Optimization design method of multi-winding regulation and control transformer for flexible interconnection

Abstract

The invention relates to an optimization design method of a multi-winding regulation and control transformer for flexible interconnection, which comprises the following steps: 1, according to a single-target optimization design mathematical model, constructing an optimization target function with the purpose of minimizing the sum of the material cost of the multi-winding transformer and the ten-year operation cost; 2, determining required constraint conditions according to basic electrical parameters of the multi-winding regulation and control transformer for flexible interconnection; under the action of the obtained optimization objective function, punishing a trend violating constraints by adopting a punishment function, so that non-constraint optimization is gradually close to a feasible region, a constraint optimization problem of the distribution transformer is adjusted into an unconstraint optimization problem, and an optimization design model of the amplitude-phase adjustment type multi-winding transformer for flexible interconnection is obtained; and 3, solving the optimal design model, obtained in the step 2, of the multi-winding regulation and control transformer for flexible interconnection by using a particle swarm optimization algorithm. According to the method, the local optimal solution and the global optimal solution of the individual can be solved, and higher solution precision can be obtained.

Description

Technical Field

[0001] The present invention belongs to the technical field of transformer optimization design, and specifically relates to a particle swarm algorithm-based optimization design method for a flexible interconnected multi-winding control transformer. Background Art

[0002] As the core equipment of the power grid or the core component of flexible control equipment, oil-immersed transformers have a wide range of applications and are in great demand. Traditional transformer design has long relied on manual operation, resulting in a long design cycle, low efficiency and cumbersome process, making it difficult to meet the high-performance design requirements of special transformers. In response to challenges such as low design efficiency and uneven product quality.

[0003] The optimization design algorithms commonly used in the transformer optimization design industry include exhaustive method, regular polyhedron method, branch and bound method, Powell method and orthogonal experimental method. The literature "Jin Ming, Qingdao. Optimization design of power transformer based on improved Powell method [J]. Transformer, 1999, (10): 12-14" uses the improved Powell method to optimize the design of power transformers, and achieves that when the optimization variable speed increases, the convergence speed can still be accelerated. The literature "Zheng Liming. Research on the optimization design of oil-immersed three-dimensional wound core transformer [D]. Guangdong: South China University of Technology, 2013" adds the loop traversal method to the optimization design program and applies it to the optimization design of oil-immersed transformers, which reduces the manufacturing cost of transformers to a certain extent. The document "Ding Fanlin, Liu Zhenkai. A new method for optimizing the design of power transformers - improved orthogonal experimental method [J]. Transformer, 1993 (10): 2-6" uses the improved orthogonal experimental method to solve the defects of the optimization method in transformer design. While improving the calculation speed, it also solves the problem of optimizing discrete variables.

[0004] It is not easy to obtain the global optimal solution when the existing algorithm is used in the actual operation of multi-winding transformers. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention proposes an optimization design method for a multi-winding control transformer for flexible interconnection.

[0006] The above-mentioned object of the present invention is achieved by the following technical solutions:

[0007] A method for optimizing the design of a multi-winding control transformer for flexible interconnection includes the following design steps:

[0008] Step 1: Based on the single-objective optimization design mathematical model, an optimization objective function is constructed with the goal of minimizing the sum of the material cost and the ten-year operating cost of the multi-winding transformer;

[0009] Step 2: Determine the required constraints based on the basic electrical parameters of the multi-winding transformer for flexible interconnection; under the action of the obtained optimization objective function, the penalty function punishes the trend of violating the constraints, so that the unconstrained optimization gradually approaches the feasible area, and the constrained optimization problem of the distribution transformer is adjusted to an unconstrained optimization problem, and the optimization design model of the phase-adjustable multi-winding transformer for flexible interconnection is obtained;

[0010] Step 3: Use the particle swarm optimization algorithm to solve the optimal design model of the flexible interconnected multi-winding control transformer obtained in step 2.

[0011] Moreover, the mathematical description of the single objective optimization model in step 1 is expressed as;

[0012]

[0013] Where f(x) represents the optimization target of transformer design; x represents the optimization variable, q i (x) represents a constraint condition.

