Optimization method suitable for time-varying error estimation of voltage transformer

Abstract

The invention provides an optimization method suitable for time-varying error estimation of a voltage transformer, and the method comprises the following steps: randomly generating an initial population based on a solution space of an optimization problem, and taking the initial population as an initial solution set of an optimization process; designing uniformly distributed reference points; initializing a feasible solution set by recording the historical state of the population and the feasibility of the marked solution; calculating a target function value and a constraint deviation of each solution in the population, judging whether the target function value and the constraint deviation are feasible, and updating a recording state of the solution; generating a new candidate solution according to the solution state of the current population in combination with the reference point association relationship and historical information to expand a search space; screening out a next generation of population from the current population and the candidate solution according to an optimization target and a constraint condition, and updating an optimization direction; repeating the process of generating the candidate solution and selecting the population until a preset number of iterations or optimization target convergence is reached; and extracting a Pareto non-dominated solution set in the final solution record matrix, and outputting the Pareto non-dominated solution set as an optimization result.

Description

Technical Field

[0001] The invention relates to the field of power system measurement, and in particular to an optimization method suitable for estimating time-varying errors of voltage transformers. Background Art

[0002] Voltage transformers are important equipment in power systems, mainly used to measure voltage and transmit signals to the control system to ensure the stability and efficient operation of the system. However, in practical applications, voltage transformers are inevitably affected by various factors such as environmental changes and equipment aging, resulting in time-varying errors. This error may have a significant impact on the monitoring and control accuracy of the power system, thereby threatening the stable operation and reliability of the system. Therefore, studying how to efficiently and accurately estimate the time-varying error of voltage transformers has become one of the important topics in the optimization design of power systems.

[0003] The estimation of time-varying errors of voltage transformers is essentially a complex multi-objective optimization problem. Specifically, the problem involves the optimization of multiple objective functions, which often conflict with each other and require finding a Pareto non-dominated solution set in the objective space. At the same time, the problem has the following characteristics: High-dimensional decision space: The error estimation problem of voltage transformer involves the optimization of multiple parameters, resulting in a high-dimensional decision space; Complex constraints: This problem has multiple complex equality constraints and inequality constraints, and the feasible solution region is often discontinuous; Difficulty in searching: Traditional analytical methods are difficult to effectively solve in high-dimensional and discontinuous decision spaces.

[0004] In view of the above difficulties, multi-objective evolutionary algorithms are gradually being applied to such optimization problems. Such algorithms simulate the natural evolution process and find a set of approximate Pareto solutions in a large search space. However, traditional multi-objective evolutionary algorithms have the following shortcomings when dealing with time-varying error estimation of voltage transformers: Failure to utilize the relative position relationship between feasible solutions and infeasible solutions: During the optimization process, the heuristic information of feasible solutions and infeasible solutions in the target space in the constraints is not fully exploited, resulting in low optimization efficiency; Insufficient adaptive search capabilities: The optimization algorithm has different search objectives at different stages. Rapid convergence is required in the early stage, while a balance between convergence and solution diversity is required in the later stage. However, existing methods fail to design adaptive search strategies for different stages. Poor generalization performance: For multi-task constrained multi-objective optimization problems, existing algorithms have difficulty maintaining strong generalization capabilities when transferring problems and switching tasks, and cannot fully utilize the correlation between multiple tasks to improve search efficiency.

[0005] Therefore, in order to deal with the complex problem of time-varying error estimation of voltage transformer, a constrained multi-task and multi-objective evolutionary optimization scheme with better performance is urgently needed. By utilizing constraints and the correlation between tasks, a balance between fast convergence and solution diversity can be achieved, providing reliable support for the optimal design of power systems. Summary of the invention

