Motor Multi-Objective Optimization Method Based on Improved Particle Swarm Algorithm

Abstract

The present invention discloses a multi-objective optimization method for motors based on an improved particle swarm optimization algorithm. First, an experimental scheme is designed based on the principles of statistical experiments; then, parametric modeling is performed on the target motor, and corresponding experimental results are obtained through simulation; a corresponding mathematical model is generated by the response surface method; then, an improved particle swarm optimization algorithm with an added mutation library is used to generate a Pareto chart to find the optimal structure of the motor; finally, the effectiveness of the optimization is verified through simulation. This method combines the respective advantages of the principles of statistical experiments, the response surface method, and the improved particle swarm optimization algorithm. By collecting data based on the principles of statistical experiments, the rationality of data collection is ensured. Then, a corresponding mathematical model is generated by the response surface method without relying on the electromagnetic formula of the motor itself. Furthermore, an improved particle swarm optimization algorithm with an added mutation library is used to find the optimal solution set. It can accurately and efficiently find the best motor structure under the target performance.

Description

Technical Field

[0001] The present invention belongs to the fields of motor magnetic field calculation, computer algorithms, and statistical experimental schemes, and relates to a method for regulating and controlling frequency coupling components under weak grid conditions. Background Art

[0002] The permanent magnet brushless DC motor is a new type of motor that has developed rapidly in recent years with the development of power electronics technology and permanent magnet materials. Compared with traditional DC motors and asynchronous motors, the rotor permanent magnet motor has higher power density and efficiency, and has received extensive attention and has been widely used. However, the rotor permanent magnet motor usually needs to take special reinforcement measures for the rotor to overcome the centrifugal force during high-speed operation, such as installing a sleeve made of non-metallic fiber material or stainless steel, which not only makes its structure complex and the manufacturing cost high, but also increases the equivalent air gap and reduces the motor performance. At the same time, the permanent magnet is placed on the rotor, and heat dissipation is difficult. The resulting temperature rise may cause irreversible demagnetization of the permanent magnet, limit the motor output, and reduce the power density. To overcome the above disadvantages of the rotor permanent magnet motor, in recent years, a stator permanent magnet brushless motor with the permanent magnet placed on the stator side has emerged and has received increasing attention. At present, the research in the field of structural optimization of flux-switching permanent magnet synchronous motors is relatively few and needs further research.

[0003] Modern optimization methods show great potential in solving problems. They can approximate the optimal solution of complex object problems within a reasonable time. Some of them are mainly based on natural phenomena and are called bionic algorithms. Among them, the particle swarm optimization algorithm (PSO) has gradually become one of the research directions that scholars focus on. Its main characteristics are simplicity, relatively fast convergence speed, and less domain knowledge required. However, PSO has a high probability of falling into local minima when optimizing high-dimensional complex problems. To address this point, a particle swarm optimization algorithm with an increased mutation library is proposed. In the algorithm, an increased mutation library is added, and the population is divided into three parts. One part is reserved, one part is uniformly mutated, and the last part has a decreasing mutation rate with the increase of the number of iterations. This improves the search ability of the population for the global optimal solution and also retains the search ability of the original population. Summary of the Invention

[0004] To solve the above problems, the present invention provides a multi-objective optimization method for motors based on an improved particle swarm algorithm. Without relying on the electromagnetic equation of the motor itself, a mathematical model is fitted by the response surface method according to the experimental scheme, and then optimized calculation is performed by the improved particle swarm algorithm, so as to achieve the multi-objective optimization of the motor.

[0005] The present patent provides a multi-objective optimization method for motors based on an improved particle swarm algorithm, which is characterized in that the specific steps are as follows:

[0006] Step 1: Select the motor size and motor performance targets to be adjusted, and generate corresponding experimental schemes through the principles of statistical experiments;

[0007] Step 2: Parametrically model the motor according to the motor size variables, and obtain the corresponding experimental simulation results;

[0008] Step 3: Generate an accurate mathematical model through the response surface method according to the experimental scheme after filling in the results;

[0009] Step 4: Substitute the mathematical model of the optimization target into the improved particle swarm optimization algorithm to search for the optimal motor structure;

[0010] Step 5: Select the required performance structure parameters according to the Pareto chart generated by the particle swarm optimization algorithm with an added mutation library;

[0011] A mutation library is added. One-third of the population remains unchanged, one-third of the population mutates uniformly, and the mutation rate of one-third of the population decreases with the increase of the number of iterations;

[0012] Among them, the MOPSO algorithm of the mutation library is improved as shown in the following formula;

[0013] per_mut = (1 - gen / maxgen) / nmut

[0014] In the formula, per_mut represents the third part of the population after mutation, gen represents the current number of iterations, maxgen represents the maximum number of iterations, and nmut represents the original population of the third part;

[0015] Step 6: Then, verify the obtained optimal motor structure parameters through the parametric motor model to ensure the effectiveness of the obtained results.

