A leakage inductance calculation method based on genetic algorithm

Abstract

The present application relates to the field of high-frequency transformer, disclose a kind of leakage inductance calculation method based on genetic algorithm, the method steps are as follows: step one, using the orthogonality of transformer layer winding and longitudinal winding, mixed winding is decomposed into the combination of two, deduced to obtain the transformer leakage inductance mathematical model based on leakage magnetic field energy method;Step two, introduce the leakage inductance calculation model into the non-dominated sorting genetic algorithm with elitist strategy, with leakage inductance and transformer size as constraint condition, with efficiency and volume as optimization target to carry out iterative optimization;Step three, select appropriate transformer structure size and winding mode in the optimized Pareto optimal solution, select appropriate transformer size and winding structure to guide the design of high-frequency transformer under the condition of meeting the leakage inductance requirement.The beneficial effects of the present application are that, in the case of obtaining accurate leakage inductance calculation model, the introduction of genetic algorithm greatly saves human resources and time.

Description

Technical Field

[0001] This invention belongs to the field of high-frequency transformers, specifically relating to a leakage inductance calculation method based on a genetic algorithm. Background Technology

[0002] As power electronic devices continue to develop towards higher frequencies and smaller sizes, isolated power electronic converters have received widespread attention. Isolated power electronic converters such as LLC converters, DAB converters, and phase-shifted full-bridge converters require the participation of high-frequency transformers and leakage inductance when regulating output voltage and power.

[0003] The structure and winding method of a transformer affect the magnitude of leakage inductance, which in turn affects the normal operation of the power electronic converter. If the leakage inductance can be accurately calculated, it can not only provide guidance for optimizing transformer design, but also realize the magnetic integration of leakage inductance.

[0004] Current leakage inductance calculation methods are only applicable to specific winding configurations and are not very accurate for complex winding situations in actual engineering. Transformer design is a multi-objective, multi-constraint, and multi-degree-of-freedom design process. Even after obtaining an accurate leakage inductance value, it is still necessary to optimize the transformer's materials, dimensions, and structure while taking into account requirements such as efficiency, volume, insulation, and parasitic parameters. Manual iteration would waste a lot of time and money.

[0005] Non-dominated sorting algorithms with elitist strategies can obtain a uniformly distributed Pareto optimal solution set while ensuring the richness of the optimization population. This allows for accurate calculation of leakage inductance values ​​and provides guidance for transformer design based on actual conditions, ensuring the normal and reliable operation of power electronic equipment. Therefore, a leakage inductance calculation method based on genetic algorithms is needed to significantly reduce the time and cost of transformer design by obtaining a general leakage inductance model. Summary of the Invention

[0006] The purpose of this invention is to introduce a leakage inductance calculation model into a non-dominated sorting genetic algorithm with an elite strategy, thereby reducing the waste of human resources and time by utilizing the powerful computing power of computers, and guiding the optimal design of transformers while ensuring accurate leakage inductance calculation.

[0007] A method for calculating leakage inductance based on a genetic algorithm. The method includes the following steps:

[0008] Step 1: Calculate the leakage magnetic field energy in the transformer winding region and the primary and secondary insulation regions respectively, to obtain the leakage inductance calculation model based on the leakage magnetic field energy method:

[0009] (1)

[0010] In the formula, The total leakage magnetic field energy, This represents the vector magnitude of the magnetic field intensity at various locations within the transformer winding region and the primary and secondary insulation regions. This is the effective value of the primary winding current. To calculate the leakage inductance value back to the original side, The permeability of free space, The excitation voltage;

[0011] Step 2: Based on the orthogonality of the winding method, calculate the leakage inductance models for layered winding and longitudinal winding respectively, and add them together to obtain a leakage inductance calculation model applicable to any winding method.

[0012] Step 3: The leakage sensing calculation model is introduced into the non-dominated sorting genetic algorithm with an elitist strategy. New populations are continuously generated through selection, crossover, and mutation operations of the genetic algorithm, and non-dominated sorting is performed.