[0006] In a first aspect of the present disclosure, there is provided an optimization method applicable to time-varying error estimation of a voltage transformer, the method comprising the following steps: Based on the solution space of the optimization problem, an initial population is randomly generated as the initial solution set of the optimization process; Design evenly distributed reference points for guiding the target space and evaluating the solution during the optimization process; By recording the historical state of the population and the feasibility of the marked solution, the feasible solution set is initialized to provide historical support and feasibility constraints for optimization; Calculate the objective function value and constraint deviation of each solution in the population, determine whether it is feasible, and update the record status of the solution; Generate new candidate solutions based on the solution status of the current population, combined with the reference point association and historical information; From the current population and candidate solutions, select the next generation population according to the optimization objectives and constraints, and update the optimization direction; Repeat the process of generating candidate solutions and selecting populations until the preset number of iterations is reached or the optimization goal converges; The Pareto non-dominated solution set in the final solution record matrix is ​​extracted and output as the optimization result.

[0007] In combination with the first aspect, the step of generating an initial population specifically includes: Determine the number of decision variables for the problem D , the number of objective functions M and population size N ; Each population solution is randomly generated by uniform distribution D dimensional variables, and determine the value range based on the upper and lower bounds defined in the problem; Constructing the initial population matrix P 0 , as the optimization initial solution set.

[0008] In combination with the first aspect, the reference points designed to be evenly distributed include: Generating matrices by mixed uniform design W , select the column with the largest centralized L2 deviation as the reference point; The reference points are distributed in the target space to ensure uniform coverage, which is used to guide the direction selection of the optimization target.

[0009] In combination with the first aspect, the initializing the feasible solution set by recording the historical state of the population and marking the feasibility of the solution includes: Create a solution record matrix to save the solutions of the current population, the previous generation population, and the previous two generations of populations; Create a marker vector to record the feasibility status of the solution; Initialize the feasible solution set matrix, each row is a negative unit vector, indicating that there is no feasible solution in the initial state.

[0010] In combination with the first aspect, the calculating the objective function value and constraint deviation of each solution in the population and judging whether it is feasible includes: Calculate the performance value of each population solution in the target space according to the objective function; Calculate the deviation value of equality constraints and inequality constraints for each solution to determine its feasibility; Update the solution record status, mark feasible solutions and infeasible solutions, and save them in the solution record matrix.

[0011] In combination with the first aspect, generating a new candidate solution according to the solution state of the current population, in combination with the reference point association relationship and historical information includes: For feasible solutions, new candidate solutions are generated by combining the solutions associated with the reference point and the historical solution information; For infeasible solutions, different mutation strategies are selected according to the current iteration status to generate new solutions.

[0012] In combination with the first aspect, the step of selecting the next generation population from the current population and the candidate solutions according to the optimization objective and the constraint conditions includes: Select solutions from the current population and the newly generated candidate solutions according to the target solution association rule for each reference point; According to the objective function value and constraint deviation, the solutions that meet the optimization conditions are selected to form the next generation population.

[0013] In combination with the first aspect, the process of repeatedly generating candidate solutions and selecting a population until a preset number of iterations is reached or the optimization target converges includes: Set the maximum number of iterations or the convergence accuracy of the objective function value as the optimization termination condition; In each iteration, the process of generating candidate solutions and selecting the population is repeated to gradually approach the optimization goal.

[0014] According to a second aspect of the present disclosure, there is provided an electronic device, comprising: one or more processors; A storage unit is used to store one or more programs, which, when executed by the one or more processors, enable the one or more processors to implement the optimization method applicable to time-varying error estimation of a voltage transformer.

[0015] According to a third aspect of the present disclosure, a computer-readable storage medium is provided, on which a computer program is stored, characterized in that when the computer program is executed by a processor, the optimization method applicable to time-varying error estimation of a voltage transformer can be implemented.

