Site selection and sizing planning method and system based on improved multi-objective differential evolution

Abstract

The invention discloses a locating and sizing planning method and system based on improved multi-objective differential evolution, and relates to the technical field of electric power system planning and optimizing.The method comprises the steps that electric power system data are collected and processed, and the electric power system data comprise network topology, line parameters, load characteristics and generator set parameters; the method comprises the following steps: establishing a static var compensator locating and sizing planning model based on power system data, setting an objective function, and formulating a constraint condition set; a self-adaptive variation strategy and an elitism strategy are introduced, and a multi-target differential evolution algorithm is improved; according to the method, a self-adaptive variation strategy and an elitism strategy are introduced, and the improved multi-target differential evolution algorithm is combined, so that the searching capability and the convergence of the algorithm are greatly improved, and the optimal locating and sizing scheme is obtained. And the optimal solution can be more efficiently searched in the complex solution space.

Description

Technical Field

[0001] The present invention relates to the technical field of power system planning and optimization, and in particular to a method and system for site selection and capacity planning based on improved multi-objective differential evolution. Background Art

[0002] With the continuous development of power systems, power grids are becoming more and more intelligent and flexible. In order to enhance the flexibility of the system and improve the stability and efficiency of the power grid, flexible AC transmission system (FACTS) equipment has become more and more common in modern power systems. Electronically controlled FACTS devices can alleviate most of the problems related to power quality and network overload. In fact, FACTS devices can avoid the upgrade of network generation and transmission capacity by planning and effectively utilizing existing facilities. Therefore, FACTS devices have an increasingly greater impact on the system, and static reactive power compensators (SVCs), as one of them, are increasingly widely used in the system. As an important power device, SVC can effectively improve the power factor of the power grid, improve power quality, and reduce network losses. Therefore, SVC is widely used in load compensation and transmission line compensation (voltage and reactive power compensation) of modern power systems. Reasonable site selection and sizing of SVC in the power grid are of great significance to the stability and performance of the system, but existing research has explored few methods for SVC site selection and sizing. Summary of the invention

[0003] In view of the problems existing in the static VAR compensator (SVC) site selection and capacity determination methods in the prior art, the present invention is proposed.

[0004] Therefore, the problem to be solved by the present invention is how to optimize the site selection and sizing of static VAR compensators (SVCs) in complex power systems to minimize system losses and voltage deviations and improve system stability and efficiency.

[0005] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0006] In the first aspect, an embodiment of the present invention provides a site selection and sizing planning method based on improved multi-objective differential evolution, which includes collecting and processing power system data, the power system data including network topology, line parameters, load characteristics and generator set parameters; establishing a static VAR compensator site selection and sizing planning model based on the power system data, setting an objective function, and formulating a set of constraints; introducing an adaptive mutation strategy and an elite retention strategy to improve the multi-objective differential evolution algorithm; using the improved multi-objective differential evolution algorithm to optimize and solve the static VAR compensator site selection and sizing planning model to obtain the optimal site selection and sizing plan.

[0007] As a preferred solution of the site selection and capacity planning method based on improved multi-objective differential evolution described in the present invention, the specific formula of the objective function is as follows:

[0008] Min[PLOSS,V D ]

[0009] Where PLOSS is the system loss, V D is the voltage deviation, the specific formula is as follows:

[0010]

[0011] Among them, N b is the total number of branches, V m is the voltage at node m, V n is the voltage at node n, δ mn is the voltage phase angle between node m and node n, G b is the conductance of branch b.

[0012] As a preferred solution of the site selection and capacity planning method based on improved multi-objective differential evolution described in the present invention, the constraint condition set includes system constraints, SVC constraints, unit operation constraints, and power flow constraints.

