Power distribution network primary and secondary collaborative planning method and system based on whale optimization algorithm

Abstract

The application discloses a power distribution network primary and secondary collaborative planning method and system based on a whale optimization algorithm. Multiple fault scenarios are constructed and classified, each fault scenario containing one or more lines; the fault recovery time of users under each type of fault scenario is calculated; a power distribution network primary and secondary network architecture collaborative planning model is constructed, which is used to calculate the optimal configuration of primary equipment and secondary equipment when the power outage loss and network loss of users under the fault scenario are the lowest; and the whale optimization algorithm is used to solve the power distribution network primary and secondary network architecture collaborative planning model to obtain the optimal configuration of the primary equipment and the secondary equipment of the power distribution network when the objective function is the minimum. Through the introduction of randomness and diversity operations, and the adjustment of the parameter balance of exploration and utilization ratio, the application can efficiently handle faults under various weather scenarios, solve the fault problems that may occur to distributed photovoltaic power sources and other power distribution network equipment under various weather scenarios, and thus significantly improve the reliability and stability of the system.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of photovoltaic power distribution network, and particularly relates to a power distribution network primary and secondary collaborative planning method and system based on whale optimization algorithm. BACKGROUND

[0002] In the power system, the primary equipment refers to the high-voltage electrical equipment directly used for producing, transmitting and distributing electric energy, and the secondary equipment refers to various auxiliary equipment for monitoring, measuring, controlling and protecting the primary equipment. The primary and secondary collaborative planning in the power distribution network can make the calculation of the primary equipment related indexes more accurate, and fully exert the auxiliary role of the secondary equipment.

[0003] With the development of the power distribution network and the improvement of the reliability requirement of the power grid, the coordinated planning of the primary and secondary equipment of the power distribution network has more and more important significance. However, in the traditional power distribution network planning, the primary and secondary planning work is isolated from each other, and lacks the interconnection relationship of mutual benefit. In the aspect of primary equipment planning, some researchers have established a multi-objective optimization planning model to plan the power grid line, effectively improving the TSC value of the power distribution network and the voltage quality of the power distribution network; some researchers plan the location and capacity of the distributed power supply from the perspective of user satisfaction and distributed power supply economy. In the aspect of secondary planning, some researchers have proposed a method for optimizing the configuration of fault indicators and sectional switches in the branch power distribution network, and some researchers have considered the objectives of cost minimization, redundancy and efficiency maximization, and proposed a method for solving the optimal PMU layout to reduce the total number of PMUs required for network complete observation.

[0004] The current research mainly focuses on the separate planning of the primary equipment and the secondary equipment, and there are some gaps in the primary and secondary system collaborative planning. With the gradual development of the distributed power supply mode, the large-scale access of distributed photovoltaic to the power distribution system will have an impact on the power flow, voltage distribution, power supply reliability, power quality and protection control of the power distribution network. At the same time, in the extreme weather scenario, the fault scenarios of the distributed photovoltaic power distribution network system show diversity and uncertainty. The traditional power distribution management system is slightly insufficient in monitoring the primary power grid energy flow and the protection and control ability of the secondary information flow. SUMMARY

[0005] In order to optimize the planning and management of the power grid, realize the accurate perception and optimal control of the operation of the power distribution network, improve the operation efficiency of the power grid, reduce the waste of energy and reduce the cost of energy supply, solve the problem of unstable power supply of the power distribution network in the large-scale access of distributed photovoltaic, and put it into the consideration range of planning and management, in order to realize more reliable, efficient and sustainable operation of the power distribution network, the present application proposes a power distribution network primary and secondary collaborative planning method and system based on whale optimization algorithm.

[0006] Whale Optimization Algorithm (WOA) is a heuristic optimization algorithm inspired by the behavior of whales in nature. The algorithm has excellent global search capability by introducing randomness and diversity operations. At the same time, by adjusting the algorithm parameters, it can balance the proportion of exploration and utilization, and show good adaptability, suitable for integrating primary equipment and secondary equipment planning, ensuring that they work in coordination and cooperation, while effectively solving the problem of unstable power supply of distribution network when large-scale distributed photovoltaic is accessed.

[0007] A power distribution network primary-secondary collaborative planning method based on whale optimization algorithm, which realizes one of the purposes of the application, comprises:

[0008] A plurality of fault scenarios are constructed and classified, each fault scenario containing one or more lines; the fault recovery time of users under each type of fault scenario is calculated;

[0009] A power distribution network primary-secondary network architecture collaborative planning model is constructed, which is used to calculate the optimal configuration of primary equipment and secondary equipment when the power loss of users and the network loss under fault scenarios are the lowest;

[0010] The whale optimization algorithm is used to solve the power distribution network primary-secondary network architecture collaborative planning model to obtain the optimal configuration of the primary equipment and the secondary equipment of the power distribution network when the objective function is the lowest.

