Design of ant colony planning algorithms for multi-stage grids of distribution networks considering network resilience

Abstract

Network Destruction Resilience is the ability of a system to maintain good operation in the event of an external attack or internal failure. The resilience of distribution network is crucial to guarantee the reliability of power supply. In this paper, we design a planning algorithm considering network destructibility for the multi-stage ant colony planning problem of distribution networks. The method establishes the multi-stage network planning objective function of distribution network from the perspectives of total investment cost and annual operation cost of multi-node network frame, destruction resistance, active power and reactive network loss of distribution network, etc. Then based on the constraints of the model, the improved ant colony algorithm is used to solve the multi-stage network planning objective function of distribution network, and the results of the anti-termite colony planning of multi-stage network frame of distribution network are obtained. In order to verify the effectiveness of the algorithm, simulation experiments are carried out on real distribution network data. The results show that the proposed ant colony planning algorithm for multi-stage grid frames can effectively improve the destruction resistance of distribution networks, and reduce the total investment cost and annual operation cost of multi-stage grid frames, and reduce the network loss rate data of multi-stage grid frames of distribution networks after application. It provides an effective method for planning the distribution network.

Keywords

Network destruction resistance distribution network multi-stage grid ant colony planning algorithm heuristic functions

1. Introduction

The distribution network in the actual operation process, it may be affected by various factors [1], such as bad weather, equipment damage, etc., resulting in network failure or even paralysis. Therefore, how to improve the destruction resistance of the power supply is a hot issue in current research [2]. In the distribution network network planning, multi-stage network planning is a common planning method, which can comprehensively consider the needs and constraints of different stages to achieve the optimization of the network structure [3].

At present, many scholars have studied the distribution network structure planning, such as Selvaraj, M, etc. [4] proposed the floating photovoltaic system method based on the Black Widow optimization, which designed a unified power quality regulator to regulate the power quality of each node in the grid by obtaining the nodes of the floating photovoltaic system. The Black Widow optimization algorithm is used to adjust the system power when grid photovoltaic is connected to the grid, so as to realize the planning of distribution network structure. This method can improve the efficiency and reliability of floating photovoltaic system, but there may be problems such as insufficient consideration of network invulnerability and neglect of complex network topology. Snoeck, A et al. [5] proposed a high response last mile distribution network optimization method based on discrete simulation. This method first simulates the operation state of the distribution network in real time through discrete time scale, and then uses advanced optimization algorithms to optimize the rapid response of the last mile line, so as to ensure that power can be quickly restored in case of emergencies. This method can improve the responsiveness of the last mile distribution network, but there may be feasibility and economic problems, as well as data uncertainty problems. Rasheed, S et al. [6] proposed an efficient operation planning method for active distribution network based on embedded uncertainty and network reconfiguration. The method first established a distribution network model including uncertainty factors, and then used an optimization algorithm based on embedded uncertainty to solve it. In the aspect of network reconfiguration, this method adopts a fast network reconfiguration algorithm, which can reconstruct the distribution network in a short time to adapt to the changes of uncertainty. This method can improve the operation efficiency and robustness of the active distribution network, but there may be feasibility and economic problems, as well as insufficient consideration of network invulnerability. Sadeghi, S, et al. [7] proposed a two-stage planning method for distribution network synchronous distributed generation, which established a distributed generation configuration model and considered protection coordination indicators, such as the action time and action range of protection devices. This method may be problems of ignoring complex network topology and data uncertainty.

This paper proposes an ant colony planning algorithm for multi-stage network frames of distribution networks, which takes into account the network destruction resistance. The algorithm combines the ant colony algorithm with the multi-stage network planning, and takes into account the actual operating conditions and constraints of the distribution network, as well as the requirements of network destruction resistance. By simulating the foraging behavior of ants in nature, the algorithm can optimize the planning of multi-stage network frames for distribution networks [8], and improve the reliability and stability of the network.

