A multi-objective optimization design method and system of a zero sequence current transformer

Abstract

This application belongs to the field of zero-sequence current transformer optimization design technology, specifically disclosing a multi-objective optimization design method and system for zero-sequence current transformers. The method includes: taking the relative error of the secondary output voltage, manufacturing cost, and overall weight as optimization objectives; selecting core parameters, winding parameters, and structural parameters as design variables; establishing constraint conditions and cost / weight calculation models; constructing a multi-objective optimization mathematical model; using a mixed real-number and integer encoding method to encode the design variables to generate an initial population; iteratively optimizing based on a multi-objective optimization algorithm to obtain a Pareto non-dominated optimal solution set; verifying the electromagnetic characteristics and engineering feasibility of the optimal solution set; eliminating invalid solutions to obtain an engineering-feasible Pareto optimal solution set; selecting the final design scheme according to the objective weights of the engineering scenario and outputting all design parameters. This application can achieve coordinated optimization of the accuracy, cost, and weight of zero-sequence current transformers.

Description

Technical Field

[0001] This application belongs to the field of zero-sequence current transformer optimization design technology, and more specifically, relates to a multi-objective optimization design method and system for zero-sequence current transformers. Background Technology

[0002] Zero-sequence current transformers are core components for ground fault detection and relay protection in power systems. The accuracy of their secondary output voltage directly determines the reliability of the protection device, while cost, weight, and size affect the economic efficiency and ease of installation in engineering applications. The design of zero-sequence current transformers must simultaneously meet the dual requirements of electrical performance compliance and engineering practicality.

[0003] Existing design methods for zero-sequence current transformers often employ trial-and-error adjustments of single parameters (such as adjusting the core cross-sectional area and the number of winding turns), which can only meet the single objective requirement of measurement accuracy and cannot simultaneously optimize objectives such as cost, weight, and volume. For example, while the design method disclosed in Chinese patent CN 119808679A solves the design error problem of traditional error calculation and achieves performance targets, it does not consider the optimization of transformer cost, weight, and volume. Furthermore, although there are attempts to apply intelligent optimization algorithms to the design of conventional current transformers, these have not been adapted to the unique characteristics of zero-sequence current transformers, such as excitation current constraints, structural size limitations, and parallel resistance-capacitor loads on the secondary side. They also lack multi-objective optimization mathematical models for accuracy, cost, and weight, making them unsuitable for direct application in the design of zero-sequence current transformers.

[0004] Therefore, how to achieve coordinated optimization of multiple design goals such as accuracy, cost, and weight of zero-sequence current transformers is an urgent problem to be solved. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of this application is to provide a multi-objective optimization design method and system for zero-sequence current transformers, which can achieve synergistic optimization of multiple design objectives such as accuracy, cost, and weight of zero-sequence current transformers.

[0006] To achieve the above objectives, in a first aspect, this application provides a multi-objective optimization design method for a zero-sequence current transformer, comprising the following steps: S10, with the relative error of the secondary output voltage of the zero-sequence current transformer, manufacturing cost and overall weight as optimization objectives, select the effective cross-sectional area of ​​the iron core, the number of turns of the secondary winding, the diameter of the secondary conductor, the average magnetic circuit length of the iron core and the magnetic permeability of the iron core material as design variables, and establish equality constraints and inequality constraints, as well as manufacturing cost calculation model and overall weight calculation model, to construct a multi-objective optimization mathematical model; S20, the design variables are encoded using a hybrid encoding method of real number encoding and integer encoding to generate an initial population, and the initial population is iteratively optimized based on a multi-objective optimization algorithm to obtain a Pareto non-dominated optimal solution set; S30, perform electromagnetic property verification and engineering feasibility verification on each solution in the Pareto non-dominated optimal solution set, remove solutions that do not meet the verification requirements, and obtain an engineering-feasible Pareto optimal solution set. S40, based on the target weight of the engineering scenario, select the final design scheme from the set of feasible Pareto optimal solutions for the engineering scenario, and output all design parameters of the final design scheme.

[0007] As a further preferred embodiment, in step S10, the optimization objective includes: using the relative error of the secondary output voltage... Minimize the accuracy target while minimizing the manufacturing cost. C For cost objectives, based on overall weight M Minimize the weight target; The design variables include: the effective cross-sectional area of ​​the iron core, which is a continuous variable. S Secondary conductor diameter d Average magnetic circuit length of the iron core L Relative permeability of core material μ r And the number of turns in the secondary winding as an integer variable. N 2.