[0016] As a further improvement of the present invention, the experimental scheme in Step 1 selects the CCD experimental scheme in statistics. The CCD experimental scheme is applicable to multi-factor and multi-level experiments and continuous variables.

[0017] As a further improvement of the present invention, Step 3 uses the RSM method to establish the corresponding mathematical model. Compared with the BBD experimental scheme, it can better fit the corresponding surface. RSM analyzes the relationship between variables through fewer experiments; it can use a quantitative model with high fitting accuracy to analyze experimental data and verify its significance; it can generate an accurate mathematical model.

[0018] As a further improvement of the present invention, the improved particle swarm optimization algorithm in Step 4 is designed as follows:

[0019] Assume:

[0020] 1) The search space is an n-dimensional space;

[0021] 2) When the number of particles is N, and when the iteration number is k, the position and velocity information of the i-th particle are respectively:

[0022]

[0023]

[0024] In the formula: i indicates the i-th particle, and there is j indicates the spatial dimension, and there is indicates the j-dimensional position component of particle i at the iteration number k; indicates the j-dimensional velocity component of particle i at the iteration number k;

[0025] Only, the optimal solution pbest encountered within the neighborhood of the particle and the optimal solution gbest encountered by the current population are expressed as:

[0026]

[0027]

[0028] In the formula: and are respectively the j-dimensional optimal position component and the global optimal component of particle i at the k-th iteration;

[0029] Calculate the position and velocity information of the i-th particle:

[0030]

[0031]

[0032] In the formula: represents the j-dimensional velocity component of particle i at the iteration number k + 1; c1 and c2 are respectively the learning factors representing the population experience and the degree of influence of the particle by the experience, and there are c1 > 0, c2 > 0; r1 and r2 indicate random numbers uniformly distributed within the range [0, 1]; ω represents the inertia weight, and its meaning is the difference between the individual velocity change and the original velocity. The traditional MOPSO algorithm is prone to falling into local optimal solutions and has poor diversity. Therefore, it is necessary to improve it to enhance the global search ability and improve the convergence.

[0033] Compared with the prior art, the significant advantages of the present invention are:

[0034] (1) By using the response surface method to generate a mathematical model, there is no need for the electromagnetic formula of the motor itself, no theoretical derivation is required, and it is convenient to solve through algorithms.

[0035] (2) The improved particle swarm optimization algorithm is used. By adding a mutation library, it prevents the algorithm from falling into local optimal solutions, improves the search ability for the global optimal solution, and also preserves the search ability of the original population. Brief Description of the Drawings

[0036] Figure 1 It is a flow schematic diagram of the present invention;

[0037] Figure 2 It is a schematic diagram of the basic particle swarm optimization algorithm of the present invention;

[0038] Figure 3 It is a Pareto chart of the present invention. Detailed Embodiment

[0039] The present invention will be further described in detail below in conjunction with the drawings and the detailed embodiment:

[0040] A multi-objective optimization method for motors based on an improved particle swarm optimization algorithm proposed by the present invention will be described in detail below in conjunction with the embodiments and the drawings. It includes the following steps. First, determine the motor performance to be optimized, and then determine the motor dimensions that have a greater impact on the corresponding performance. Generate an experimental plan through the CCD principle, perform parametric modeling on the motor, and simulate to obtain the results. According to the experimental plan, generate a mathematical model through the response surface method. Then solve it through the improved particle swarm optimization algorithm with an added mutation library to obtain a Pareto chart, thereby selecting the optimal dimensions. The flow schematic diagram is as Figure 1 shown:

[0041] Step 1: Determine the structure to be adjusted and the optimization objectives:

[0042] Taking a 12 / 10 FSPM motor as an example, the optimization objectives are as large an electromagnetic torque as possible and as small a cogging torque as possible. The specific parameters are shown in Table 1.