2. Ant colony planning algorithm for multi-phase grids in distribution networks

2.1 Multi-stage grid modeling of distribution networks

The multi-stage network frame planning of distribution network includes two stages of economic and distribution network to meet the stable operation, under the consideration of the premise of destruction resistance of distribution network.

2.1.1 The objective function for cost planning of the main distribution network frame

Distribution network radiation range is wide, so its network erection line topology across the mountains, rivers, highways and other geographic areas, taking into account the impact of different geographic barriers to the distribution network main frame cost planning [9], the establishment of the planning objective function, the expression of the formula is as follows:

$\displaystyle F_{1}=\min({e_{I}+e_{O}})$ (1)

In the above formula, the $F_{1}$ denotes the minimum value of the sum of annual investment and operating costs of the main frame of the distribution network. $e_{I}$ and $e_{O}$ denote the annual investment cost of the main frame, respectively. The annual investment cost of the main frame is the equivalent annual value of the time value of money discounted by the investment cost of new lines, order $x_{i}$ represent the decision variable of the $i$ th grid line, $k_{i}$ indicates the tortuous coefficient of the $i$ th grid line, $A_{Di}$ denotes the geographical barrier factor, $L_{i}$ indicates the length of the line $i$ , then the formula of the annual investment cost $e_{I}$ of the medium main grid is as follows:

$\displaystyle e_{I}=x_{i}o_{t,i}k_{i}L_{i}A_{Di}\cdot y_{0}(1+y_{0})^{T_{i}}$ (2)

In the above formula, the $t$ denotes the type of distribution network line, $o_{t,i}$ is the investment cost of line $i$ per unit length in this type; $T_{i}$ is the service life cycle of line $i$ ; $y_{0}$ indicates the current annual interest rate on savings.

The annual operating cost of the main grid frame is calculated on the basis of the active power losses in the transmission lines during the transmission of electrical energy [10], order $\zeta_{\max,i}$ indicate the maximum annual load loss hours of the distribution line $i$ , $R_{i}$ represents the resistance of line $i$ , the formula of the annual operating costs $f_{O}$ of the main grid is as follows:

$\displaystyle e_{O}=\sum{x_{i}\tilde{o}3I_{i}^{2}k_{i}L_{i}R_{i}\zeta_{\max,i}}$ (3)

In the above formula, the $\tilde{o}$ indicates the net loss tariff. $I_{i}$ indicates the line current.

In order to guarantee the normal operation of the distribution network in the state of cost minimization of the distribution network [11], its constraints are set as follows:

(1) Upper and lower voltage constraints at distribution network grid nodes

Make $U_{j\max}$ and $U_{j\min}$ denote the maximum and minimum values of the voltage at the location of node $j$ under the distribution network frame in the normal operating state, then the upper and lower constraints on the voltage at the nodes of the distribution network grid is expressed as follows:

$\displaystyle U_{j\min}\leqslant U_{j}\leqslant U_{j\max}$ (4)

In the above formula, the $U_{j}$ represents the current voltage value at the position of the distribution network node $j$ .

(2) Upper and lower line current constraints

Make $I_{i\max}$ denote the maximum value of the transmission line current of the distribution network, and its minimum value is 0. The upper and lower limit constraints of the line current is expressed as follows:

$\displaystyle 0\leqslant I_{i}\leqslant I_{i\max}$ (5)

2.1.2 Distribution network reactive network loss planning objective function

In order to guarantee the normal operation of the multi-stage grid of the distribution network, the objective function of the reactive network loss planning objective function of this distribution network is expressed as follows:

$\displaystyle F_{2}=\min\{{P_{\textit{loss}}+\Gamma}\}\varepsilon$ (6) $\displaystyle\varepsilon=\frac{\sum\limits_{i=1}^{n}{U_{i}}}{\sum\limits_{i=1}% ^{n}{(U_{i\max}+U_{i\min})}}$ (7)

In the above formula, the $F_{2}$ denotes the minimum network loss value of the multi-stage grid of the distribution network. $\varepsilon$ denotes the node voltage crossing penalty term; the $U_{i}$ and $U_{i\max}$ and $U_{i\min}$ denote, respectively, the current voltage value of the node and the upper and lower values of the node $i$ ’s voltage.