[0013] The specific formula of system constraints is as follows:

[0014]

[0015] in, are the upper and lower limits of the voltage at node m, V m is the voltage at node m, is the maximum transmission capacity of line b, S b is the transmission capacity of line b;

[0016] The specific formula of SVC constraint is as follows:

[0017]

[0018] in, is the upper and lower limits of reactive power that SVC can compensate, Q SVC is the reactive power that the SVC can compensate;

[0019] The specific formula of unit operation constraints is as follows:

[0020] P max ≥P≥P min

[0021] Q max ≥Q≥Q min

[0022] Among them, P max , P min is the upper and lower limits of the active output of the generator set, Q max , Q min The upper and lower limits of reactive power output of the generator set;

[0023] The specific formula of power flow constraint is as follows:

[0024]

[0025] Among them, P m , Q m are the active and reactive output of node m, respectively, Fm , Q Fm are the active and reactive loads of node m, Q SVC is the reactive power that the SVC at node m can compensate, V m 、V n are the voltages at nodes m and n, respectively, s is the total number of nodes, Y mn is the element in the mth row and nth column of the admittance matrix.

[0026] As a preferred solution of the site selection and sizing planning method based on improved multi-objective differential evolution described in the present invention, wherein: improving the multi-objective differential evolution algorithm includes the following steps: designing a calculation formula for the adaptive scaling factor F and a calculation formula for the adaptive crossover probability CR; establishing an elite archive, which is used to store non-dominated solutions in each iteration; designing an elite archive update mechanism, which includes adding new non-dominated solutions and an archive clipping method based on non-dominated sorting and crowding calculation; formulating a strategy for elite individuals to participate in evolution, selecting a preset proportion of individuals from the elite archive to participate in mutation operations; designing an improved mutation operation formula and an adaptive adjustment formula for the crowding distance; formulating a local search strategy, and performing a local search on a preset proportion of solutions in the non-dominated solution set every preset number of iterations.

[0027] As a preferred solution of the site selection and capacity planning method based on improved multi-objective differential evolution described in the present invention, the calculation formula of the adaptive scaling factor F is:

[0028]

[0029] Among them, F min is the minimum value of the scaling factor, F max is the maximum value of the scaling factor, t is the current number of iterations, T is the maximum number of iterations, and α is the control parameter;

[0030] The calculation formula of adaptive crossover probability CR is:

[0031]

[0032] Among them, CR min is the minimum crossover probability, CR max is the maximum value of the crossover probability, β is the control parameter, d i For the current individual X i To the optimal individual X best The normalized Euclidean distance of ;

[0033] The specific formula of the mutation operation formula is as follows:

[0034]

[0035] Among them, V i is the individual after mutation, X i is the current individual, X best is the best individual in the current population or elite archive, and are different individuals selected randomly, and F is the adaptive scaling factor.

[0036] As a preferred solution of the site selection and sizing planning method based on improved multi-objective differential evolution described in the present invention, wherein: formulating a local search strategy includes the following steps: setting a preset number of iterations according to the problem scale and computing resources; determining a preset ratio based on a balance between algorithm performance and convergence speed; considering the value range and accuracy requirements of the decision variables, determining the radius of the local search as a first preset value; each time an integer multiple of the preset number of iterations is reached, randomly selecting a preset ratio of solutions from the non-dominated solution set for local search; for each selected solution, performing a random search in a hypersphere with the solution as the center and the first preset value as the radius to generate a new candidate solution; evaluating the newly generated candidate solution, and if it is better than or non-dominated by the original solution, replacing the original solution with the new solution.

[0037] As a preferred solution of the site selection and sizing planning method based on improved multi-objective differential evolution described in the present invention, wherein: using the improved multi-objective differential evolution algorithm to optimize and solve the static VAR compensator site selection and sizing planning model includes the following steps: initializing the multi-objective differential evolution algorithm parameters, the multi-objective differential evolution algorithm parameters include the population size N, the maximum number of iterations FEs_max, the crossover probability CR and the scaling factor F; randomly generating an initial population, each individual includes the operating parameters of the generator set, the SVC installation location and capacity; evaluating the objective function value and the default value of each individual in the initial population quantity; establish and initialize elite archives, and iterate the optimization process; in each iteration, calculate adaptive parameters, generate and evaluate offspring populations, update parent populations and elite archives, and perform local search at a preset number of iterations; when the termination condition is reached, output the Pareto optimal solution set from the elite archives; select a site selection and sizing scheme from the Pareto optimal solution set according to the preset decision preference; analyze the system loss and voltage deviation of the site selection and sizing scheme, and verify whether the site selection and sizing scheme meets all constraints; if all constraints are met, output the site selection and sizing scheme as the optimal site selection and sizing scheme.

