Volume optimization design method for low-harmonic magnetically controlled reactor

Abstract

The invention relates to the field of reactor volume optimization design, in particular to a low-harmonic magnetically controlled reactor volume optimization design method. According to the scheme, the method comprises the following steps: selecting parameter variables of the low-harmonic magnetically controlled reactor, wherein the parameter variables comprise iron core length, iron core height, iron core cross section side length, single-side air gap length, total winding turns and single-side winding layer number; according to the selected parameter variables of the low-harmonic magnetically controlled reactor, variables needed in the optimization process are calculated; setting constraint conditions; and the optimal parameter combination enabling the iron core volume to be minimum is optimized and solved through the improved genetic algorithm. The objective function aims to minimize the outer volume of an iron core, punishment is applied to inductance deviation, and various constraint conditions including wire constraint, winding turn number constraint, winding thickness constraint, inter-winding insulation and appearance constraint, maximum inductance value constraint and peak magnetic flux density constraint are set. And performance failure caused by pure pursuit of volume minimization is avoided. The method is suitable for reactor volume optimization design.

Description

Technical Field

[0001] The present invention relates to the field of reactor volume optimization design, and in particular to a method for volume optimization design of a low-harmonic magnetically controlled reactor. Background Art

[0002] In the field of power system equipment, tuned-inductance series resonance test systems are widely used for AC withstand voltage testing of power transformers, power cables, and other capacitive equipment. Low-harmonic magnetically controlled reactors, with their ability to smoothly adjust their reactance, effectively achieve series resonance with the test equipment, making them a key component of this test system. Given the frequent movement required in practical applications, such equipment places stringent requirements on compactness. However, as a specialized electromagnetic device, low-harmonic magnetically controlled reactors lack a comprehensive design process. Currently, the determination of core window size and winding turns relies primarily on simulation results, lacking systematic design criteria. Existing design methods fail to prioritize reactor size minimization, resulting in widespread redundancy in core length design. This not only wastes material but also increases equipment cost and mobility. Furthermore, the optimization design of low-harmonic magnetically controlled reactors involves a mixture of continuous and discrete variables. This complex nature further complicates achieving minimum design size, necessitating the development of efficient optimization methods to overcome existing technical bottlenecks. Summary of the Invention

[0003] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a volume optimization design method for a low-harmonic magnetic-controlled reactor, thereby realizing a design with minimized volume of the low-harmonic magnetic-controlled reactor.

[0004] The present invention adopts the following technical solutions to achieve the above-mentioned purpose. The present invention provides a volume optimization design method for a low-harmonic magnetically controlled reactor, comprising: S1. Select the parameter variables of the low harmonic magnetic controlled reactor, including the core length, core height, core cross-section side length, single-side air gap length, total number of winding turns, and number of single-side winding layers; S2. Calculate the variables required in the optimization process based on the selected low harmonic magnetically controlled reactor parameter variables; S3. Set the objective function to minimize the outer volume of the core while imposing a penalty on inductance deviation. S4. Set constraints; S5. Optimize and solve the optimal parameter combination that minimizes the core volume through an improved genetic algorithm.

[0005] Furthermore, step S2 specifically includes: Calculate the maximum inductance; ; Where, represents the total magnetic circuit length, Indicates the core length, Indicates the core height; ; Where, represents the cross-sectional area of ​​the core, Indicates the cross-sectional side length of the core; ; Where, Indicates the magnetic resistance of the core part at maximum inductance; represents the air gap length, and the BH magnetization curve is fitted into a two-fold line model. It represents the slope of the linear section of the BH magnetization curve of the core material, that is, the unsaturated magnetic permeability of the core; ; Where, represents the magnetic resistance of the air gap part, Indicates the magnetic permeability at the air gap, that is, the magnetic permeability of air; The maximum inductance is: ; Where, Indicates the maximum inductance, N indicates the total number of winding turns; Calculate the minimum inductance; ; Where, Indicates the magnetic resistance of the core part at minimum inductance; ; Where, represents the magnetic resistance of the orthogonal core, and the BH magnetization curve is fitted into a two-fold line model. It represents the slope of the saturation section of the BH magnetization curve of the core material, that is, the saturation permeability of the core; Then the minimum inductance is: ; Calculate the peak flux density at maximum and minimum inductance; The core magnetic flux and the effective magnetic flux density of the core under the maximum inductance state are: ; ; Where, Indicates the core magnetic flux at maximum inductance, Indicates the effective magnetic flux density of the core under the maximum inductance state, I 0 Indicates the effective value of the winding current under the maximum inductance state; Then the peak flux density at maximum inductance is: ; Where, Indicates the peak magnetic flux density at maximum inductance; The core magnetic flux and the effective magnetic flux density of the core under the minimum inductance state are: ; ; Where, Indicates the core magnetic flux in the minimum inductance state, Indicates the effective magnetic flux density of the core under the minimum inductance state, I 1 Indicates the effective value of the winding current in the minimum inductance state; Then the peak flux density in the minimum inductance state is: ; Where, Indicates the peak magnetic flux density at minimum inductance; Calculate the inductance variation range; ; Where, is the inductance variation range, 、 are the maximum inductance and the minimum inductance respectively.

