Optimization design method for air gap of transformer iron core
By using genetic algorithms and clear objective functions in the transformer core air gap design, the problems of magnetic flux loss and temperature rise are solved, and the transformer performance optimization is achieved.
Patent Information
- Application Number
- CN202510252610.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-05
- Publication Date
- 2025-06-06
AI Technical Summary
In the existing transformer core design, the presence of air gaps leads to flux loss and temperature rise, and it is difficult to achieve optimal performance in determining the number and thickness of the core laminations.
Search for the optimal solution in multi-parameter space through clear objective functions and genetic algorithms, optimize the core air gap design, reduce magnetic flux loss and temperature rise, and improve the overall performance of the transformer.
It significantly improves the flexibility and accuracy of the design process, dynamically adjusts the design parameters to meet different specifications and application needs, reduces flux loss and temperature rise, and optimizes transformer performance.
Smart Images
Figure CN120105906A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of transformers, and in particular to a transformer core air gap optimization design method. Background Art
[0002] The design of the transformer core is particularly critical, and its performance directly affects the transmission and conversion efficiency of electric energy, especially the design and optimization of the air gap. The existence of the air gap can effectively reduce the magnetic saturation of the core and improve the working efficiency of the transformer, but it will also cause leakage and loss of magnetic flux. At present, the optimization design of the transformer core mainly focuses on the core size, material, core cross-sectional area, cost and manufacturing process.
[0003] Since the core is made of thin steel sheets, it is very important to completely fill the area inside the inner winding. Ideally, using an unlimited number of core laminations of different widths in circular and elliptical cores would form a perfectly circular area without any gaps between the windings and the active part of the core. However, this approach is not practical considering the time and cost involved in transformer core construction. To address this challenge, the core is designed with a specific number of core laminations, where each lamination has a uniform width. In this case, it becomes crucial to determine the number of laminations in the transformer core design as well as determine the optimal thickness of each core lamination. Therefore, it is necessary to design a method for optimizing the air gap design of the transformer core. Summary of the invention
[0004] The purpose of the present invention is to provide a transformer core air gap optimization design method, which searches for the optimal solution in a multi-parameter space through a clear objective function and a genetic algorithm to reduce flux loss and temperature rise and optimize the overall performance of the transformer.
[0005] To achieve the above object, the present invention provides the following solutions:
[0006] A transformer core air gap optimization design method comprises the following steps:
[0007] Obtaining fixed parameter data of the transformer, and calculating the net cross-sectional area of the core of the magnetic flux path according to the fixed parameter data;
[0008] Determine the preset transformer core initial value;
[0009] Determine whether the initial value of the transformer core satisfies the constraint conditions, and obtain the set value according to the determination result; the constraint conditions include the physical constraint of the core and the constraint of the net cross-sectional area of the core;
[0010] Obtain the target value of the set value through the objective function;
[0011] The target value is iteratively calculated through genetic algorithm to obtain the minimum target function;
[0012] The core air gap optimization scheme is determined based on the minimum objective function.
[0013] Optionally, the fixed parameter data include: transformer rated power, transformer operating frequency, saturation magnetic flux density, primary winding rated voltage and primary winding turns.
[0014] Optionally, the calculation formula for the net cross-sectional area of the core is: Among them, S net is the net cross-sectional area of the core, V 1 is the rated voltage of the primary winding, B m is the saturation flux density, f is the transformer operating frequency, N 1 is the number of turns of the primary winding.
[0015] Optionally, the initial values of the transformer core include: core radius, lamination thickness and number of laminations.
[0016] Optionally, the expression of the core physical constraint is: Among them, x i is the thickness of the i-th layer of the core, n is the number of laminations, and R is the radius of the core.
[0017] Alternatively, the constraint on the net cross-sectional area of the core is expressed as: Among them, S net is the net cross-sectional area of the core, K s is the core stacking factor, x i is the thickness of the i-th core layer, R is the core radius, and n is the number of laminations.
[0018] Optionally, judging whether the initial value of the transformer core satisfies the constraint condition, and obtaining a set value according to the judgment result, includes:
[0019] If the initial value of the transformer core satisfies the constraint condition, the initial value of the transformer core is determined as the set value;
[0020] If the initial value of the transformer core does not satisfy the constraint condition, the initial value of the transformer core is re-determined until the initial value of the transformer core satisfies the constraint condition, and then the initial value of the transformer core is determined as the set value.
[0021] Optionally, the objective function is expressed as: Among them, G is the air gap between the winding and the core, R is the radius of the core, S net is the net cross-sectional area of the core, K s is the core stacking coefficient, and min(·) is the minimum function.