[0011] Further, the objective function of the power distribution network primary-secondary network architecture collaborative planning model comprises:

[0012]

[0013] In the formula:

[0014] weight k is the weight of the kth type of fault scenario;

[0015] G is the total number of fault scenarios;

[0016] is the fault recovery time of user i under the kth type of fault scenario;

[0017] W is the set of all users;

[0018] r i is the load of user i;

[0019] C out is the average cost of unit power outage loss;

[0020] P loss is the total network loss;

[0021] σ is the network loss optimization coefficient.

[0022] Further, the constraint conditions of the power distribution network primary and secondary network architecture collaborative planning model include:

[0023] C D Ginv +C D Gom +C DTinv +C DTom ≤B

[0024] p DGi -∑ i∈W r i -p loss >0

[0025]

[0026]

[0027] In the formula:

[0028] C D Ginv , C D Gom , C DTinv and C DTom respectively represent the investment cost of the power distribution network, the operation and maintenance cost of the power distribution network, the investment cost of the power distribution terminal and the operation and maintenance cost of the power distribution terminal;

[0029] B is the maximum budget of the equipment;

[0030] P DGi is the photovoltaic power output of island i;

[0031] W is the set of all users;

[0032] r i is the load of user i;

[0033] p loss represents the network loss of island;

[0034] is the maximum capacity of the power distribution network;

[0035] P i is the active power of node i in the distributed photovoltaic;

[0036] π(i) represents the parent node of node i;

[0037] represents the operating state from node k to node i;

[0038] Ω represents the power supply node.

[0039] Further, the capacity and position of the distributed power supply in the primary equipment and the position and type of the power distribution terminal in the secondary equipment are taken as the position vectors of the whales in the whale optimization algorithm.

[0040] Further, the method for constructing multiple fault scenarios comprises:

[0041] According to the fault rate of the line under different weather scenarios, a non-sequential Monte Carlo simulation method is used to simulate the operation of the line to generate a fault scenario set, the fault scenario set contains multiple fault scenarios, each fault scenario contains one or more lines and their fault states, and the non-sequential Monte Carlo simulation determines whether each line fault state is normal by sampling the corrected line fault rate λ.

[0042] Further, it also includes correcting the line fault rate according to the weather scenario, and the correction method comprises:

[0043] λ=λ0[ρ+σe η(Q-ω) ]Q≥ω

[0044] In the formula:

[0045] λ is the line fault rate corrected based on real-time weather conditions;

[0046] λ0 is the initial fault rate of the line;

[0047] ρ, σ and η are set parameters for correcting the line fault rate;

[0048] Q is the value of the comprehensive meteorological factor; the larger the value of the comprehensive meteorological factor, the greater the risk of weather to the transmission line, and the greater the influence on the line fault rate;

[0049] ω is the minimum threshold of the comprehensive meteorological factor for the line fault rate to meet the health index model.

[0050] Further, it also includes screening the fault scenarios in the fault scenario set and extracting typical fault scenarios, and the method comprises:

[0051] Hierarchical clustering is performed on the similarity between each two fault scenarios as the distance between clustering variables to obtain multiple clusters;

[0052] The proportion of the number of fault scenarios contained in each cluster to the total number of fault scenarios is calculated, and the proportion is taken as the weight of the cluster;

[0053] Each fault scenario in each cluster is traversed, the sum of the similarity between each fault scenario and other fault scenarios in the cluster is calculated, and the fault scenario with the smallest sum of similarity is selected as the typical fault scenario extracted from each cluster.

[0054] Further, the method for calculating the similarity between each two fault scenarios comprises:

[0055] The sum of the nearest fault distances between all lines in the fault scenario m and another fault scenario n is obtained

[0056] Sum of all lines in fault scenario n and the nearest fault distance of fault scenario m

[0057] ER m and ER n are the set of fault lines in fault scenario m and fault scenario n respectively;

[0058] FD i,n represents the nearest fault distance from fault scenario n to fault line i;

[0059] FD k,m represents the nearest fault distance from fault scenario m to fault line k;

[0060] and The sum of the two fault scenarios m and n is the similarity.

[0061] Further, the calculation method of the distance between two lines includes:

[0062] According to the length of each line, the electrical distance between two lines i and j is calculated; the calculation method includes:

[0063]

[0064] In the formula:

[0065] D ij is the electrical distance between line i and line j;

[0066] B ij is the set of the shortest lines from line i to line j;

[0067] h m is the length of line m.

