A method for calculating the inductance value of a reactor

Abstract

The present invention provides a method for calculating the inductance value of a reactor, comprising the following steps: S1, establishing an inductance calculation gray box model formula containing undetermined parameters according to the structure of the reactor; S2, obtaining an inductance data set with different structural parameters using a numerical simulation method; S3, performing parameter identification on the inductance data set using an improved differential evolution algorithm, obtaining the final undetermined parameters, and determining the final inductance calculation formula; S4, testing the new inductance calculation formula. The method for calculating the inductance value of a reactor described in the present invention effectively combines the gray box model with parameter identification, and achieves the purpose of high precision and low error compared with the traditional inductance calculation model.

Description

Technical Field

[0001] The invention belongs to the technical field of design and production of electrical equipment, and in particular relates to a method for calculating the inductance value of a reactor. Background Art

[0002] At present, with the development and progress of the electrical engineering industry, reactors play a vital role in power systems as the main equipment for improving voltage distribution, reducing line power loss, preventing self-excited resonance and generating high voltage. As an important parameter of the reactor, the inductance value plays a decisive role in the quality effect of the reactor.

[0003] Oil-immersed air-core reactors are basic components of power systems and are widely used in the power transmission and distribution network of power systems. Air-core reactors play the role of current limiting, voltage stabilization, and reactive power compensation in use. The inductance calculation and analysis methods of inductors include analytical method, finite element method, and experimental method. Air-core reactors do not include iron core structures. The analytical method commonly used in industrial design and production at this stage usually has an error of about 1%, with large errors, fast calculation speed, and complex derivation. The finite element method is based on modeling and simulates the reactor model. The error is usually between 0.1% and 0.5%, with small errors, complex modeling, and slow calculation speed. Therefore, how to reduce the calculation error and calculation speed of inductance and the inductance calculation method that can take the measured value into consideration has become a problem worthy of attention.

[0004] In summary, in order to effectively improve the accuracy of inductance calculation, a high-precision and dynamic inductance calculation model is established to further improve the quality of oil-immersed air-core reactors;

[0005] Traditional inductance calculation often adopts analytical method; one of the main disadvantages of analytical method is low accuracy and complex modeling; therefore, the present invention proposes an inductance calculation gray box model based on differential evolution algorithm. Summary of the invention

[0006] In view of this, the present invention aims to propose a method for calculating the inductance value of a reactor to solve the problem that the existing inductance calculation using an analytical method has low accuracy and complex modeling.

[0007] To achieve the above object, the technical solution of the present invention is achieved as follows:

[0008] A method for calculating the inductance value of a reactor comprises the following steps:

[0009] S1. According to the structure of the reactor, a gray box model formula for inductance calculation containing unknown parameters is established;

[0010] S2, using numerical simulation method to obtain inductance data sets with different structural parameters;

[0011] S3. Use the improved differential evolution algorithm to perform parameter identification on the inductance data set, obtain the final undetermined parameters, and determine the final inductance calculation formula;

[0012] S4. Verify the new inductance calculation formula.

[0013] Furthermore, the specific process of establishing the gray box model formula for inductance calculation in step S1 is as follows:

[0014] The number of coil turns N, inner diameter Rin, height H and winding thickness W of the reactor are selected as the overall design parameters. The inductance value is determined to be in a square relationship with the number of turns, in a proportional relationship with the inner diameter of the coil and the winding thickness of the coil, and in an inversely proportional relationship with the height through the control variable method.

[0015] Based on the above parameters and proportional relationships, the gray box model formula for inductance calculation containing undetermined parameters is initially constructed as follows:

[0016] Among them, D av =2×R in +W is the average diameter of the solenoid.

[0017] Furthermore, the numerical simulation method in step S2 is to establish a three-dimensional finite element field-circuit coupling model of the reactor for simulation.