Set the distribution network reactive network loss planning objective function power balance constraint, such that $P_{i}$ denotes the active power, the $G_{ij}$ is the value of the resistance between distribution network nodes $i$ and $j$ , the distribution network reactive network loss planning objective function power balance constraints is expressed as follows:

$\displaystyle P_{i}=U_{i}\left({\sum\limits_{j=1}^{N}{U_{j}G_{ij}\cos U_{ij}}+% \sum\limits_{j=1}^{N}{U_{j}C_{ij}\sin U_{ij}}}\right)$ (8)

In the above formula, the $U_{ij}$ denotes the voltage between node $i$ and $j$ ; and $C_{ij}$ denotes the value of the capacitance between node $i$ and $j$ .

2.1.3 Distribution network active power planning objective function

Let $P_{\textit{load}}$ denote the load power of the multi-stage grid of the distribution network, the $P_{\textit{DGi}}$ denotes the output power of distributed power sources within the multi-stage grid of the distribution network, then the expression formula of active power planning objective function $F_{3}$ of the distribution network is as follows:

$\displaystyle F_{3}=\max({P_{\textit{load}}+P_{\textit{loss}}})=\max\left[{% \left({\sum\limits_{i\in DG}{P_{\textit{DGi}}}+\sum\limits_{i\in MG}{P_{% \textit{MGi}}}}\right)+P_{\textit{grd}}}\right]$ (9)

In the above formula, the $P_{\textit{MGi}}$ denotes the interaction power between branches within the multi-stage grid of the distribution network; the $P_{\textit{grd}}$ indicates the value of the purchased power from the multi-stage grid of the distribution network to the higher grid.

The constraints for setting the active power planning objective function for the distribution network are as follows:

(1)

Let $P_{in}$ and $P_{\textit{out}}$ denotes the upper and lower output power limits of the multi-stage grid frame of the distribution network, then the expression formula of the interaction power constraints between the branches of the multi-stage grid frame of the distribution network is as follows:

$\displaystyle-P_{in}<P_{MG}<P_{\textit{out}}$ (10)

Among them, $P_{MG}$ represents the interaction power between the branches of the multi-stage grid of the distribution network.

(2)

The distributed power output constraints of distributed power sources in the multi-stage grid of the distribution network are expressed as follows:

$\displaystyle-P_{\textit{DGi}\_\min}<P_{\textit{DGi}}<P_{\textit{DGi}\_\max}$ (11)

Among them, $P_{\textit{DGi}\_\max}$ and $P_{\textit{DGi}\_\min}$ indicate the upper and lower output power limits of the distributed power supply.

2.1.4 Distribution network destruction resilience objective planning objective function establishment

Destruction resistance of distribution network refers to the recovery ability and stability of the distribution network when it suffers from faults or attacks, which can describe the ability of the distribution network to resist damage, in the process of optimizing the multi-stage network framework of the distribution network [12], it is necessary to take into account the destruction resistance of the distribution network, the cost of different stages of the distribution network, as well as the reactive network loss and active power for planning. In order to obtain the destruction resistance of the distribution network, the destruction resistance of the current distribution network structure is evaluated, and the detailed process is as follows:

The distribution network topology is described as an undirected graph, where the point set and edge set of the distribution network topology are given by $V$ and $E$ respectively, then the undirected graph of the distribution network topology is $G=(V,E)$ , within this undirected graph, the number of nodes and edges are given by $m$ and $n$ respectively. Set $W$ be the set of connecting edges $(i,j)$ distances from nodes $i$ and $j$ , which is expressed as follows:

$\displaystyle W=\{{w_{ij}>0|{i,j=1,2,\ldots,m}}\}$ (12)

Based on the elements in the set of Eq. (1), the adjacency matrix of the topological undirected graph, the matrix is represented by $A$ . The elements of this matrix are expressed as follows:

$\displaystyle A_{ij}=\left\{{\begin{array}[]{ll}w_{ij}&i\neq j\cup i\text{ and% }j\text{ are connected}\\ \infty&\text{else}\\ \end{array}}\right.$ (13)

Among them, $A_{ij}\in A$ .