[0006] Furthermore, the objective function is: ; ; ; Where, represents the objective function, represents the outer volume of the core, Indicates that a penalty is imposed on the inductance deviation. represents the target inductance.

[0007] Furthermore, step S4 specifically includes: Wire Constraints: Select the appropriate wire size based on the given current as follows: ; Where, Indicates the effective value of the reactor's rated voltage; f Indicates the rated frequency of the reactor, usually 50 Hz.

[0008] According to the calculated maximum current , look up the table to obtain the wire cross-sectional area, and select the corresponding wire specification according to the wire cross-sectional area; Winding turns constraint: Number of turns per layer n and wire diameter The relationship is: ; The winding wrapping position cannot exceed 90% of the core height; Winding thickness constraints: ; ; Where, Indicates the distance between the outer side of the winding and the surface of the core. represents the margin coefficient, Indicates the winding thickness, Indicates the frame thickness, m indicates the number of winding layers on one side, Indicates the thickness of the insulation between layers; Inter-winding insulation and shape constraints: ; Maximum inductance constraint: ; Peak flux density constraint: ; ; Where, It is the dividing point of the two broken line model of the BH magnetization curve.

[0009] Furthermore, step S5 specifically includes: Initialize the population: For continuous variables 、 、 and , generates random values ​​within a defined range; For discrete variables N and m, generate random integers within the defined integer range; choose: First, use the elite strategy to select the best-fit individuals from the current population as elite individuals; Then, the tournament selection method is used to randomly select multiple individuals from the remaining individuals to compete, and the individual with the best fitness is selected as the parent; cross: For continuous variables 、 、 and , using simulated binary crossover, during which the genes of two parent individuals are exchanged and mixed to produce new offspring; For discrete variables N and m, single-point crossover is used to randomly select the crossover point and exchange the corresponding parts of the parent individuals to produce new offspring; Mutations: In the new generation, for continuous variables 、 、 and ,Using polynomial mutation, continuous variables undergo small-scale random changes within their defined range with a certain set probability. During the mutation process, the gene value is adjusted according to the distribution index to generate new mutant individuals; For discrete variables N and m, uniform mutation is used to achieve mutation by randomly selecting a new integer value within the allowed range to generate new mutant individuals; Combine new mutant individuals with elite individuals to obtain a new generation of population; termination: An early stopping strategy is adopted. When the fitness improvement is less than the improvement threshold after the set number of iterations is reached, the optimization process is terminated in advance to obtain the optimal parameter combination that minimizes the core volume.

[0010] The beneficial effects of the present invention are: The present invention sets an objective function, the goal of which is to minimize the outer volume of the iron core, while imposing a penalty on inductance deviation, and sets various constraints, including wire constraints, winding turn constraints, winding thickness constraints, inter-winding insulation and shape constraints, and maximum inductance value constraints, to ensure that the core functions of the inductor meet the standards, avoid performance failure caused by simply pursuing volume minimization, and prevent design parameters from violating physical laws or process limits.

[0011] In order to process different types of decision variables, the present invention adopts a hybrid coding strategy, that is, processing continuous variables and discrete variables at the same time, and using simulated binary crossover for continuous variables, and single-point crossover for discrete variables. The simulated binary crossover can maintain the excellent properties of continuous variables and has adaptive search capabilities. If the current optimal solution is small and the inductance meets the standard, the simulated binary crossover will conduct a fine search near it to avoid blind disturbances.