[0014] Moreover, the optimization objective function f(X)min obtained in step 1 is:

[0015] f(X)min=CF Fe G Fe +CF h G h +CF l G l +F W (1)

[0016] In formula (1), X represents the optimization variable; CF Fe Indicates the unit price of silicon steel sheet; G Fe Indicates the total weight of the core; CF h Indicates the unit price of high-voltage conductors; indicates G h ——Total weight of high-voltage conductor; CF l Indicates the unit price of low-voltage conductor; G l Indicates the total weight of the low-voltage conductor; F W Indicates the operating cost over ten years.

[0017] Moreover, in step 1, the optimization variables should include the core diameter, the number of coil turns on the low-voltage side, the wire size of the low-voltage side, and the wire size of the high-voltage side.

[0018] Moreover, in step 2, the constraints include performance constraints, material constraints and process constraints;

[0019] The performance constraints include that the load loss and short-circuit loss are not greater than 1.02 times the standard value, the specified range of the impedance voltage is (1±0.05) times the standard value, and the no-load current is not greater than 1.05 times the standard value;

[0020] The material constraints include that the coil temperature rise should not exceed the standard value, the magnetic flux density of the core should be within the specified range, and the current density of the conductor should be within the specified range;

[0021] The process constraints include that the core diameter, core window height and core center distance should be multiples of 5, the number of coil turns is an integer, and the wire specifications of the winding are selected according to the specified table.

[0022] Moreover, the optimal design model obtained in step 2 is:

[0023]

[0024] In the formula, h i (x) represents the penalty function. When the constraint is met, m i (h i ) is 0; on the contrary, when the constraint condition is not met, m i (h i ) is 1.

[0025] Furthermore, step 3 includes the following steps:

[0026] Step 3.1: Initialize the speed and position of all particles. The starting position of each particle will be directly assigned the optimal position Qbest recorded in its individual history. i ; Then, the optimal positions of all particles in the population are compared and analyzed, and the position with the best performance is selected, denoted as Pbest, as the global optimal position of the entire population; each particle represents one of the optimal design schemes for multi-winding control transformers for flexible interconnection; each design scheme contains basic information of design variables, which is presented in different dimensions of the particle swarm in the particle swarm algorithm, and particles of different dimensions represent different optimization variables;

[0027] Step 3.2, initialize the number of iterations k, and set the maximum number of iterations to K;

[0028] Step 3.3, iterate the particles in the particle swarm, and construct a particle swarm through random search to achieve global search in the feasible domain of the optimization variable;

[0029] Step 3.4: Set a penalty function in the particle swarm to punish trend particles that violate the constraints, so as to better explore the optimal position of local individuals in the particle swarm;

[0030] Step 3.5: In the current particle state analysis, according to the established mathematical model and formula, the movement speed and position of the particles are dynamically calibrated and optimized to ensure the accuracy of the simulation or experiment;

[0031] Step 3.6, update the individual positions of particles in the particle swarm and compare them with the previously recorded optimal positions; if the current position shows better performance or characteristics, update it to the best known position of the particle; if the current position fails to meet the best record, continue to use the previous optimal position as a reference;

[0032] Step 3.7: During the population optimization evaluation process, compare the best position of the individual with the global optimal solution; if the individual optimal solution of a particle exceeds the overall optimal position of the current population, it will be set as the new global optimal solution; otherwise, the global optimal solution will continue to maintain its current state;

[0033] Step 3.8, check the current number of iterations k. If the current number of iterations k is less than the maximum number of iterations K, return to step 3.3 to iterate again; if the number of iterations k is greater than the maximum number of iterations K, output the optimal function value as the sum of the material cost and the ten-year operating cost of the amplitude-phase-regulated multi-winding transformer for flexible interconnection, and output the global optimal position of the particle as the optimization variable combination.

[0034] Furthermore, step 3.1 is specifically:

[0035] The parameters of the particle swarm algorithm include the population size N, the population dimension D, the moving step length C for adjusting the particle to move to the individual optimal position, and the weight factor w represents the influence of the particle's past speed information on the current moving speed. The expression formula is:

[0036]

[0037] In the formula, rand() represents a random number that is uniformly varied in the interval [0,1]. The use of inertia weights is very useful for solving nonlinear problems.