[0038] In the second aspect, an embodiment of the present invention provides a site selection and sizing planning system based on improved multi-objective differential evolution, which includes a data collection and processing module for collecting and processing power system data, the power system data including network topology, line parameters, load characteristics and generator set parameters; a model building module for establishing a static VAR compensator site selection and sizing planning model based on the power system data, setting the objective function, and formulating a set of constraints; an algorithm improvement module for introducing an adaptive mutation strategy and an elite retention strategy to improve the multi-objective differential evolution algorithm; an optimization solution module for optimizing and solving the static VAR compensator site selection and sizing planning model using an improved multi-objective differential evolution algorithm to obtain the optimal site selection and sizing solution.

[0039] In a third aspect, an embodiment of the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: when the computer program instructions are executed by the processor, the steps of the site selection and capacity planning method based on improved multi-objective differential evolution as described in the first aspect of the present invention are implemented.

[0040] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program instructions are executed by a processor, the steps of the site selection and capacity planning method based on improved multi-objective differential evolution as described in the first aspect of the present invention are implemented.

[0041] The beneficial effects of the present invention are as follows: by introducing an adaptive mutation strategy and an elite retention strategy, combined with an improved multi-objective differential evolution algorithm, the algorithm's search capability and convergence are greatly improved, enabling it to more efficiently find the optimal solution in a complex solution space. This method simultaneously optimizes the two objectives of system loss and voltage deviation, achieving a comprehensive evaluation and improvement of the performance of the power system. In addition, the introduction of local search strategies and adaptive parameter adjustment mechanisms enhances the algorithm's ability to conduct refined exploration in the later stages of the search, and increases the probability of obtaining a global optimal solution. Finally, through carefully designed objective functions and constraints, this method can accurately evaluate the impact of the installation location and capacity of the static VAR compensator on the performance of the entire power system, ensuring that the resulting site selection and sizing scheme not only meets the technical requirements, but also maximizes system performance, thereby providing strong decision-making support for the planning and operation of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0043] Figure 1 This is a framework flow chart of the site selection and capacity planning method based on improved multi-objective differential evolution.

[0044] Figure 2 This is the system wiring diagram of the site selection and capacity planning method based on improved multi-objective differential evolution.

[0045] Figure 3 This is a comparison chart of network losses based on the site selection and capacity planning method based on improved multi-objective differential evolution.

[0046] Figure 4 This is a comparison chart of network losses based on the site selection and capacity planning method based on improved multi-objective differential evolution.

[0047] Figure 5 Computer equipment diagram for the site selection and capacity planning method based on improved multi-objective differential evolution. DETAILED DESCRIPTION

[0048] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the accompanying drawings.

[0049] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0050] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

[0051] Example 1

[0052] Reference Figure 1 to Figure 5 , which is the first embodiment of the present invention, and provides a method for site selection and capacity planning based on improved multi-objective differential evolution, comprising:

[0053] S1: Collect and process power system data.

[0054] Specifically, the power system data includes network topology, line parameters, load characteristics, and generator set parameters.

[0055] S2: Establish a static VAR compensator site selection and sizing planning model based on power system data, set the objective function, and formulate a set of constraint conditions.