[0012] The present invention adopts polynomial mutation, controls the disturbance amplitude through the mutation exponent, and fine-tunes the parameters in small steps, which is suitable for refined optimization and can also automatically suppress the parameters from crossing the boundary after mutation. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 This is a flow chart of a volume optimization design method for a low-harmonic magnetically controlled reactor provided by an embodiment of the present invention; Figure 2 This is a schematic diagram of the AC port-shaped core structure of a low-harmonic magnetically controlled reactor provided by an embodiment of the present invention; Figure 3This is a schematic diagram of the structure of the U-shaped iron core of the DC port of the low harmonic magnetically controlled reactor provided by an embodiment of the present invention; Figure 4 1 is a schematic diagram of the winding structure of a low-harmonic magnetically controlled reactor provided by an embodiment of the present invention; Figure 5 1 is a schematic diagram of a low harmonic magnetically controlled reactor model before optimization provided by an embodiment of the present invention; Figure 6 Schematic diagram of an optimized low-harmonic magnetically controlled reactor model provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0014] To make the objectives, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0015] The present invention provides a method for optimizing the volume design of a low harmonic magnetic controlled reactor. Figure 1 As shown, specifically including: S1. Select the parameter variables of the low harmonic magnetic controlled reactor, including the core length, core height, core cross-section side length, single-side air gap length, total number of winding turns, and number of single-side winding layers; S2. Calculate the variables required in the optimization process based on the selected low harmonic magnetically controlled reactor parameter variables; Calculate the maximum inductance; ; Where, represents the total magnetic circuit length, Indicates the core length, Indicates the core height; ; Where, represents the cross-sectional area of ​​the core, Indicates the cross-sectional side length of the core; ; Where, Indicates the magnetic resistance of the core part at maximum inductance; represents the air gap length; the BH magnetization curve is fitted into a two-fold line model, It represents the slope of the linear section of the BH magnetization curve of the core material, that is, the unsaturated magnetic permeability of the core; ; Where, represents the magnetic resistance of the air gap part, Indicates the magnetic permeability at the air gap, that is, the magnetic permeability of air; The maximum inductance is: ; Where, Indicates the maximum inductance, N indicates the total number of winding turns; Calculate the minimum inductance; ; Where, Indicates the magnetic resistance of the core part at minimum inductance; ; Where, represents the magnetic resistance of the orthogonal core, and the BH magnetization curve is fitted into a two-fold line model. It represents the slope of the saturation section of the BH magnetization curve of the core material, that is, the saturation permeability of the core; Then the minimum inductance is: ; Calculate the peak flux density at maximum and minimum inductance; The core magnetic flux and the effective magnetic flux density of the core under the maximum inductance state are: ; ; Where, Indicates the core magnetic flux at maximum inductance, Indicates the effective magnetic flux density of the core under the maximum inductance state, I 0 Indicates the effective value of the winding current under the maximum inductance state; Then the peak flux density at maximum inductance is: ; Where, Indicates the peak magnetic flux density at maximum inductance; The core magnetic flux and the effective magnetic flux density of the core under the minimum inductance state are: ; ; Where, Indicates the core magnetic flux in the minimum inductance state, Indicates the effective magnetic flux density of the core under the minimum inductance state, I 1 Indicates the effective value of the winding current in the minimum inductance state; Then the peak flux density in the minimum inductance state is: ; Where, Indicates the peak magnetic flux density at minimum inductance; Calculate the inductance variation range; ; Where, is the inductance variation range, 、 are the maximum inductance and the minimum inductance respectively.

[0016] S3. Set the objective function to minimize the outer volume of the core while imposing a penalty on inductance deviation. ; ; ; Where, represents the objective function, represents the outer volume of the core, Indicates that a penalty is imposed on the inductance deviation. represents the target inductance.

[0017] S4. Set constraints; Wire Constraints: Select the appropriate wire size based on the given current as follows: ; Where, Indicates the effective value of the reactor's rated voltage; f Indicates the rated frequency of the reactor, usually 50 Hz.

[0018] According to the calculated maximum current , look up the table to obtain the wire cross-sectional area, and select the corresponding wire specification according to the wire cross-sectional area; Winding turns constraint: Number of turns per layer n and wire diameter The relationship is: ; The winding wrapping position cannot exceed 90% of the core height; Winding thickness constraints: ; ; Where, Indicates the distance between the outer side of the winding and the surface of the core. represents the margin coefficient, Indicates the winding thickness, Indicates the frame thickness, m indicates the number of winding layers on one side, Indicates the thickness of the insulation between layers. The winding structure of the low harmonic adjustable reactor is as follows: Figure 4 shown.