[0008] As a further preferred embodiment, in step S10, based on the electromagnetic design principle of zero-sequence current transformers, equation constraints are established for parameters such as secondary output voltage, excitation impedance, and magnetic flux density to obtain the secondary side output voltage of the transformer. U 2. The calculation formula is:

[0009] in, I 1 is the effective value of the primary side current-carrying conductor current; Z 2n It is the rated load impedance; Z 2 is the total impedance of the secondary circuit; N 1 represents the number of turns of the primary conductor; N 2 represents the number of turns in the secondary winding; Z 0 represents the magnetizing impedance; θ It is the core loss angle; φ 2 is the power factor angle of the secondary circuit; The inequality constraints include: secondary conductor current density. J ≤2A / mm², wire diameter d ≥0.1mm, number of turns in the secondary winding N2≥100; Core magnetic flux density B ≤saturation magnetic flux density B max Excitation current I 0≤ I 1; Effective cross-sectional area of ​​the iron core S Within a preset range, the average magnetic circuit length of the iron core L Within the preset range; relative error of secondary output voltage ≤ Rated error limit max Relative permeability of core material μ r Within the preset range.

[0010] As a further preferred embodiment, in step S10, the manufacturing cost calculation model is as follows:

[0011] in, C Fe1 The unit weight cost of the first type of core material; M Fe1 This refers to the weight of the first type of core material; C Fe2 The unit weight cost of the second type of core material; M Fe2 This refers to the weight of the second type of core material; C Cu Cost per unit weight of winding; M Cu This refers to the weight of the winding. C Fix To fix processing costs.

[0012] As a further preferred embodiment, in step S10, the overall weight calculation model is as follows:

[0013] in, M Fe1 = ρ Fe1 V Fe1 , ρ Fe1 The density of the first core material, V Fe1 This represents the volume of the first type of core material; M Fe2 = ρ Fe2 V Fe2 , ρ Fe2 The density of the second type of core material,V Fe2 This refers to the volume of the second type of core material; M Cu = ρ Cu V Cu , ρ Cu Copper wire density, V Cu This represents the volume of the copper wire.

[0014] As a further preferred embodiment, in step S20, the multi-objective optimization algorithm is one of the following: Fast Elite Non-Dominated Sorting Genetic Algorithm (NSGA-II), Reference Point Guided Multi-Objective Non-Dominated Sorting Genetic Algorithm (NSGA-III), or Particle Swarm Optimization-Genetic Algorithm Hybrid Algorithm.

[0015] As a further preferred embodiment, when the multi-objective optimization algorithm is the NSGA-II algorithm, the iterative optimization of the initial population based on the multi-objective optimization algorithm to obtain the Pareto non-dominated optimal solution set specifically involves: The initial population is sorted by non-dominated order. Based on the Pareto non-dominated relation, the non-dominated individuals are divided into the first layer. The remaining individuals are sorted repeatedly to obtain the non-dominated solution sets of each layer. The crowding degree of the non-dominated individuals in each layer is calculated. A progeny population is generated through genetic operations, which include: selecting individuals from the parent generation using a tournament selection method; applying simulated binary crossover and polynomial mutation to the core effective cross-sectional area, secondary conductor diameter, core average magnetic circuit length, and core material relative permeability as continuous variables; and applying integer crossover and random integer mutation to the number of turns in the secondary winding as an integer variable. The crossover probability ranges from 0.8 to 0.9, and the mutation probability ranges from 0.01 to 0.05. The parent population and the offspring population are merged to obtain a new population. The new population is then re-sorted for non-dominance and crowding, and a preset number of individuals with the highest sorting values ​​are selected as the next generation of parent population. Repeat the above steps until the preset maximum number of iterations is reached, and use the final non-dominated solution set as the Pareto non-dominated optimal solution set.

[0016] As a further preferred embodiment, in step S20, the hybrid encoding method of real number encoding and integer encoding is specifically as follows: for the effective cross-sectional area of ​​the iron core S Secondary conductor diameter d Average magnetic circuit length of the iron core L Relative permeability of core material μ r Real number encoding is used to determine the number of turns in the secondary winding. N 2. Integer encoding is used.

[0017] As a further preferred embodiment, in step S30, the electromagnetic characteristic verification includes: substituting the solution into the electromagnetic formula of the zero-sequence current transformer to calculate the secondary output voltage, magnetic flux density, and excitation current parameters, and verifying whether all constraints are met; the engineering feasibility verification includes: verifying whether the design variables meet the actual engineering requirements, which include processing technology, material supply, and installation space requirements.