Let $B_{i}$ represent the set of edges directly connected to the distribution network topology node $i$ , the edge weight calculation formula of the node is as follows:

$\displaystyle\omega_{i}=\sum\limits_{(i,j)\in B_{i}}{\frac{1}{w_{ij}}}$ (14)

Among them, $\omega_{i}$ denotes the edge weights of node $i$ .

Make $l_{ij}$ denote the minimum path distance between the distribution network topology node $i$ and $j$ , then the formula for calculating the positional importance of the current node $i$ is as follows:

$\displaystyle l_{i}=\frac{\sum\limits_{j=1,j\neq i}^{m}{l_{ij}}}{m}$ (15)

Among them, $l_{i}$ denotes the positional importance of node $i$ . From this formula, the higher the value of the positional importance of the node $i$ , the greater the role it plays within the distribution network topology and the more other nodes it connects [13].

Based on the results of Eqs (14) and (15), calculate the integrated importance $\Psi(i)$ of the distribution network topology node $i$ and expressed as follows:

$\displaystyle\Psi(i)=\frac{\omega_{i}}{l_{i}}$ (16)

By Eq. (16), the importance of all nodes in the undirected graph $G=(V,E)$ of the distribution network topology can be calculated, summed and processed to get the sum $\sum\limits_{i=1}^{m}{\Psi(i)}$ of the importance of all nodes. Based on the sum of these importance degrees [14], the destructive degree is calculated and expressed as follows:

$\displaystyle H(G)=\sum\limits_{i=1}^{m}{\Psi(i)}\cdot\frac{1}{\sum\limits_{i=% 1}^{m}{\Psi_{\textit{full}}(i)}}$ (17)

Among them, $H(G)$ denotes the degree of destruction resistance of the topological undirected graph of the distribution network; the $\sum\limits_{i=1}^{m}{\Psi_{\textit{full}}(i)}$ denotes the sum of node importance of distribution network topology nodes in fully connected state. In the fully connected state of the distribution network nodes the value of destruction resistance of the distribution network is 1. When there are individual nodes that are not connected, then, the $H(G)$ will have a value less than 1, and therefore, the range of value $H(G)$ is between 0 and 1. The closer the value of destruction resistance of the distribution network is to 1, the more resistant the distribution network is to destruction [15].

Considering the network destruction resistance of multi-node network frame of distribution network, based on Eq. (17), the maximum value of network destruction resistance of multi-stage network frame of distribution network is taken as the planning target, and the planning objective function of multi-stage destruction resistance of distribution network is established, and the expression formula is as follows:

$\displaystyle F_{4}=\max({H(G)})$ (18)

Combining the above steps, the planning objective function of the multi-stage grid mathematical model of distribution network is expressed as follows:

$\displaystyle F=F_{1}+F_{2}+F_{3}+F_{4}$ (19)

Multi-stage network planning for distribution networks can be realized by optimally solving Eq. (19) based on the constraints corresponding to the mathematical model.

2.2 Optimized solution of multi-stage grid model

After establishing the objective function of multi-stage grid planning for distribution networks, the mathematical model is optimized and solved by using the ant colony algorithm, and the ant colony algorithm has the problems of slow convergence in the early stage, unable to jump out of the local optimal region and sensitive to the pheromone volatilization, ant number and other parameters [16], and the improved ant colony algorithm is used to optimize and solve the multi-stage grid model of the cultivation unit, and the details are as follows. The detailed procedure is as follows:

