Multi-objective optimization design method of power inductors based on good point set genetic algorithm

Abstract

The present invention relates to a multi-objective optimization design method for power inductors based on a good point set genetic algorithm, and belongs to the field of power electronics technology. The method comprises: determining the parameters to be optimized and their search space according to actual application requirements; determining the constraints and their boundaries; determining the objective function expression according to the parameters to be optimized; using the good point set algorithm to implement population initialization, and using a multi-objective optimization genetic algorithm under multiple constraints to search for the optimal value of the objective function, and finally obtaining the corresponding parameter value to be optimized. The present invention not only ensures the uniformity of the initial population distribution, helps the algorithm to search for the optimal solution, and improves the algorithm performance, but also effectively solves the problem of a single optimization target for power inductors, reflects the trade-off relationship between multiple targets, and is conducive to the design of power inductors considering different working scenarios and design requirements.

Description

Technical Field

[0001] The invention belongs to the technical field of power electronics and relates to a multi-objective optimization design method of a power inductor based on a good point set genetic algorithm. Background Art

[0002] Inductor components are one of the core supporting components in the field of power electronics technology. With power electronic devices as carriers, they play the roles of inversion (converting DC to AC), chopping (converting DC to DC), frequency conversion (changing power supply frequency), switching and intelligent control. However, inductor components are usually large devices in power electronic equipment. With the application of new electromagnetic materials, power inductors designed for specific applications are currently developing in the direction of miniaturization, high energy density and low cost. The biggest challenge facing the miniaturization of power inductors is how to minimize the volume of the inductor under the condition of the maximum temperature rise of the inductor, while improving the efficiency of the inductor and reducing the cost. These performances conflict and restrict each other, making the complex optimization problem of power inductors with multiple objectives, uncertainty, nonlinearity and multiple parameters difficult to achieve in traditional optimization methods. It is impossible to guarantee the accuracy of each parameter by empirical judgment. How to use rigorous mathematical methods to select appropriate parameters and deal with the multi-objective optimization problem of power inductors to achieve the best comprehensive performance is of great significance to the reliable operation of devices and the sustainable development of energy. Therefore, multi-objective optimization design for power inductors is imperative. Summary of the invention

[0003] In view of this, the purpose of the present invention is to provide a multi-objective optimization design method for power inductors based on a good point set genetic algorithm to solve the problem of a single optimization target for power inductors. The present invention enables the design of power inductors to reflect the trade-off relationship between various indicators and to design the optimal power inductor according to different requirements.

[0004] In order to achieve the above object, the present invention provides the following technical solutions:

[0005] The multi-objective optimization design method of power inductor based on good point set genetic algorithm specifically includes the following steps:

[0006] S1: Determine the parameters to be optimized according to the actual application requirements and determine the search space of each parameter;

[0007] S2: Determine the constraints and their boundaries;

[0008] S3: define the objective function: the present invention takes the cost, volume and temperature rise of the power inductor as an example, and determines the expressions of each objective function based on the parameters to be optimized in step S1;

[0009] S4: Based on the parameters to be optimized and their search range, the population is initialized using the good point set algorithm;

[0010] S5: Taking the cost, volume and temperature rise of power inductors as low as possible as the optimization goal, a multi-objective genetic algorithm is used to find the optimal solution for the optimization parameters under multiple constraints;

[0011] S6: After multiple iterations, the Pareto frontier surface is obtained, and finally the optimal value of the objective function and its corresponding optimization parameter value are obtained.