[0013] Step four: With leakage inductance as a constraint and transformer efficiency and volume as optimization targets, select the transformer structure size and winding method while ensuring accurate leakage inductance.

[0014] A computing device includes: at least one processor and a memory storing program instructions; when the program instructions are read and executed by the processor, the computing device performs the aforementioned leakage inductance calculation method based on a genetic algorithm.

[0015] A readable storage medium storing program instructions, which, when read and executed by a computing device, cause the computing device to perform the aforementioned leakage inductance calculation method based on a genetic algorithm.

[0016] Beneficial effects:

[0017] 1) This method can calculate the leakage inductance of transformers with irregular windings;

[0018] 2) This method introduces a non-dominated sorting genetic algorithm with an elitist strategy, which saves human resources and time;

[0019] 3) This method can guide the optimization of transformer structure dimensions and winding method while ensuring accurate calculation of leakage inductance value. Attached Figure Description

[0020] Figure 1 This is a schematic flowchart of the leakage inductance calculation method based on genetic algorithm of the present invention;

[0021] Figure 2 This is a schematic diagram of the transformer winding method provided by the present invention;

[0022] Figure 3 The flowchart of the non-dominated sorting genetic algorithm with elitist strategy provided by this invention is shown below.

[0023] Figure 4 The Pareto optimization results provided by this invention;

[0024] Figure 5 This is the result of the leakage inductance test. Detailed Implementation

[0025] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0026] This invention provides a method for calculating leakage inductance based on a genetic algorithm. Figure 1 This is a schematic flowchart of the leakage inductance calculation method based on genetic algorithm of the present invention, as shown below. Figure 1 As shown, the method includes the following steps:

[0027] Step 1: Calculate the leakage magnetic field energy in the transformer winding region and the primary and secondary insulation regions respectively, and obtain the leakage inductance calculation model based on the leakage magnetic field energy method as shown in Equation (1):

[0028] (1)

[0029] In the formula, The total leakage magnetic field energy, This represents the vector magnitude of the magnetic field intensity at various locations within the transformer winding region and the primary and secondary insulation regions. This is the effective value of the primary winding current. To calculate the leakage inductance value back to the original side, It is the vacuum permeability. It is the excitation voltage.

[0030] Common transformer winding methods include Figure 2 As shown, where, This refers to the number of turns in the primary winding. The diameter of the primary winding. For the secondary winding wire diameter, This is the insulation distance between the primary and secondary windings. , The distance from the secondary winding to the core window is given. In layered winding, the primary and secondary windings are arranged sequentially along the vertical direction of the transformer core, with the same height. In longitudinal winding, the primary and secondary windings are arranged sequentially along the horizontal direction of the transformer core, with the same width. Hybrid winding combines both methods. Leakage inductance calculation is affected by the winding form. The leakage magnetic field energy method shown in equation (1) is used to calculate the leakage inductance under different winding methods. The leakage magnetic field of layered winding is longitudinal, the leakage magnetic field of longitudinal winding is transverse, and the leakage magnetic field of hybrid winding consists of both longitudinal and transverse magnetic fields. The leakage magnetic field energy in the transformer winding region and the primary and secondary insulation regions is calculated separately, and then the transformer leakage inductance value can be calculated.

[0031] Step 2: Based on the orthogonality of the winding method, calculate the leakage inductance models for layered winding and longitudinal winding respectively, and add them together to obtain a leakage inductance calculation model applicable to any winding method.

[0032] When calculating the leakage inductance of a layered winding, the primary and secondary winding heights must be consistent. , for , , The sum of the leakage magnetic field energy per unit length of the insulation zone and the primary and secondary windings are shown in equations (2), (3), and (4), respectively.

