi}=U_i{\displaystyle \sum _{j=1}^m}{U}_j\left(G_{ij}\cos {\delta }_{ij}+B_{ij}\sin {\delta }_{ij}\right)+P_{Li}\\ Q_i+Q_{DGi}=U_i{\displaystyle \sum _{j=1}^m}{U}_j\left(G_{ij}\sin {\delta }_{ij}-B_{ij}\cos {\delta }_{ij}\right)+Q_{Li}\end{array}$$

(7)

$P_i$ and $Q_i$ respectively represent the active and reactive power injected by the system at node i; $P_{Di}$ and $Q_{Di}$ respectively, represent the active and reactive power injected at node i of the distributed power-generation DG access; $P_{Li}$ and $Q_{Li}$ represent the active and reactive power of the load at node i, respectively; $U_i$ and $U_j$ represent the effective voltage values of nodes i and j, respectively; $G_{ij}$ and $B_{ij}$ are the real and imaginary parts of the node admittance matrix, respectively; ${\delta }_{ij}$ represents the voltage phase difference between node i and node j.

(3)

Power constraints on branch lines:

$$S_i\le S_{i\max }$$

(8)

In the formula, $S_i$ represents the actual power flowing through branch i and $S_{i\max }$ represents the maximum power allowed to flow through branch i.

(4)

DG-capacity constraints

$$S_{DGi}\le S_{DGi\max }$$

(9)

In the formula, $S_{DGi}$ represents the actual power injected by DG into branch i and $S_{DGi\max }$ represents the maximum capacity of DG.

(5)

Network-topology constraints

$$g_n\in G_n$$

(10)

Here, $g_n$ is the reconstructed network structure and $G_n$ is the set of all allowed radial network structures in the distribution-network system. After the reconstruction of the distribution network is completed, its structure should comply with the operational rules of the power grid; that is, the topology structure should be radial, acyclic, and islanded.

2.3. Method for Judging the Structure of Distribution Networks

One of the most important constraints in the reconstruction of distribution networks is that the power grid structure must not have islands or loops; that is, its radial structure must operate, in a manner similar to the tree structure in graph theory. A tree is a special structure in which any two points are connected and there is no loop between them. When all switches in the power grid are closed, the system structure forms a connected graph, denoted as G, and the radial distribution-network structure is a spanning tree of the connected graph G. A connected graph contains n nodes in the graph, but only (n − 1) edges are needed to form a tree. If the number of branches in the graph is more than (n − 1), it indicates the existence of a ring network. If it is less than (n − 1), there must be solitons in the graph. To carry out distribution-network reconstruction, it is necessary to ensure that the distribution-network structure is radial.

In the reconstruction of distribution networks, the structure of the distribution network is often complex, with a large number of switches present [12]. In the process of algorithm optimization, many solutions that do not meet the structural requirements will be generated. Judging the structure of these solutions is beneficial for improving the efficiency of algorithm processing.

To avoid the occurrence of a ring-network structure, it is assumed that all switches in the distribution network are closed, forming some circuits, each with only one switch open. In order to avoid islanding, at most one switch is disconnected in the common branch of the loop and at most n-1 switches are disconnected around nodes where n loops converge. This ensures that the reconstructed distribution network maintains a radial topology.

3. Algorithm Research

3.1. Algorithm Selection

In the reconfiguration of distribution networks in modern power systems, multi-objective optimization plays a vital role. In a difference from traditional single-objective optimization, multi-objective optimization needs to consider multiple performance indicators, such as reducing network loss, reducing voltage offset, reducing the number of switching actions, and increasing the output of distributed power supply, at the same time. There are often conflicts among these goals. For example, reducing network loss may increase the number of switching actions, and increasing the output of distributed power may affect the voltage quality. Therefore, finding a balance point to achieve the coordinated optimization of these goals is a major challenge in distribution-network reconfiguration.

In order to solve the above multi-objective optimization problem, this paper uses an improved binary particle swarm optimization algorithm (GA-BPSO). Binary particle swarm optimization (BPSO) is an optimization algorithm based on swarm intelligence. It searches for the optimal solution by simulating the social behavior of birds. The BPSO algorithm shows good performance with optimization problems in discrete space, but it may fall into local optimal solutions when dealing with complex constraints and multi-objective problems. The reasons for choosing GA-BPSO as a multi-objective optimization method in this paper follow.