The ant colony algorithm solves the problem characteristics according to Eq. (19), establishes the feasible solution space of the multi-stage grid model of the distribution network and generates a set of initial feasible solutions of the multi-stage grid model of the distribution network, and the initial feasible solutions satisfy all the constraints of the initial feasible solutions. The feasible solution in the feasible space is regarded as an ant running node, then there exists $n$ ant running nodes in the feasible solution space, placed simultaneously in the feasible solution space $m$ artificial ants, through the ants according to the pheromone concentration of optimization, can obtain the optimal solution of the multi-stage grid model of the distribution network. Let $t$ denote the moments, the feasible solution space complexity function $P(v)$ is introduced to improve the ant transition probability, then the probability $P_{uv}^{k}(t,t+1)$ of the $k$ th ant moving from the feasible solution $u$ to $v$ is expressed as follows:

$\displaystyle P_{uv}^{k}(t,t+1)=\left\{{\begin{array}[]{ll}P(v)^{-1}\cdot\frac% {[{\delta_{uv}(t)}]^{\alpha}[{\sigma_{uv}(t)}]^{\beta}}{\sum\limits_{w\in J_{k% }}{[{\delta_{uv}(t)}]^{\alpha}[{\sigma_{uv}(t)}]^{\beta}}}&J_{k}\in\textit{ % allowed}_{k}\\ 0&\text{other}\\ \end{array}}\right.$ (20)

In the above formula, the $\sigma_{uv}(t)$ denotes the heuristic function; the $\alpha$ and $\beta$ denote the pheromone concentration importance factor and the heuristic function importance factor, respectively; the $\delta_{uv}(t)$ denotes pheromone concentrations from a feasible solution $u$ to $v$ . $\textit{allowed}_{k}$ denotes the set of feasible solutions for the $k$ -th ant. By introducing the feasible solution space complexity function $P(v)$ , which can constrain the ants to choose the shortest path to run.

When searching for the optimal solution, artificial ants need to search globally in the feasible solution space, and design the bidirectional search strategy of the ant colony algorithm, i.e., set up two groups of ant colonies respectively, and start searching in parallel from the initial point and the end position of the feasible solution space at the same time [17]. Let $A$ and $B$ denote two groups of artificial ants respectively, each group has the same number of artificial ants, and a single ant within each of the two groups is labeled as $A_{r}$ and $B_{r}$ , when paired, form ant pairs $(A_{r},B_{r})$ , choose a set of ant pairs to start together from the feasible solution initial point and the end position respectively [18], and at the same time let $\textit{tabu}_{A_{r}}$ denotes the set of nodes of the location of the feasible solutions passed through $A_{r}$ , then the intersection of the two ants passing through the feasible solutions is expressed by the following formula:

$\displaystyle\Upsilon=\textit{tabu}_{A_{r}}\cap\textit{tabu}_{B_{r}}$ (21)

In the above formula, $\Upsilon$ represents the intersection of two ants $A_{r}$ and $B_{r}$ via feasible solutions; $\textit{tabu}_{B_{r}}$ represents the set of feasible solution position nodes via $B_{r}$ . When the result of Eq. (21) is not null, then it means that the ants that $A_{r}$ and $B_{r}$ encounter, at which point the search stops [19]. Walking path lengths $L_{A_{r}}$ and $L_{B_{r}}$ are calculated for ants $A_{r}$ and $B_{r}$ , based on the length of the path, calculate the total length $L$ of the ant’s walk. The formula is as follows:

$\displaystyle L=L_{A_{r}}+L_{B_{r}}$ (22)

The result of Eq. (22) is a solution of the multi-stage grid model of distribution network. However, when the result of Eq. (21) is empty, the search result of the pair of ants in the feasible solution space is discarded and another pair of ants is re-selected for searching [20].

