Method for optimizing double random PWM (Pulse Width Modulation)

Abstract

The invention relates to the technical field of PWM (Pulse Width Modulation), and discloses a method for optimizing double random PWM, which comprises the following steps: randomizing a carrier frequency fc and a pulse position to obtain double random PWM, performing parameter setting on random distribution of the carrier frequency and the pulse position by adopting a Sigmoid function, improving a genetic algorithm by utilizing a particle swarm algorithm, and optimizing the double random PWM. Optimizing a minimum value fmin of a random number of a carrier frequency or a pulse position, a maximum value fmax of the random number of the carrier frequency or the pulse position and a curve transverse adjustment parameter sigma of random number Sigmoid distribution in the double random PWM by adopting an improved genetic particle swarm algorithm; according to the method, harmonic energy is dispersed from frequency and phase dimensions to a wider range through double random PWM, the switching frequency and the harmonic amplitude at the integral multiple of the switching frequency are reduced, random numbers are distributed in a Sigmoid mode, and the carrier frequency and the pulse position can more easily avoid a sensitive area by means of the nonlinear probability density characteristic that samples are more on the two sides and less in the middle, so that the switching efficiency is improved. And EMI peaks caused by extreme parameters in traditional uniform distribution are reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of PWM modulation, in particular to a method for optimizing double random PWM. Background Art

[0002] Motor drive systems are widely used in industrial automation, electric vehicles, and household appliances. However, the power electronics (such as IGBTs and MOSFETs) in motor drive systems generate high-frequency electromagnetic interference (EMI) during switching. This interference not only affects the stability of the system itself but can also interfere with surrounding electronic devices. Furthermore, as semiconductor power devices develop towards miniaturization, lightweighting, and higher efficiency, the ultra-high-frequency switching performance leads to even more severe EMI.

[0003] Pulse-width modulation (PWM) technology, as a strategy for suppressing EMI in motor drive systems from noise sources, offers significant advantages in spectrum dispersion, harmonic suppression, switching noise reduction, and power density improvement. However, traditional fixed-frequency PWM technology, due to the strict periodicity of switching cycles and pulse positions, causes harmonic energy to concentrate at specific frequencies, generating high-amplitude electromagnetic interference (EMI) peaks. This makes it difficult to meet the stringent electromagnetic compatibility (EMC) requirements of modern power electronics systems (such as new energy inverters and high-precision motor drives).

[0004] Single random PWM disperses harmonic energy by randomizing a single parameter (such as carrier frequency or pulse position), but it has significant limitations: by adjusting only the frequency domain (random carrier frequency) or time domain (random pulse position), residual harmonic energy may still be locally concentrated, limiting EMI peak suppression effectiveness; drastic random changes in a single parameter can trigger transient load disturbances, increasing the risk of control loop instability; and PWM with a fixed pulse position or carrier frequency is prone to circuit parasitic parameter coupling, inducing high-frequency resonance and other problems. The dual random PWM proposed in this invention combines randomization of carrier frequency and pulse position to disperse harmonic energy from multiple angles, offering the advantages of collaborative optimization, wideband distribution, and enhanced dynamic stability.

[0005] Algorithm-optimized random PWM technology provides an innovative path for achieving electromagnetic compatibility (EMC) in high-performance motor drives. Regarding harmonic characteristic control, while the genetic algorithm (GA) possesses strong global exploration capabilities through crossover and mutation operations, its selection pressure mechanism can easily lead to premature loss of population diversity and convergence stagnation in complex solution spaces. While the particle swarm algorithm (PSO) relies on a social cognitive model for rapid neighborhood development, it is susceptible to local extremum traps due to the sensitivity of its inertia weight parameters. The genetic particle swarm algorithm, by combining the global search capabilities of the genetic algorithm with the local search capabilities of the particle swarm algorithm, demonstrates significant advantages in terms of convergence speed, solution quality, robustness, and search efficiency. It can effectively avoid premature convergence and adapt to complex optimization problems. Therefore, a method for optimizing dual random PWM is proposed to address these issues. Summary of the Invention