[0012] Further, in step S1, the parameters to be optimized include core parameters, winding parameters and air duct parameters;

[0013] The magnetic core parameters include magnetic core material type parameters and magnetic core geometric structure parameters; the magnetic core material type parameters include the unit price P of various magnetic core materials cd and density ρ cd The core geometry parameters include the core stack thickness l c , Width of magnetic chip w e , Yoke width w i , number of air gaps n and thickness g1, radial electrical clearance c w and axial electrical clearance c d ;

[0014] The winding parameters include wire material type parameters and wire geometry parameters; the wire material type parameters include the unit price P of various wire materials cr , density ρ cr and resistivity ρ lv The conductor geometry parameters include the conductor height h, the conductor thickness c, the number of coil turns N, the number of axial parallel connections of a single turn of conductor N A And radial parallel number N R ;

[0015] The air duct parameters include the number of air ducts and the size of air ducts.

[0016] Further, in step S2, the constraints determined include:

[0017] (1) Geometric size constraints: mainly include core geometric size constraints and winding geometric size constraints. To ensure that the size of the power inductor is suitable for the limited space, the constraint condition expression formed by the reasonable value of the power inductor is:

[0018] ①Core geometry constraints:

[0019] Window height: d s,mn ≤d s ≤d s,mx , where d s Indicates the core window height, d s,mn d s,mx They represent the minimum and maximum values ​​of the core window height respectively;

[0020] Window width: w s,mn ≤w s ≤w s,mx , where w s Indicates the core window width, w s,mn 、w s,mx They represent the minimum and maximum values ​​of the core window width respectively;

[0021] Core stack thickness: l c,mn ≤l c ≤l c,mx , where l c Indicates the core stack thickness, l c,mn , l c,mx They represent the minimum and maximum values ​​of the core stack thickness respectively;

[0022] ③ Winding geometry constraints:

[0023] Coil left and right gap: Wzy mn ≤Wzy≤Wzy mx , where Wzy represents the gap between the coil and Wzy mn 、Wzy mx They represent the minimum and maximum values ​​of the left and right gaps of the coil respectively;

[0024] Coil front and rear clearance: Wqh mn ≤Wqh≤Wqh mx , where Wqh represents the gap between the front and rear of the coil, Wqh mn ,Wqh mx They represent the minimum and maximum values ​​of the gap between the front and rear of the coil respectively;

[0025] (2) Air gap size constraints: Among them, l g represents the total air gap size, Indicates the size of the reserved air gap;

[0026] (3) Temperature rise constraint: T r ≤T r,mx , where T r Indicates the temperature rise of the power inductor, T r,mx Indicates the maximum allowable temperature rise of the power inductor;

[0027] (4) Inductance constraint: k1L n ≤L r ≤k2L n , where L r Indicates the actual inductance value, L n Indicates the rated inductance value, k1 and k2 represent the minimum and maximum coefficients respectively;

[0028] (5) Magnetic density confinement at fundamental frequency: B0≤B mx , where B0 represents the magnetic flux density at the fundamental frequency, B mx Indicates the maximum magnetic flux density at the fundamental frequency;

[0029] The above constraints are calculated based on the parameters to be optimized, where the air gap is reserved According to experience, the value can be within the range of 1-2mm; the minimum coefficient k1 and the maximum coefficient k2 are determined according to design requirements.

[0030] Further, in step S3, temperature rise is defined as the objective function, specifically including: according to Newton's cooling law, the calculation formula of temperature rise ΔT is:

[0031] ΔT=P loss / ∑(α×A)

[0032] Among them, P loss Indicates the winding loss P w Or core loss P c , α is the convection heat transfer coefficient, A represents the area of ​​each heat dissipation surface of the power inductor. ΔT is the maximum temperature rise of the core and the winding.

[0033] For the winding loss P w , the following formula is used to sum the losses of the windings at the fundamental frequency and harmonic frequency. The calculation formula is:

[0034]

[0035] Among them, I 1,rms Indicates the effective value of the fundamental current flowing through the winding. When n>1, I n,rms is the effective value of the nth harmonic current; R ACn is the AC resistance of the winding under a given current, and its value can be calculated according to the Dowell equation;

[0036] For the core loss P c , the Steinmetz formula is used to sum the core losses at the fundamental frequency and harmonic frequency. The calculation formula is:

[0037]

[0038] Where k, α′, and β are the Steinmetz parameters provided by the core manufacturer. When n=1, f n Indicates the fundamental frequency. When n>1, f n Indicates the harmonic frequency, B n Indicates the maximum magnetic flux density at the corresponding frequency, V core Indicates the volume of the magnetic core.