[0016] Beneficial effects: The present invention utilizes the relative position relationship between feasible solutions and infeasible solutions in the target space to provide heuristic information for evolutionary search, thereby improving the convergence speed of the algorithm; balances fast convergence with solution diversity through adaptive strategies at different stages of the search process to improve the overall optimization performance; utilizes the correlation between multiple tasks and transfer learning capabilities to enhance the generalization performance of the algorithm, significantly improving the optimization efficiency in high-dimensional decision spaces and complex constraints, and providing a more accurate, stable and efficient solution for voltage transformer time-varying error estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A schematic flow chart of an optimization method for estimating time-varying errors of voltage transformers according to an embodiment of the present disclosure; Figure 2 It is a TREE problem instance setting for an embodiment of the present disclosure; Figure 3 is the mean value and standard deviation of the hypervolume (HV) value of each test algorithm of the embodiment of the present disclosure; Figure 4 A heat map plotting the median of each algorithm in the embodiments of the present disclosure on each TREE test case; Figure 5 An electronic device according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0018] Here, exemplary embodiments are described in detail, and examples thereof are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the embodiments of the present disclosure.

[0019] The terms used in the disclosed embodiments are only for the purpose of describing specific embodiments and are not intended to limit the disclosed embodiments. The singular forms of "a", "said" and "the" used in the disclosed embodiments and the appended claims are also intended to include plural forms unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0020] It should be understood that although the terms first, second, third, etc. may be used to describe various information in the disclosed embodiments, these information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the disclosed embodiments, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0021] like Figure 1 The figure is a flow chart of an optimization method for estimating a time-varying error of a voltage transformer according to an embodiment of the present disclosure, comprising: S101: Based on the solution space of the optimization problem, an initial population is randomly generated as an initial solution set of the optimization process; S102: Design evenly distributed reference points for guiding the target space and evaluating the solution during the optimization process; S103: Initialize the feasible solution set by recording the historical state of the population and the feasibility of the marked solution, and provide historical support and feasibility constraints for optimization; S104: Calculate the objective function value and constraint deviation of each solution in the population, determine whether it is feasible, and update the record status of the solution; S105: Generate a new candidate solution based on the solution state of the current population, combined with the reference point association relationship and historical information; S106: Select the next generation population from the current population and candidate solutions according to the optimization objectives and constraints, and update the optimization direction; S107: Repeat the process of generating candidate solutions and selecting populations until a preset number of iterations is reached or the optimization target converges; S108: extracting a set of Pareto non-dominated solutions from the final solution record matrix and outputting it as an optimization result.

[0022] Specific: S101: Randomly generate an initial population.

[0023] Assume that the number of decision variables to be optimized is D , the number of objective functions is M , initialize the population, and get the population Assume that the population size is N , then for any initial solution , the values ​​of any dimension are generated according to uniform distribution, that is:

[0024] in is a function that generates random real numbers from a uniform distribution, represents the minimum value on the dth dimension, Represents the maximum value in the dth dimension.

[0025] Beneficial effects: Based on the solution space of the optimization problem, the initial population is generated in a uniformly distributed random manner, and each individual in the population represents a potential solution. The generation of the initial population is the starting point of the entire optimization process. Its purpose is to provide sufficient diversity for the subsequent optimization process and ensure that the search can cover the main area of ​​the solution space. By randomly generating the initial solution set, the problem of the initial solution being too concentrated in a specific area is avoided, providing a comprehensive exploration basis for the optimization process.

[0026] S102: Design evenly distributed reference points.

[0027] set up is a row vector consisting of all positive integers less than or equal to N and relatively prime to N, .set up ,from Select columns, forming a matrix O ,Right now , so that according to formula (2) O The centralized L2 deviation of is maximized.

[0028] , (2) in Representation Matrix O No. i Line j Order the matrix S is a set of reference points, S The i Point j dimension , which is consistent with the matrix O The relationship is shown in formula (3):

[0029] Generated reference point set S is uniformly distributed in the target space. N points will be used for subsequent solution evaluation and selection.

[0030] Beneficial effects: A set of reference points in the target space is generated by a mixed uniform design method. These reference points are evenly distributed and used to guide the evaluation of the objective function and the screening of solutions in the optimization process. The existence of reference points helps to maintain the uniformity of the distribution of the population in the target space, avoid the concentration of solutions in certain specific areas, and improve the diversity of optimization results and global exploration capabilities.