[0018] Furthermore, in step S3, the improved differential evolution algorithm is used to identify parameters of the inductance data set to obtain the final undetermined parameters, including the following steps:

[0019] S301, performing an initialization operation according to the inductance data set in step S2 to generate an initialization population;

[0020] S302, calculating the fitness value of each inductance parameter in the initialized population;

[0021] S303, performing mutation operation on individuals in the initialization population according to the individualized mutation formula to obtain mutated individuals;

[0022] S304, using a population crossover formula to perform a population crossover operation on the mutated individual and the parent individual to obtain a population individual after the crossover;

[0023] S305, according to the set objective function, compare the individuals after the crossover with the individuals in the parent population, and select the dominant individuals as the individuals of the next generation;

[0024] S306, judging whether the number of iterations at this time has reached the maximum number of iterations, if so, outputting the optimal result; if not, repeating steps S302-S306;

[0025] Furthermore, the initialization operation process in step S301 is as follows:

[0026] Initialize the inductance data set using the formula of the parameter to be identified;

[0027] The formula for the parameters to be identified is as follows:

[0028] Where i = 1, 2, ... NP; j = 1, 2, ... D; D is the total number of to-be-identified in the model, NP is the population size in the improved differential evolution algorithm, and Respectively represent the upper and lower limits of the parameters, rand j [0,1] is a random value in the range 0-1.

[0029] Furthermore, the process of calculating the fitness value of each inductor parameter in the initialization population in step S302 is as follows:

[0030] The expectation is calculated by taking the sum of the squares of the difference between the parameter estimate and the true value. The specific formula is as follows:

[0031]

[0032] Y i (θ) and L i (θ) are the output inductance value of this model and the actual inductance value respectively.

[0033] Furthermore, the individualized variation formula in step S303 is:

[0034] u i,G =λθ best,G +(1-λ)·θ i,G +F·(θ r1,G -θ r2,G );

[0035] Among them, λ and F are the introduced adaptive mutation factors, θ r1,G is the model parameter value of the r1th individual in the Gth generation, θ r2,G is the model parameter value of the r2th individual in the Gth generation, i≠r1≠r2.

[0036] Furthermore, the population crossover formula used in step S304 is as follows:

[0037]

[0038] u is the individual after mutation, j is the jth parameter, j rand A random number selected from (1, NP), cr is the crossover rate of this population, and cr is the crossover rate of this population.

[0039] Furthermore, the process of checking the new inductance calculation formula in step S4 is as follows:

[0040] The reactor parameters are simulated using Comsol simulation software to obtain the simulated inductance value, and Origin is used to draw a curve graph. At the same time, the reactor parameters are substituted into the new inductance calculation formula to obtain the inductance value, and Origin is used to draw a curve graph. The curve of the calculation formula is compared with the simulation curve to obtain a fitting curve. The validity of the new inductance calculation formula is obtained based on the fitting curve.

[0041] Compared with the prior art, the method for calculating the inductance value of a reactor described in the present invention has the following advantages:

[0042] (1) The method for calculating the inductance value of a reactor described in the present invention effectively combines the gray box model and parameter identification, and achieves the purpose of high precision and low error compared with the traditional inductance calculation model;

[0043] (2) The method for calculating the inductance value of a reactor described in the present invention can obtain an inductance formula with high credibility when there are fewer samples; compared with the commonly used BP neural network algorithm, elite-retaining genetic algorithm, and particle swarm algorithm, the improved differential evolution algorithm introduces an adaptive mutation factor and the optimal individual of the current population, thereby avoiding the destruction of population diversity and the occurrence of premature maturity, and the optimal solution finally obtained is relatively ideal. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The accompanying drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings:

[0045] Figure 1 A schematic diagram of a flow chart of a method for calculating the inductance value of a reactor according to an embodiment of the present invention;

[0046] Figure 2 This is a simulation diagram of the fitting curve of the tall and thin reactor described in an embodiment of the present invention;

[0047] Figure 3 This is a simulation diagram of the fitting curve of the short and fat reactor described in an embodiment of the present invention. DETAILED DESCRIPTION

[0048] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0049] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and the like are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0050] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood by specific circumstances.

[0051] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0052] like Figure 1 As shown, a method for calculating the inductance value of a reactor includes the following steps:

[0053] First, determine the gray box model for inductance calculation.