[0068] The sum of the shortest electrical distance from line i to line j or the sum of the shortest electrical distance from line j to line i is taken as the distance between lines i and j.

[0069] A power distribution network primary and secondary collaborative planning system based on whale optimization algorithm for achieving the second purpose of the application, comprising a fault recovery time calculation module, a power distribution network primary and secondary network frame collaborative planning model construction module and an optimal configuration solution module of primary and secondary equipment;

[0070] The fault recovery time calculation module is used to construct multiple fault scenarios and classify them, each fault scenario containing one or more lines; the fault recovery time of users under each type of fault scenario is calculated;

[0071] The power distribution network primary and secondary network architecture collaborative planning model construction module is configured to construct a power distribution network primary and secondary network architecture collaborative planning model, which is used to calculate the optimal configuration of primary equipment and secondary equipment when the power loss of users and the network loss are lowest under a fault scenario.

[0072] The optimal configuration of primary and secondary equipment solving module is configured to solve the power distribution network primary and secondary network architecture collaborative planning model by using a whale optimization algorithm to obtain the optimal configuration of primary equipment and secondary equipment in the power distribution network when the value of the objective function is the lowest.

[0073] The beneficial effects of the present application include:

[0074] 1. By introducing randomness and diversity operations, and adjusting the balance of exploration and utilization of parameters, the system can efficiently handle faults under various weather scenarios and ensure the reliability and stability of the power distribution network system.

[0075] 2. The problem of possible faults of power distribution network equipment under various weather scenarios is solved, thereby significantly improving the reliability and stability of the system. By using meteorological data and failure rates, the influence of different weather conditions on the power distribution network system is simulated, and based on the above typical scenarios and fault outage time calculation model, a power distribution system primary and secondary collaborative planning model is built. By using the global optimization ability of the whale optimization algorithm in this model and fully considering diversified solutions, high-quality solutions can be found in the complex search space. Through iteration and adaptive mechanism, the algorithm constantly adjusts the search strategy and gradually approaches the optimal solution, better balancing the exploration possibility and the use of known information, thereby improving the efficiency and accuracy of the power distribution network primary and secondary collaborative planning.

[0076] 3. By using the whale optimization algorithm to solve the primary and secondary collaborative planning model, the operation state of the power distribution network equipment can be quickly adjusted under various weather conditions to deal with problems such as photovoltaic component damage and line faults. This greatly shortens the fault repair time, significantly reduces the system outage time, and improves the power supply reliability of users. At the same time, it reduces system loss and energy cost, bringing significant planning effects to the power distribution network system. BRIEF DESCRIPTION OF DRAWINGS

[0077] Figure 1 is the whale optimization algorithm flowchart of the embodiment of the present application;

[0078] Figure 2 is the typical power distribution network topology of the embodiment of the present application;

[0079] Figure 3 is the contraction and enclosure mechanism of the embodiment of the present application;

[0080] Figure 4Spiral update position of the embodiment of the application. DETAILED DESCRIPTION

[0081] The following detailed description is provided as an enabling teaching of the technical solutions of the claims of the present application, in order to allow those skilled in the art to understand the technical solutions of the claims of the present application. The protection scope of the present application is not limited to the following specific implementation structure. The technical solutions of the claims of the present application that are different from the following specific implementation are also within the protection scope of the present application, which are made by those skilled in the art.

[0082] 1. Generating a typical fault scenario

[0083] The power distribution network in the embodiment is a distributed photovoltaic power distribution network. Since weather can affect multiple line devices such as photovoltaic power supply and thus affect the fault rate of the line, the fault rate of the power line is corrected according to meteorological data:

[0084] λ=λ0[ρ+σe η(Q-ω) ] Q≥ω (1)

[0085] In the formula:

[0086] λ is the line fault rate corrected based on real-time weather conditions;

[0087] λ0 is the initial fault rate of the line. In the embodiment, the initial fault rate is derived from historical real data;

[0088] ρ, σ, and η are parameters for correcting the line fault rate;

[0089] Q is a comprehensive meteorological factor. Each meteorological factor (including air temperature, air flow, air humidity, air pressure, etc.) is respectively standardized, and the entropy value and weight are calculated to obtain; the greater the value of the comprehensive meteorological factor, the greater the risk of weather to the power transmission line, and thus the greater the impact on the line fault rate;

[0090] ω is the minimum threshold of the comprehensive meteorological factor for the line fault rate to meet the health index model; when Q < ω, the impact of weather on the power transmission line is not considered;

[0091] In the embodiment, ρ = 1, σ = 3.4491, η = 1.1989, and ω = 0.2.