[0018] Secondly, this application provides a multi-objective optimization design system for a zero-sequence current transformer, used to implement the steps of any one of the above methods, including: The model building module is used to optimize the relative error of the secondary output voltage, manufacturing cost and overall weight of the zero-sequence current transformer. It selects the effective cross-sectional area of ​​the iron core, the number of turns of the secondary winding, the diameter of the secondary conductor, the average magnetic circuit length of the iron core and the magnetic permeability of the iron core material as design variables, and establishes equality constraints and inequality constraints, as well as manufacturing cost calculation model and overall weight calculation model to construct a multi-objective optimization mathematical model. The optimization solution module is used to encode the design variables using a hybrid encoding method of real number encoding and integer encoding to generate an initial population, and to iteratively optimize the initial population based on a multi-objective optimization algorithm to obtain a Pareto non-dominated optimal solution set. The verification and filtering module is used to verify the electromagnetic properties and engineering feasibility of each solution in the Pareto non-dominated optimal solution set, and to remove solutions that do not meet the verification requirements to obtain an engineering-feasible Pareto optimal solution set. The scheme selection output module is used to select the final design scheme from the set of feasible Pareto optimal solutions for the engineering scenario based on the target weight of the engineering scenario, and output all design parameters of the final design scheme.

[0019] This application has the following beneficial effects: 1) Achieve multi-objective collaborative optimization: Establish a mathematical model for the optimization of accuracy, cost, and weight for zero-sequence current transformers. This solves the limitations of single-objective optimization in traditional design methods. Under the premise of meeting the accuracy requirements of relay protection, it minimizes cost and weight, and takes into account the reliability, economy, and practicality of engineering applications. 2) High optimization efficiency and strong optimization ability. The NSGA-II algorithm is used for global optimization. The algorithm is adapted to the mixed variable characteristics of the zero-sequence current transformer. This avoids the problems of traditional trial calculation methods relying on experience and low efficiency. It can quickly find the global optimal solution and significantly improve design efficiency. 3) Adapts to diverse engineering needs. The output Pareto non-dominated optimal solution set contains multiple sets of collaborative optimal solutions. It can be flexibly selected and highly adaptable according to the target weight of different engineering scenarios, such as prioritizing lightweight outdoor installation, prioritizing low-cost industrial power distribution, and prioritizing high-precision precision protection. 4) Comprehensive constraints: Constraints covering electromagnetic characteristics, process requirements, and structural limitations are established to ensure the engineering feasibility of the optimization results and avoid the problem of the theoretical optimality being out of touch with engineering practice. 5) It has strong versatility. The parameters and constraints of the optimization model can be adjusted according to different zero-sequence current transformer design requirements, such as different rated current, rated voltage, load parameters, and installation space. It is suitable for the design of zero-sequence current transformers of different voltage levels and application scenarios in power systems. Attached Figure Description

[0020] Figure 1 This is the equivalent magnetic circuit of the zero-sequence current transformer provided in the embodiments of this application; Figure 2 This is the equivalent circuit of the zero-sequence current transformer provided in the embodiments of this application; Figure 3 This is a flowchart of the multi-objective optimization design method provided in the embodiments of this application; Figure 4 This is the iterative convergence curve of the NSGA-II algorithm provided in the embodiments of this application; Figure 5 This is a scatter plot of the Pareto front of the NSGA-II algorithm provided in the embodiments of this application. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0022] This application provides a multi-objective optimization design method for zero-sequence current transformers based on the NSGA-II algorithm. By establishing a multi-objective optimization mathematical model adapted to the characteristics of zero-sequence current transformers and combining the global optimization capability of the NSGA-II algorithm, a set of non-dominated optimal design schemes is output, which engineers can select according to the objective weights of the actual engineering scenario. This achieves collaborative optimization with high accuracy, lowest cost, and lightest weight, while improving design efficiency and reducing reliance on experience.

[0023] The core technical solution of this application is as follows: taking the relative error of the secondary output voltage, manufacturing cost, and overall weight of the zero-sequence current transformer as optimization objectives, and the core parameters, winding parameters, and structural parameters as design variables, an optimization mathematical model is established in combination with the electromagnetic characteristic constraints, process constraints, and structural constraints of the zero-sequence current transformer; the NSGA-II algorithm is used to perform global optimization on the model, and the non-dominated optimal solution set is obtained through encoding, initializing the population, non-dominated sorting, congestion calculation, and genetic operations; the optimal solution set is verified and screened to obtain the optimal design scheme of the zero-sequence current transformer that meets the engineering requirements.