[0043] Table 1 Initial design reference data of 12 / 10 FSPM motor

[0044]

[0045]

[0046] Perform per-unit value processing on the variables. Standardize with a pole arc coefficient of 1 / 4 as the reference. The selected dimension variables and ranges are shown in Table 2.

[0047] Table 2 Dimension parameters of 12 / 10 FSPM motor

[0048]

[0049] Step 2: Generate an experimental plan based on the CCD test principle, perform parametric modeling and simulation to obtain the results, as shown in Table 3:

[0050] Table 3 Partial experimental plan of CCD

[0051]

[0052] At this time, the variance of the mathematical model of electromagnetic torque is 0.9973, and the variance of cogging torque is 0.935. The accuracy of the mathematical model is very high, ensuring the reliability of the mathematical model.

[0053] The obtained mathematical model of electromagnetic torque is:

[0054] -16.24155 + 35.05538*kst + 14.47201*hpm + 6.59308*krt + 0.15162*krty - 6.5375*kst*hpm + 0.91062*kst*krt + 0.89052*kst*krty - 2.77062*hpm*krt + 0.13948*hpm*krty - 0.19742*krt*krty - 15.57431*kst 2 -4.18764*hpm 2 -1.2218* krt 2 -0.16498*krty 2

[0055] The obtained mathematical model of cogging torque is:

[0056] 125.71016 - 78.41709*kst - 76.9526*hpm - 55.3697*krt - 5.26739*krty + 31.30194*kst*hpm + 21.86562*kst*krt + 0.51969*kst*krty + 24.69521*hpm*krt + 0.61198*hpm*krty + 0.71555*krt*krty + 5.99431*kst 2 +5.22097 *hpm 2 +2.84023*krt 2 +0.55115*krty 2

[0057] Step 3: Obtain the optimal solution through the MOPSO algorithm:

[0058] The traditional MOPSO algorithm is prone to falling into local optimal solutions and has poor diversity. Therefore, it is necessary to improve it to enhance the global search ability and improve the convergence. Before improving it, the following assumptions are made: 1) The search space is an n-dimensional space; 2) The number of particles is N. When the number of iterations is k, the position and velocity information of the i-th particle are respectively:

[0059]

[0060]

[0061] In the formula: i represents the i-th particle, and j represents the space dimension, and represents the j-dimensional position component of particle i at the k-th iteration; represents the j-dimensional velocity component of particle i at the k-th iteration.

[0062] Only, the optimal solution pbest encountered within the neighborhood of the particle and the optimal solution gbest encountered by the current population are expressed as:

[0063]

[0064]

[0065] In the formula: and are respectively the j-dimensional optimal position component and the global optimal component of particle i at the k-th iteration.

[0066] Calculate the position and velocity information of the i-th particle:

[0067]

[0068]

[0069] In the formula: represents the j-dimensional velocity component of particle i at the (k + 1)-th iteration; c1 and c2 are learning factors representing the population experience and the degree to which the particle is affected by the experience respectively, and c1 > 0, c2 > 0; r1 and r2 represent random numbers uniformly distributed within the range [0, 1]; ω represents the inertia weight, and its meaning is the difference between the individual velocity change and the original velocity.

[0070] To improve the MOPSO algorithm, a mutation library is added to prevent the algorithm from falling into a local optimal solution. All populations are evenly divided into three parts. For the first part of the population, it remains unchanged without mutation, preserving the original search ability and direction of the population. For the second part, global mutation is performed. The population size is directly multiplied by the mutation rate, and the initial positions and velocities of the mutation targets are randomly reset to let them search again. The mutation rate of the third part decreases as the number of iterations increases. Because when the iteration reaches the later stage, the population is basically getting closer and closer to the optimal solution, and a large number of mutations are not conducive to finding the optimal solution. Therefore, the mutation rate decreases as the number of iterations increases, as shown in the following formula.

[0071] per_mut = (1 - gen / maxgen) / nmut (7)

[0072] In the formula, per_mut represents the third part of the population after mutation, gen represents the current number of iterations, maxgen represents the maximum number of iterations, and nmut represents the original population of the third part.