[0038] Assume that the particles in the population move in the d-dimensional search space, and the current position of particle i is x i , the particle's current moving speed is v i ; The optimal position that particle i can reach is Qbest i , this position is called the optimal position of the individual particle; let g(x) be the objective function of the particle population, then the current optimal position of the particle can be expressed as:

[0039]

[0040] Let the number of particles in the population be n, and the optimal position Pbest(t) passed by all particles be the optimal position in the global space, then:

[0041] Pbest(t)=min{g(Qbest 1 (t)),g(Qbest 2 (t)),...,g(Qbest n (t))

[0042] The moving speed and moving position of particles in the population can be dynamically adjusted based on the past historical experience of the individual and the population. The updating formula of the particle speed and position is as follows:

[0043] v ij (t+1)=wv ij (t)+C 1 R 1 (Qbest ij (t)-x ij (t))+C 2 R 2 (Qbest j (t)-x ij (t))

[0044] x ij (t+1)=x ij (t)+v ij (t+1)

[0045] The i-th particle is represented by the letter i, j indicates that the particle is in the j-th dimension, and v ij (t+1) represents the moving speed of particle i when it evolves to generation t, x ij (t) represents its j-dimensional position in the tth generation, Qbest ij (t) indicates the optimal position of particle i in the jth dimension of the tth generation, Qbest j (t) indicates the j-dimensional component of the best position of the entire population when it evolves to generation t. w in the formula represents the inertia weight, C 1 and C 2 Become a learning factor or acceleration factor, R 1 and R 2 is any random number in the range [0,1].

[0046] The advantages and positive effects of the present invention are:

[0047] 1. When optimizing the design of a multi-winding transformer for flexible interconnection, the present invention uses different optimal variables to perform a global search in a feasible domain at different speeds and in different directions to achieve the maximum probability of finding the optimal electrical parameter value of the amplitude-phase adjustable multi-winding transformer for flexible interconnection, and has the excellent performance of low cost, high flexibility and high accuracy.

[0048] 2. This application proposes a particle swarm algorithm to optimize the multi-winding control transformer for flexible interconnection, which effectively improves the optimization design accuracy and design efficiency of the multi-winding transformer, reduces the material cost and operating cost of the multi-winding transformer, and further improves the economy of the multi-winding transformer.

[0049] 3. This application proposes two types of updates: speed and position, which make the global search capability of particles stronger and the obtained optimal position more reliable. In the iterative process, the individual local optimal solution and the global optimal solution are solved according to the position characteristics of the particles.

[0050] 4. Compared with the existing transformer design method, the multiple target parameters of the present application will not affect each other, so multiple parameters can be optimized and solved, making the solution accuracy of the flexible interconnection multi-winding regulation transformer higher.

[0051] 5. Compared with the existing transformer design technology, this application proposes a new probabilistic search technology with greater flexibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 The present invention is a flow chart of using the particle swarm algorithm of the present invention to design a multi-winding control transformer for flexible interconnection. DETAILED DESCRIPTION

[0053] The structure of the present invention is further described below with reference to the accompanying drawings and by way of examples. It should be noted that the present examples are descriptive rather than restrictive.

[0054] A method for optimizing the design of a multi-winding control transformer for flexible interconnection, see Figure 1 , the method comprises the following steps:

[0055] Step 1: Based on the single-objective optimization design mathematical model, an optimization objective function f(X)min is constructed with the goal of minimizing the sum of the material cost and the ten-year operating cost of the multi-winding transformer:

[0056] f(X)min=CF Fe G Fe +CF h G h +CF l G l +F W (1)

[0057] In formula (1), X represents the optimization variable; CF Fe Indicates the unit price of silicon steel sheet; G Fe Indicates the total weight of the core; CF h Indicates the unit price of high-voltage conductors; indicates G h ——Total weight of high-voltage conductor; CF l Indicates the unit price of low-voltage conductor; G l Indicates the total weight of the low-voltage conductor; F W It represents the operating cost for ten years;

[0058] Preferably, the mathematical description of the single objective optimization model in step 1 can be expressed as formula (2);

[0059]

[0060] In formula (2), f(x) represents the optimization target of transformer design; x represents the optimization variable, q i (x) represents a constraint condition.

[0061] Preferably, the selection of optimization variables in step 1 should follow the selection principle of optimization variables, that is, variables closely related to the objective function and constraints should be considered, and the optimization variables should be independent of each other and not affected by each other.