[0024] exist Figure 1 In the equivalent magnetic circuit of the mutual inductor, R m1 It is the leakage magnetic reluctance of the current-carrying conductor in phase A. R m2 It is the leakage magnetic reluctance of the B-phase current-carrying conductor. R m3 It is the leakage magnetic reluctance of the C-phase current-carrying conductor. R m4 It is the main magnetic circuit reluctance of the transformer core. , and These are the current phasors for phases A, B, and C. This is the current phasor of the secondary winding. According to the duality principle, we can obtain... Figure 2 The equivalent circuit of the mutual inductor shown is as follows, in which, , and These are the voltage phasors of phases A, B, and C. R 1 is the equivalent resistance of a primary current-carrying conductor. X 1A , X 1B and X 1C It is the leakage reactance corresponding to the magnetic reluctance of the leakage magnetic circuit. X m It is the magnetizing reactance corresponding to the magnetic reluctance of the main magnetic circuit. R m It is the excitation resistance corresponding to the core loss. It is a zero-sequence current phasor. It is the secondary winding current phasor referred to the primary side. It is the excitation current phasor. It is an induced electromotive force. It is the secondary induced electromotive force referred to the primary side. This is the voltage at the secondary load terminal, which is attributed to the primary side. and This refers to the secondary winding resistance and leakage reactance attributed to the primary side. and It is the load impedance referred to the primary side.

[0025] like Figure 3 As shown, the overall design process includes: Step 1, Input Design Requirements: Input the rated electrical parameters of the zero-sequence current transformer (rated frequency, primary rated input current, secondary rated output voltage, load parameters, etc.), error limits, installation space constraints, material selection range, etc. Step 2, Determine the optimization model: Determine the optimization objectives (accuracy, cost, weight), design variables, constraints, and establish cost and weight calculation models; Step 3, NSGA-II algorithm parameter settings: Set algorithm parameters such as population size, number of iterations, crossover / mutation probability, and encoding method; Step 4, Initialize the population: Generate an initial population with hybrid encoding based on the design variable constraints. Step 5, Objective function and constraint calculation: Calculate the accuracy, cost, and weight objective function values ​​for each individual in the population, verify whether the constraints are met, and penalize individuals that do not meet the constraints; Step 6, Non-dominated sorting and crowding calculation: Perform Pareto non-dominated sorting on the population and calculate the crowding of individuals at each level. Step 7, Genetic operations: Generate offspring populations through selection, crossover, and mutation; Step 8, Iteration judgment: Merge the parent and child populations, reorder and select a new population, and determine whether the maximum number of iterations has been reached. If not, return to step 5 to continue iterating; if so, proceed to step 9. Step 9, Optimal Solution Verification: Verify the electromagnetic properties and engineering feasibility of the Pareto non-dominated optimal solution set, and eliminate invalid solutions; Step 10, Output the optimal solution set: Output the set of Pareto optimal solutions that are feasible for the project, including the design parameters and performance indicators of each solution set; Step 11, Engineering Scheme Selection: Based on the target weights of the actual engineering scenario, select the final design scheme from the set of optimal solutions; Step 12, Design Complete: Output all parameters of the final design scheme to guide the fabrication and manufacturing of the zero-sequence current transformer.

[0026] Specifically, the following steps are included: (a) Determine the optimization objective A three-objective optimization function is established to minimize the relative error of the secondary output voltage, minimize manufacturing cost, and minimize overall weight, while also supporting the adjustment of objective weights according to engineering scenarios: (1) Precision target Secondary output voltage relative error , The objective function is: (The given error limit is missing from the original text.) (minimize).

[0027] (2) Cost target Taking into account the costs of core materials, winding copper materials, and processing costs, the objective function is: (minimize).

[0028] (3) Weight target Taking into account the core weight and the winding copper weight, the objective function is: (minimize).

[0029] In this embodiment, the operating frequency is 50Hz. N 1 represents 1 turn. I 1 represents a rated current of 100mA. U 2 is rated at 150mV. It is 3%.

[0030] (II) Determine the optimization objective: The parameters that have a significant impact on the three optimization objectives and are engineering-achievable are selected as design variables, denoted as:

[0031] in, x 1 is the effective cross-sectional area of ​​the iron core. S (cm 2 ), which are continuous variables; x 2 is the number of turns in the secondary winding of the current transformer. N 2 is an integer variable; x 3 is the diameter of the secondary winding conductor. d (mm) is a continuous variable; x 4 is the average magnetic circuit length of the iron core. L (cm) is a continuous variable; x 5 is the relative permeability of the core material. μ r , is a continuous variable.