[0092] According to the fault rate of the line under different weather scenarios, a non-sequential Monte Carlo simulation method is used to simulate the operation of the line to generate a fault scenario set. The fault scenario set includes the fault state of each line in multiple fault scenarios. In the embodiment, each line is a simulated line based on an IEEE example. The non-sequential Monte Carlo simulation determines the state S m of each line whether normal or not, as shown in the following formula:

[0093]

[0094] wherein:

[0095] S m represents the state of line m, 1 for normal, 0 for fault;

[0096] U m is the failure rate of the mth line, in this embodiment a random number between 0 and 1, L is the set of lines.

[0097] In order to reduce the complexity of subsequent calculations, the generated fault scenarios are clustered and reduced, and typical fault scenarios are extracted.

[0098] First, the similarity of each fault scenario is calculated, and the specific steps are as follows:

[0099] 1) Calculate the electrical distance between two lines according to the length of each line in the region:

[0100]

[0101] wherein:

[0102] D ij is the electrical distance between line i and line j;

[0103] B ij is the set of shortest lines from line i to line j;

[0104] h m is the length of line m, in km.

[0105] 2) Calculate the similarity of each two fault scenarios:

[0106] The similarity between fault scenarios is calculated according to the nearest fault distance (denoted by FD) of the fault lines in the fault scenario. When calculating the similarity between fault scenario m and fault scenario n, find the fault line j in fault scenario n that is closest to line i in fault scenario m in terms of electrical distance, and then calculate the distance between the two lines, as follows:

[0107]

[0108] wherein:

[0109] ER n denotes the set of fault lines in fault scenario n;

[0110] FD i,n denotes the nearest fault distance from fault scenario n to fault line i.

[0111] The sum of the nearest fault distance (FD value) of all fault lines in m and n in the fault scenario is added to obtain the similarity of the two scenarios:

[0112]

[0113] In the formula:

[0114] P m,n is the similarity between the two fault scenarios m and n;

[0115] ER m and ER n are the sets of fault lines in the fault scenario m and the fault scenario n, respectively.

[0116] Then, each fault scenario is regarded as a clustering variable to be classified, and the similarity of the two fault scenarios is regarded as the distance between the clustering variables, and hierarchical clustering is performed.

[0117] After the fault scenarios are classified into several classes, the proportion of each class of fault scenarios in the total number of fault scenarios is calculated and used as the weight of the fault scenario for subsequent calculation of the objective function:

[0118] weight k = N k / N (5)

[0119] In the formula:

[0120] weight k is the weight of the kth class of fault scenarios;

[0121] N k is the number of fault scenarios included in the kth class of fault scenarios;

[0122] N is the total number of fault scenarios.

[0123] Finally, on the basis of clustering, a method based on the total similarity distance within the class (denoted by DC) is used for scenario number reduction. The sum of the similarity between the scenario m in the kth class of fault scenarios and all other fault scenarios in the same class is obtained by the following formula:

[0124]

[0125] In the formula:

[0126] DC m,k denotes the total similarity distance of the scenario m in the kth class of fault scenarios and other fault scenarios within the class;

[0127] M k is the set of the kth class of fault scenarios;

[0128] P m,nsimilarity between fault scenarios m and n;

[0129] For all fault scenarios in the kth fault scenario type, the fault scenario with the minimum DC value is selected as the typical fault scenario (denoted as F k The set of fault lines in the kth typical fault scenario is denoted as FL k .

[0130] 2. Calculation model of user fault recovery time under fault condition

[0131] In power grid, the installation of distributed power and distributed terminal will affect the outage loss time of users. Figure 2 A typical distribution network topology is shown in the figure. It contains distributed power, circuit breaker and tie switch.

[0132] When calculating the outage time, the main path and sub-path of the user need to be determined. The main path is defined as the shortest path from the user to the power point. The sub-path is the path other than the main path.

[0133] 1) Calculate the fault recovery time in the user sub-path

[0134] When the line on the user sub-path fails, the island can be formed by operating the circuit breaker. The operation of the island is relative to the network operation. The island refers to a local independent system temporarily disconnected from the main network operation. The distributed power (DG) supplies power to the users in the island. When the sub-path of the user fails, the circuit breaker and distribution terminal installed on the line in the sub-path terminal search set can isolate the fault. The sub-path terminal search set is defined as: when line l fails and user i is disconnected, find the intersection point of the main path of the user at the end of the fault line and the main path of user i; search for the shortest path from the intersection point to the fault line l. The searched path is the sub-path terminal search set SP i,l .