[0056] It should be noted that the static VAR compensator (SVC) can help the system reduce losses and reduce voltage deviations. Therefore, when considering the site selection and capacity determination of the static VAR compensator, the method of the present invention takes into account the impact of the introduction of the static VAR compensator on system losses and voltage deviations. This consideration is directly reflected in the static VAR compensator site selection and capacity planning model of the present invention, especially in the setting of the objective function and the formulation of constraints. In this way, the method of the present invention can more accurately evaluate the impact of the installation location and capacity of the static VAR compensator on the performance of the entire power system, thereby obtaining a better site selection and capacity determination plan, so the specific formula of the objective function is as follows:

[0057] Min[PLOSS,V D ]

[0058] Where PLOSS is the system loss, V D is the voltage deviation, the specific formula is as follows:

[0059]

[0060] Among them, N b is the total number of branches, V mis the voltage at node m, V n is the voltage at node n, δ mn is the voltage phase angle between node m and node n, G b is the conductance of branch b.

[0061] Furthermore, the constraint condition set includes system constraints, SVC constraints, unit operation constraints, and power flow constraints, where the specific formula of the system constraints is as follows:

[0062]

[0063] in, are the upper and lower limits of the voltage at node m, V m is the voltage at node m, is the maximum transmission capacity of line b, S b is the transmission capacity of line b;

[0064] The specific formula of SVC constraint is as follows:

[0065]

[0066] in, is the upper and lower limits of reactive power that SVC can compensate, Q SVC is the reactive power that the SVC can compensate;

[0067] The specific formula of unit operation constraints is as follows:

[0068] P max ≥P≥P min

[0069] Q max ≥Q≥Q min

[0070] Among them, P max , P min is the upper and lower limits of the active output of the generator set, Q max , Q min The upper and lower limits of reactive power output of the generator set;

[0071] The specific formula of power flow constraint is as follows:

[0072]

[0073] Among them, P m , Q m are the active and reactive output of node m, respectively, Fm , Q Fm are the active and reactive loads of node m, Q SVCis the reactive power that the SVC at node m can compensate, V m 、V n are the voltages at nodes m and n, respectively, N s is the total number of nodes, Y mn is the element in the mth row and nth column of the admittance matrix.

[0074] It should be noted that the decision variables of the system layout planning model include: the active and reactive output of the generator (P m and Q m ), SVC installation location and capacity (Q SVC ), node voltage amplitude and phase angle (V m and V n ).

[0075] S3: Introduce adaptive mutation strategy and elite retention strategy to improve the multi-objective differential evolution algorithm.

[0076] Specifically, the following steps are included:

[0077] S3.1: Design a calculation formula for the adaptive scaling factor F.

[0078]

[0079] Among them, F min is the minimum value of the scaling factor, F max is the maximum value of the scaling factor, t is the current number of iterations, T is the maximum number of iterations, and α is the control parameter.

[0080] S3.2: Design a calculation formula for the adaptive crossover probability CR.

[0081]

[0082] Among them, CR min is the minimum crossover probability, CR max is the maximum value of the crossover probability, β is the control parameter, d i For the current individual X i To the optimal individual X best The normalized Euclidean distance of .

[0083] S3.3: Create an elite file to store the non-dominated solutions in each iteration.

[0084] S3.4: Design an elite archive update mechanism, including adding new non-dominated solutions and an archive pruning method based on non-dominated sorting and crowding calculation.

[0085] S3.5: Formulate a strategy for elite individuals to participate in evolution, and select a preset proportion of individuals from the elite archive to participate in the mutation operation.

[0086] S3.6: Design improved mutation operation formulas.

[0087]

[0088] Among them, V i is the individual after mutation, X i is the current individual, X best is the best individual in the current population or elite archive, and are different individuals selected randomly, and F is the adaptive scaling factor.

[0089] S3.7: Design an adaptive adjustment formula for the crowding distance to increase population diversity.

[0090]

[0091] Among them, CD i For the current individual X i The crowding distance is , γ is the adjustment coefficient, t is the current number of iterations, and T is the maximum number of iterations.

[0092] S3.8: Formulate a local search strategy to perform a local search on a preset proportion of solutions in the non-dominated solution set every preset number of iterations.