[0032] (iii) Establishing constraints Constraints are established based on the electromagnetic characteristics, process requirements, and structural limitations of the zero-sequence current transformer, and are divided into equality constraints and inequality constraints.

[0033] (1) Equality constraints Based on the electromagnetic design principle of zero-sequence current transformer, combined with Figure 1 and Figure 2 Using the equivalent magnetic circuit and equivalent circuit shown, establish equation constraints for parameters such as secondary output voltage, excitation impedance, and magnetic flux density to obtain the secondary output voltage of the current transformer.

[0034] in, I 1 is the effective value of the primary side current-carrying conductor current. Z 2n It is the rated load impedance. Z 2 is the total impedance of the secondary circuit. N 1 represents the number of turns of the primary conductor. N 2 represents the number of turns in the secondary winding. Z 0 represents the magnetizing impedance. θ It is the core loss angle. φ 2 is the power factor angle of the secondary circuit.

[0035] (2) Inequality constraints Process constraints: Secondary conductor current density J ≤ 2A / mm 2 wire diameter d ≥ 0.1mm, number of turns in the secondary winding N 2≥100, ensuring the winding process; Electromagnetic confinement: core flux density B ≤ B max (Saturation magnetic flux density), to avoid core saturation, excitation current I 0≤ I 1. Avoid calculation errors caused by the excitation current exceeding the primary current; Structural constraints: Effective cross-sectional area of ​​the iron core Average magnetic circuit length of iron core Suitable for the installation space of current transformers; Accuracy constraint: Relative error of secondary output voltage ; Material constraints: relative permeability .

[0036] In the embodiment, the constraint ranges for each variable are as follows: , , , , .

[0037] (iv) Establish a cost and weight calculation model (1) Cost calculation model The cost is calculated based on the comprehensive cost of core materials, winding copper materials, and processing costs, according to the actual project pricing standard:

[0038] in, C Fe1 This is the cost per unit weight of the first type of core material (yuan / kg). MFe1 It is the weight (kg) of the first type of iron core. C Fe2 This is the cost per unit weight (yuan / kg) of the second type of core material. M Fe2 It is the second type of iron core weight (kg). C Cu It is the cost per unit weight of the winding (yuan / kg). M Cu It is the weight of the winding (kg). C Fix It is the fixed processing cost (yuan).

[0039] The reason for considering two types of core materials here is that the soft magnetic materials used for the transformer core and the magnetic shielding layer are usually different. Let's assume that the first type of material is used for the transformer core and the second type of core material is used for the magnetic shielding layer.

[0040] (2) Weight calculation model The overall weight of a zero-sequence current transformer is the sum of the weight of the core and the weight of the winding copper materials, excluding auxiliary components such as the casing and insulation. It can be expanded according to project requirements.

[0041] Among them, the weight of the iron core M Fe1 = ρ Fe1 V Fe1 , ρ Fe1 It is the density of the first type of core material. V Fe1 It refers to the volume of the first type of core material; the weight of the core. M Fe2 = ρ Fe2 V Fe2 , ρ Fe2 It is the density of the second type of core material. V Fe2 It refers to the volume of the second type of core material; the winding weight. M Cu = ρ Cu V Cu , ρ Cu It is the copper wire density. V Cu It is the volume of the copper wire.

[0042] (V) Multi-objective optimization based on NSGA-II algorithm For the established multi-objective optimization model of the zero-sequence current transformer:

[0043] The NSGA-II algorithm is used for global optimization, and the algorithm is adapted to the mixed-variable (continuous + integer) characteristics of zero-sequence current transformers. The iterative convergence curve of the NSGA-II algorithm is shown below. Figure 4 As shown, the Pareto front scatter plot is as follows: Figure 5 As shown. In the embodiment, the population size... N The maximum number of iterations is 150. G The crossover probability is 0.85, and the mutation probability is 0.02. The specific steps include: (1) Encoding A hybrid encoding method of "real number encoding + integer encoding" is adopted for the cross-sectional area of ​​the iron core. S Wire diameter d Magnetic circuit length L Relative permeability μ r Continuous variables are encoded using real numbers; the number of turns in the secondary winding is... N 2. Integer encoding is used to ensure the engineering feasibility of design variables.

[0044] (2) Initialize the population Based on the constraints of the design variables, an initial population is randomly generated. P 0, population size is N (For engineering design, the range is 100-200), with each individual representing a set of design variable combinations. X .