[0031] S103: Initialize a feasible solution set.

[0032] Create separately matrix and , used to record the solutions of the previous generation and the previous two generations; create N Dimensional vector and , used to mark whether each solution is feasible, creating matrix H Used to save feasible solutions. The matrix represents the feasible solution set, which is used to record the optimal feasible solution associated with each reference vector. It is initialized so that each row is a negative unit vector, indicating that there is no feasible solution at the time of initialization.

[0033] Beneficial effects: By recording the historical state of the population and marking the feasibility of each solution, a set of feasible solutions is constructed. The historical records provide a dynamic feedback mechanism for the algorithm, and marking the feasibility ensures that the algorithm can distinguish between feasible solutions and infeasible solutions, so as to adjust the search strategy in a targeted manner. The initialization of the feasible solution set provides basic constraints for subsequent steps and lays the foundation for the migration and utilization of solutions in multi-task optimization.

[0034] S104: Calculate the objective function value and the constraint deviation.

[0035] The objective function and constraint function For evaluation, assuming that the objective functions are arrive , then for any solution , which corresponds to a M Dimensional vector .

[0036] For any solution , on the jth constraint, if it is an equality constraint, then:

[0037] in is the equality constraint function.

[0038] If it is an inequality constraint, then we have

[0039] in is the inequality constraint function, .

[0040] For each reference vector , construct the function according to formula (6):

[0041] in is an M-dimensional vector, each dimension of which is the optimal value of each objective function currently found. and Calculate according to formula (7) and (8) respectively.

[0042]

[0043] For each reference vector , in the associated population, in the corresponding function A solution that achieves the optimal value on .

[0044] Beneficial effects: For each solution in the current population, its objective function value and constraint deviation are calculated to determine whether it meets the constraints of the problem. For infeasible solutions, its constraint deviation is used as reference information for improvement; for feasible solutions, its objective function performance is recorded. This process realizes the quantitative evaluation of the solution quality and feasibility of the population, and provides a basis for subsequent solution generation and screening.

[0045] S105: Generate new candidate solutions.

[0046] Assume that the population is , for any solution , if it is a feasible solution, generate a new candidate solution The method is:

[0047] in and are random real numbers between 0 and 1, and Respectively and distance The reference point associated with the M A randomly selected solution from the solutions associated with the reference points.

[0048] like If it is an infeasible solution, a candidate solution is generated. The method is shown in formula (10).

[0049] ,(10) in , and are random real numbers between 0 and 1, For belong to the same sub-problem, and They are the current iteration number and the maximum iteration number of the algorithm respectively.

[0050] for ,Will Join the population ,at this time Contains 2 N A solution.

[0051] Beneficial effects: Combine the solution status of the current population, the association relationship of the reference points, and the historical records to generate new candidate solutions. For feasible solutions, the differential evolution strategy is used to update the solution to improve the diversity and exploration ability of the population; for infeasible solutions, combined with constraint deviation information, its position is adjusted through mutation and crossover operations to guide its transformation to the feasible area. This step aims to expand the search space while balancing local development and global exploration under multiple objectives and constraints.

[0052] S106: Screening the next generation population.

[0053] According to formulas (6), (7), (8), For each reference point, select a solution associated with it. N , forming the next generation population .

[0054] renew , , , and H .

[0055] Beneficial effects: From the current population and the newly generated candidate solutions, the optimal solution is selected according to the optimization objectives and constraints to form the next generation population. The screening process comprehensively considers the feasibility of the solution, the objective function value, and the distribution of the solution in the target space to ensure that the selected solution achieves the best balance between performance and diversity. This process iteratively optimizes the population quality so that the algorithm gradually converges to the Pareto optimal frontier of the problem.

[0056] S107: Repeat the iteration.

[0057] Repeat steps (7) to (10) until the algorithm termination condition is reached.