[0006] In response to the shortcomings of the existing technology, the present invention provides a method for optimizing dual-random PWM, which has the advantages of broadband balanced distribution of EMI energy, precise suppression of harmonic spikes, and dynamic probability adaptive control. It solves the problems of insufficient high-frequency suppression of single random modulation, sudden changes in harmonic energy caused by fixed probability distribution, and lack of dynamic optimization capabilities of traditional strategies.

[0007] To achieve the above object, the present invention provides the following technical solution: a method for optimizing double random PWM, comprising the following steps: S1: Randomize carrier frequency f c and pulse position to get double random PWM, Among them, the random distribution of carrier frequency and pulse position uses Sigmoid function to set parameters respectively; S2: Improve the genetic algorithm using particle swarm optimization; S3: Use the improved genetic particle swarm optimization algorithm to find the minimum value f of the random number of the carrier frequency or pulse position of the random number Sigmoid distribution in the double random PWM min , the maximum value f of the random number of carrier frequency or pulse position max And the curve horizontal adjustment parameter σ is optimized.

[0008] Preferably, the step S1 is specifically as follows: Random carrier frequency PWM uses a central symmetrical triangular carrier and changes the carrier frequency f c To compare the traditional SVPWM carrier period T c Randomization, get random wave carrier period T i , random carrier period T i Compared with the traditional SVPWM carrier period T c The relationship is: ; Among them, Tc =1 / f c , y is a random number between -1 and 1, and ΔT is the distribution range of the random number; f ac is the center frequency of the carrier, set the center frequency of the carrier f ac Serves as a reference point for frequency randomization.

[0009] Preferably, the step S1 is specifically as follows: Based on the randomized carrier frequency PWM, the randomized pulses are generated in each carrier period T i Position within; The random offset method with a fixed starting position is used. The starting moment of the PWM cycle (a=0) is used as the phase reference. A random offset Δa is generated in each cycle, where 0≤Δa <T i , T i is the carrier period, so that the pulse is i Randomize the position within.

[0010] Preferably, the step S1 is specifically as follows: The traditional uniformly distributed random numbers are mapped through the Sigmoid function to generate a distribution with more samples in the two side areas and fewer samples in the middle area. The algorithm objective function expression is set as follows: ; Among them, S(n) is the random number sample value of the carrier frequency or pulse position, n is the subscript value of the sample, and n is changes, N0 is the total number of samples, f min is the minimum value of the random number of carrier frequency or pulse position, which is the lower limit of the distribution, f max is the maximum value of the random number of carrier frequency or pulse position, which is the upper limit of the distribution. is the horizontal adjustment parameter of the curve, and e is a constant.