[0039] Furthermore, in step S4, the population is initialized by using the good point set algorithm, and an initial population evenly distributed in the search space can be designed to maintain good diversity of the population. Specifically, the present invention uses the following formula to find the best point containing s parameters to be optimized by using the circle domain:

[0040]

[0041] Among them, r k represents the kth parameter to be optimized, and p is the smallest prime number satisfying p≥2s+3;

[0042] Then the good point set containing m good points in s-dimensional space is:

[0043] P(i)={(r1*i,r2*i,…,r s *i),i=1,2,…,m}

[0044] The above m optimal points are the initial population.

[0045] Further, in step S5, a multi-objective optimization algorithm based on a genetic algorithm is used to solve the optimal Pareto frontier, and the algorithm steps are as follows:

[0046] S51: Set the population size N, the number of iterations M, and initialize the population P0;

[0047] S52: Calculate the objective function and constraints;

[0048] S53: Calculate and evaluate the fitness function value;

[0049] S54: Determine whether the maximum number of iterations has been reached, if so, output the Pareto optimal solution frontier, otherwise go to step S55;

[0050] S55: Select, crossover, and mutate to generate a new population, and return to step S52.

[0051] The beneficial effects of the present invention are: the present invention solves the problem of a single optimization target for power inductors, shows the trade-offs between multiple targets, and is conducive to making the design of power inductors take into account different working scenarios and design requirements. Compared with the prior art, the advantages of the method of the present invention are:

[0052] 1) The population is initialized through the good point set algorithm, which ensures the uniformity of the initial population distribution, helps the algorithm search for the optimal solution, and improves the algorithm performance.

[0053] 2) The temperature rise is calculated based on Newton's cooling law, which improves the accuracy of temperature rise calculation.

[0054] 3) The cost and volume issues that are of greatest concern in actual use of power inductors are taken into consideration, reflecting the trade-offs between multiple objectives.

[0055] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0057] Figure 1 It is a flow chart of the multi-objective optimization design method of power inductor based on the good point set genetic algorithm of the present invention;

[0058] Figure 2 A schematic diagram of the structure of a power inductor provided in an embodiment of the present invention,

[0059] Figure 3 It is the core geometry diagram;

[0060] Figure 4 is the winding geometry diagram;

[0061] Figure 5 This is the geometric structure diagram of the air duct. DETAILED DESCRIPTION

[0062] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0063] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0064] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is 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 operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0065] See also Figure 1 to Figure 5 , Figure 1 A multi-objective optimization design method for power inductors based on a good point set genetic algorithm is proposed, which specifically includes the following steps:

[0066] S1: Determine the parameters to be optimized according to the actual application requirements and determine the search space of each parameter;

[0067] The parameters to be optimized include core parameters, winding parameters and air duct parameters. The core parameters include core material type parameters and core geometry parameters, such as Figure 3 As shown; the core material type parameters include the unit price P of various core materials cd and density ρ cd ; The core geometry parameters include the core stack thickness l c , Width of magnetic chip w e , Yoke width w i , number of air gaps n and thickness g1, radial electrical clearance c w and axial electrical clearance c d The winding parameters include the wire material type parameters and the wire geometry parameters, such as Figure 4 As shown; the conductor material type parameters include the unit price P of various conductor materials cr , density ρ cr and resistivity ρ lv ; The conductor geometry parameters include the conductor height h, the wire thickness c, the number of coil turns N, and the number of axial parallel connections of a single turn of conductor N A And radial parallel number N R The air duct parameters include the number of air ducts and the air duct size, such as Figure 5 shown.