[0058] Beneficial effect: Based on the previous generation of population, the candidate solution generation and population screening process are repeated to continuously optimize the quality and distribution of the solution. When the preset number of iterations is reached or the objective function value converges to the expected range, the algorithm stops. The iterative process is the core of the optimization algorithm. By continuously updating the population, the solution space is gradually narrowed to ensure that the optimal solution is found.

[0059] S108: Output the Pareto non-dominated solution.

[0060] Output Matrix H The Pareto non-dominated solutions saved in .

[0061] Beneficial effects: The Pareto non-dominated solution set is extracted from the final solution record matrix and output as the optimization result. These solutions are not mutually dominant in the objective function value and reflect the optimal solution set of the problem. By outputting the non-dominated solutions, users can obtain diversified solutions that meet the needs of multi-objective optimization and provide reference for actual engineering design and implementation.

[0062] Exemplarily, the present invention is used to solve six voltage transformer time-varying error estimation examples, named TREE1-TREE6, respectively. The settings of each problem example are as follows: Figure 2 As shown, M represents the number of objective functions, J represents the number of constraints, K represents the sum of the primary / secondary voltage phases, P represents the number of voltage transformer sets involved in the TREE problem, and T represents the length of the measured data sequence. Data types 1, 2, and 3 represent data containing only primary voltage values, data containing both primary and secondary voltage values, and data containing both voltage and phase angle values.

[0063] The decision space of the test case is defined as shown in formula (11), where represents the voltage of the i-th stage at time j, and the number of decision variables is .

[0064]

[0065] The time series data collected from the i-th group of voltage transformers can be expressed in the form of formula (12):

[0066] in and represents the pth data measured at time q. Then, the transformation ratio errors of these voltage transformers can be calculated according to formula (13).

[0067]

[0068] Further simplifying formula (13), the ratio error can be expressed as shown in formula (14): , (14) Therefore, the time-varying error is expressed as shown in formula (15):

[0069] , (15) For TREE6, the phase angle information measured from the primary and secondary sides of the transformer is expressed as shown in formula (16): , (16) in: , (17)

[0070] As shown in formula (18), the first objective function is the total relative time-varying error of all uncalibrated voltage transformers, which represents the matching degree between the true voltage value and the measured value. The time-varying relative error on the voltage transformer should be as small as possible.

[0071] , (18) in The calculation method is shown in formula (13).

[0072] As shown in formula (19), the second objective function is the sum of time-varying errors, which represents the time-varying relationship between the true voltage value and the measured value. This objective value should be as small as possible.

[0073] , (19) For TREE1-5, L is set to K, and for TREE6, L is set to .

[0074] As shown in formula (20), unlike the first two objectives which only consider the voltage value, the third objective reveals the true voltage value, the measured phase angle value, and the phase angle relationship between the measured voltage values. The smaller the value of this optimization objective, the higher the quality of the solution.

[0075]

[0076] Topological constraints: Topological constraints are derived from the three-phase balance principle, which maintains the true three-phase main line voltage balance when the power grid is controlled. This balance is described by a coefficient called voltage unbalance factor (VUF), which represents the balance between the three-phase impedances. Since the three-phase impedances are balanced and change slowly (especially in high-voltage power grids), the VUF value and its fluctuation can be limited to the range shown in formula (21).

[0077]

[0078] In addition, since the primary voltage value is proportional to the secondary voltage value, all the proportions of the three-phase voltages should be the same. Therefore, we can derive the second constraint condition through its fluctuation as shown in formula (22).

[0079]

[0080] The calculation method of VUF is shown in formula (23):

[0081] Series constraints: Series constraints describe the time-varying relationship of the same decision variable. The basic assumption is that the decision variable changes slowly and continuously, rather than suddenly. j The change of the decision vector x at is defined as:

[0082] in and The corresponding constraints are shown in formula (15):

[0083] Where std() represents the function for finding the standard deviation.

[0084] In addition, due to the imbalance between the primary and secondary sides, for TREE3-6, the primary and secondary voltages are constrained as shown in formula (26):

[0085] Phase constraint: The basic assumption of phase constraint is that the phase angle difference of the three phases in the voltage transformer system remains constant. Therefore, the first phase constraint represents the tolerance of phase angle imbalance, and its expression is:

[0086] in Given in formula (16). According to the phase and voltage balance in the transmission system, the matrix shown in formula (28) can be obtained.