[0011] Preferably, the step S2 specifically includes: S2.1: Set the population size, number of iterations, and carrier center frequency f ac Sum value range, pulse position value range and evolution termination algebra; S2.2: Initialize the particle swarm population size, particle dimensions, and initial position and velocity. The particle dimensions correspond to random number sample values ​​S(n) of the carrier frequency or pulse position. S2.3: Let weighted total harmonic distortion WTHD be the fitness function of the particle swarm algorithm, and evaluate the particle fitness value according to the fitness function. The expression is: ; Among them, φ is the harmonic order, V1, Vφ are the fundamental voltage amplitude and φ subharmonic voltage amplitude respectively; S2.4: Update the velocity and position of each particle based on the particle swarm algorithm. The expression is: ; Where ω is the inertia weight, V i (t) is the velocity of particle i at time t, X i (t) is the position of particle i at time t, C1 and C2 are the individual acceleration factor and the global acceleration factor, r 1、 r2 is a random number between [0,1], pbest i is the individual optimal position found by particle i so far, gbest i is the global optimal position found by particle i so far; S2.5: By dynamically adjusting the inertia weight ω, balancing the global search and local optimization of the solution space, the dynamic inertia weight ω' is obtained, which is expressed as: ; Among them, ω max 、ω min are the maximum inertia weight and the minimum inertia weight, r3 is a random number in (0,1), N' is the total number of iterations, n' is the current number of iterations, η is the function switching threshold, and its value range is (0,1); S2.6: Use tournament selection to select parents from the population based on fitness; Use simulated binary crossover method to generate beta crossover parents based on normal distribution; Using the polynomial mutation method, the individual values ​​are reset according to the probability Pm to achieve mutation; Through the replacement operation, the population individuals are replaced with new offspring; Adopting the elite retention strategy, the best individuals are recorded and retained in each generation; S2.7: Select excellent individuals based on fitness values ​​for crossover and mutation operations to generate new individuals and increase population diversity. Leverage the search experience of the particle swarm algorithm to adjust the method and scope of crossover and mutation to prevent the genetic algorithm from falling into a local optimum. S2.8: Fuse the results of the particle swarm algorithm guidance and genetic algorithm operation to generate a new population. During the fusion process, retain the best individuals among the new individuals in the fitness step S2.7 to ensure the overall quality of the population. S2.9: Based on the updated population, the particle swarm algorithm’s speed and position update formula is used again to update the particle speed and position, further guiding the population to evolve in a more optimal direction.

[0012] Preferably, the step S3 is specifically as follows: After completing the update of steps S2.4-S2.9, determine whether the preset termination condition is met. If so, terminate the search and output the Sigmoid distribution parameter f of the random number of the optimal carrier frequency and pulse position. min 、f max and the curve horizontal adjustment parameter σ. If not satisfied, return to step S2.3.

[0013] Preferably, the termination condition includes reaching a maximum number of iterations or the fitness value converging to a preset threshold.

[0014] Compared with the prior art, the present invention provides a method for optimizing dual random PWM, which has the following beneficial effects: 1. This method optimizes dual-random PWM by dispersing harmonic energy over a wider range in both frequency and phase dimensions, reducing harmonic amplitudes at the switching frequency and its integer multiples. The random numbers adopt a Sigmoid distribution, leveraging its nonlinear probability density characteristic of more samples on both sides and fewer in the middle. This allows the carrier frequency and pulse position to more easily avoid sensitive areas, reducing EMI spikes caused by extreme parameters in traditional uniform distribution.

[0015] 2. This method for optimizing dual-random PWM integrates the advantages of particle swarm algorithm through an improved genetic particle swarm algorithm, making up for the defects of genetic algorithm that are prone to falling into local optimality and slow convergence, significantly improving the convergence speed and local search ability, and accurately optimizing the key parameters of the random number distribution function in a vast solution space to generate the optimal random number distribution model for dual-random PWM modulation. By precisely controlling the dual randomization mode of carrier frequency and pulse position, the frequency band harmonic energy distribution during the PWM drive process of the motor system is made more uniform, ultimately achieving effective suppression of EMI in the motor system. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 A schematic diagram of a method for optimizing double random PWM proposed in the present invention; Figure 2 A schematic diagram of a method for optimizing double random PWM proposed in the present invention; Figure 3 A schematic diagram of a method for optimizing double random PWM proposed in the present invention; Figure 4 A schematic diagram of the topology of a motor drive system using a method for optimizing dual random PWM proposed in the present invention; Figure 5 This is an optimization iteration diagram of the GAPSO algorithm for optimizing dual random PWM proposed in the present invention; Figure 6 This is a GA algorithm optimization iteration diagram for a method of optimizing double random PWM proposed in the present invention; Figure 7 This is a distribution curve diagram after optimization of the GAPSO algorithm, a method for optimizing double random PWM proposed in the present invention; Figure 8 This is a distribution curve diagram after optimization of the GAPSO algorithm, a method for optimizing double random PWM proposed in the present invention; Figure 9 This is a traditional SVPWM line voltage FFT analysis diagram of a method for optimizing dual random PWM proposed in the present invention; Figure 10 This is a random carrier frequency PWM line voltage FFT analysis diagram of a method for optimizing dual random PWM proposed in the present invention; Figure 11 This is a method for optimizing dual random PWM proposed by the present invention. The dual random PWM line voltage FFT analysis diagram; Figure 12 This is a method for optimizing dual random PWM proposed by the present invention, using the GAPSO algorithm to optimize the dual random PWM line voltage FFT analysis diagram. DETAILED DESCRIPTION