[0033] (2)

[0034] (3)

[0035] (4)

[0036] in, It is the leakage magnetic field energy per unit length of the insulation region. It is the leakage magnetic field energy per unit length of the primary winding. It is the leakage magnetic field energy per unit length of the secondary winding. It is the number of turns in the primary winding. It is the primary winding current. It is the height of the magnetic field.

[0037] Considering that in practice the winding height will be lower than the core window height This leads to a decrease in the magnetomotive force at the winding ends, hence the introduction of the Rockwell coefficient. For magnetic field height Corrections are needed. Lochte coefficient. The expression is:

[0038] (5)

[0039] The Rockwell height within the window, constrained by the magnetic yoke, is:

[0040] (6)

[0041] The Rockwell height outside the window, unrestricted by the magnetic yoke, is:

[0042] (7)

[0043] The leakage magnetic field energy inside and outside the window differs only in the Rockwell height during calculation. The leakage magnetic field energy per unit length of the winding is shown in equation (8). Multiplying the leakage magnetic field energy by the winding length yields the total leakage inductance, as shown in equation (9).

[0044] (8)

[0045] (9)

[0046] In the formula, and These represent the average winding lengths inside and outside the window, respectively. It is the leakage magnetic field energy of the winding inside the window. The leakage magnetic field energy of the winding outside the window is calculated using formulas (2)-(4).

[0047] When calculating the leakage inductance of longitudinally wound wires, the widths of the primary and secondary windings must be consistent, both being... , , , These are the heights of the primary winding, secondary winding, and insulation region, respectively. for , , The sum of the leakage magnetic field energy per unit length of the insulation zone and the primary and secondary windings is shown in equations (10), (11), and (12).

[0048] (10)

[0049] (11)

[0050] (12)

[0051] in, It is the winding width.

[0052] Considering that the winding width is smaller than the core window width, a Rockwell coefficient is introduced. Adjust winding width. Rockwell coefficient within the window. Represented as:

[0053] (13)

[0054] Lochte coefficient outside the window Represented as:

[0055] (14)

[0056] in, It is a correction of the winding width factor. It is the window-outside correction winding distance factor. It is the distance from the outer winding of the window to the magnetic post. , This is the distance from the secondary winding to the core window. , This is the correction winding distance coefficient from the window to the two magnetic posts. It is the width of the primary and secondary windings. for , , sum.

[0057] The corrected expression for the winding width is:

[0058] (15)

[0059] The leakage magnetic field energy inside and outside the window differs only in the Rockwell height during calculation. The leakage magnetic field energy per unit length of the winding is shown in equation (16). Multiplying the leakage magnetic field energy by the winding length yields the total leakage inductance, as shown in equation (17).

[0060] (16)

[0061] (17)

[0062] In the formula, and These represent the average winding lengths inside and outside the window, respectively. It is the leakage magnetic field energy of the winding inside the window. The leakage magnetic field energy of the winding outside the window is calculated using formulas (10)-(12).

[0063] However, in practical engineering applications, transformer windings are usually not regular windings, but a mixture of longitudinal and layered windings. To better meet actual needs and improve the calculation accuracy of transformer leakage inductance, the mixed windings are decomposed into a superposition of longitudinal and layered windings. The total leakage magnetic field energy inside and outside the window is calculated separately and then added together, which has a universal effect. Therefore, for transformers with arbitrary windings in practical engineering, they can be decomposed into several longitudinally arranged and several layered windings. Based on equations (8) and (9), the leakage magnetic field energy of the layered windings inside the window is calculated separately. Window outer layer winding leakage magnetic field energy Based on equations (16) and (17), the leakage magnetic field energy of the longitudinal winding within the window is calculated respectively. Window-out longitudinal winding leakage magnetic field energy Thus, the general analytical model for leakage inductance is obtained as shown in equation (18):

[0064] (18)

[0065] in, It is the leakage magnetic field energy of the inner layer of the window winding. It is the leakage magnetic field energy of the longitudinally wound wire inside the window. It is the leakage magnetic field energy of the outer layer of the window winding. It is the leakage magnetic field energy of the longitudinal winding outside the window. It is the length of the winding inside the window. It is the length of the outer winding of the window.