[0087]

[0088] in As shown in formula (29).

[0089]

[0090] in:

[0091] From this we can see that:

[0092] The change over time can be expressed as:

[0093] Therefore, the constraint representing the tolerance of phase angle variation can be expressed as:

[0094] TREE1 to TREE5 contain two objectives, while TREE6 contains three optimization objectives. All test cases are subject to multiple constraints, which can be divided into topology constraints, time series constraints, and phase constraints. The data length and the number of decision variables of the test cases vary. According to the type of data involved, TREE problems can be divided into three categories. The first category involves only primary voltage data, including TREE1 to TREE3, with two objectives and three constraints. TREE4 and TREE5 belong to the second category, which contains primary and secondary voltage data and involves four constraints. TREE6 combines voltage and phase angle data, with three objectives and six constraints.

[0095] The proposed method was compared with the most advanced algorithms such as EMCMO, AGEMOEA-II, C3M, CMOEMT, and LMOCSO. Simulated binary crossover (SBX) and polynomial mutation (PM) were used in offspring generation. The crossover and mutation probabilities were set to pc=1.0 and pm=1 / D, respectively, where D is the number of decision variables. The population size was set to 100 in the two-objective test instance and to 105 in the three-objective test instance. As the termination criterion, the number of evaluations (FEs) for TREE1 to TREE5 was set to 10000 and for TREE6 to 400000. Figure 3 The mean and standard deviation of the hypervolume (HV) value for each tested algorithm are shown. Higher HV values ​​indicate better results.

[0096] Figure 4 The heat map is drawn for the median of each algorithm on each TREE test case. Figure 4 It can be seen that the method proposed in the present invention has a higher HV median value than other algorithms when optimizing the TREE problem, indicating that the experimental results obtained by the method proposed in the present invention in independent repeated experiments are better than those of other compared algorithms.

[0097] The present invention utilizes the relative position relationship between feasible solutions and infeasible solutions in the target space to provide heuristic information for evolutionary search, thereby improving the convergence speed of the algorithm; balances fast convergence and solution diversity through adaptive strategies at different stages of the search process to improve the overall optimization performance; utilizes the correlation between multiple tasks and transfer learning capabilities to enhance the generalization performance of the algorithm, significantly improves the optimization efficiency in high-dimensional decision spaces and complex constraints, and provides a more accurate, stable and efficient solution for voltage transformer time-varying error estimation.

[0098] The electronic device 500 may be a desktop computer, a notebook, a PDA, a cloud server, or other electronic device. The electronic device 500 may include, but is not limited to, a processor 501 and a memory 502. Those skilled in the art will appreciate that Figure 5It is only an example of the electronic device 500 and does not constitute a limitation of the electronic device 500. It may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the electronic device may also include input and output devices, network access devices, buses, etc.

[0099] Processor 501 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or the processor may be any conventional processor, etc.

[0100] The memory 502 may be an internal storage unit of the electronic device 500, for example, a hard disk or memory of the electronic device 500. The memory 502 may also be an external storage device of the electronic device 500, for example, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. equipped on the electronic device 500. Further, the memory 502 may also include both an internal storage unit of the electronic device 500 and an external storage device. The memory 502 is used to store the computer program 503 and other programs and data required by the electronic device. The memory 502 may also be used to temporarily store data that has been output or is to be output.

[0101] In the embodiments provided in the present disclosure, it should be understood that the disclosed devices / electronic devices and methods can be implemented in other ways. For example, the device / electronic device embodiments described above are merely schematic. For example, the division of modules or units is only a logical function division. There may be other division methods in actual implementation. Multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed may be through some interfaces, indirect coupling or communication connection of devices or units, which may be electrical, mechanical or other forms.