[0093] Specifically, according to the problem scale and computing resources, a preset number of iterations is set, and this value represents the number of interval iterations for performing local search; based on the balance between algorithm performance and convergence speed, a preset ratio is determined, and this ratio determines the number of non-dominated solutions selected each time a local search is performed; considering the value range and accuracy requirements of the decision variables, the radius of the local search is determined to be a first preset value; each time an integer multiple of the preset number of iterations is reached, a preset ratio of solutions is randomly selected from the non-dominated solution set for local search; for each selected solution, a random search is performed in a hypersphere with the solution as the center and the first preset value as the radius to generate a new candidate solution; the newly generated candidate solution is evaluated, and if it is better than or non-dominated by the original solution, the original solution is replaced by the new solution.

[0094] S4: An improved multi-objective differential evolution algorithm is used to optimize and solve the static VAR compensator site selection and sizing planning model to obtain the optimal site selection and sizing plan.

[0095] Specifically, the following steps are included:

[0096] S4.1: Initialize the parameters of the multi-objective differential evolution algorithm, including the population size N, the maximum number of iterations FEs_max, the crossover probability CR, and the scaling factor F.

[0097] S4.2: Randomly generate an initial population, each individual contains the operating parameters of the generator set, the SVC installation location and capacity.

[0098] S4.3: Evaluate the objective function value (system loss and voltage deviation) and default amount of each individual in the initial population.

[0099] Preferably, the default amount is calculated by a feasible solution technique, and the specific formula is as follows:

[0100]

[0101] Among them, x is the individual to be evaluated, N F is the total number of constraints, Y F is the default value of the Fth constraint, Y F max is the maximum default value of the Fth constraint.

[0102] It should be noted that the smaller the value of the default indicator WY(x), the higher the feasibility of the solution. When the default indicator WY(x) of the solution is equal to 0, the solution is a feasible solution.

[0103] S4.4: Create and initialize elite profiles, and iterate the optimization process.

[0104] S4.5: In each iteration, the adaptive parameters are calculated, the offspring population is generated and evaluated, the parent population and elite archive are updated, and the local search is performed for a preset number of iterations.

[0105] Specifically, the adaptive scaling factor F and crossover probability CR of the current iteration are calculated using the formulas of S3.1 and S3.2; the offspring population is generated: a mating pool is generated from the current population using a binary tournament selection strategy, mutation operations and crossover operations are performed on the individuals in the mating pool to generate an offspring population; the objective function value and default amount of each individual in the offspring population are evaluated; the initial population and the offspring population are merged to form a joint population, non-dominated sorting and crowding calculations are performed on the joint population, and the crowding distance of the individuals is adjusted using an adaptive adjustment formula; N optimal individuals are selected to form a new parent population, and the update mechanism in S3.4 is applied to update the elite archive; if the current number of iterations is an integer multiple of the preset number of iterations, a local search strategy is executed.

[0106] It should be noted that the specific operation of generating a mating pool is: randomly select two individuals, compare their fitness, put the individual with higher fitness into the mating pool, and repeat this process until the size of the mating pool is equal to the current population size.

[0107] Furthermore, performing mutation and crossover operations on individuals in the mating pool includes the following steps: applying the improved mutation operation formula designed in S3.6 to perform mutation operations on each individual in the mating pool; performing crossover operations on the mutated individuals, and for each decision variable, deciding whether to perform crossover with the adaptive crossover probability CR calculated in S3.2, and if crossover is performed, replacing the variables of the original individual with the corresponding variables of the mutated individual; applying the elite individual participation evolution strategy formulated in S3.5 to select individuals from the elite archives with a preset probability to participate in mutation and crossover operations; for each new individual generated, checking whether it meets the constraints of the problem, if not, applying a repair strategy or regenerating the individual; and forming a descendant population with all new individuals that pass mutation, crossover and inspection.

[0108] It should be noted that the current population is the population selected at the end of the previous iteration, and the initial population in the first iteration.

[0109] S4.6: When the termination condition is reached (i.e., the number of iterations reaches FEs_max), the Pareto optimal solution set is output from the elite file.

[0110] S4.7: Select a site selection and capacity determination plan from the Pareto optimal solution set based on preset decision preferences.