[0068] S2: Determine the constraints and their boundaries;

[0069] The constraints determined include:

[0070] (1) Geometric size constraints: mainly include core geometric size constraints and winding geometric size constraints. To ensure that the size of the power inductor is suitable for the limited space, the constraint condition expression formed by the reasonable value of the power inductor is:

[0071] ①Core geometry constraints:

[0072] Window height: d s,mn ≤d s ≤d s,mx , where d s Indicates the core window height, d s,mn d s,mx They represent the minimum and maximum values ​​of the core window height respectively;

[0073] Window width: w s,mn ≤w s ≤w s,mx , where w s Indicates the core window width, w s,mn 、w s,mx They represent the minimum and maximum values ​​of the core window width respectively;

[0074] Core stack thickness: l c,mn ≤l c ≤l c,mx , where l c Indicates the core stack thickness, l c,mn , l c,mx They represent the minimum and maximum values ​​of the core stack thickness respectively;

[0075] ② Winding geometric size constraints:

[0076] Coil left and right gap: Wzy mn ≤Wzy≤Wzy mx , where Wzy represents the gap between the coil and Wzy mn 、Wzy mx They represent the minimum and maximum values ​​of the left and right gaps of the coil respectively;

[0077] Coil front and rear clearance: Wqh mn ≤Wqh≤Wqh mx , where Wqh represents the gap between the front and rear of the coil, Wqh mn ,Wqh mx They represent the minimum and maximum values ​​of the gap between the front and rear of the coil respectively;

[0078] (2) Air gap size constraints: Among them, l g represents the total air gap size, Indicates the size of the reserved air gap;

[0079] (3) Temperature rise constraint: Tr ≤T r,mx , where T r Indicates the temperature rise of the power inductor, T r,mx Indicates the maximum allowable temperature rise of the power inductor;

[0080] (4) Inductance constraint: k1L n ≤L r ≤k2L n , where L r Indicates the actual inductance value, L n Indicates the rated inductance value, k1 and k2 represent the minimum and maximum coefficients respectively;

[0081] (5) Magnetic density confinement at fundamental frequency: B0≤B mx , where B0 represents the magnetic flux density at the fundamental frequency, B mx Indicates the maximum magnetic flux density at the fundamental frequency;

[0082] The above constraints are calculated based on the parameters to be optimized, where the air gap is reserved According to experience, the value can be taken in the range of 1-2mm, and the minimum coefficient k1 and the maximum coefficient k2 are taken according to design requirements.

[0083] S3: Define the objective function: Take the cost, volume and temperature rise of the power inductor as the objective function, and determine the expression of each objective function based on the parameters to be optimized in step S1.

[0084] The temperature rise is defined as the objective function, specifically including: According to Newton's cooling law, the calculation formula of the temperature rise ΔT is:

[0085] ΔT=P loss / ∑(α×A)

[0086] Among them, P loss Indicates the winding loss P w Or core loss P c , α is the convection heat transfer coefficient, A represents the area of ​​each heat dissipation surface of the power inductor. ΔT is the maximum temperature rise of the core and the winding.

[0087] For the winding loss P w , the following formula is used to sum the losses of the windings at the fundamental frequency and harmonic frequency. The calculation formula is:

[0088]

[0089] Among them, I 1,rms Indicates the effective value of the fundamental current flowing through the winding. When n>1, I n,rms is the effective value of the nth harmonic current; R ACnis the AC resistance of the winding under a given current, and its value can be calculated according to the Dowell equation;

[0090] For the core loss P c , the Steinmetz formula is used to sum the core losses at the fundamental frequency and harmonic frequency. The calculation formula is:

[0091]

[0092] Where k, α′, and β are the Steinmetz parameters provided by the core manufacturer. When n=1, f n Indicates the fundamental frequency. When n>1, f n Indicates the harmonic frequency, B n Indicates the maximum magnetic flux density at the corresponding frequency, V core Indicates the core volume.