The enlightening function of the ant colony algorithm can guide the moving direction of ants, and improve the adjacent relationship between nodes of the current multi-stage network model. The expression formula is as follows:

$\displaystyle\delta_{uv}=\left.\left(\frac{Q_{Su}}{Q_{SG}}\right)\right/(Q_{uv% }+Q_{vT})$ (23)

In the above formula, the $S$ and $G$ are the initial and end points of the feasible solution space; the $Q_{SG}$ is the distance between the initial point and the end point. $T$ denotes the location of the feasible solution goal; the $Q_{uv}$ denotes the distance from a feasible solution $u$ to the next feasible solution $v$ , the $Q_{Su}$ denotes the the distance between the initial point to a feasible solution $u$ . $Q_{vT}$ denotes the distance from the next feasible solution $v$ to the location of the feasible solution target $T$ .

Pheromone concentration is the key factor affecting the movement direction of ants, designing the ant colony algorithm adaptive pheromone concentration updating function, the process is as follows.

Make $\chi(Z)$ denote the volatilization factor of adaptive pheromone concentration, which is expressed as follows:

$\displaystyle\chi(Z)=\left\{{\begin{array}[]{ll}\frac{\chi_{0}\exp\left\{{-% \frac{Z^{2}}{2\sigma^{2}}}\right\}}{\sigma\sqrt{2\pi}}&Z\geqslant\omega\\ \chi_{0}&Z<\omega\\ \end{array}}\right.$ (24)

In the above formula, the $\chi_{0}$ denotes the initial pheromone concentration; the $Z$ denotes the number of ant colony iterations; the $\omega$ is a threshold for the number of iterations; the $\sigma$ denotes the pheromone volatilization constraint parameter.

The updated expression for the pheromone concentration of ants operating in the feasible solution space based on the results of Eq. (24) is given as follows:

$\displaystyle\delta_{uv}(t+1)=\delta_{uv}(t)\cdot(1-\chi(Z))+\Delta\delta_{uv}$ (25)

Among them, $\Delta\delta_{uv}$ is the pheromone concentration increment.

The detailed steps of the improved ant colony algorithm to find the multi-stage grid model of distribution network through the above path searching strategy and pheromone concentration updating method are as follows:

Step 1:

Initialization parameters, including the initial pheromone of the number of ants.

Step 2:

Build the solution space according to the characteristics of the problem.

Step 3:

Initial solution: according to the characteristics of the solution space, a group of initial solutions are randomly generated, which should meet the constraint conditions.

Step 4:

Iterative search, move in the feasible solution space according to the ant search strategy and pheromone concentration update method, record the current optimal solution, and then judge whether the current solution is globally optimal or whether the current iteration times are met, if so, output the optimal solution, otherwise continue to search until the stop condition is met.

3. Experimental analysis

A city distribution network as an experimental object, the city distribution network by two branches of the network frame, its network topology is shown in Fig. 1.

Figure 1.

Schematic diagram of distribution network topology.

There are 6 distributed photovoltaic accesses in the distribution network, including 2 distributed photovoltaic accesses in two branch grids, and a total of 25 nodes exist in the whole distribution network topology. The method of this paper is used to plan the multi-stage network frame of the distribution network and verify the application effect of the method in practice.

Calculating the annual operating cost of multi-stage network frame of distribution network is the basis of establishing the objective function of multi-stage network frame planning of distribution network, due to the wide range of distribution network erection, spanning different types of geography, test the method of this paper in the case of different geographic obstacle factors of multi-stage network frame of distribution network, the method of this paper calculates the annual operating cost of multi-stage network frame of distribution network, and the test results are shown in Fig. 2.

Figure 2.

Annual operating cost of multi-stage distribution network framework.

As can be seen from the analyzed Fig. 2, the results of calculating the annual operating costs of multi-stage grids of distribution grids using the methodology of this paper are in full agreement with the actual values, which further confirms the strong capability of the methodology of this paper in multi-stage cost planning of distribution grids. This method provides a reliable basis for the operation and management of distribution grids and helps to realize more efficient and economical grid operation.

In this paper, the method uses the improved ant colony algorithm to solve the multi-stage grid model of distribution network, and takes the path of ants to find the optimal path as a measure to test whether the ants can find the shortest path in the feasible solution space of the multi-stage grid model of distribution network, and the results are shown in Fig. 3.