[0019] Inter-winding insulation and shape constraints: ; Maximum inductance constraint: ; Peak flux density constraint: ; ; Where, It is the dividing point of the two broken line model of the BH magnetization curve.

[0020] S5. Optimize and solve the optimal parameter combination that minimizes the core volume through an improved genetic algorithm.

[0021] Initialize the population: For continuous variables 、 、 and , generates random values ​​within a defined range; For discrete variables N and m, generate random integers within the defined integer range; choose: First, use the elite strategy to select the best-fit individuals from the current population as elite individuals; Then, the tournament selection method is used to randomly select multiple individuals from the remaining individuals to compete, and the individual with the best fitness is selected as the parent; The above process helps to maintain the diversity of the population and avoid falling into local optimality. The advantage of tournament selection is that it is simple and can better avoid the degeneration of elite individuals.

[0022] cross: For continuous variables 、 、 and , using simulated binary crossover, during which the genes of two parent individuals are exchanged and mixed to produce new offspring; For discrete variables N and m, single-point crossover is used to randomly select the crossover point and exchange the corresponding parts of the parent individuals to produce new offspring; Mutations: In the new generation, for continuous variables 、 、 and ,Using polynomial mutation, continuous variables undergo small-scale random changes within their defined range with a certain set probability. During the mutation process, the gene value is adjusted according to the distribution index to generate new mutant individuals; For discrete variables N and m, uniform mutation is used to achieve mutation by randomly selecting a new integer value within the allowed range to generate new mutant individuals; Combine new mutant individuals with elite individuals to obtain a new generation of population; termination: An early stopping strategy is adopted. When the fitness improvement is less than the improvement threshold after the set number of iterations, the optimization process is terminated in advance to avoid unnecessary resource computing consumption and obtain the optimal parameter combination that minimizes the core volume.

[0023] The following is an explanation with reference to specific design cases.

[0024] Design of low harmonic magnetic controlled reactor, rated voltage RMS , , , , the maximum inductance required is 0.1 H, and the inductance variation range is .

[0025] The AC port-shaped iron core structure of the low harmonic magnetic control reactor is as follows Figure 2 As shown, the DC port shaped core structure is as follows Figure 3 The following takes the AC square core as an example.

[0026] The bounds on the decision variables are as follows: AC port core length: ; AC port-shaped core height: ; Side length of the core cross section square: ; Single-side air gap length: ; Total number of turns of AC winding: N∈[200,1000]; Number of layers of single-sided AC winding: m∈[1,5]; Genetic algorithm parameters: population size 5000, number of iterations 200, elite ratio 0.1, number of randomly selected competing individuals in the tournament 3, crossover probability 0.8, and mutation probability 0.1.

[0027] Early stopping strategy parameters: improvement threshold 0.001, minimum number of iterations 60.

[0028] Table 1 below shows the comparison of parameters before and after optimization: Table 1 Comparison of parameters before and after optimization The low harmonic magnetic controlled reactor models before and after optimization are as follows: Figure 5 and Figure 6 shown.

[0029] The foregoing description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein and should not be construed as excluding other embodiments. Rather, the present invention can be used in various other combinations, modifications, and environments and can be modified within the scope of the concept described herein through the above teachings or techniques or knowledge in the relevant field. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention are intended to be protected by the appended claims.

Claims

1. A volume optimization design method for a low harmonic magnetic controlled reactor, characterized in that: include: S1. Select the parameter variables of the low harmonic magnetic controlled reactor, including the core length, core height, core cross-section side length, single-side air gap length, total number of winding turns, and number of single-side winding layers; S2. Calculate the variables required in the optimization process based on the selected low harmonic magnetically controlled reactor parameter variables; S3. Set the objective function to minimize the outer volume of the core while imposing a penalty on inductance deviation. S4. Set constraints; S5. Optimize and solve the optimal parameter combination that minimizes the core volume through an improved genetic algorithm.