[0066] Step 3: The leakage sense calculation model is introduced into the non-dominated sorting genetic algorithm with an elitist strategy. New populations are continuously generated through selection, crossover, and mutation operations of the genetic algorithm, and the richness of the population is ensured by non-dominated sorting to avoid single convergence.

[0067] The non-dominated sorting genetic algorithm with an elitist strategy mainly solves multi-objective, multi-constraint, and multi-degree-of-freedom problems as shown in equation (18):

[0068] (19)

[0069] In the formula, It is a p-dimensional vector. It is to optimize the objective function. and Here, n is the number of objective functions f(X); J is the number of constraint functions g(X), and j is its index; K is the number of constraint functions h(X), and k is its index.

[0070] Non-dominated sorting is a hierarchical sorting of each variable in a function. The specific steps are as follows: Let... ;for and ,Compare and The relationship of domination and non-domination; Then, the comparison is repeated until all non-dominated individuals are found.

[0071] To maintain the rich diversity of the population, the concept of crowding is introduced. The perimeter of two adjacent points of an individual is calculated for evaluation. Thus, each individual i has two attributes: dominance level and crowding level. During genetic optimization, if individuals have different dominance levels, the one with the lower dominance level is selected; if two individuals have the same dominance level, the one with the higher crowding level is selected.

[0072] After obtaining a leakage inductance calculation model applicable to any winding method, it is introduced into a non-dominated sorting genetic algorithm with an elitist strategy and iterated, where:

[0073] Optimize objective function ,in It's core loss. It is winding loss;

[0074] Optimize objective function , It refers to the transformer volume;

[0075] Constraint functions:

[0076] g(X) = =Target leakage inductance value, with core size parameters, number of winding turns, and arrangement as free variables.

[0077] Then according to such Figure 3 The following steps are performed using a non-dominated sorting genetic algorithm with an elitist strategy: An initial population is randomly generated. Its scale is Then, through non-dominated sorting and selection, crossover, and mutation in the genetic algorithm, a group of the same size is generated. offspring population The two populations are mixed to form a population of size population Then, a fast non-dominated ordination is performed on the individuals in the population, and the crowding degree of individuals in each ordination layer is calculated. Based on the non-dominated relationship and the crowding degree of individuals, suitable individuals are selected to form a new parent population. New offspring are generated through the basic operations of the genetic algorithm. They merged into a new generation of populations. Repeat the above steps until the optimization conditions are met.

[0078] Step four: With leakage inductance as a constraint and transformer efficiency and volume as optimization objectives, select appropriate transformer structural dimensions and winding method while ensuring accurate leakage inductance.

[0079] To verify the effectiveness of the proposed method, a high-frequency transformer with a leakage inductance requirement of 9μH was designed, and the optimization results are as follows: Figure 4As shown. Considering the actual processing difficulty, while also taking into account efficiency and size, the more centrally located black dot was selected as the optimized result. The transformer was then processed and manufactured. The leakage inductance test results are shown below. Figure 5 As shown, the error between the theoretical and measured values ​​is less than 1%. Power tests were also conducted on the transformer, demonstrating that it meets the normal operating requirements of the power electronic converter.

[0080] The present invention also provides a computing device, comprising: at least one processor and a memory storing program instructions; when the program instructions are read and executed by the processor, the computing device performs the aforementioned leakage inductance calculation method based on a genetic algorithm.

[0081] The present invention also provides a readable storage medium storing program instructions, which, when read and executed by a computing device, cause the computing device to perform the aforementioned leakage inductance calculation method based on a genetic algorithm.

[0082] Although the invention has been described with respect to a limited number of embodiments, those skilled in the art will understand from the foregoing description that other embodiments are conceivable within the scope of the invention described herein. Furthermore, it should be noted that the language used in this specification has been chosen primarily for readability and instructional purposes, and not for the purpose of explaining or limiting the subject matter of the invention.