By analyzing Fig. 3, it can be seen that the improved ant colony algorithm has the shortest value of multi-stage grid planning for distribution networks. This indicates that the path length from the starting point to the end point is the shortest, which proves that the method of this paper obtains the most accurate feasible solution in solving the model. This result further confirms the superiority of this paper’s method in multi-stage network planning for distribution networks.

In this paper, the method of multi-stage network planning of distribution network from the cost, distribution network destruction resistance and active power and reactive network loss and other stages, the following are from the above perspective on the practical application of the method of this paper to verify the effect. First of all, from the distribution network annual investment and total operating cost sum as a measure of indicators, test this paper after the application of the method, the distribution network two stages of the annual investment and total operating cost of the network frame compared with the same period of the previous year, the results are shown in Table 1.

Table 1

Cost planning results of multi stage grid model for distribution network

Cost		Stage 1 Grid	Stage 2 Grid
Total cost of the previous year	Original annual investment cost	204.55 (Ten thousand yuan)	183.66 (Ten thousand yuan)
	Original total operating cost	18.24 (Billion)	10.56 (Billion)
Compared to the same period	Current investment cost	2.31% (Ten thousand yuan)	1.36% (Ten thousand yuan)
last year, the decline rate	Current total operating costs	5.09% (Billion)	3.48% (Billion)

Figure 3.

Ant colony algorithm for solving the path of multi stage grid model in distribution network.

Analysis of Table 1 can be seen, using the method of this paper on the distribution network multi-stage network frame model planning, the distribution network multi-stage network frame of the current annual investment cost compared to the same period of the previous year decreased ratio of 231% million yuan and 136% million yuan, respectively, while the current total operating costs compared to the same period of the previous year decreased ratio of 5.09% of 100 million yuan and 348% of 100 million yuan. The above values show that: after applying the method of this paper to plan the cost stage of multi-stage network framework of distribution network, the total investment and operation cost and annual investment cost of multi-stage network framework of distribution network have been effectively reduced, which shows that the method of this paper has strong cost planning ability of multi-stage network framework of distribution network.

The network loss rate of the distribution network multi-stage network frame line operation as a measure of the index, test the line running time is different, the application of this paper’s method after the network loss rate changes, in order to make the experimental results more adequate, at the same time, using the reference [4] method, the reference [5] method, the reference [6] method and the reference [7] method to start the test, the test results are shown in Fig. 4.

Figure 4.

Changes in network loss rate after multi-stage network planning in distribution network.

By analyzing Fig. 4, it is obvious that the network loss rate of the multi-stage network structure of the distribution network increases with the increase of operation time. When comparing the five methods, the network loss rate of the method in this paper shows a slow and small growth trend when the distribution network operates in a multi-stage grid. More importantly, under the same running time, the network loss rate value after applying this method is significantly lower than that of other methods. This result shows that this method can effectively reduce the network loss rate of multi-stage distribution network structure, thus reducing the line loss. This not only proves the planning ability of this method for the total investment and operation cost of multi-stage distribution network, but also highlights its remarkable effect in practical application. By adopting the method in this paper, we can more effectively manage and optimize the operation of the multi-stage network structure of the distribution network, achieve energy conservation and emission reduction, and also save operating costs for enterprises.

Taking the fluctuation power of the multi-stage grid of the distribution network as a measurement index, and taking the distributed photovoltaic cells in the multi-stage grid of the distribution network as a measurement index, the fluctuation power of the multi-stage grid of the distribution network is tested to verify the change of the fluctuation power by the method of the present paper in the different cases of the loading state of the photovoltaic cells, and the results of the test are shown in Table 2.