2. The volume optimization design method of a low harmonic magnetic controlled reactor according to claim 1, characterized in that: Step S2 specifically includes: Calculate the maximum inductance; ； Where, represents the total magnetic circuit length, Indicates the core length, Indicates the core height; ； Where, represents the cross-sectional area of ​​the core, Indicates the cross-sectional side length of the core; ； Where, Indicates the magnetic resistance of the core part at maximum inductance; represents the air gap length; the BH magnetization curve is fitted into a two-fold line model, It represents the slope of the linear section of the BH magnetization curve of the core material, that is, the unsaturated magnetic permeability of the core; ； Where, represents the magnetic resistance of the air gap part, Indicates the magnetic permeability at the air gap, that is, the magnetic permeability of air; The maximum inductance is: ； Where, Indicates the maximum inductance, N indicates the total number of winding turns; Calculate the minimum inductance; ； Where, Indicates the magnetic resistance of the core part at minimum inductance; ； Where, represents the magnetic resistance of the orthogonal core, and the BH magnetization curve is fitted into a two-fold line model. It represents the slope of the saturation section of the BH magnetization curve of the core material, that is, the saturation permeability of the core; Then the minimum inductance is: ； Calculate the peak flux density at maximum and minimum inductance; The core magnetic flux and the effective magnetic flux density of the core under the maximum inductance state are: ； ； Where, Indicates the core magnetic flux at maximum inductance, Indicates the effective magnetic flux density of the core under the maximum inductance state, Indicates the effective value of the winding current under the maximum inductance state; Then the peak flux density at maximum inductance is: ； Where, Indicates the peak magnetic flux density at maximum inductance; The core magnetic flux and the effective magnetic flux density of the core under the minimum inductance state are: ； ； Where, Indicates the core magnetic flux in the minimum inductance state, Indicates the effective magnetic flux density of the core under the minimum inductance state, I 1 Indicates the effective value of the winding current in the minimum inductance state; Then the peak flux density in the minimum inductance state is: ； Where, Indicates the peak magnetic flux density at minimum inductance; Calculate the inductance variation range; ； Where, is the inductance variation range, 、 are the maximum and minimum inductance values ​​respectively.

3. The volume optimization design method of a low harmonic magnetic controlled reactor according to claim 2, characterized in that: The objective function is: ； ； ； Where, represents the objective function, represents the outer volume of the core, Indicates that a penalty is imposed on the inductance deviation. represents the target inductance.

4. The volume optimization design method of a low harmonic magnetic controlled reactor according to claim 3, characterized in that: Step S4 specifically includes: Wire Constraints: Select the appropriate wire size based on the given current as follows: ； Where, Indicates the effective value of the reactor's rated voltage; f Indicates the rated frequency of the reactor; According to the calculated maximum current , look up the table to obtain the wire cross-sectional area, and select the corresponding wire specification according to the wire cross-sectional area; Winding turns constraint: Number of turns per layer n and wire diameter The relationship is: ; The winding wrapping position cannot exceed 90% of the core height; Winding thickness constraints: ； ； Where, Indicates the distance between the outer side of the winding and the surface of the core. represents the margin coefficient, Indicates the winding thickness, Indicates the frame thickness, m indicates the number of winding layers on one side, Indicates the thickness of the insulation between layers; Inter-winding insulation and shape constraints: ; Maximum inductance constraint: ; Peak flux density constraint: ； ； Where, It is the dividing point of the two broken line model of the BH magnetization curve.

5. The volume optimization design method of a low harmonic magnetic controlled reactor according to claim 1, characterized in that: Step S5 specifically includes: Initialize the population: For continuous variables 、 、 and , generates random values ​​within a defined range; For discrete variables N and m, generate random integers within the defined integer range; choose: First, use the elite strategy to select the best-fit individuals from the current population as elite individuals; Then, the tournament selection method is used to randomly select multiple individuals from the remaining individuals to compete, and the individual with the best fitness is selected as the parent; cross: For continuous variables 、 、 and , using simulated binary crossover, during which the genes of two parent individuals are exchanged and mixed to produce new offspring; For discrete variables N and m, single-point crossover is used to randomly select the crossover point and exchange the corresponding parts of the parent individuals to produce new offspring; Mutations: In the new generation, for continuous variables 、 、 and ,Using polynomial mutation, continuous variables undergo small-scale random changes within their defined range with a certain set probability. During the mutation process, the gene value is adjusted according to the distribution index to generate new mutant individuals; For discrete variables N and m, uniform mutation is used to achieve mutation by randomly selecting a new integer value within the allowed range to generate new mutant individuals; Combine new mutant individuals with elite individuals to obtain a new generation of population; termination: An early stopping strategy is adopted. When the fitness improvement is less than the improvement threshold after reaching the set number of iterations, the optimization process is terminated in advance to obtain the optimal parameter combination that minimizes the core volume.

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