[0045] (3) Non-dominated ordering Calculate the objective function value for each individual in the population and rank them according to Pareto non-dominance: if individuals A All goals are superior to the individual B ,but A Dominate B , B Eliminated; the non-dominated individuals are divided into the first layer, and the remaining individuals are sorted repeatedly to obtain the non-dominated solution sets of each layer.

[0046] (4) Crowding Calculation To ensure the diversity of the solution set, the crowding degree is calculated for each layer of non-dominated individuals, which represents the density of individuals in the target space. The greater the crowding degree, the better the diversity of individuals, thus avoiding the algorithm from converging to a local optimum.

[0047] (5) Genetic manipulation Genetic operations such as tournament selection, simulated binary crossover (SBX), and polynomial mutation are used to generate offspring populations. Qt : Selection: Select individuals with high crowding and high non-dominance level from the parent population as parents; Crossover: Use SBX crossover for continuous variables and crossover for integer variables. N 2. Integer crossover is used, with a crossover probability of 0.8 to 0.9; Mutation: Multinomial mutation is used for continuous variables, and random integer mutation is used for integer variables, with mutation probabilities ranging from 0.01 to 0.05.

[0048] (6) Population merging and iteration parental population P t and offspring population Q t Merge into a new population R t ,right R t Recalculate the non-dominated sort and crowding, and select the previous one. N Each individual serves as the parent population for the next generation. P t+1 Repeat steps ③ to ⑥ until the maximum number of iterations is reached. G (For engineering design, use 200~300), then stop iterating.

[0049] In an embodiment, such as Figure 4 and Figure 5 As shown, the algorithm iteration results are that after 250 iterations, a Pareto non-dominated optimal solution set is obtained, which contains 28 sets of non-dominated solutions. The target space is uniformly distributed and there is no dominion relationship.

[0050] (vi) Optimal solution verification and screening After iteration, a Pareto non-dominated optimal solution set is obtained. Each solution in this set is a cooperatively optimal solution in terms of accuracy, cost, and weight; that is, no single solution can improve any objective without sacrificing other objectives. Electromagnetic properties and engineering feasibility are then verified for each solution in the optimal solution set. I. Electromagnetic Characteristics Verification: Substitute the electromagnetic formula of the zero-sequence current transformer, calculate the secondary output voltage, magnetic flux density, excitation current and other parameters, and verify whether all constraints are met. II. Project Feasibility Verification: Verify whether the design variables meet the actual requirements of the project, such as processing technology, material supply, and installation space.

[0051] By eliminating solutions that fail verification, a set of Pareto optimal solutions that are feasible for engineering is obtained. Engineers can then select the final design scheme based on the target weights of the actual engineering scenario, such as prioritizing high precision, low cost, or lightweight design.

[0052] In this embodiment, electromagnetic and engineering verifications were performed on 28 sets of non-dominated solutions. Three sets of solutions with saturated magnetic flux density and two sets with excessive conductor current density were eliminated, resulting in 23 sets of engineering-feasible optimal solutions. Then, from these 23 sets of solutions, three typical schemes were selected based on the priority of three common engineering objectives, such as... Figure 5 The solutions shown in the diagram represent the high-precision priority, low-cost optimization, and lightweight optimization schemes, respectively. All three typical schemes satisfy all constraints and achieve optimality under their respective priority objectives, verifying the effectiveness and engineering applicability of the method presented in this invention.

[0053] (vii) Design scheme determination and parameter output Based on the target requirements of the engineering scenario, the optimal design scheme is selected from the set of feasible Pareto optimal solutions, and the core parameters are output. S , L , μ r ), winding parameters ( N 2. d The secondary circuit parameters are given, along with performance indicators such as the relative error of the secondary output voltage, manufacturing cost, and overall weight, thus completing the multi-objective optimization design of the zero-sequence current transformer.