[0093] S4: Based on the parameters to be optimized and their search range, the good point set algorithm is used to initialize the population.

[0094] Among them, the best point set algorithm is used to realize population initialization, and an initial population evenly distributed in the search space can be designed to maintain good diversity of the population. Specifically, the present invention uses the following formula to find the best point containing s parameters to be optimized using the circle domain:

[0095]

[0096] Among them, r k represents the kth parameter to be optimized, and p is the smallest prime number satisfying p≥2s+3;

[0097] Then the good point set containing m good points in s-dimensional space is:

[0098] P(i)={(r1*i,r2*i,…,r s *i),i=1,2,…,m}

[0099] The above m optimal points are the initial population.

[0100] S5: Taking the cost, volume and temperature rise of power inductors as low as possible as the optimization goal, a multi-objective genetic algorithm is used to find the optimal solution for the optimization parameters under multiple constraints.

[0101] The multi-objective optimization algorithm based on genetic algorithm solves the optimal Pareto frontier. The algorithm steps are as follows:

[0102] S51: Set the population size, number of iterations, and initialize the population;

[0103] S52: Calculate the objective function and constraints;

[0104] S53: Calculate and evaluate the fitness function value;

[0105] S54: Determine whether the maximum number of iterations has been reached, if so, output the Pareto optimal solution frontier, otherwise go to step S55;

[0106] S6: After multiple iterations, the Pareto frontier surface is obtained, and finally the optimal value of the objective function and its corresponding optimization parameter value are obtained.

[0107] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A multi-objective optimization design method for power inductors based on a good point set genetic algorithm, characterized in that: The method specifically comprises the following steps: S1: Determine the parameters to be optimized according to the actual application requirements and determine the search space of each parameter; S2: Determine the constraints and their boundaries; S3: define the objective function: calculate the cost, volume and temperature rise of the power inductor, and determine the expression of each objective function based on the parameters to be optimized in step S1; Define temperature rise as the objective function, specifically including: According to Newton's law of cooling, the calculation formula for temperature rise ΔT is: ΔT=P loss / Σ(α×A) Among them, P loss Indicates the winding loss P w Or core loss P c , α is the convection heat transfer coefficient, A represents the area of ​​each heat dissipation surface of the power inductor; ΔT is the maximum temperature rise of the core and the winding; For the winding loss P w , the following formula is used to sum the losses of the windings at the fundamental frequency and harmonic frequency. The calculation formula is: Among them, I 1,rms Indicates the effective value of the fundamental current flowing through the winding. When n>1, I n,rms is the effective value of the nth harmonic current; R ACn is the AC resistance of the winding at a given current; For the core loss P c , the Steinmetz formula is used to sum the core losses at the fundamental frequency and harmonic frequency. The calculation formula is: Where k, α′, and β are the Steinmetz parameters provided by the core manufacturer. When n=1, f n Indicates the fundamental frequency. When n>1, f n Indicates the harmonic frequency, B n Indicates the maximum magnetic flux density at the corresponding frequency, V core Indicates the volume of the magnetic core; S4: According to the parameters to be optimized and their search range, the population is initialized using the good point set algorithm, which specifically includes: the formula for finding the good point containing s parameters to be optimized using the circle domain is as follows: Among them, r k represents the kth parameter to be optimized, and p is the smallest prime number satisfying p≥2s+3; Then the good point set containing m good points in s-dimensional space is: P(i)={(r1*i,r2*i,…,r s *i),i=1,2,…,m} The above m optimal points are the initial population; S5: Taking the cost, volume and temperature rise of power inductors as low as possible as the optimization goal, a multi-objective genetic algorithm is used to find the optimal solution for the optimization parameters under multiple constraints; S6: After multiple iterations, the Pareto frontier surface is obtained, and finally the optimal value of the objective function and its corresponding optimization parameter value are obtained.