[0022] Optionally, the target value is iteratively calculated by a genetic algorithm to obtain a minimum target function, including:
[0023] Randomly generate the initial population;
[0024] The constraint conditions are optimized through the penalty coefficient to obtain the fitness function;
[0025] Calculate the fitness of the initial population according to the fitness function;
[0026] Select and replace according to fitness to obtain the initial generation population;
[0027] Perform genetic crossover operation on the initial population to obtain the iterative population;
[0028] The selection, replacement and genetic crossover operations are repeated until the maximum number of iterations is reached and the minimum objective function is returned.
[0029] The present invention discloses the following technical effects: the transformer core air gap optimization design method provided by the present invention comprises: obtaining the fixed value parameter data of the transformer, and calculating the net cross-sectional area of the core of the magnetic flux path according to the fixed value parameter data; determining the preset initial value of the transformer core; judging whether the initial value of the transformer core satisfies the constraint condition, and obtaining the set value according to the judgment result; obtaining the target value of the set value through the objective function; iteratively calculating the target value through the genetic algorithm to obtain the minimum objective function; and determining the core air gap optimization scheme according to the minimum objective function. The method searches for the optimal solution in the multi-parameter space through a clear objective function and a genetic algorithm, reduces the magnetic flux loss and temperature rise, and optimizes the overall performance of the transformer. BRIEF DESCRIPTION OF THE DRAWINGS
[0030] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.
[0031] Figure 1 It is a flow chart of the core air gap optimization design method of the present invention;
[0032] Figure 2 A schematic diagram of the core modeling of the present invention;
[0033] Figure 3 It is the genetic algorithm optimization flow chart of the present invention;
[0034] Figure 4 It is a schematic diagram of the relationship between the number of core laminations and the minimum air gap of the present invention. DETAILED DESCRIPTION
[0035] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0036] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and understandable, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.
[0037] like Figure 1 As shown, the present invention provides a transformer core air gap optimization design method, comprising the following steps:
[0038] Step 100: obtaining fixed parameter data of the transformer, and calculating the net cross-sectional area of the core of the magnetic flux path according to the fixed parameter data;
[0039] Specifically, the fixed parameter data include: transformer rated power, transformer operating frequency, saturation magnetic flux density, primary winding rated voltage and primary winding turns.
[0040] Specifically, the calculation formula for the net cross-sectional area of the core is:
[0041]
[0042] Among them, S net is the net cross-sectional area of the core, V 1 is the rated voltage of the primary winding, B m is the saturation flux density, f is the transformer operating frequency, N 1 is the number of turns of the primary winding.
[0043] Step 200: Determine the initial value of the transformer core according to the net cross-sectional area of the core;
[0044] Specifically, the initial values of the transformer core include: core radius, lamination thickness and number of laminations.
[0045] Step 300: determine whether the initial value of the transformer core satisfies the constraint conditions, and obtain a set value according to the determination result; the constraint conditions include the physical constraint of the core and the constraint of the net cross-sectional area of the core;
[0046] Specifically, the expression of the core physical constraint is:
[0047]
[0048] Among them, x iis the thickness of the i-th layer of the core, n is the number of laminations, and R is the radius of the core.
[0049] Specifically, the constraint expression of the net cross-sectional area of the core is:
[0050]
[0051] Among them, S net is the net cross-sectional area of the core, K s is the core stacking factor, x i is the thickness of the i-th layer of the core, and R is the radius of the core. The actual meaning of each parameter is as follows Figure 2 As shown, x 1 and x 2 are the thickness of the first and second core layers respectively.
[0052] Specifically, the specific process of judging whether the initial value of the transformer core satisfies the constraint conditions is as follows: if the initial value of the transformer core satisfies the constraint conditions, the initial value of the transformer core is determined as the set value; if the initial value of the transformer core does not satisfy the constraint conditions, the initial value of the transformer core is re-determined until the initial value of the transformer core satisfies the constraint conditions, and the initial value of the transformer core is determined as the set value.
[0053] Step 400: obtaining a target value of a set value through an objective function;
[0054] Specifically, the objective function is the minimum value of the air gap between the transformer winding and the core, expressed as:
[0055]
[0056] Among them, G is the air gap between the winding and the core, R is the radius of the core, S net is the net cross-sectional area of the core, K s is the core stacking coefficient, and min(·) is the minimum function.
[0057] Step 500: Iterate the target value through genetic algorithm to obtain the minimum target function; Figure 3 As shown, including:
[0058] Step 501: randomly generate an initial population;
[0059] Furthermore, this embodiment also adds feasible design data obtained by designers based on experience into the initial population, thereby improving the quality of the initial population.
[0060] Step 502: Optimize the constraint conditions by using the penalty coefficient to obtain a fitness function;
[0061] Specifically, by introducing the penalty coefficient λ, the penalty term is constructed in combination with the constraint conditions and reflected in the fitness function. The expression of the fitness function is:
[0062]
[0063] Step 503: Calculate the fitness of each individual in the initial population according to the fitness function and judge its quality;
[0064] Step 504: select individuals with relatively high fitness in the initial population and pass them on to the next generation population. In the next generation population, adopt the optimal retention strategy to save the individuals with the highest fitness function value in the initial population and replace the individuals with the lowest fitness value in the next generation population, thereby obtaining the initial generation population.