[0135] The specific fault recovery duration can be divided into the following cases: when the user is not in the DG island, and there is no circuit breaker installed on the line of the sub-path terminal search set, the user needs to wait until the power supply is restored after the fault is recovered, as shown in formula (7); when the user is in the DG island, and a circuit breaker is installed on the line of the sub-path terminal search set, but no distribution terminal is installed, the user needs to wait until the fault is located, manually operate the circuit breaker to isolate the fault to form an island, and obtain power supply, as shown in formula (8); when the user is in the DG island, and a distribution terminal without remote control function is installed on the line of the sub-path terminal search set, but a distribution terminal with remote control function is not installed, the user needs to manually operate the circuit breaker to isolate the fault, and similarly, if the island switch does not install a distribution terminal with remote control function, the user needs to manually operate to obtain power supply, as shown in formula (9); when the user is in the DG island, and a circuit breaker with remote control function and a distribution terminal are installed on the line of the path terminal search set, the user can quickly restore the power supply, as shown in formula (10):

[0136]

[0137]

[0138]

[0139]

[0140] In the formula:

[0141] t

[0142] t repair , t loc and t iso represent the time of fault repair, fault location and manual switch operation, respectively;

[0143] t

[0144] and t represent the installation state of the circuit breaker, the distribution terminal without remote control function and the distribution terminal with remote control function of line m, respectively;

[0145] t

[0146] and t represent the installation state of the distribution terminal without remote control function and the distribution terminal with remote control function of the island switch of user i, respectively.

[0147] 2) Calculate the recovery time of the user main path fault

[0148] When a line on the user main path fails, an island can be formed by operating the circuit breaker, and the DG can supply power to the users on the island. At the same time, due to the blocking of the power supply path of the main power supply, after repairing the failed line or transferring the load, the power supply of the user can be restored. In order to transfer the load, the fault should be isolated first. When using a switch to isolate the fault and calculate the impact of the distribution terminal, the main path terminal search set is defined: when the line l fails and the user i is powered off, the intersection of the main path of the user at the end of the fault line l and the main path of the user at the head of the tie line for transfer needs to be found; search for the shortest path from the intersection to the fault line l, and the searched path is part of the main path terminal search set Another part of the main path terminal search set Defined as the line set from the end of the fault line l to the user i.

[0149] The specific fault recovery time can be divided into the following cases: when the user is not in the DG island, and there is no circuit breaker installed on the main path terminal search set line, the user needs to wait for the fault to be repaired before the power supply can be restored, as shown in equation (11); when the user is in the DG island, but the distribution terminal is not installed on the island switch, the user needs to wait for the fault to be located, and manually operate the island switch to form an island to obtain power supply. Similarly, when the main path terminal search set line is installed with a circuit breaker but no distribution terminal, the time for fault location and manual switch operation is needed to isolate the fault, as shown in equation (12); when the user is in the DG island, and the island switch is installed with a distribution terminal without remote control function, the user needs to manually operate the island switch. Similarly, when the main path terminal search set line is installed with a circuit breaker without remote control function, the user needs to manually operate the switch to isolate the fault, as shown in equation (13); when the user is in the DG island, and the line on the path terminal search set is installed with a circuit breaker and a distribution terminal with remote control function, the user can quickly restore power supply, as shown in equation (14); after fault isolation, the tie switch can be used to transfer the load, as shown in equation (15):

[0150]

[0151]

[0152]

[0153]

[0154]

[0155] In the formula:

[0156] Indicates the installation status of the remote control function distribution terminal on the selected load transfer tie line;

[0157] Indicates the outage duration of user i when line l fails.

[0158] Finally, the fault recovery duration is defined as:

[0159]

[0160] where, is the fault recovery duration of user i under the kth fault scenario.

[0161] 3. Build a primary and secondary grid coordination planning model

[0162] A primary and secondary grid coordination planning model is built, which is used to optimize the planning objective in the background of the typical fault scenario and user fault recovery duration calculation model described above. The objective function of the coordination planning model is to minimize the weighted annual outage loss and network loss under multiple typical fault scenarios. The related parameters of the model are as follows:

[0163] 1) Objective function

[0164] In the power distribution system, the decision variable of the primary planning is the capacity and location of the distributed power supply; the decision variable of the secondary planning is the location and type of the distribution terminal. The planning objective is to minimize the weighted annual outage loss and network loss under multiple typical scenarios:

[0165]

[0166] where,

[0167] G is the total number of fault scenarios;

[0168] weight k is the weight of the kth fault scenario, and the specific algorithm is shown in formula (5);

[0169] is the fault recovery duration of user i under the kth fault scenario, and the specific algorithm is shown in formula (16);

[0170] W is the set of all users;

[0171] r i is the load of user i;

[0172] C out is the average cost of unit power outage loss;

[0173] P loss is the total network loss;

[0174] σ is a net loss optimization coefficient.