[0062] At the same time, the choice of transformer design variables determines the efficiency and cycle of the design. If the choice is inappropriate, it will lead to a series of problems such as low efficiency and unreasonable solutions. When the number of design variables increases, the amount of calculation increases exponentially. When the number of designs decreases, it is more difficult to find a design solution that meets the expectations. Therefore, when determining the design variables, its relationship with the objective function and the constraints should be considered. Only variables that are closely related to the two are reasonable design choices.

[0063] The variables often selected for optimization in transformer optimization design include: core diameter, current density, magnetic flux density, wire size, and other settings such as core structure and core cross-section to complete the variable selection.

[0064] According to the selection principle, the optimization variables that minimize the material cost and ten-year operating cost of the phase-adjustable multi-winding transformer for flexible interconnection should include the core diameter, the number of coil turns on the low-voltage side, the low-voltage wire size, and the high-voltage wire size.

[0065] Step 2: According to the basic electrical parameters of the transformer controlled by flexible interconnection and multi-winding, the required constraints are determined; under the action of the new objective function, the penalty function penalizes the trend of violating the constraints, so that the unconstrained optimization gradually approaches the feasible area, and then the constrained optimization problem of the distribution transformer is adjusted to an unconstrained optimization problem, and the optimization design model of the multi-winding transformer is obtained as follows:

[0066]

[0067] In formula (3), h i (x) represents the penalty function. When the constraint is met, m i (h i ) is 0. On the contrary, when the constraint condition is not met, m i (h i ) is 1.

[0068] Preferably, in step 2, the constraints include performance constraints, material constraints and process constraints.

[0069] The performance constraints include that the load loss and short-circuit loss should not be greater than 1.02 times the standard value, the impedance voltage should be within the specified range of (1±0.05) times the standard value, and the no-load current should not be greater than 1.05 times the standard value;

[0070] The material constraints include that the coil temperature rise should not exceed the standard value, the magnetic flux density of the core should be within the specified range, and the current density of the conductor should be within the specified range;

[0071] The process constraints include that the core diameter, core window height and core center distance should be multiples of 5, the number of coil turns should be an integer, and the wire specifications of the winding should be selected according to the specified table.

[0072] Step 3: Using a particle swarm optimization algorithm to solve the optimal design model of the flexible interconnection multi-winding control transformer obtained in step 2, including the following steps:

[0073] Step 3.1: Initialize the speed and position of all particles. The starting position of each particle will be directly assigned the optimal position Qbest recorded in its individual history. i . Then, in order to determine the global optimal starting point of the entire population, the optimal positions of all particles in the population are compared and analyzed, and the position with the best performance is selected, denoted as Pbest, as the global optimal position of the entire population;

[0074] Preferably, in step 3.1, the parameters of the particle swarm algorithm include the population size N, the population dimension D, and the moving step length C for adjusting the particles to move to the individual optimal position. At the same time, in order to speed up the convergence speed and improve the convergence accuracy, the weight factor w is set to represent the influence of the particle's past speed information on the current moving speed, and its expression formula is:

[0075]

[0076] In formula (4), rand() represents a random number that is uniformly varied in the interval [0,1]. The use of inertia weight is very beneficial for solving nonlinear problems.

[0077] Preferably, step 3.1 can be understood that the particle swarm algorithm is an optimization algorithm based on swarm intelligence, which is often used to solve search and optimization problems. It searches by simulating the behavior of the cooperation of biological groups such as bird flocks or fish schools. Each solution in its solution space is called a particle, and these particles find the optimal solution by moving in the solution space. Its basic idea is to continuously adjust the speed and position of each particle so that it searches for the best solution in the solution space. The speed and position of each particle will be updated according to its own past experience and the best experience in the group. In the process of searching, particles tend to move towards the position that has performed better in their history and the position that has performed best in the history of the entire group. Each time the particle swarm algorithm is iterated, the particle will move to the current optimal position, and then adjust its own moving direction and moving speed, and further move towards the optimal position. Therefore, sometimes the position found is not the global optimal, and it may only be an optimal solution in a local range, so it is called a local optimal solution.