By combining the crossover and mutation operations of the genetic algorithm (GA), GA-BPSO enhances the global search ability of the algorithm and helps it jump out of the local optimal solution, which is particularly important for multi-objective problems. There is a large number of constraints in the distribution-network reconfiguration problem. GA-BPSO can effectively deal with these constraints and avoid the generation of invalid solutions. In this paper, the objective function is normalized by random weight distribution such that the contribution weights of different objective functions to the optimization results are evenly distributed, so as to evaluate the performance of the algorithm more objectively and fairly. The GA-BPSO algorithm has a fast convergence speed while maintaining search accuracy, which is particularly important for large-scale power-system optimization problems.

3.2. Binary Particle Swarm Optimization Algorithm

Traditional particle swarm optimization (PSO) achieves iterative updates by updating the velocities and positions of particles [16]. The inspiration for this algorithm comes from bird swarm behavior, which combines the strategies of individual birds with those of other birds to ultimately search for food in a collective manner. The PSO algorithm exhibits highly efficient performance in optimization problems in continuous spatial domains. When it is necessary to optimize a problem in a discrete spatial domain, the standard PSO algorithm is no longer applicable [17]. To address this issue, Kennedy et al. proposed the binary particle swarm optimization (BPSO) algorithm in 1997 [18]. The BPSO algorithm uses binary encoding to represent the solution space in the search space, and its speed and position updates are done in the same way as in standard PSO algorithms. Due to the fact that the variable switch-state variables in the optimization of distribution-network reconstruction are a set of discrete variables, it is more suitable to use the BPSO algorithm. The formula for updating the velocities and positions of its particles is as follows:

$$\begin{array}{l}\begin{array}{l}{v}_{i,j}\left(k+1\right)=w\cdot v_{i,j}\left(k\right)+c_1\cdot ran{d}_1\cdot \\ \left(p_{i,j}\left(k\right)-x_{i,j}\left(k\right)\right)+c_2*ran{d}_2*\left(g_j\left(k\right)-x_{i,j}\left(k\right)\right)\end{array}\hfill \\ x_{i,j}\left(k+1\right)=\left\{\begin{array}{c}1,rand<sigmoid\left(v_i\left(k+1\right)\right)\\ 0,rand\ge sigmoid\left(v_i\left(k+1\right)\right)\end{array}\right.\hfill \end{array}$$

(11)

In the formula, the j-th dimensional velocity of the i-th particle at the k-th iteration is $v_{i,j}$, where $x_{i,j}(k)$ represents the j-th dimensional position of the i-th particle at the k-th iteration. The individual’s historical optimal position is $p_{i,j}(k)$; the global optimal position is $g_j(k)$; $\omega$ is the inertia weight; and $c_1$ and $c_2$ are the adaptive acceleration constants. The values of particle position and velocity are represented by converting real numbers to binary encoding, so particles need to first perform binary encoding and decoding when updating their position and velocity. That is, each particle uses a binary string to represent its position and velocity, and some of the operations in the update equation are performed in binary space.

3.3. Improved Binary Particle Swarm Optimization Algorithm

In dealing with the problem of reconstruction of a power-distribution network, the BPSO algorithm has better search and convergence capabilities compared to the PSO algorithm. However, there are still many problems in practical applications, one of which is that the network structure needs to meet a large number of constraint conditions, which results in a large number of invalid solutions arising during the search process and seriously affects search efficiency. Another is that the algorithm easily falls into local optima in distribution-network-reconstruction problems. To address these issues, this study introduces the concepts of “inheritance” and “mutation” from the genetic algorithm (GA) into the algorithm. The position of attractor p(k) will inherit the optimal individual solution P(k) and the global optimal solution G(k) with a certain probability [19], and non-optimal genes will be mutated with a certain probability. Therefore, the iterative process can be described in the following form:

$$\begin{array}{cc}\begin{array}{c}{v}_{i,j}(k+1)=\omega \cdot v_{i,j}(k)+ran{d}_1\cdot [p_{i,j}(k)-x_{i,j}(k)]+\\ ran{d}_2\cdot [g_j(k)-x_{i,j}(k)]+F_1\cdot [P_{i,j}(k)-x_{i,j}(k)]+\\ \hspace{1em}{F}_2\cdot [V_{i,j}(k)-x_{i,j}(k)]\end{array}& \\ x_{i,j}(k+1)=\left\{\begin{array}{c}1,\hspace{1em}{P}_{i,j}(k)+Q_{i,j}(k)<rand\\ 0,\hspace{1em}{P}_{i,j}(k)+Q_{i,j}(k)\ge rand\end{array}\right.& \end{array}$$