[0017] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0018] See also Figures 1-12 , a method for optimizing double random PWM, comprising the following steps: As shown in the motor drive system topology diagram, it includes a linear impedance network, SiC MOSFET driver, cables, and motor. The linear impedance network is used to isolate power supply interference and provide stable test impedance. The SiC MOSFET driver has high-frequency switching characteristics and requires PWM modulation to suppress EMI.

[0019] S1: Randomize carrier frequency f c and pulse position to get double random PWM, Among them, the random distribution of carrier frequency and pulse position uses Sigmoid function to set parameters respectively; The harmonic energy originally concentrated in the switching frequency and its integer multiples is dispersed to a wider frequency band, such as Figure 1 As shown in the figure, random pulse position PWM will randomly adjust the offset of the cycle start position, so that the harmonic energy is further spread in the frequency domain, as shown in the figure. Figure 2 As shown, the dual random PWM combined with the two is as follows Figure 3 shown.

[0020] S2: improving the genetic algorithm by using a particle swarm algorithm; S3: optimizing the minimum value f min , the maximum value f max of the random number of the carrier frequency or pulse position, and the curve transverse adjustment parameter σ of the Sigmoid distribution of the random number in the double-random PWM by using the improved genetic particle swarm algorithm.

[0021] Step S1 is specifically: The random carrier frequency PWM adopts a center-symmetrical triangular carrier, and the carrier frequency f c is changed to randomize the carrier period T c of the traditional SVPWM, to obtain a random wave carrier period T i . i The relationship between the random wave carrier period T c and the carrier period T c of the traditional SVPWM is as follows: ; wherein, T c =1 / f ac , y is a random number between -1 and 1, and ΔT is the distribution range of the random number. f ac is the center frequency of the carrier, and the center frequency f i of the carrier is set as the reference point of the frequency randomization.

[0022] Secondly, on the basis of the randomization of the carrier frequency PWM, the position of the pulse in each carrier period T i is randomized. The random offset method with a fixed starting position is adopted, the starting time (a=0) of the PWM period is taken as the phase reference, a random offset Δa is generated in each period, wherein 0≤Δa<T i , and T i is the carrier period, so as to realize the randomization of the position of the pulse in the carrier period T min .

[0023] The traditional uniformly distributed random number is mapped through a Sigmoid function to generate a distribution with more samples in the two side regions and fewer samples in the middle region, and the algorithm objective function expression is as follows: ; wherein, S(n) is the random sample value of the carrier frequency or pulse position, n is the index value of the sample, n changes in , N0 is the total number of samples, f max is the minimum value of the random number of the carrier frequency or pulse position, and is the lower limit of the distribution.is the maximum value of the random number of carrier frequency or pulse position, which is the upper limit of the distribution. is the horizontal adjustment parameter of the curve, and e is a constant.