[0078] Assume that the particles in the population move in the d-dimensional search space, and the current position of particle i is x i , the particle's current moving speed is v i The optimal position that particle i can reach is Qbest i , and this position is called the optimal position of the individual particle. Let g(x) be the objective function of the particle population, then the current optimal position of the particle can be expressed as:

[0079]

[0080] Let the number of particles in the population be n, and the optimal position Pbest(t) passed by all particles be the optimal position in the global space, then:

[0081] Pbest(t)=min{g(Qbest 1 (t)),g(Qbest 2 (t)),...,g(Qbest n (t)) (6)

[0082] The moving speed and moving position of particles in the population can be dynamically adjusted according to the past historical experience of individuals and the past historical experience of the population. The updating formulas of the particle speed and position are as follows:

[0083] v ij (t+1)=wv ij (t)+C 1 R 1 (Qbest ij (t)-x ij (t))+C 2 R 2 (Qbest j (t)-x ij (t)) (7)

[0084] x ij (t+1)=x ij (t)+v ij (t+1) (8)

[0085] The i-th particle is represented by the letter i, j indicates that the particle is in the j-th dimension, and v ij (t+1) represents the moving speed of particle i when it evolves to generation t, x ij (t) represents its j-dimensional position in the tth generation, Qbest ij (t) indicates the optimal position of particle i in the jth dimension of the tth generation, Qbest j (t) indicates the j-dimensional component of the best position of the entire population when it evolves to generation t. w in the formula represents the inertia weight, C 1 and C 2 Become a learning factor or acceleration factor, R 1 and R 2 is any random number in the range [0,1].

[0086] In this implementation example, each particle represents one of the optimized designs of the multi-winding control transformer for flexible interconnection, which is a feasible design scheme for the multi-winding transformer. Each design scheme contains basic information of the design variables, which is mainly presented in the particle swarm algorithm through different dimensions of the particle swarm, and particles of different dimensions represent different optimization variables.

[0087] Step 3.2, initialize the number of iterations k, and set the maximum number of iterations to K;

[0088] Step 3.3, iterate the particles in the particle swarm, and construct a particle swarm through random search, so as to realize global search in the feasible domain of the optimization variable;

[0089] Step 3.4: Set a penalty function in the particle swarm to punish trend particles that violate the constraints, so as to better explore the optimal position of local individuals in the particle swarm;

[0090] Step 3.5: In the current particle state analysis, according to the established mathematical model and formula, the movement speed and position of the particles are dynamically calibrated and optimized to ensure the accuracy of the simulation or experiment;

[0091] Step 3.6, update the individual positions of the particles in the particle swarm and compare them with the previously recorded optimal position. If the current position shows better performance or characteristics, update it to the best known position of the particle. If the current position fails to meet the best record, continue to use the previous optimal position as a reference;

[0092] Step 3.7: During the population optimization evaluation process, compare the individual best position with the global optimal solution. If the individual optimal solution of a particle exceeds the overall optimal position of the current population, it will be set as the new global optimal solution; otherwise, the global optimal solution will continue to maintain its current state;

[0093] Step 3.8, check the current number of iterations k. If the current number of iterations k is less than the maximum number of iterations K, return to step 3.3 and iterate again; if the number of iterations k is greater than the maximum number of iterations K, output the optimal function value as the sum of the material cost and the ten-year operating cost of the multi-winding transformer, and output the global optimal position of the particle as the optimization variable combination.

[0094] The multi-winding transformer designed by the method of the present invention is a flexible control transformer, and the flexible interconnection device constructed by it is more reasonable and has better performance. The transformer uses transformer oil as a filling material to effectively protect the insulating cardboard from oxidation, extend the service life of the transformer, and at the same time make the transformer have good heat dissipation, strong stability and simple manufacturing process and other performance characteristics. The multi-winding transformer designed by the method of the present invention mainly realizes the adjustment of voltage amplitude and phase angle, and can be used in scenarios such as flexible interconnection and power grid reconstruction. The present invention is mainly used for the optimization design of multi-winding transformers, improving the production performance of transformers and their high adaptability in usage scenarios.

[0095] Embodiment:

[0096] A multi-winding control transformer for flexible interconnection (the number of low-voltage windings is 4) is taken as an example for example optimization design. The main parameters of the multi-winding transformer are shown in Table 1.

[0097] Table 1

[0098]

[0099] The particle swarm algorithm is used to conduct simulation experiments with the sum of material cost and ten-year operating cost as the objective function. The target optimization is performed on multi-winding transformers, and the results are compared with the data given by the manufacturer's design plan to obtain the comparison results of the transformer's structural parameters, performance parameters and economic indicators.