[0054] The influence of various structural parameters in the reactor on the inductance value is analyzed, the main parameters are selected as variables in the gray box model calculation formula, and the inductance calculation formula containing unknown coefficients is established; then, by establishing a field-circuit coupling model of the reactor, the finite element concept (establishing a three-dimensional finite element field-circuit coupling model of the reactor) is used to simulate the model to obtain a set of simulated inductance values.

[0055] Second, the improved differential evolution algorithm is used to obtain the parameters of the corresponding gray box model.

[0056] Before parameter identification, the obtained inductance value sample set is divided into two parts, one part is used for training parameter identification of the gray box model, and the other part is used as a test set to evaluate and check the accuracy of the model.

[0057] During the identification process, the main flow of the improved differential evolution algorithm includes: (1) inputting the obtained inductance value; (2) randomly initializing the population and setting the parameters to be identified; (3) calculating the fitness value of the inductance parameter vector; (4) performing mutation operations on the individuals in the above initial population to obtain mutated individuals; (5) performing population crossover operations on the mutated individuals in (4) and the parent individuals to obtain the population individuals after crossover; (6) according to the set objective function, comparing the individuals after crossover with the individuals in the parent population, and selecting the dominant individuals as the individuals of the next generation; (7) judging whether the number of iterations at this time has reached the maximum number of iterations. If so, outputting the optimal result; if not, returning to (3) to continue.

[0058] Third, according to the results of parameter identification, the value of the unknown coefficient is determined and a new inductance calculation formula is obtained.

[0059] Fourth, the reliability and accuracy of the inductance calculation formula are verified through simulation of the inductance model.

[0060] like Figures 1 to 3 As shown, the embodiments are as follows:

[0061] The gray box model and the improved algorithm are used to describe the performance of two types of reactors: tall and thin type and short and fat type. The so-called tall and thin type and short and fat type refer to the factors that affect the shape of the reactor, which is the ratio of its height to its outer diameter. Different ratios will result in different shapes of the reactor.

[0062] The structural parameters of the reactor in the present invention include: a rated capacity of 2500 kVar, a round wire diameter of 1.9 mm, and a rated voltage of 500 kV.

[0063] (1) By analyzing the influence of each structure on the inductance parameters, the number of coil turns N, inner diameter Rin, height H and winding thickness W are selected as the overall design parameters; here, the units of inner diameter, height and winding thickness are all mm, and the variable unit of the subsequent inductance calculation formula is also mm. Through the control variable method, it can be basically determined that the inductance value is approximately in a square relationship with the number of turns, is approximately proportional to the inner diameter of the coil and the winding thickness of the coil, and is inversely proportional to the height.

[0064] (2) Based on the parameters and proportional relationships in (1), the gray box model formula for inductance calculation containing unknown parameters is initially constructed as follows: Among them, D av =2× R in +W is the average diameter of the solenoid.

[0065] In subsequent operations, it is mainly necessary to determine the values ​​of parameters θ1-θ7.

[0066] (3) A three-dimensional finite element field-circuit coupling model of the reactor is established, and the simulated inductance value is obtained through simulation.

[0067] (4) 30 groups of data samples under different parameter structures are selected, and the corresponding inductance model parameters are identified by improving the differential evolution algorithm: the parameter to be identified in the model is the inductance value, and the identification process is the process of continuously reducing the error and obtaining the optimal solution. In the differential evolution algorithm, an individual in a population refers to a single vector, and each element in the vector is called a gene. Obviously, the individual in the present invention refers to all the inductance values ​​to be identified, and the gene is each inductance value to be identified.

[0068] The improved differential evolution algorithm is used to obtain the parameter identification results of the gray box model. The specific steps are as follows: In the first step, according to the obtained inductance data set, a random initialization operation is performed to generate an initialized population.

[0069] The jth parameter to be identified in the i-th individual can be expressed as:

[0070]

[0071] Among them, θ ij represents the jth parameter to be identified in the i-th individual,

[0072] i=1,2,...NP;j=1,2,...D. D is the total number of to-be-identified in the model, NP is the population size in the improved differential evolution algorithm, and Respectively represent the upper and lower limits of the parameters, rand j [0,1] is a random value in the range 0-1.