[0111] S4.8: Analyze the system losses and voltage deviations of the selected site selection and sizing scheme, and verify whether the selected site selection and sizing scheme meets all constraints.

[0112] S4.9: If all constraints are met, the solution is output as the optimal site selection and capacity determination solution.

[0113] It should be noted that the active and reactive output (P m and Q m ), SVC installation location and capacity (Q SVC ), node voltage amplitude and phase angle (V m and V n ), as well as optimized system losses and voltage deviations.

[0114] Furthermore, this embodiment also provides a site selection and sizing planning system based on improved multi-objective differential evolution, including a data collection and processing module for collecting and processing power system data, the power system data including network topology, line parameters, load characteristics and generator set parameters; a model building module for establishing a static VAR compensator site selection and sizing planning model based on the power system data, setting the objective function, and formulating a set of constraints; an algorithm improvement module for introducing an adaptive mutation strategy and an elite retention strategy to improve the multi-objective differential evolution algorithm; an optimization solution module for optimizing and solving the static VAR compensator site selection and sizing planning model using an improved multi-objective differential evolution algorithm to obtain the optimal site selection and sizing solution.

[0115] This embodiment also provides a computer device, which is suitable for the site selection and capacity planning method based on improved multi-objective differential evolution, including a memory and a processor; the memory is used to store computer executable instructions, and the processor is used to execute computer executable instructions to implement the site selection and capacity planning method based on improved multi-objective differential evolution as proposed in the above embodiment.

[0116] The computer device may be a terminal, and the computer device includes a processor, a memory, a communication interface, a display screen and an input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, an operator network, NFC (near field communication) or other technologies. The display screen of the computer device may be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device may be a touch layer covering the display screen, or a key, trackball or touchpad provided on the housing of the computer device, or an external keyboard, touchpad or mouse, etc.

[0117] This embodiment also provides a storage medium on which a computer program is stored. When the program is executed by a processor, the method for site selection and capacity planning based on improved multi-objective differential evolution as proposed in the above embodiment is implemented.

[0118] In summary, this method greatly improves the search ability and convergence of the algorithm by introducing adaptive mutation strategy and elite retention strategy, combined with the improved multi-objective differential evolution algorithm, so that it can more efficiently find the optimal solution in the complex solution space. This method optimizes the two goals of system loss and voltage deviation at the same time, and realizes the comprehensive evaluation and improvement of the performance of the power system. In addition, the introduction of local search strategy and adaptive parameter adjustment mechanism enhances the algorithm's refined exploration ability in the later stage of search and increases the probability of obtaining the global optimal solution. Finally, through carefully designed objective functions and constraints, this method can accurately evaluate the impact of the installation location and capacity of the static VAR compensator on the performance of the entire power system, ensuring that the obtained site selection and sizing scheme not only meets the technical requirements, but also can maximize the improvement of system performance, thereby providing strong decision-making support for the planning and operation of the power system.

[0119] Example 2

[0120] Reference Figure 1 to Figure 5 , which is the second embodiment of the present invention, provides a site selection and capacity planning method based on improved multi-objective differential evolution. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.

[0121] Specifically, the wiring diagram of the embodiment system is as follows Figure 2 As shown in Figure 1, the network contains 30 nodes, 6 thermal power units, and 4 transformers. The information of SVC is shown in Table 1. Since the generator can generate reactive power, SVC is not installed at the generator node.

[0122] Table 1 SVC information

[0123] quantity Compensation maximum value Compensation minimum Install node scope 1 10Mvar -10Mvar [1,30]

[0124] The relevant parameters of the existing non-dominated sorting genetic algorithm II (NSGA-II) are set as follows: the population size is set to 50, the number of iterations is set to 50 generations, the mutation factor PM is 1 / 13, the crossover factor PC is 0.9, and the mutation parameter DM and the crossover parameter DC are both 20; the parameters of the improved multi-objective differential evolution algorithm are set as follows: the population size is set to 50, the number of iterations is set to 50 generations, the scaling factor F is a random number between 0.1 and 1, and the crossover probability factor CR is a random number between 0 and 1. Each algorithm is run independently 30 times. In addition, in order to compare the performance of the algorithm, the Hypervolume (HV) indicator is used to evaluate the algorithm, and its calculation method is as follows:

[0125]

[0126] Among them, rd is the reference point (1,1), which represents the size of the hypercube enclosed by x and rd. The higher the HV value, the better the performance of the algorithm.