[0054] The beneficial effects of the technical solution in this embodiment include: 1) Achieve multi-objective collaborative optimization: Establish a mathematical model for the optimization of accuracy, cost, and weight for zero-sequence current transformers. This solves the limitations of single-objective optimization in traditional design methods. Under the premise of meeting the accuracy requirements of relay protection, it minimizes cost and weight, and takes into account the reliability, economy, and practicality of engineering applications. 2) High optimization efficiency and strong optimization ability. The NSGA-II algorithm is used for global optimization. The algorithm is adapted to the mixed variable characteristics of the zero-sequence current transformer. This avoids the problems of traditional trial calculation methods relying on experience and low efficiency. It can quickly find the global optimal solution and significantly improve design efficiency. 3) Adapts to diverse engineering needs. The output Pareto non-dominated optimal solution set contains multiple sets of collaborative optimal solutions. It can be flexibly selected and highly adaptable according to the target weight of different engineering scenarios, such as prioritizing lightweight outdoor installation, prioritizing low-cost industrial power distribution, and prioritizing high-precision precision protection. 4) Comprehensive constraints: Constraints covering electromagnetic characteristics, process requirements, and structural limitations are established to ensure the engineering feasibility of the optimization results and avoid the problem of the theoretical optimality being out of touch with engineering practice. 5) It has strong versatility. The parameters and constraints of the optimization model can be adjusted according to different zero-sequence current transformer design requirements, such as different rated current, rated voltage, load parameters, and installation space. It is suitable for the design of zero-sequence current transformers of different voltage levels and application scenarios in power systems.

[0055] In addition, while keeping the optimization objective and parameter variation range of the zero-sequence current transformer unchanged, other multi-objective optimization algorithms, such as the NSGA-II algorithm, the NSGA-III algorithm, and the particle swarm optimization-genetic algorithm hybrid algorithm, can also be used to replace the NSGA-II algorithm in this embodiment.

[0056] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A multi-objective optimization design method for a zero-sequence current transformer, characterized in that, Includes the following steps: S10, with the relative error of the secondary output voltage of the zero-sequence current transformer, manufacturing cost and overall weight as optimization objectives, select the effective cross-sectional area of ​​the iron core, the number of turns of the secondary winding, the diameter of the secondary conductor, the average magnetic circuit length of the iron core and the magnetic permeability of the iron core material as design variables, and establish equality constraints and inequality constraints, as well as manufacturing cost calculation model and overall weight calculation model, to construct a multi-objective optimization mathematical model; S20, the design variables are encoded using a hybrid encoding method of real number encoding and integer encoding to generate an initial population, and the initial population is iteratively optimized based on a multi-objective optimization algorithm to obtain a Pareto non-dominated optimal solution set; S30, perform electromagnetic property verification and engineering feasibility verification on each solution in the Pareto non-dominated optimal solution set, remove solutions that do not meet the verification requirements, and obtain an engineering-feasible Pareto optimal solution set. S40, based on the target weight of the engineering scenario, select the final design scheme from the set of feasible Pareto optimal solutions for the engineering scenario, and output all design parameters of the final design scheme.

2. The multi-objective optimization design method for zero-sequence current transformers as described in claim 1, characterized in that, In step S10, the optimization objective includes: using the relative error of the secondary output voltage... Minimize the accuracy target while minimizing the manufacturing cost. C For cost objectives, based on overall weight M Minimize the weight target; The design variables include: the effective cross-sectional area of ​​the iron core, which is a continuous variable. S Secondary conductor diameter d Average magnetic circuit length of the iron core L Relative permeability of core material μ r and the number of turns of the secondary winding as an integer variable. N 2.

3. The multi-objective optimization design method for zero-sequence current transformers as described in claim 1, characterized in that, In step S10, based on the electromagnetic design principle of zero-sequence current transformers, equation constraints are established for parameters such as secondary output voltage, excitation impedance, and magnetic flux density to obtain the secondary output voltage of the transformer. U 2. The calculation formula is: in, I 1 is the effective value of the primary side current-carrying conductor current; Z 2n It is the rated load impedance; Z 2 is the total impedance of the secondary circuit; N 1 represents the number of turns of the primary conductor; N 2 represents the number of turns in the secondary winding; Z 0 represents the magnetizing impedance; θ It is the core loss angle; φ 2 is the power factor angle of the secondary circuit; The inequality constraints include: secondary conductor current density. J ≤2A / mm², wire diameter d ≥0.1mm, number of turns in the secondary winding N 2≥100; Core magnetic flux density B ≤saturation magnetic flux density B max Excitation current I 0≤ I 1; Effective cross-sectional area of ​​the iron core S Within a preset range, the average magnetic circuit length of the iron core L Within the preset range; relative error of secondary output voltage ≤ Rated error limit max Relative permeability of core material μ r Within the preset range.

4. The multi-objective optimization design method for zero-sequence current transformers as described in claim 1, characterized in that, In step S10, the manufacturing cost calculation model is as follows: in, C Fe1 The unit weight cost of the first type of core material; M Fe1 This refers to the weight of the first type of core material; C Fe2 The unit weight cost of the second type of core material; M Fe2 This refers to the weight of the second type of core material; C Cu Cost per unit weight of winding; M Cu This refers to the weight of the winding. C Fix To fix processing costs.