[0175] 2) Constraint

[0176] The budget of the distributed photovoltaic and distribution terminal is limited to the following formula:

[0177] C D Ginv +C D Gom +C DTinv +C DTom ≤B (18)

[0178] In the formula:

[0179] C D Ginv , C D Gom , C DTinv and C DTom respectively represent the distributed photovoltaic investment cost, distributed photovoltaic operation and maintenance cost, distribution terminal investment cost and distribution terminal operation and maintenance cost;

[0180] B is the maximum budget of the equipment.

[0181] The power balance on the island:

[0182] p DGi -∑ i∈W r i -p loss >0 (19)

[0183] In the formula:

[0184] P DGi is the photovoltaic power output of island i;

[0185] W is the set of all users;

[0186] p loss represents the net loss of the island.

[0187] The installation capacity constraint of a single distributed photovoltaic:

[0188]

[0189] In the formula:

[0190] is the maximum capacity of the distributed photovoltaic;

[0191] P i is the active power of node i in the distributed photovoltaic;

[0192] π(i) represents the parent node of node i.

[0193] Topology constraint of distribution network:

[0194]

[0195] wherein:

[0196] represents the operation state from node k to node i, and represents the power supply node.

[0197] 4. Solving the power distribution network and secondary network architecture collaborative planning model

[0198] The whale optimization algorithm (WOA) is an intelligent swarm algorithm simulating the surrounding and hunting of a whale group, has the advantages of few parameters and easy implementation, and has higher solution accuracy and speed than the particle swarm algorithm and the gravitational search algorithm. The whale optimization algorithm is used to solve the power distribution network and secondary network architecture planning model, different dimensions of a whale position vector are used to represent the installation of a distributed photovoltaic and a terminal, in the optimization process of the algorithm, the whale position is constantly adjusted, that is, the capacity and position of the distributed power supply and the position and type of the power distribution terminal are constantly adjusted, and finally the optimal whale position vector is found to achieve the optimization target of minimizing the weighted power failure loss and network loss.

[0199] The meanings of different dimensions of the whale position vector are as follows:

[0200] For the dimension representing the distributed photovoltaic, a value greater than 0 and less than or equal to 1 represents the installation of one distributed photovoltaic, and the value can represent the active power output proportion of the photovoltaic power supply; a value of 0 represents no installation of the distributed photovoltaic.

[0201] For the dimension representing the distribution terminal, when the value is greater than or equal to 0 and less than 1, a terminal without remote control function is installed; when the value is greater than or equal to 1 and less than 2, a distributed terminal with a remote control terminal is installed.

[0202] In the WOA algorithm, the humpback whale in the search space is a candidate solution to the optimization problem, also known as a search agent, and WOA uses a group of search agents to determine the possible or approximate global optimal solution. The search process for a given problem starts from a group of random solutions, and the candidate solutions are updated through optimization rules until the final condition is met. The WOA algorithm can be divided into three main stages: surrounding hunting, bubble net attack and hunting prey.

[0203] 1) Surrounding hunting: In the initial stage, the humpback whale does not know the best position in the search space when the prey is surrounded. In WOA, the current best solution is considered as the target prey, and the whale closest to the prey, that is, the whale with the minimum objective function value calculated from its position vector, is considered as the best search agent. Then, other whale individuals approach the target prey and gradually update their positions. The above process is represented by equations (22) and (23):

[0204]

[0205]

[0206] where:

[0207] denotes the distance vector from the search agent to the target prey;

[0208] t is the current iteration number;

[0209] is the local optimal solution at the tth iteration, i.e., the best position of the current whale;

[0210] and are the position vectors at the (t+1)th iteration and the tth iteration, respectively, d is the dimension of the position vector; p denotes the number of installable distributed power sources; d-p denotes the number of installable power distribution terminals.

[0211] C and A are coefficient vectors, defined as follows:

[0212] C = 2 x r (24)

[0213] A = 2a x r - a (25)

[0214] where:

[0215] r is a random number between 0 and 1;

[0216] a represents a decreasing value related to the iteration number t, which gradually decreases from 2 to 0 as the iteration number increases;

[0217] t max maximum iteration number;

[0218]

[0219] 2) Bubble net attack (exploitation phase): The bubble net attack behavior of the whale is modeled based on the idea of shrinking the encircling circle and spiral position update.