[0100] The structural parameter data of the multi-winding transformer are shown in Table 2.

[0101] Table 2

[0102]

[0103] The performance parameter data of the multi-winding transformer are shown in Table 3.

[0104] Table 3

[0105]

[0106] The structural parameter data of the multi-winding transformer are shown in Table 4.

[0107] Table 4

[0108]

[0109] By analyzing the above comparative data, it can be found that under the premise of meeting the constraints, the total loss of the proposed algorithm is reduced from 4096.09W to 3716.21W, a decrease of 379.88W, a full 9.27% ​​reduction, compared with the solution given by the existing conventional method of 4096.09W. Among them, the no-load loss and load loss have both decreased to a certain extent. At the same time, although the weight of the core has decreased slightly, the weight of the coil has increased to a higher degree, resulting in an increase in material costs. Compared with the existing method, the increase in the cross-section of the wire also reduces the load loss.

[0110] From the perspective of ten-year operating costs, the optimized operating costs were reduced from 88,160.78 yuan to 82,010.22 yuan. Therefore, the total cost after optimization was reduced by 5,673.44 yuan compared with the original solution, a decrease of 5.63%. Through the above analysis of the comparative data, it can be seen that applying the proposed method to the optimization design of multi-winding regulating transformers for flexible interconnection can not only reduce losses to protect the environment, but also reduce operating costs to increase manufacturers' profits.

[0111] Although the embodiments and drawings of the present invention are disclosed for illustrative purposes, those skilled in the art will appreciate that various substitutions, changes and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A method for optimizing the design of a multi-winding control transformer for flexible interconnection, characterized in that: The design steps include: Step 1: Based on the single-objective optimization design mathematical model, an optimization objective function is constructed with the goal of minimizing the sum of the material cost and the ten-year operating cost of the multi-winding transformer; Step 2: Determine the required constraints based on the basic electrical parameters of the transformer controlled by the flexible interconnection multi-winding; Under the action of the obtained optimization objective function, a penalty function is used to punish the trend of violating constraints, so that the unconstrained optimization gradually approaches the feasible area, and the constrained optimization problem of the distribution transformer is adjusted to an unconstrained optimization problem, and the optimization design model of the phase-adjustable multi-winding transformer for flexible interconnection is obtained: Step 3: Use the particle swarm optimization algorithm to solve the optimal design model of the flexible interconnected multi-winding control transformer obtained in step 2.

2. The particle swarm algorithm-based optimization design method for a flexible interconnected multi-winding control transformer according to claim 1 is characterized in that: The mathematical description of the single objective optimization model in step 1 is expressed as; Where f(x) represents the optimization target of transformer design; x represents the optimization variable, q i (x) represents a constraint condition.

3. The particle swarm algorithm-based optimization design method for a flexible interconnected multi-winding control transformer according to claim 2 is characterized in that: The optimization objective function f(X)min obtained in step 1 is: f(X)min=CF Fe G Fe +CF h G h +CF l G l +F W (1) In formula (1), X represents the optimization variable; CF Fe Indicates the unit price of silicon steel sheet; G Fe Indicates the total weight of the core; CF h Indicates the unit price of high-voltage conductors; indicates G h ——Total weight of high-voltage conductor; CF l Indicates the unit price of low-voltage conductor; G l Indicates the total weight of the low-voltage conductor; F W Indicates the operating cost over ten years.

4. The optimization design method for a multi-winding control transformer for flexible interconnection according to claim 3 is characterized in that: In step 1, the optimization variables should include the core diameter, the number of coil turns on the low-voltage side, the low-voltage wire size, and the high-voltage wire size.

5. The optimization design method for a multi-winding control transformer for flexible interconnection according to claim 1 is characterized in that: In step 2, the constraints include performance constraints, material constraints and process constraints; The performance constraints include that the load loss and short-circuit loss are not greater than 1.02 times the standard value, the specified range of the impedance voltage is (1±0.05) times the standard value, and the no-load current is not greater than 1.05 times the standard value; The material constraints include that the coil temperature rise should not exceed the standard value, the magnetic flux density of the core should be within the specified range, and the current density of the conductor should be within the specified range; The process constraints include that the core diameter, core window height and core center distance should be multiples of 5, the number of coil turns is an integer, and the wire specifications of the winding are selected according to the specified table.