[0073] The second step is to find the fitness value. The fitness value is calculated by taking the square sum of the difference between the parameter estimate and the true value. Its solution formula is: Y i (θ) and L i (θ) are the output inductance value of this model and the actual inductance value respectively.

[0074] The third step is to randomly select two individuals from the parent generation and make a difference, add the vector difference and the third individual, and the next generation individual after mutation is obtained. The mutated individual is:

[0075] u i,G =λθ best,G +(1-λ)·θ i,G +F·(θ r1,G -θ r2,G ). λ and F are the introduced adaptive variation factors. In this expression, θ r1,G is the model parameter value of the r1th individual in the Gth generation, θr2,G is the model parameter value of the r2th individual in the Gth generation, and it must be ensured that i≠r1≠r2. If the individual value range exceeds the specified upper and lower limits during the mutation operation, the upper and lower limits will be used as the values ​​of the subsequent mutation individuals.

[0076] The fourth step is to perform population crossover operation. The expression of population crossover is: cr is the crossover rate of this population. This formula means: for each inductance value to be identified in each individual, a random number is generated. If its value is less than or equal to the crossover rate, the crossover operation is performed; if its value is greater than the crossover rate, the crossover is abandoned.

[0077] The fifth step is to select the population. After the objective function is introduced, the function values ​​of the new generation and the previous generation are determined, and the smaller one is selected as the next generation.

[0078] Step 6: After obtaining the optimal individual of the new generation population, compare it with the optimal individual of the previous generation population. Determine whether the number of iterations at this time has reached the maximum number of iterations. If the conditions are met, terminate the above process and output the optimal individual at this time as the parameter identification result of the improved differential evolution algorithm; if the conditions are not met, return to the second step and repeat the subsequent process.

[0079] Finally, according to the results of parameter identification, the new inductance calculation formula is determined as:

[0080]

[0081] Combining the performance of the tall and thin type and the short and fat type reactors, the following uses Comsol to simulate the inductance model and illustrate and verify the inductance calculation formula:

[0082] A two-dimensional axisymmetric coil model is designed in comsol, and the calculation is set in the frequency domain field with a frequency of 50Hz. A geometric model is constructed, and four parameters, namely the number of coil turns N, the inner diameter Rin, the height H, and the winding thickness W, are set in the global parameters. The shape of the reactor model is adjusted by changing the inner diameter and height of the coil, and the ratio of the two is continuously adjusted to obtain the simulated inductance value in post-processing. The simulated inductance value is plotted using origin. At the same time, the inductance calculation formula is substituted, and the curve of the calculated value and the curve of the simulated value are compared to obtain a fitting curve. Then the performance of the inductance calculation formula under the two reactors is explained.

[0083] For the tall and thin reactor, the fitting curve is as shown in the attached figure. Figure 2As shown. The height is controlled unchanged, and the inner diameter of the coil is gradually changed to increase the ratio of the two, and the shape of the reactor gradually tends to be taller and thinner. It can be found that as the ratio increases, the change trends of the two curves remain highly consistent, the deviation of the inductance calculation formula is small, and the calculated inductance value has a high reliability. It is proved that the formula performs well in tall and thin reactors, and the inductance calculation formula is suitable for tall and thin reactors.

[0084] For the short and fat reactor, the fitting curve is as shown in the attached figure. Figure 3 As shown. Similarly, the shape of the reactor is changed by changing the ratio. The shape of the reactor gradually tends to be short and fat. It is found that the curve obtained by the inductance formula calculation value and the curve obtained by the simulation value almost keep overlapping when the ratio changes. The inductance calculation formula performs well under the condition of short and fat reactors, indicating that the calculation accuracy of the formula has been fully verified and affirmed. Therefore, the inductance calculation formula is also applicable to short and fat reactors.