[0220] Shrinking the encircling circle: Starting from equation (23), it can be seen that when |A| < 1, the encircling circle of the whale will shrink. This means that the whale individual will approach the prey at the current best position, i.e., swim around the prey in a gradually shrinking circle. The larger the value of |A|, the larger the step the whale will take, and vice versa. As shown in FIG. 2, it shows the approach from (X1, X2) to all possible positions in 2D space when 0 ≤ A ≤ 1. Figure 3 Spiral position update: Each humpback whale first calculates its distance from the current best whale, and then moves along a spiral path, as shown in FIG. 3.

[0221] FIG. 3 shows the spiral position update of the whale.​Figure 4 The mathematical model of the position updating process is described as follows:

[0222]

[0223] In the formula:

[0224] is a vector, representing the distance from the best position of the current whale to the current whale position at the tth iteration;

[0225] b is a constant;

[0226] l is a random number whose value is between -1 and 1.

[0227] In order to simultaneously imitate the two behaviors, it is assumed that the whales update their positions according to the possibility of the contraction path and the spiral path, respectively, which is 0.5, and it can be described as:

[0228]

[0229] In the formula, p is a randomly generated number between 0 and 1.

[0230] 3) Hunting for prey (exploration phase): In order to ensure that the approximate global optimal solution can be achieved, when |A|>1, the search agents are pushed away from each other. In this case, the position of the current optimal search agent will be replaced by a randomly selected search agent, and the position of the search agent in the exploration phase is updated according to the randomly selected search agent:

[0231]

[0232] In the formula, is the position vector of the randomly selected search agent.

[0233] The WOA execution process is summarized as follows: first, a specified number of whale populations are randomly generated, and the fitness value corresponding to each whale is calculated, then it is judged whether the current calculation satisfies the established iteration termination condition, if not, the position of each whale in the population is updated by using the above calculation method, and the position of the optimal whale in this update is recorded, otherwise the calculation is terminated, and the position of the whale corresponding to the historical optimal fitness value in the population is the configuration of the primary device and the secondary device, and the flow chart is as shown in Figure 1 .

[0234] It should be understood that the size of the serial number of each step in the above embodiment does not mean the order of execution, the execution order of each process should be determined according to its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present application.

[0235] The embodiment of the present application also provides a power distribution network primary and secondary collaborative planning system based on a whale optimization algorithm, comprising a fault recovery duration calculation module, a power distribution network primary and secondary network architecture collaborative planning model construction module and an optimal configuration solution module of primary and secondary equipment.

[0236] The fault recovery duration calculation module is used for constructing multiple fault scenarios and classifying them, each fault scenario containing one or more lines; and the fault recovery duration of users under each type of fault scenario is calculated.

[0237] The power distribution network primary and secondary network architecture collaborative planning model construction module is used for constructing a power distribution network primary and secondary network architecture collaborative planning model, which is used for calculating the optimal configuration of primary and secondary equipment when the power loss of users and the network loss under a fault scenario are the lowest.

[0238] The optimal configuration solution module of primary and secondary equipment is used for solving the power distribution network primary and secondary network architecture collaborative planning model by using a whale optimization algorithm, so as to obtain the optimal configuration of primary and secondary equipment in the power distribution network when the objective function is the lowest.

[0239] The contents not described in detail in the specification belong to the prior art known to those skilled in the art.

Claims

1. A method for primary and secondary collaborative planning of distribution networks based on the whale optimization algorithm, characterized in that, include: Construct and classify multiple fault scenarios, each fault scenario containing one or more lines; Calculate the user's fault recovery time for each type of fault scenario; A collaborative planning model for the primary and secondary network of the power distribution network is constructed. The model is used to calculate the optimal configuration of primary and secondary equipment when the power outage loss and network loss of users are minimized under fault scenarios. The whale optimization algorithm is used to solve the primary and secondary network collaborative planning model of the distribution network to obtain the optimal configuration of primary and secondary equipment in the distribution network when the objective function value is minimized. The objective function of the primary and secondary network collaborative planning model for the distribution network includes: ； In the formula: weight k Let be the weight of the k-th type of fault scenario; G represents the total number of fault scenarios; Let be the fault recovery time for user i under the k-th fault scenario; W represents the set of all users; The table shows the load of user i; The average cost per unit of power outage loss; Total network loss; This is the optimization coefficient for network loss; Methods for constructing multiple failure scenarios include: Based on the line failure rates under different weather scenarios, a non-sequential Monte Carlo simulation method is used to simulate line operation, generating a fault scenario set. This set contains multiple fault scenarios, each including one or more lines and their fault states. The non-sequential Monte Carlo simulation then modifies the line failure rate. Sampling is performed to determine whether the fault status of each line is normal.