5. The multi-objective optimization design method for zero-sequence current transformers as described in claim 1, characterized in that, In step S10, the overall weight calculation model is as follows: in, M Fe1 = ρ Fe1 V Fe1 , ρ Fe1 The density of the first core material, V Fe1 This represents the volume of the first type of core material; M Fe2 = ρ Fe2 V Fe2 , ρ Fe2 The density of the second type of core material, V Fe2 This refers to the volume of the second type of core material; M Cu = ρ Cu V Cu , ρ Cu Copper wire density, V Cu Let V be the volume of the copper wire.

6. The multi-objective optimization design method for zero-sequence current transformers as described in claim 1, characterized in that, In step S20, the multi-objective optimization algorithm is one of the following: fast elite non-dominated sorting genetic algorithm, reference point guided multi-objective non-dominated sorting genetic algorithm, or particle swarm optimization-genetic algorithm hybrid algorithm.

7. The multi-objective optimization design method for zero-sequence current transformers as described in claim 6, characterized in that, When the multi-objective optimization algorithm is a fast elite non-dominated sorting genetic algorithm, the iterative optimization of the initial population based on the multi-objective optimization algorithm to obtain the Pareto non-dominated optimal solution set is specifically as follows: The initial population is sorted by non-dominated order. Based on the Pareto non-dominated relation, the non-dominated individuals are divided into the first layer. The remaining individuals are sorted repeatedly to obtain the non-dominated solution sets of each layer. The crowding degree of the non-dominated individuals in each layer is calculated. A progeny population is generated through genetic operations, which include: selecting individuals from the parent generation using a tournament selection method; applying simulated binary crossover and polynomial mutation to the core effective cross-sectional area, secondary conductor diameter, core average magnetic circuit length, and core material relative permeability as continuous variables; and applying integer crossover and random integer mutation to the number of turns in the secondary winding as an integer variable. The crossover probability ranges from 0.8 to 0.9, and the mutation probability ranges from 0.01 to 0.

05. The parent population and the offspring population are merged to obtain a new population. The new population is then re-sorted for non-dominance and crowding, and a preset number of individuals with the highest sorting values ​​are selected as the next generation of parent population. Repeat the above steps until the preset maximum number of iterations is reached, and use the final non-dominated solution set as the Pareto non-dominated optimal solution set.

8. The multi-objective optimization design method for zero-sequence current transformers as described in claim 1, characterized in that, In step S20, the hybrid encoding method of real number encoding and integer encoding specifically refers to: for the effective cross-sectional area of ​​the iron core... S Secondary conductor diameter d Average magnetic circuit length of the iron core L Relative permeability of core material μ r Real number encoding is used to determine the number of turns in the secondary winding. N 2. Integer encoding is used.

9. The multi-objective optimization design method for zero-sequence current transformers as described in claim 1, characterized in that, In step S30, the electromagnetic characteristic verification includes: substituting the solution into the electromagnetic formula of the zero-sequence current transformer to calculate the secondary output voltage, magnetic flux density, and excitation current parameters, and verifying whether all constraints are met; the engineering feasibility verification includes: verifying whether the design variables meet the actual engineering requirements, which include processing technology, material supply, and installation space requirements.

10. A multi-objective optimization design system for a zero-sequence current transformer, characterized in that, The steps for implementing the method as described in any one of claims 1 to 9 include: The model building module is used to optimize the relative error of the secondary output voltage, manufacturing cost and overall weight of the zero-sequence current transformer. It selects the effective cross-sectional area of ​​the iron core, the number of turns of the secondary winding, the diameter of the secondary conductor, the average magnetic circuit length of the iron core and the magnetic permeability of the iron core material as design variables, and establishes equality constraints and inequality constraints, as well as manufacturing cost calculation model and overall weight calculation model to construct a multi-objective optimization mathematical model. The optimization solution module is used to encode the design variables using a hybrid encoding method of real number encoding and integer encoding to generate an initial population, and to iteratively optimize the initial population based on a multi-objective optimization algorithm to obtain a Pareto non-dominated optimal solution set. The verification and filtering module is used to verify the electromagnetic properties and engineering feasibility of each solution in the Pareto non-dominated optimal solution set, and to remove solutions that do not meet the verification requirements to obtain an engineering-feasible Pareto optimal solution set. The scheme selection output module is used to select the final design scheme from the set of feasible Pareto optimal solutions for the engineering scenario based on the target weight of the engineering scenario, and output all design parameters of the final design scheme.

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