[0024] Step S2 specifically includes: S2.1: Set the population size, number of iterations, and carrier center frequency f ac Sum value range, pulse position value range and evolution termination algebra; S2.2: Initialize the particle swarm population size, particle dimension, and initial position velocity. The particle dimension corresponds to the random number sample value S(n) of the carrier frequency or pulse position. S2.3: Let weighted total harmonic distortion WTHD be the fitness function of the particle swarm algorithm, and evaluate the particle fitness value according to the fitness function. The expression is: ; Among them, φ is the harmonic order, V1, V φ are the fundamental voltage amplitude and φ subharmonic voltage amplitude respectively; S2.4: Update the velocity and position of each particle based on the particle swarm algorithm. The expression is: ; Where ω is the inertia weight, V i (t) is the velocity of particle i at time t, X i (t) is the position of particle i at time t, C1 and C2 are the individual acceleration factor and the global acceleration factor, r 1、 r2 is a random number between [0,1], pbest i is the individual optimal position found by particle i so far, gbest i is the global optimal position found by particle i so far; S2.5: By dynamically adjusting the inertia weight ω, balancing the global search and local optimization of the solution space, the dynamic inertia weight ω' is obtained, which is expressed as: ; Among them, ω max 、ω min are the maximum inertia weight and the minimum inertia weight, r3 is a random number in (0,1), N' is the total number of iterations, n' is the current number of iterations, η is the function switching threshold, and its value range is (0,1); S2.6: Use tournament selection to select parents from the population based on fitness; Use simulated binary crossover method to generate beta crossover parents based on normal distribution; Using the polynomial mutation method, the individual values ​​are reset according to the probability Pm to achieve mutation; Through the replacement operation, the population individuals are replaced with new offspring; Adopting the elite retention strategy, the best individuals are recorded and retained in each generation; S2.7: Select excellent individuals based on fitness values ​​for crossover and mutation operations to generate new individuals and increase population diversity. Leverage the search experience of the particle swarm algorithm to adjust the method and scope of crossover and mutation to prevent the genetic algorithm from falling into a local optimum. S2.8: Fuse the results of the particle swarm algorithm guidance and genetic algorithm operation to generate a new population. During the fusion process, retain the best individuals among the new individuals in the fitness step S2.7 to ensure the overall quality of the population. S2.9: Based on the updated population, the particle swarm algorithm’s speed and position update formula is used again to update the particle speed and position, further guiding the population to evolve in a more optimal direction.

[0025] Step S3 is specifically as follows: After completing the update of steps S2.4-S2.9, determine whether the preset termination condition is met. If so, terminate the search and output the Sigmoid distribution parameter f of the random number of the optimal carrier frequency and pulse position. min 、f max and the curve horizontal adjustment parameter σ. If not satisfied, return to step S2.3.

[0026] Termination conditions include reaching the maximum number of iterations or the fitness value converging to a preset threshold.

[0027] The algorithm iteration results are as follows: GA algorithm optimization iteration diagram is as follows Figure 6 As shown in the figure, the algorithm converges quickly in the first 200 generations but falls into a local optimum between 200 and 600 generations, with the final fitness value being 0.3040. Figure 5 As shown in the figure, the algorithm converges more evenly throughout the entire iteration process, and the final fitness value is 0.2488. It can be seen that adding the PSO algorithm to the GA algorithm can accelerate the convergence speed and enhance the local search ability.

[0028] The distribution curve after GAPSO algorithm optimization is as follows Figures 7-8 As shown, Figure 7 This is the carrier frequency distribution curve after optimization. Figure 8 The pulse position distribution curve after optimization shows that both of them show the characteristics of Sigmoid distribution, that is, the samples are dense on both sides and fewer in the middle.

[0029] The optimal sample distribution data after algorithm optimization is imported into MATLAB / Simulink for simulation verification. First, the traditional SVPWM, random carrier frequency PWM and double random PWM simulation models are run, and the obtained line voltage FFT analysis diagrams are as follows:Figures 9-12 As shown in the figure, the harmonic components of traditional SVPWM are concentrated at the switching frequency and its integer multiples, with high harmonic peaks. The maximum harmonic amplitude can reach 37.61, and the THD is 80.18%. Random carrier frequency PWM increases the fundamental amplitude from 203.5 to 213, but reduces the THD from 80.18% to 78.35%, and suppresses the harmonic amplitude peak from 37.61 to 4.69.