(12)

Here, $F_1$ and $F_2$ are the “genetic” and “mutation” factors of the genetic algorithm; $P_{i,j}(k)$ is the best position of the ith particle in the individual historical optimum at the kth iteration; $V_{i,j(k)}$ is the velocity corresponding to the global historical optimum at the kth iteration; and $Q_{i,j}(k)$ is the mutation value of the ith particle at the kth iteration.

The specific process of GA-BPSO algorithm is shown in the figure.

(1)

To initialize the algorithm model, this article considers the topology constraints of the distribution network when initializing and updating particles, which can narrow the particle search range and enhance the algorithm’s convergence ability.

(2)

To initialize the population, note that in GA-BPSO, the population is composed of particles from BPSO. First, randomly select some seed points to initialize the population, with each particle representing a potential solution.

(3)

When defining a fitness function, the objective function of distribution-network reconstruction should be used as the main reference indicator to evaluate the power system.

(4)

In the selection operation, use a fitness function to evaluate the fitness of each particle, select the optimal particle, and make a selection based on the fitness.

(5)

In the genetic and mutation operations, to increase randomness and assist in the global search, mutation operations are performed on certain particles in a new population.

(6)

In the particle swarm update, based on the characteristics of the BPSO algorithm in the population, update the positions and velocities of particles in the population according to the strategy of the BPSO algorithm.

(7)

If the constraint is satisfied, then determine whether the termination condition is satisfied; if not, repeat steps 3–6 until the stopping condition is reached.

4. Simulation Analysis

To verify the performance of the GA-BPSO algorithm applied in the optimization and reconstruction of distribution networks, an IEEE33 node distribution-network system was used as an example, and simulation analysis based on the GA-BPSO algorithm in Figure 1 was conducted using MATLAB. The original topology structure of the IEEE33 node distribution network system is shown in Figure 2, which includes 33 nodes, 32 segmented switches (all closed), and 5 tie switches (all open). The system reference voltage is 12.66 kV, the active load is 3.72 MW, the reactive load is 2.32 Mvar, and the reference capacity is set to 10 MVA. The initial population size of the GA-BPSO algorithm is set to 50, and the maximum number of iterations is 40. The convergence accuracy is 10⁻⁶. In order to verify the performance of the proposed method in distribution-network reconstruction, this paper conducts simulations under two different application scenarios: one considering distributed power sources and one not considering distributed power sources.

4.1. Improved Binary Particle Swarm Optimization Algorithm

This scenario involves an IEEE33 node distribution network without distributed power sources. We applied this method to the reconstruction problem of this type of distribution network, and the reconstructed system-network diagram is shown in Figure 3. The disconnect switches for the pre-refactoring system were 33, 34, 35, 36, and 37, while the disconnect switches for the post-refactoring system were 7, 9, 14, 32, and 37.

In order to better verify the role of the algorithm in the distribution-network reconfiguration, the GA-BPSO algorithm is compared with the ant colony algorithm, the PSO algorithm, and the BPSO algorithm. It can be seen from Figure 4 that the performance of the GA-BPSO algorithm is better than those of the ant colony algorithm, the particle swarm algorithm and the binary particle swarm algorithm. The ant colony algorithm, the particle swarm algorithm and the binary particle swarm algorithm all converge to the local optimal solution and do not find the global optimal solution. The GA-BPSO algorithm has lower fitness and faster convergence speed. The particle swarm optimization algorithm converges after 28 iterations, the binary particle swarm optimization algorithm converges after 19 iterations, and the improved binary algorithm converges after 5 iterations.

Table 1. Reconstruction results of a distribution network without distributed power sources.