[0065] Step 505: traverse all individuals in the initial population, perform genetic crossover operations to generate new individuals, and then perform genetic variation processing on the generated new individuals to achieve population evolution and generate an iterative population;
[0066] Step 506: Repeat steps 504 and 505 until the maximum number of iterations is reached, then stop and return to the minimum objective function.
[0067] Step 600: Determine a core air gap optimization solution according to a minimum objective function.
[0068] Specifically, the genetic algorithm is used to optimize the number of core laminations of different sizes, and the minimum objective function output is the minimum air gap of the current number of core laminations. The relationship between the two is as follows: Figure 4 In this embodiment, considering the time and man-hours required for cutting the core laminations, 6-8 laminations are selected as the core design of the transformer.
[0069] The beneficial effects of the present invention are as follows:
[0070] 1) By combining genetic algorithm with the optimization design of transformer core air gap, the flexibility and accuracy of the design process are significantly improved;
[0071] 2) Design parameters such as core radius, lamination thickness and number of laminations can be adjusted dynamically, which can more accurately adapt to different specifications and application requirements, improving the adaptability and efficiency of the design;
[0072] 3) By defining a clear objective function, the air gap is minimized, the flux loss and temperature rise are reduced, and the overall performance of the transformer is optimized;
[0073] 4) The genetic algorithm is used to search for the optimal solution in the multi-parameter space, overcoming the limitations of traditional design methods and enhancing the reliability and accuracy of the design results.
[0074] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.
[0075] The present invention uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the method and core ideas of the present invention. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.
Claims
1. A transformer core air gap optimization design method, characterized in that: The steps include: Obtaining fixed parameter data of the transformer, and calculating the net cross-sectional area of the core of the magnetic flux path according to the fixed parameter data; Determine the preset transformer core initial value; Determine whether the initial value of the transformer core satisfies the constraint condition, and obtain the set value according to the determination result; the constraint condition includes the physical constraint of the core and the constraint of the net cross-sectional area of the core; Obtaining a target value of the set value through an objective function; Iteratively calculating the target value through a genetic algorithm to obtain a minimum target function; The core air gap optimization scheme is determined according to the minimum objective function.
2. The transformer core air gap optimization design method according to claim 1, characterized in that: The fixed parameter data include: transformer rated power, transformer operating frequency, saturation magnetic flux density, primary winding rated voltage and primary winding turns.
3. The transformer core air gap optimization design method according to claim 1, characterized in that: The calculation formula of the net cross-sectional area of the core is: Among them, S net is the net cross-sectional area of the core, V1 is the rated voltage of the primary winding, B m is the saturation flux density, f is the operating frequency of the transformer, and N1 is the number of turns of the primary winding.
4. The transformer core air gap optimization design method according to claim 1, characterized in that: The transformer core initial values include: core radius, lamination thickness and lamination quantity.
5. The transformer core air gap optimization design method according to claim 1, characterized in that: The expression of the core physical constraint is: Among them, x i is the thickness of the i-th layer of the core, n is the number of laminations, and R is the radius of the core.
6. The transformer core air gap optimization design method according to claim 1, characterized in that: The expression for the core net cross-sectional area constraint is: Among them, S net is the net cross-sectional area of the core, K s is the core stacking factor, x i is the thickness of the i-th core layer, R is the core radius, and n is the number of laminations.
7. The transformer core air gap optimization design method according to claim 1, characterized in that: Determining whether the initial value of the transformer core satisfies the constraint condition, and obtaining a set value according to the determination result, including: If the initial value of the transformer core satisfies the constraint condition, determining the initial value of the transformer core as the set value; If the initial value of the transformer core does not satisfy the constraint condition, the initial value of the transformer core is re-determined until the initial value of the transformer core satisfies the constraint condition, and then the initial value of the transformer core is determined as the set value.
8. The transformer core air gap optimization design method according to claim 1, characterized in that: The expression of the objective function is: Among them, G is the air gap between the winding and the core, R is the radius of the core, S net is the net cross-sectional area of the core, K s is the core stacking coefficient, and min(·) is the minimum function.
9. The transformer core air gap optimization design method according to claim 1, characterized in that: The target value is iteratively calculated by a genetic algorithm to obtain a minimum target function, including: Randomly generate the initial population; The constraint condition is optimized by a penalty coefficient to obtain a fitness function; Calculating the fitness of the initial population according to the fitness function; Perform selection and replacement according to the fitness to obtain an initial generation population; Performing a genetic crossover operation on the initial population to obtain an iterative population; The selection, replacement and genetic crossover operations are repeated until a maximum number of iterations is reached and then the minimum objective function is returned.