[0030] On this basis, random pulse position PWM is added, Figure 11 It can be seen that the harmonic components are dispersed into the random number distribution range of the switching frequency and its integer multiples. The fundamental amplitude is slightly reduced to 212.9, and the THD is slightly reduced to 76.39%. It can be seen that the harmonic amplitude peak is further suppressed from 4.69 to 4.47. The harmonic components of the switching frequency and its integer multiples are further reduced, but the harmonic components in the non-random number distribution range have increased. The effect of the proposed strategy is as follows Figure 12 As shown in the figure, the amplitude is slightly reduced to 212.7, the THD is slightly reduced to 76.36%, and the harmonic peak amplitude is reduced from 4.47 to 3.19. The proposed method has the effect of reducing the superposition of harmonics in the frequency domain, thereby distributing the energy originally concentrated on the switching frequency and its multiple harmonics more evenly throughout the frequency domain, further improving the shortcomings of traditional random PWM.

[0031] In summary, this optimized dual-random PWM method uses dual-random PWM to disperse harmonic energy over a wider range in both frequency and phase dimensions, reducing harmonic amplitudes at the switching frequency and its integer multiples. The random number adopts a Sigmoid distribution, leveraging its nonlinear probability density characteristic of more samples on both sides and fewer in the middle, allowing the carrier frequency and pulse position to more easily avoid sensitive areas, thus reducing EMI spikes caused by extreme parameters in traditional uniform distribution. Moreover, the advantages of the particle swarm algorithm are integrated through the improved genetic particle swarm algorithm to make up for the defects of the genetic algorithm that it is easy to fall into local optimality and slow convergence, significantly improve the convergence speed and local search ability, and accurately optimize the key parameters of the random number distribution function in the vast solution space to generate the optimal random number distribution model of double random PWM modulation. By accurately controlling the dual randomization mode of carrier frequency and pulse position, the frequency band harmonic energy distribution in the PWM drive process of the motor system is made more uniform, and ultimately the EMI of the motor system is effectively suppressed.

[0032] It is to be understood that the terminology "including", "comprising", or any other variation thereof, is intended to cover a non-exclusive inclusion such that process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises a... " does not, without more constraints, exclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element.

[0033] While embodiments of the application have been shown and described, it is to be understood that the application is not limited to the details of the embodiments described, since numerous modifications and changes can be made to the embodiments without departing from the spirit and scope of the application as defined by the appended claims and their equivalents.

Claims

1. A method for optimizing dual random PWM, characterized in that: The following steps are involved: S1: Randomize carrier frequency f c and pulse position to get double random PWM, Among them, the random distribution of carrier frequency and pulse position uses Sigmoid function to set parameters respectively; S2: Improve the genetic algorithm using particle swarm optimization; S3: Use the improved genetic particle swarm optimization algorithm to find the minimum value f of the random number of the carrier frequency or pulse position of the random number Sigmoid distribution in the double random PWM min , the maximum value f of the random number of carrier frequency or pulse position max and the curve lateral adjustment parameter σ is optimized; After completing the update in step S2, determine whether the preset termination condition is met. If so, terminate the search and output the Sigmoid distribution parameter f of the random number of the optimal carrier frequency and pulse position. min 、f max and the curve horizontal adjustment parameter σ. If not satisfied, return to step S2.

3.

2. The method for optimizing dual random PWM according to claim 1, wherein: The step S1 is specifically as follows: Random carrier frequency PWM uses a central symmetrical triangular carrier and changes the carrier frequency f c To compare the traditional SVPWM carrier period T c Randomization, get random wave carrier period T i , random carrier period T i Compared with the traditional SVPWM carrier period T c The relationship is: ； Among them, T c =1 / f c , y is a random number between -1 and 1, and ΔT is the distribution range of the random number; f ac is the center frequency of the carrier, set the center frequency of the carrier f ac Serves as a reference point for frequency randomization.