[0102] If the integrated module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present disclosure implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. The computer program may include computer program code, and the computer program code may be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electric carrier signals and telecommunication signals.

[0103] The above embodiments are only used to illustrate the technical solutions of the present disclosure, rather than to limit them. Although the present disclosure has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present disclosure, and should all be included in the protection scope of the present disclosure.

Claims

1. An optimization method for estimating time-varying errors of voltage transformers, characterized in that: The method comprises the following steps: Based on the solution space of the optimization problem, an initial population is randomly generated as the initial solution set of the optimization process; Design evenly distributed reference points for guiding the target space and evaluating the solution during the optimization process; By recording the historical state of the population and the feasibility of the marked solution, the feasible solution set is initialized to provide historical support and feasibility constraints for optimization; Calculate the objective function value and constraint deviation of each solution in the population, determine whether it is feasible, and update the record status of the solution; Generate new candidate solutions based on the solution status of the current population, combined with the reference point association and historical information; From the current population and candidate solutions, select the next generation population according to the optimization objectives and constraints, and update the optimization direction; Repeat the process of generating candidate solutions and selecting populations until the preset number of iterations is reached or the optimization goal converges; The Pareto non-dominated solution set in the final solution record matrix is ​​extracted and output as the optimization result.

2. The method according to claim 1, characterized in that The step of generating the initial population specifically includes: Determine the number of decision variables for the problem D , the number of objective functions M and population size N ; Each population solution is randomly generated by uniform distribution D dimensional variables, and determine the value range based on the upper and lower bounds defined in the problem; Constructing the initial population matrix P 0 , as the optimization initial solution set.

3. The method according to claim 1, characterized in that The reference points for the design to be evenly distributed include: Generating matrices by mixed uniform design W , select the column with the largest centralized L2 deviation as the reference point; The reference points are distributed in the target space to ensure uniform coverage, which is used to guide the direction selection of the optimization target.

4. The method according to claim 1, characterized in that The process of initializing the feasible solution set by recording the historical state of the population and marking the feasibility of the solution includes: Create a solution record matrix to save the solutions of the current population, the previous generation population, and the previous two generations of populations; Create a marker vector to record the feasibility status of the solution; Initialize the feasible solution set matrix, each row is a negative unit vector, indicating that there is no feasible solution in the initial state.

5. The method according to claim 1, characterized in that The calculation of the objective function value and constraint deviation of each solution in the population and determining whether it is feasible include: Calculate the performance value of each population solution in the target space according to the objective function; Calculate the deviation value of equality constraints and inequality constraints for each solution to determine its feasibility; Update the solution record status, mark feasible solutions and infeasible solutions, and save them in the solution record matrix.

6. The method according to claim 1, characterized in that The generating of new candidate solutions according to the solution state of the current population, combined with the reference point association relationship and historical information, includes: For feasible solutions, new candidate solutions are generated by combining the solutions associated with the reference point and the historical solution information; For infeasible solutions, different mutation strategies are selected according to the current iteration status to generate new solutions.

7. The method according to claim 1, characterized in that The step of selecting the next generation population from the current population and candidate solutions according to the optimization objectives and constraints includes: Select solutions from the current population and the newly generated candidate solutions according to the target solution association rule for each reference point; According to the objective function value and constraint deviation, the solutions that meet the optimization conditions are selected to form the next generation population.

8. The method according to claim 1, characterized in that The process of repeatedly generating candidate solutions and selecting a population until a preset number of iterations is reached or the optimization target converges includes: Set the maximum number of iterations or the convergence accuracy of the objective function value as the optimization termination condition; In each iteration, the process of generating candidate solutions and selecting the population is repeated to gradually approach the optimization goal.

9. An electronic device, characterized in that: include: one or more processors; A storage unit, used to store one or more programs, which, when executed by the one or more processors, enable the one or more processors to implement the optimization method for estimating time-varying errors of voltage transformers according to any one of claims 1 to 8.

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 optimization method for estimating time-varying errors of voltage transformers according to any one of claims 1 to 8 can be implemented.

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