Claims

1. A leakage inductance calculation method based on a genetic algorithm, characterized in that, The method includes the following steps: Step 1: Calculate the leakage magnetic field energy in the transformer winding region and the primary and secondary insulation regions respectively, to obtain the leakage inductance calculation model based on the leakage magnetic field energy method: （1） In the formula, The total leakage magnetic field energy, This represents the vector magnitude of the magnetic field intensity at various locations within the transformer winding region and the primary and secondary insulation regions. This is the effective value of the primary winding current. To calculate the leakage inductance value back to the original side, The permeability of free space, The excitation voltage; Step 2: Based on the orthogonality of the winding method, calculate the leakage inductance models for layered winding and longitudinal winding respectively, and add them together to obtain a leakage inductance calculation model applicable to any winding method. Step 3: The leakage sensing calculation model is introduced into the non-dominated sorting genetic algorithm with an elitist strategy. New populations are continuously generated through selection, crossover, and mutation operations of the genetic algorithm, and non-dominated sorting is performed. Step four: With leakage inductance as a constraint and transformer efficiency and volume as optimization targets, select the transformer structure size and winding method while ensuring accurate leakage inductance.

2. The leakage inductance calculation method based on genetic algorithm according to claim 1, characterized in that, The calculation model for the layered winding leakage inductance in step two is as follows: The leakage magnetic field energy per unit length in the insulation region, primary winding, and secondary winding are respectively shown in the following formulas: （2） （3） （4） in, It is the leakage magnetic field energy per unit length of the insulation region. It is the leakage magnetic field energy per unit length of the primary winding. It is the leakage magnetic field energy per unit length of the secondary winding. It is the primary winding current. It is the height of the magnetic field; This refers to the number of turns in the primary winding. The diameter of the primary winding. For the secondary winding wire diameter, This is the insulation distance between the primary and secondary windings; The leakage magnetic field energy per unit length of the winding is shown in equation (8). Multiplying the leakage magnetic field energy by the winding length yields the total leakage inductance, as shown in equation (9). （8） （9） In the formula, and These represent the average winding lengths inside and outside the window, respectively. It is the leakage magnetic field energy of the winding inside the window. It is the leakage magnetic field energy of the winding outside the window.

3. The leakage inductance calculation method based on genetic algorithm according to claim 2, characterized in that, In step two, the Lochte coefficient is introduced. For magnetic field height Corrections are made for the Lochte coefficient. The expression is: （5） The Rockwell height within the window, constrained by the magnetic yoke, is: （6） The Rockwell height outside the window, unrestricted by the magnetic yoke, is: （7） in, for , , The sum of It is the height of the primary and secondary windings. It is the height of the magnetic core window.

4. The leakage inductance calculation method based on genetic algorithm according to claim 2, characterized in that, The calculation model for longitudinal winding leakage inductance in step two is as follows: The leakage magnetic field energy per unit length of the insulation region and the primary and secondary windings are shown in equations (10), (11), and (12): （10） （11） （12） in, It is the leakage magnetic field energy per unit length of the insulation region. It is the leakage magnetic field energy per unit length of the primary winding. It is the leakage magnetic field energy per unit length of the secondary winding. It is the number of turns in the primary winding. It is the primary winding current. It is the winding width. , , These are the heights of the primary winding, secondary winding, and insulation region, respectively. The leakage magnetic field energy per unit length of the winding is shown in equation (15). Multiplying the leakage magnetic field energy by the winding length yields the total leakage inductance, as shown in equation (16). （16） （17） In the formula, and These represent the average winding lengths inside and outside the window, respectively. It is the leakage magnetic field energy of the winding inside the window. It is the leakage magnetic field energy of the winding outside the window.