2. The multi-objective optimization design method for power inductors according to claim 1, characterized in that: In step S1, the parameters to be optimized include core parameters, winding parameters and air duct parameters; The magnetic core parameters include magnetic core material type parameters and magnetic core geometric structure parameters; the magnetic core material type parameters include the unit price P of various magnetic core materials cd and density ρ cd The core geometry parameters include the core stack thickness l c , Width of magnetic chip w e , Yoke width w i , number of air gaps n and thickness g1, radial electrical clearance c w and axial electrical clearance c d ; The winding parameters include the wire material type parameters and the wire geometry parameters; the wire material type parameters include the unit price P of various wire materials cr , density ρ cr and resistivity ρ lv The conductor geometry parameters include the conductor height h, the conductor thickness c, the number of coil turns N, the number of axial parallel connections of a single turn of conductor N A And radial parallel number N R ; The air duct parameters include the number of air ducts and the size of air ducts.

3. The multi-objective optimization design method for power inductors according to claim 1, characterized in that: In step S2, the constraints determined include: (1) Geometric size constraints: including core geometric size constraints and winding geometric size constraints. To ensure that the size of the power inductor is suitable for a limited space, the constraint condition expression formed by the reasonable value of the power inductor is: ①Core geometry constraints: Window height: d s,mn ≤d s ≤d s,mx , where d s Indicates the core window height, d s,mn d s,mx They represent the minimum and maximum values ​​of the core window height respectively; Window width: w s,mn ≤w s ≤w s,mx , where w s Indicates the core window width, w s,mn 、w s,mx They represent the minimum and maximum values ​​of the core window width respectively; Core stack thickness: l c,mn ≤l c ≤l c,mx , where l c Indicates the core stack thickness, l c,mn , l c,mx They represent the minimum and maximum values ​​of the core stack thickness respectively; ② Winding geometric size constraints: Coil left and right gap: Wzy mn ≤Wzy≤Wzy mx , where Wzy represents the gap between the coil and Wzy mn 、Wzy mx They represent the minimum and maximum values ​​of the left and right gaps of the coil respectively; Coil front and rear clearance: Wqh mn ≤Wqh≤Wqh mx , where Wqh represents the gap between the front and rear of the coil, Wqh mn ,Wqh mx They represent the minimum and maximum values ​​of the gap between the front and rear of the coil respectively; (2) Air gap size constraint: l g ≤n×g1+2×g dmx , where l g Indicates the total air gap size, g dmx Indicates the size of the reserved air gap; (3) Temperature rise constraint: T r ≤T r,mx , where T r Indicates the temperature rise of the power inductor, T r,mx Indicates the maximum allowable temperature rise of the power inductor; (4) Inductance constraint: k1L n ≤L r ≤k2L n , where L r Indicates the actual inductance value, L n Indicates the rated inductance value, k1 and k2 represent the minimum and maximum coefficients respectively; (5) Magnetic density confinement at fundamental frequency: B0≤B mx , where B0 represents the magnetic flux density at the fundamental frequency, B mx Indicates the maximum magnetic flux density at the fundamental frequency; The above constraints are calculated based on the parameters to be optimized, where the reserved air gap g dmx The minimum coefficient k1 and the maximum coefficient k2 are determined based on experience and design requirements.

4. The multi-objective optimization design method for power inductors according to claim 1, characterized in that: The AC resistance R of the winding at a given current ACn The calculations were performed according to Dowell's equation.

5. The multi-objective optimization design method for power inductors according to claim 1, characterized in that: In step S5, a multi-objective optimization algorithm based on a genetic algorithm is used to solve the optimal Pareto frontier, and the algorithm steps are as follows: S51: Set the population size, number of iterations, and initialize the population; S52: Calculate the objective function and constraints; S53: Calculate and evaluate the fitness function value; S54: Determine whether the maximum number of iterations has been reached, if so, output the Pareto optimal solution frontier, otherwise go to step S55; S55: Select, crossover, and mutate to generate a new population, and return to step S52.

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