[0073] Step 4: Select the optimal solution according to the Pareto diagram obtained by the improved particle swarm algorithm. First, initialize the original velocities and positions of all particles, calculate the objective vector values of the particles, and store them. Then determine the local optimal solution and global optimal solution of the particles. Update the positions and velocities of the particles according to the fitness function of each particle, adjust the local optimal solution, and update the global optimal solution of the particles until the iteration ends. The schematic diagram of the basic particle swarm algorithm is as Figure 2 shown. The finally obtained Pareto result diagram has the cogging torque on the abscissa and the electromagnetic torque on the ordinate. The algorithm calculates an optimal solution library and displays all the results in the diagram to facilitate the selection of the optimal structure. The specific Pareto diagram is as Figure 3 shown:

[0074] The optimal structure found by the improved particle swarm algorithm is shown in Table 4.

[0075] Table 4 Optimal solutions found according to the improved MOPSO algorithm

[0076]

[0077] Compared with the original dimensions, it can be found that the electromagnetic torque of the FSPM motor has increased by 0.9% and basically remains unchanged, but the cogging torque has decreased by 69.5%. The optimization effect is obvious, greatly improving the stability of the motor torque.

[0078] In summary, the calculation method of the present invention uses the experimental principle CCD to generate an experimental scheme, then establishes an accurate mathematical model through the response surface method, and then searches for the optimal solution through the improved particle swarm algorithm. It has good application value in the optimization of the stator permanent magnet synchronous motor.

[0079] The above are only the preferred embodiments of the present invention, and do not constitute any other form of limitation to the present invention. Any modification or equivalent change made according to the technical essence of the present invention still belongs to the scope protected by the present invention.

Claims

1. Motor multi-objective optimization method based on improved particle swarm algorithm, Characterized in that, The specific steps are as follows: Step 1: Select the motor size and motor performance objectives to be adjusted, and generate corresponding experimental schemes through the principle of statistical experiments; Step 2: Parametrically model the motor according to the motor size variables, and run the corresponding experimental simulation results; Step 3: Generate an accurate mathematical model through the response surface method according to the experimental scheme after filling in the results; Step 4: Substitute the mathematical model of the optimization objective into the improved particle swarm algorithm to find the optimal motor structure; The improved particle swarm algorithm in Step 4 is designed as follows: Assume: 1) The search space is an n-dimensional space; 2) The number of particles is N. When the iteration number is k, the position and velocity information of the i-th particle are respectively: where: i denotes the i-th particle, and we have j denotes the spatial dimension, and we have denotes the j-th dimensional position component of particle i at iteration k; denotes the j-th dimensional velocity component of particle i at iteration k; Only, the optimal solution pbest encountered within the particle neighborhood and the optimal solution gbest encountered by the current population are expressed as: Wherein: and are respectively the j - dimensional optimal position component and the global optimal component of particle i at the k - th iteration; Calculate the position and velocity information of the i-th particle: In the formula: represents the j-dimensional velocity component of particle i at the (k + 1)-th iteration; c1 and c2 are learning factors representing the population experience and the degree of influence of the particle by the experience, respectively, and c1 > 0, c2 > 0; r1 and r2 are random numbers uniformly distributed in the range [0, 1]; ω represents the inertia weight, which means the difference between the individual velocity change and the original velocity; Step 5: Select the required performance structure parameters according to the Pareto diagram generated by the particle swarm algorithm with an added mutation library; An additional mutation library is added. One-third of the population remains unchanged, one-third of the population mutates uniformly, and one-third of the population has a mutation rate that decreases with the increase in the number of iterations; Among them, the MOPSO algorithm of the mutation library is improved as shown in the following formula; per_mut = (1 - gen / maxgen) / nmut In the formula, per_mut represents the third part of the population after mutation, gen represents the current number of iterations, maxgen represents the maximum number of iterations, and nmut represents the third part of the original population; Step 6: Then verify the obtained optimal motor structure parameters through the parametric motor model to ensure the effectiveness of the obtained results.

2. The motor multi-objective optimization method based on the improved particle swarm algorithm according to claim 1, Characterized in that, The experimental scheme in Step 1 selects the CCD experimental scheme in statistics.

3. The motor multi-objective optimization method based on the improved particle swarm algorithm according to claim 1, Characterized in that, Step 3 adopts the RSM method to establish the corresponding mathematical model.

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