Table 2

Fluctuation power changes (kW) of multi stage grid structures in distribution networks

State of charge value of photovoltaic cells%	Before planning	After planning
0.1	402.36	102.41
0.2	411.54	98.66
0.3	369.58	131.24
0.4	251.63	125.51
0.5	234.19	87.59
0.6	424.37	106.35
0.7	406.55	111.24
0.8	367.85	99.67

It can be seen from the analysis of Table 2 that the fluctuating power of photovoltaic cells under different state of charge values shows a significant reduction trend after the multi-stage grid planning of the distribution network using this method. This result means that through reasonable planning, the fluctuating power of the photovoltaic part in the distribution network has been effectively controlled, thus improving the stability of the power grid. This indirectly proves that the invulnerability of distribution network has been significantly improved through the planning of this method. This discovery has important practical significance for ensuring the stability and reliability of power supply.

To verify the anti-destruction performance of the multi-stage grid frame of the distribution network after the application of the method in this paper, 10 nodes of the multi-stage grid frame of the distribution network were used as experimental objects to calculate the anti-destruction values before and after the planning of the multi-stage grid frame of the distribution network, and the results are shown in Fig. 5.

Figure 5.

Test results of multi-stage network frame durability performance in distribution network.

By comparing the data in Fig. 5, it is obvious that the invulnerability of the multi-stage grid structure of the distribution network has been significantly improved after the application of the method proposed in this paper. Especially for the node coded 9, its invulnerability value has increased from about 0.8 to more than 0.95, indicating that the stability of the node in the face of failure or attack has been enhanced. This is due to the optimization design of the grid structure by the method in this paper, which improves the anti destruction performance of the whole distribution network multi-stage grid structure. Such improvement is of great significance to ensure the stability and security of power supply, especially in the complex and changeable power environment. Therefore, the method in this paper has a significant effect on enhancing the invulnerability of multi-stage distribution grids.

The network to be planned within the multi-stage network frame of the distribution network as an experimental object, the network node topology is shown in Fig. 6, using the method of this paper to plan the multi-stage network frame of the distribution network, the planning results are shown in Fig. 7, to analyze the practical application of the method of this paper.

Figure 6.

Topology of network nodes to be planned.

Figure 7.

Planning results of multi stage network structure nodes in distribution network.

Analysis of Fig. 6 shows that the use of this paper’s method of multi-stage network frame node planning for distribution networks, individual nodes are not directly connected to each other, but through the other nodes can be realized through the connection between each node, and at the same time after the planning of the entire network within the path less, can effectively save the distribution network multi-stage network frame of the annual operating costs and total investment costs. Taking node 5 as an example, the original planning line node 5 connects the nodes coded as 3, 4, 8, once node 5 fails, it will directly affect the normal operation of the nodes coded as 3, 4, 8, and after using the method of this paper for planning, even if the node 5 fails, the nodes 3, 4, 8 can still be connected through other nodes, so it strengthens the multi-stage network framework of the distribution network. Therefore, the damage resistance of the multi-stage grid is strengthened. In summary, the method of this paper has a strong ability to plan the nodes of the multi-stage network framework of the distribution network.

4. Conclusion

As an important part of the power network, the distribution network has a decisive influence on the reliability and stability of power supply. As a new type of optimization algorithm, the multi-stage network ant colony planning algorithm can simulate the pheromone transfer mechanism in the ant foraging process, and search for the optimal network structure scheme through continuous iterative updating. In this paper, an ant colony planning algorithm for multi-stage grid structure of distribution network is designed to consider the network destructibility. The algorithm firstly divides the distribution network into multiple phases, and then optimizes the network structure of each phase by using the ant colony planning algorithm. In the optimization process, not only the traditional indexes such as reliability and economy are considered, but also the destructive capability of the network, i.e., the recovery ability and stability of the network when it suffers from faults or attacks, is also taken into account. Through experimental verification, the algorithm is able to improve the destruction resistance. This provides a new idea and method for the design and optimization of power network. However, the algorithm still has some limitations, such as the optimization effect for large-scale networks needs to be further improved. Future research can improve and optimize the algorithm to address these shortcomings.

Data sharing agreement

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, author-ship, and/or publication of this article.

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