5. The leakage inductance calculation method based on genetic algorithm according to claim 4, characterized in that, Introducing the Lochte coefficient Adjust winding width, Rockwell coefficient within window Represented as: （13） Lochte coefficient outside the window Represented as: （14） In the formula, It is a correction of the winding width factor. It is the window-outside correction winding distance factor. It is the distance from the outer winding of the window to the magnetic post. , This is the distance from the secondary winding to the core window. , This is the correction winding distance coefficient from the window to the two magnetic posts. It is the width of the primary and secondary windings. for , , sum; The corrected expression for the winding width is: （15）。 6. The leakage inductance calculation method based on genetic algorithm according to claim 4, characterized in that, For transformers with arbitrary windings in practical engineering, they are decomposed into a superposition of longitudinally wound and layered wound windings. The leakage magnetic field energy of the layered windings within the window is calculated based on equations (8) and (9). Window outer layer winding leakage magnetic field energy Based on equations (16) and (17), the leakage magnetic field energy of the longitudinal winding within the window is calculated respectively. Window-external longitudinal winding leakage magnetic field energy Thus, the leakage inductance calculation model for any winding method in step two is obtained as shown in equation (18): （18） in, It is the leakage magnetic field energy of the inner layer of the window winding. It is the leakage magnetic field energy of the longitudinally wound wire inside the window. It is the leakage magnetic field energy of the outer layer of the window winding. It is the leakage magnetic field energy of the longitudinal winding outside the window. It is the length of the winding inside the window. It is the length of the outer winding of the window.

7. The leakage inductance calculation method based on genetic algorithm according to claim 1, characterized in that, The non-dominated sorting genetic algorithm with an elite strategy in step three is as follows: The non-dominated sorting genetic algorithm with an elitist strategy mainly solves multi-objective, multi-constraint, and multi-degree-of-freedom problems as shown in equation (19): （19） In the formula, It is a p-dimensional vector. It is to optimize the objective function. and Here, n is the number of objective functions f(X); J is the number of constraint functions g(X), and j is its index; K is the number of constraint functions h(X), and k is its index. Non-dominated sorting is a hierarchical sorting of each variable in a function. The specific steps are as follows: Let... ;for and ,Compare and The relationship of domination and non-domination; Then compare again until all non-dominated individuals are found; Introducing crowding degree: The perimeter of two adjacent points of an individual is calculated for evaluation. Thus, each individual i has two attributes: dominance level and crowding degree. During genetic optimization, if the individuals have different dominance levels, the one with the smaller dominance level is selected; if the two individuals have the same dominance level, the one with the larger crowding degree is selected.

8. The leakage inductance calculation method based on genetic algorithm according to claim 7, characterized in that, The specific model in step three is as follows: Optimize objective function ,in It's core loss. It is winding loss; Optimize objective function , This refers to the volume of a high-frequency transformer; Constraint functions: g(X) = =Target leakage inductance value; Then, the process is carried out according to the non-dominated sorting genetic algorithm with elitist strategy: an initial population is randomly generated. Its scale is Then, through non-dominated sorting and selection, crossover, and mutation in the genetic algorithm, a group of the same size is generated. offspring population The two populations are mixed to form a population of size population Then, a fast non-dominated ordination is performed on the individuals in the population, and the crowding degree of individuals in each ordination layer is calculated. Based on the non-dominated relationship and the crowding degree of individuals, suitable individuals are selected to form a new parent population. New offspring are generated through the basic operations of the genetic algorithm. They merged into a new generation of populations. Repeat the above steps until the optimization conditions are met.

9. A computing device, characterized in that, include: At least one processor and a memory storing program instructions; When the program instructions are read and executed by the processor, the computing device performs a leakage inductance calculation method based on a genetic algorithm as described in any one of claims 1-8.

10. A readable storage medium storing program instructions, characterized in that, When the program instructions are read and executed by the computing device, the computing device performs a leakage inductance calculation method based on a genetic algorithm as described in any one of claims 1-8.

Images