[0085] The new inductance calculation formula has good applicability for both tall and thin reactors and short and fat reactors. The fitting degree was studied and it was found that within the allowable error range, the fitting degree of the short and fat reactor was higher than that of the tall and thin reactor. In this example, the two fitting curves met the accuracy requirements, which proved that the new inductance calculation formula is effective.

[0086] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating the inductance value of a reactor, characterized in that The following steps are involved: S1. According to the structure of the reactor, a gray box model formula for inductance calculation containing unknown parameters is established; S2, using numerical simulation method to obtain inductance data sets with different structural parameters; S3. Use the improved differential evolution algorithm to perform parameter identification on the inductance data set, obtain the final undetermined parameters, and determine the final inductance calculation formula; S4. Test the new inductance calculation formula; In step S3, the improved differential evolution algorithm is used to identify the parameters of the inductance data set, and the final undetermined parameters are obtained, which includes the following steps: S301, performing an initialization operation according to the inductance data set in step S2 to generate an initialization population; S302, calculating the fitness value of each inductance parameter in the initialized population; S303, performing mutation operation on individuals in the initialization population according to the individualized mutation formula to obtain mutated individuals; S304, using a population crossover formula to perform a population crossover operation on the mutated individual and the parent individual to obtain a population individual after the crossover; S305, according to the set objective function, compare the individuals after the crossover with the individuals in the parent population, and select the dominant individuals as the individuals of the next generation; S306, judging whether the number of iterations at this time has reached the maximum number of iterations, if so, outputting the optimal result; if not, repeating steps S302-S306; The initialization operation process in step S301 is as follows: Initialize the inductance data set using the formula of the parameter to be identified; The formula for the parameters to be identified is as follows: Where i = 1, 2, ... NP; j = 1, 2, ... D; D is the total number of to-be-identified in the model, NP is the population size in the improved differential evolution algorithm, and Respectively represent the upper and lower limits of the parameters, rand j [0,1] is a random value in the range of 0-1; The process of calculating the fitness value of each inductor parameter in the initialized population in step S302 is as follows: The expectation is calculated by taking the sum of the squares of the difference between the parameter estimate and the true value. The specific formula is as follows: Y i (θ) and L i (θ) are the output inductance value of this model and the actual inductance value respectively; The individualized variation formula in step S303 is: you i,G =λθ best,G +(1-λ)·θ i,G +F·(θ r1,G -θ r2,G ); Among them, λ and F are the introduced adaptive mutation factors, θ r1,G is the model parameter value of the r1th individual in the Gth generation, θ r2,G is the model parameter value of the r2th individual in the Gth generation, i≠r1≠r2; The population crossover formula used in step S304 is as follows: u is the individual after mutation, j is the jth parameter, j rand A random number selected from (1, NP), cr is the crossover rate of this population.

2. The method for calculating the inductance of a reactor according to claim 1, characterized in that: The specific process of establishing the gray box model formula for inductance calculation in step S1 is as follows: The number of coil turns N, inner diameter Rin, height H and winding thickness W of the reactor are selected as the overall design parameters. The inductance value is determined to be in a square relationship with the number of turns, in a proportional relationship with the inner diameter of the coil and the winding thickness of the coil, and in an inversely proportional relationship with the height through the control variable method. Based on the above parameters and proportional relationships, the gray box model formula for inductance calculation containing undetermined parameters is initially constructed as follows: Among them, D av =2×R in +W is the average diameter of the solenoid.

3. The method for calculating the inductance of a reactor according to claim 1, characterized in that: The numerical simulation method in step S2 is to establish a three-dimensional finite element field-circuit coupling model of the reactor for simulation.

4. The method for calculating the inductance of a reactor according to claim 1, characterized in that: The process of checking the new inductance calculation formula in step S4 is as follows: The reactor parameters are simulated using Comsol simulation software to obtain the simulated inductance value, and Origin is used to draw a curve graph. At the same time, the reactor parameters are substituted into the new inductance calculation formula to obtain the inductance value, and Origin is used to draw a curve graph. The curve of the calculation formula is compared with the simulation curve to obtain a fitting curve. The validity of the new inductance calculation formula is obtained based on the fitting curve.

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