6. The optimization design method of a multi-winding control transformer for flexible interconnection according to claim 1 is characterized in that: The optimized design model obtained in step 2 is: In the formula, h i (x) represents the penalty function. When the constraint is met, m i (h i ) is 0; On the contrary, when the constraints are not met, m i (h i ) is 1.

7. The optimization design method of a multi-winding control transformer for flexible interconnection according to claim 1 is characterized in that: Step 3 includes the following steps: Step 3.1: Initialize the speed and position of all particles. The starting position of each particle will be directly assigned the optimal position Qbest recorded in its individual history. i ; Then, the optimal positions of all particles in the population are compared and analyzed, and the position with the best performance is selected, denoted as Pbest, as the global optimal position of the entire population; each particle represents one of the optimal design schemes for multi-winding control transformers for flexible interconnection; each design scheme contains basic information of design variables, which is presented in different dimensions of the particle swarm in the particle swarm algorithm, and particles of different dimensions represent different optimization variables; Step 3.2, initialize the number of iterations k, and set the maximum number of iterations to K; Step 3.3, iterate the particles in the particle swarm, and construct a particle swarm through random search to achieve global search in the feasible domain of the optimization variable; Step 3.4: Set a penalty function in the particle swarm to punish trend particles that violate the constraints, so as to better explore the optimal position of local individuals in the particle swarm; Step 3.5: In the current particle state analysis, according to the established mathematical model and formula, the movement speed and position of the particles are dynamically calibrated and optimized to ensure the accuracy of the simulation or experiment; Step 3.6, update the individual positions of particles in the particle swarm and compare them with the previously recorded optimal positions; if the current position shows better performance or characteristics, update it to the best known position of the particle; if the current position fails to meet the best record, continue to use the previous optimal position as a reference; Step 3.7: During the population optimization evaluation process, compare the best position of the individual with the global optimal solution; if the individual optimal solution of a particle exceeds the overall optimal position of the current population, it will be set as the new global optimal solution; otherwise, the global optimal solution will continue to maintain its current state; Step 3.8, check the current number of iterations k. If the current number of iterations k is less than the maximum number of iterations K, return to step 3.3 to iterate again; if the number of iterations k is greater than the maximum number of iterations K, output the optimal function value as the sum of the material cost and the ten-year operating cost of the amplitude-phase-regulated multi-winding transformer for flexible interconnection, and output the global optimal position of the particle as the optimization variable combination.

8. The optimization design method for a multi-winding control transformer for flexible interconnection according to claim 7 is characterized in that: Step 3.1 is as follows: The parameters of the particle swarm algorithm include the population size N, the population dimension D, the moving step length C for adjusting the particle to move to the individual optimal position, and the weight factor w represents the influence of the particle's past speed information on the current moving speed. The expression formula is: In the formula, rand() represents a random number that is uniformly varied in the interval [0,1]. The use of inertia weights is very useful for solving nonlinear problems. Assume that the particles in the population move in the d-dimensional search space, and the current position of particle i is x i , the particle's current moving speed is v i ; The optimal position that particle i can reach is Qbest i , this position is called the optimal position of the individual particle; let g(x) be the objective function of the particle population, then the current optimal position of the particle can be expressed as: Let the number of particles in the population be n, and the optimal position Pbest(t) passed by all particles be the optimal position in the global space, then: Pbest(t)=min{g(Qbest1(t)),g(Qbest2(t)),...,g(Qbest n (t)) The moving speed and moving position of particles in the population can be dynamically adjusted based on the past historical experience of the individual and the population. The updating formula of the particle speed and position is as follows: v ij (t+1)=wv ij (t)+C1R1(Qbest ij (t)-x ij (t))+C2R2(Qbest j (t)-x ij (t)) x ij (t+1)=x ij (t)+v ij (t+1) The i-th particle is represented by the letter i, j indicates that the particle is in the j-th dimension, and v ij (t+1) represents the moving speed of particle i when it evolves to generation t, x ij (t) represents its j-dimensional position in the tth generation, Qbest ij (t) indicates the optimal position of particle i in the jth dimension of the tth generation, Qbest j (t) indicates the j-dimensional component of the best position of the entire population when it evolves to the tth generation. w in the formula represents the inertia weight, C1 and C2 become learning factors or acceleration factors, and R1 and R2 are any random numbers in the range of [0,1].

Images