[0127] The optimal planning solution obtained by using the improved differential evolution algorithm and NSGA-II is shown in Table 2.

[0128] Table 2 Optimization results

[0129]

[0130] From the results after optimization, it can be seen that in the solution provided by IMODE, the optimal voltage deviation and optimal loss are 5.5759MW and 0.4205 respectively, and both target values ​​are better than those obtained by NSGAII. In the compromise solution, both targets obtained by IMODE are also better than those obtained by NSGAII. In addition, by comparing the Hypervolumes of the two, the performance of IMODE is significantly better than that of NSGAII. This shows that when IMODE takes voltage deviation and loss as the optimization targets, the solution provided by NSGAII is more effective than NSGAII, and it can effectively select the location and set the parameters for SVC, so that the system can maximize the use of SVC.

[0131] In summary, the use of the improved multi-objective differential evolution algorithm for planning can obtain the optimal planning scheme, which has a certain guiding role in the site selection and capacity determination of SVC in actual engineering practice.

[0132] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A site selection and capacity planning method based on improved multi-objective differential evolution, characterized by: include, Collect and process power system data, including network topology, line parameters, load characteristics, and generator set parameters; Based on the power system data, a static VAR compensator site selection and capacity planning model is established, the objective function is set, and a set of constraint conditions is formulated; Adaptive mutation strategy and elite retention strategy are introduced to improve the multi-objective differential evolution algorithm; An improved multi-objective differential evolution algorithm is used to optimize and solve the static VAR compensator site selection and sizing planning model to obtain the optimal site selection and sizing plan.

2. The site selection and capacity planning method based on improved multi-objective differential evolution according to claim 1, characterized in that: The specific formula of the objective function is as follows: Min[PLOS,V D ] Where PLOSS is the system loss, V D is the voltage deviation, the specific formula is as follows: Among them, N b is the total number of branches, V m is the voltage at node m, V n is the voltage at node n, δ mn is the voltage phase angle between node m and node n, G b is the conductance of branch b.

3. The site selection and capacity planning method based on improved multi-objective differential evolution according to claim 1, characterized in that: The constraint condition set includes system constraints, SVC constraints, unit operation constraints, and power flow constraints. The specific formula of the system constraint is as follows: in, are the upper and lower limits of the voltage at node m, V m is the voltage at node m, is the maximum transmission capacity of line b, S b is the transmission capacity of line b; The specific formula of the SVC constraint is as follows: in, is the upper and lower limits of reactive power that SVC can compensate, Q SVC is the reactive power that the SVC can compensate; The specific formula of the unit operation constraint is as follows: P max ≥P≥P min Q max ≥Q≥Q min Among them, P max , P min is the upper and lower limits of the active output of the generator set, Q max , Q min The upper and lower limits of reactive power output of the generator set; The specific formula of the power flow constraint is as follows: Among them, P m , Q m are the active and reactive output of node m, respectively, Fm , Q Fm are the active and reactive loads of node m, Q SVC is the reactive power that the SVC at node m can compensate, V m 、V n are the voltages at nodes m and n, respectively, N s is the total number of nodes, Y mn is the element in the mth row and nth column of the admittance matrix.

4. The site selection and capacity planning method based on improved multi-objective differential evolution according to claim 1, characterized in that: The improvement of the multi-objective differential evolution algorithm comprises the following steps: Design a calculation formula for the adaptive scaling factor F and a calculation formula for the adaptive crossover probability CR; Establishing an elite file, wherein the elite file is used to store non-dominated solutions in each iteration; Designing an elite file update mechanism, wherein the elite file update mechanism includes adding new non-dominated solutions and a file pruning method based on non-dominated sorting and congestion calculation; Formulate strategies for elite individuals to participate in evolution, and select a preset proportion of individuals from the elite archives to participate in mutation operations; Design an improved mutation operation formula and an adaptive adjustment formula for crowding distance; A local search strategy is formulated to perform a local search on a preset proportion of solutions in the non-dominated solution set every preset number of iterations.