2. The distribution network primary and secondary collaborative planning method based on the whale optimization algorithm as described in claim 1, characterized in that, The constraints of the primary and secondary network collaborative planning model for the distribution network include: ； ； ； ； In the formula: , , and These represent the investment cost of the distribution network, the operation and maintenance cost of the distribution network, the investment cost of the distribution terminal, and the operation and maintenance cost of the distribution terminal, respectively. B represents the maximum budget for the equipment; P DGi For the photovoltaic power output of island i; W represents the set of all users; For user i's load; For the island's network loss; P n For the installation capacity constraint of a single distributed photovoltaic system; This represents the maximum capacity of the distribution network. (i) represents the parent node of node i; P i Let be the active power of node i in a distributed photovoltaic system; This represents the operation state from node k to node i; Indicates a power node.

3. The distribution network primary and secondary collaborative planning method based on the whale optimization algorithm as described in claim 1, characterized in that, The capacity and location of distributed power sources in primary equipment, and the location and type of power distribution terminals in secondary equipment are used as the position vector of the whale in the whale optimization algorithm.

4. The distribution network primary and secondary collaborative planning method based on the whale optimization algorithm as described in claim 1, characterized in that, It also includes adjusting the line failure rate based on weather conditions, the adjustment method including: ； In the formula: This is the line failure rate corrected based on real-time weather conditions. It is the initial failure rate of the line; , and These are the setting parameters for correcting line failure rates; It is a comprehensive meteorological factor value; the higher the comprehensive meteorological factor value, the greater the risk that the weather poses to the transmission line, and the greater the impact on the line failure rate. It is the lowest threshold for the line failure rate to conform to the comprehensive meteorological factors of the health index model.

5. The distribution network primary and secondary collaborative planning method based on the whale optimization algorithm as described in claim 1 or 4, characterized in that, It also includes filtering fault scenarios from a fault scenario set to extract typical fault scenarios. Methods include: Hierarchical clustering is performed by using the similarity between two fault scenarios as the clustering variable to obtain multiple clusters; Calculate the proportion of the number of fault scenarios contained in each cluster to the total number of fault scenarios, and use this proportion as the weight of the cluster. Iterate through each fault scenario in each cluster, calculate the sum of similarities between each fault scenario and other fault scenarios within the same cluster, and select the fault scenario with the smallest sum of similarities as the typical fault scenario extracted from each cluster.

6. The distribution network primary and secondary collaborative planning method based on the whale optimization algorithm as described in claim 5, characterized in that, The methods for calculating the similarity between two failure scenarios include: Obtain the sum of the nearest fault distances between all lines in fault scenario m and another fault scenario n. ; Obtain the sum of the nearest fault distances between all lines in fault scenario n and fault scenario m. ; and These are the sets of faulty lines in fault scenarios m and n, respectively. This represents the shortest fault distance from fault scenario n to faulty line i; This represents the shortest fault distance from fault scenario m to faulty line k; and The sum represents the similarity between the two fault scenarios m and n.

7. The distribution network primary and secondary collaborative planning method based on the whale optimization algorithm as described in claim 6, characterized in that, The methods for calculating the distance between two lines include: Calculate the electrical distance between two lines i and j based on the length of each line; The distance between lines i and j is the sum of the shortest electrical distances from line i to line j or the sum of the shortest electrical distances from line j to line i.

8. A primary and secondary collaborative planning system for a distribution network based on the whale optimization algorithm, employing the method described in claim 1, characterized in that, It includes a fault recovery time calculation module, a distribution network primary and secondary network collaborative planning model construction module, and an optimal configuration solution module for primary and secondary equipment; The fault recovery time calculation module is used to construct and classify multiple fault scenarios, each fault scenario containing one or more lines; and to calculate the fault recovery time for users under each type of fault scenario. The distribution network primary and secondary network collaborative planning model construction module is used to construct the distribution network primary and secondary network collaborative planning model. The model is used to calculate the optimal configuration of primary and secondary equipment when the power outage loss and network loss of users are minimized under fault scenarios. The optimal configuration solution module for primary and secondary equipment is used to solve the collaborative planning model of the primary and secondary network of the distribution network using the whale optimization algorithm, so as to obtain the optimal configuration of primary and secondary equipment in the distribution network when the objective function is minimized.

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