3. The method for optimizing dual random PWM according to claim 1, wherein: The step S1 is specifically as follows: Based on the randomized carrier frequency PWM, the randomized pulses are generated in each carrier period T i Position within; The random offset method with a fixed starting position is used. The starting moment of the PWM cycle (a=0) is used as the phase reference. A random offset Δa is generated in each cycle, where 0≤Δa <T i , T i is the carrier period, so that the pulse is i Randomize the position within.

4. The method for optimizing dual random PWM according to claim 1, wherein: The step S1 is specifically as follows: The traditional uniformly distributed random numbers are mapped through the Sigmoid function, and the algorithm objective function expression is set as follows: ； Among them, S(n) is the random number sample value of the carrier frequency or pulse position, n is the subscript value of the sample, and n is changes, N0 is the total number of samples, f min is the minimum value of the random number of carrier frequency or pulse position, which is the lower limit of the distribution, f max is the maximum value of the random number of carrier frequency or pulse position, which is the upper limit of the distribution. is the horizontal adjustment parameter of the curve, and e is a constant.

5. The method for optimizing dual random PWM according to claim 1, wherein: The specific steps in step S2 are: S2.1: Set the population size, number of iterations, and carrier center frequency f ac Sum value range, pulse position value range and evolution termination algebra; S2.2: Initialize the particle swarm population size, particle dimensions, and initial position and velocity. The particle dimensions correspond to random number sample values ​​S(n) of the carrier frequency or pulse position. S2.3: Let weighted total harmonic distortion WTHD be the fitness function of the particle swarm algorithm, and evaluate the particle fitness value according to the fitness function. The expression is: ； Among them, φ is the harmonic order, V1, V φ are the fundamental voltage amplitude and φ subharmonic voltage amplitude respectively; S2.4: Update the velocity and position of each particle based on the particle swarm algorithm. The expression is: ； Where ω is the inertia weight, V i (t) is the velocity of particle i at time t, X i (t) is the position of particle i at time t, C1 and C2 are the individual acceleration factor and the global acceleration factor, r 1、 r2 is a random number between [0,1], pbest i is the individual optimal position found by particle i so far, gbest i is the global optimal position found by particle i so far; S2.5: By dynamically adjusting the inertia weight ω, balancing the global search and local optimization of the solution space, the dynamic inertia weight ω' is obtained, which is expressed as: ； Among them, ω max 、ω min are the maximum inertia weight and the minimum inertia weight, r3 is a random number in (0,1), N' is the total number of iterations, n' is the current number of iterations, η is the function switching threshold, and its value range is (0,1); S2.6: Use tournament selection to select parents from the population based on fitness; Use simulated binary crossover method to generate beta crossover parents based on normal distribution; Using the polynomial mutation method, the individual values ​​are reset according to the probability Pm to achieve mutation; Through the replacement operation, the population individuals are replaced with new offspring; Adopting the elite retention strategy, the best individuals are recorded and retained in each generation; S2.7: Select excellent individuals based on fitness values ​​for crossover and mutation operations to generate new individuals and increase population diversity. Leverage the search experience of the particle swarm algorithm to adjust the method and scope of crossover and mutation to prevent the genetic algorithm from falling into a local optimum. S2.8: Fuse the results of the particle swarm algorithm guidance and genetic algorithm operation to generate a new population. During the fusion process, retain the best individuals among the new individuals in the fitness step S2.7 to ensure the overall quality of the population. S2.9: Based on the updated population, the particle swarm algorithm’s speed and position update formula is used again to update the particle speed and position, further guiding the population to evolve in a more optimal direction.

6. The method for optimizing dual random PWM according to claim 1, characterized in that: The termination condition includes reaching a maximum number of iterations or the fitness value converging to a preset threshold.

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