5. The site selection and capacity planning method based on improved multi-objective differential evolution according to claim 4 is characterized in that: The calculation formula of the adaptive scaling factor F is: Among them, F min is the minimum value of the scaling factor, F max is the maximum value of the scaling factor, t is the current number of iterations, T is the maximum number of iterations, and α is the control parameter; The calculation formula of the adaptive crossover probability CR is: Among them, CR min is the minimum crossover probability, CR max is the maximum value of the crossover probability, β is the control parameter, d i For the current individual X i To the optimal individual X best The normalized Euclidean distance of ; The specific formula of the mutation operation formula is as follows: Among them, V i is the individual after mutation, X i is the current individual, X best is the best individual in the current population or elite archive, and are different individuals selected randomly, and F is the adaptive scaling factor.

6. The site selection and capacity planning method based on improved multi-objective differential evolution according to claim 4, characterized in that: The local search strategy comprises the following steps: Set a preset number of iterations based on the problem size and computing resources; Determine the preset ratio based on the balance between algorithm performance and convergence speed; Considering the value range and accuracy requirements of the decision variable, determining the radius of the local search to be a first preset value; Each time when the number of iterations reaches an integer multiple, a preset proportion of solutions are randomly selected from the non-dominated solution set for local search; For each selected solution, a random search is performed within a hypersphere with the solution as the center and a first preset value as the radius to generate a new candidate solution; Evaluate the newly generated candidate solution, and if it is better than or non-dominated by the original solution, replace the original solution with the new solution.

7. The site selection and capacity planning method based on improved multi-objective differential evolution according to claim 1, characterized in that: The method of optimizing and solving the static VAR compensator site selection and capacity planning model by using an improved multi-objective differential evolution algorithm comprises the following steps: Initialize multi-objective differential evolution algorithm parameters, wherein the multi-objective differential evolution algorithm parameters include population size N, maximum number of iterations FEs_max, crossover probability CR, and scaling factor F; The initial population is randomly generated, and each individual contains the operating parameters of the generator set, the SVC installation location and capacity; Evaluate the objective function value and default amount of each individual in the initial population; Establish and initialize elite profiles, and iterate the optimization process; In each iteration, adaptive parameters are calculated, the offspring population is generated and evaluated, the parent population and elite archive are updated, and local search is performed for a preset number of iterations; When the termination condition is reached, the Pareto optimal solution set is output from the elite archive; Select a location and capacity solution from the Pareto optimal solution set based on preset decision preferences; Analyze the system loss and voltage deviation of the site selection and sizing scheme to verify whether the site selection and sizing scheme meets all constraints; If all constraints are met, the site selection and capacity determination plan is output as the optimal site selection and capacity determination plan.

8. A site selection and capacity planning system based on improved multi-objective differential evolution, based on the site selection and capacity planning method based on improved multi-objective differential evolution according to any one of claims 1 to 7, characterized in that: Also includes, A data collection and processing module, used to collect and process power system data, wherein the power system data includes network topology, line parameters, load characteristics and generator set parameters; A model building module, used to establish a static VAR compensator site selection and capacity planning model based on the power system data, set an objective function, and formulate a set of constraint conditions; Algorithm improvement module, used to introduce adaptive mutation strategy and elite retention strategy to improve the multi-objective differential evolution algorithm; The optimization solution module is used to optimize and solve the static VAR compensator site selection and capacity planning model using an improved multi-objective differential evolution algorithm to obtain the optimal site selection and capacity solution.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the site selection and capacity planning method based on improved multi-objective differential evolution described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the site selection and capacity planning method based on improved multi-objective differential evolution described in any one of claims 1 to 7 are implemented.

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