	Disconnect Branch Combination	Active Network Loss/kW	Minimum Node Voltage/(p.u.)	Voltage Offset/(p.u.)	Switching Frequency
Pre-reconfiguration	33, 34, 35, 36, 37	202.6471	0.9131	0.13438	\
After reconfiguration	7, 9, 14, 32, 37	139.4731	0.9378	0.08503	8

lists the reconstruction results of the distribution network before and after reconstruction, where the reconstructed data were obtained by using GA-BPSO for reconstruction. According to the table, the network loss after reconstruction is 139.4731 kW, which is 31.4% lower than the 202.6471 kW from before the reconstruction. The minimum node voltage increased from 0.9131 p.u. to 0.9378 p.u., an increase of 2.63%. The voltage offset decreased from 0.13438 p.u. to 0.08503 p.u., a decrease of 36.72%. Figure 5 shows the voltage curves of each node before and after reconstruction, indicating a certain improvement in node voltage. This indicates that using the method proposed in this article for distribution-network reconstruction can effectively reduce network losses and provide some support for node voltages. At the same time, the GA-BPSO algorithm used in this article has better search ability and convergence speed.

4.2. Reconstruction with Distributed Power Sources

To verify whether the algorithm proposed in this article is applicable to the optimization and reconstruction of distribution networks containing distributed power sources, five distributed power sources were connected to the system, with access nodes including node 6, node 13, node 18, node 22, and node 25. The installed capacity and active output of 5 distributed power sources were 400 kVA and 300 kW. During simulation analysis, the power node was treated as a PQ node for processing. We used the algorithm proposed in this article to optimize and reconstruct the distribution system and obtain the reconstructed topology structure, as shown in Figure 6.

The relevant parameters of the distribution network before and after reconstruction with distributed power sources are shown in

Table 2. Distribution-grid-reconfiguration results with distributed power sources.

	Disconnect Branch Combination	Active Network Loss/kW	Minimum Node Voltage/(p.u.)	Voltage Offset/(p.u.)	Switching Frequency
Pre-reconfiguration	34, 35, 36, 37, 38	114.3275	0.9321	0.11762	\
After reconfiguration	8, 14, 33, 34, 35	51.5273	0.9461	0.07034	6

and Figure 7. The output of five distributed power sources are as follows: the DG output at node 6 is 91.0 kvar, the DG output at node 13 is 104.6 kvar, the DG output at node 18 is 62.7 kvar, the DG output at node 22 is 102.9 kvar, and the DG output at node 25 is 103.6 kvar. Based on Table 1 and Table 2, it can be seen that after the IEEE33 node is connected to the distributed power source, the active power loss decreases from 202.6471 kW to 114.3275 kW, and the minimum node voltage increases from 0.9131 p.u. to 0.9364 p.u. After the method described in this article was used to reconstruct and optimize the distribution network system, the active power loss decreased to 51.5273 kW, a decrease of 74.57%, the lowest node voltage increased to 0.9461 p.u., an increase of 3.61%, and the voltage offset decreased to 0.07034, a decrease of 47.66%. From our simulation results, it can be seen that although the voltage levels of each node have been significantly improved after the introduction of distributed power sources, the improvement in network losses is not significant. After using the method described in this article for reconstruction, the node voltage level has been significantly improved, and the active power loss has also been further reduced. This indicates that our proposed algorithm can effectively optimize and reconstruct the distribution network, improving its efficiency and performance.

5. Conclusions

In this paper, an improved binary particle swarm optimization algorithm (GA-BPSO) is proposed to study the multi-objective optimization reconfiguration problem of a distribution network with distributed generation. It was found that the algorithm effectively improves the global search ability and convergence speed by including the strategy of the genetic algorithm and reduces the risk of falling into a local optimum. Through the simulation of the IEEE33 node system, it was proved that GA-BPSO algorithm has a significant effect in reducing network loss, improving voltage level and optimizing distributed power output. Based on these findings, we can infer that the algorithm is universal and may be applicable to larger scales or different types of distribution-network reconfiguration problems. However, in order to further promote the findings of this study, future research should focus on dynamic reconfiguration, consider the volatility of load and distributed power output, evaluate the robustness of the algorithm, and apply it to the actual power grid. In addition, research should also consider environmental impact and sustainability, as well as integrated applications with other smart-grid technologies to achieve more comprehensive grid optimization.