A carrier phase-shifted modulation method of a cascaded H-bridge multi-level power amplifier

Abstract

The application discloses a carrier phase shift modulation method of a cascade H-bridge multilevel power amplifier, and comprises the following steps: 1, detecting the DC side voltage and modulation degree of each H-bridge unit for the cascade H-bridge multilevel power amplifier under the condition of DC side input voltage imbalance; 2, solving the nonlinear transcendental equation set related to the phase shift angle by using a neural network-genetic hybrid algorithm to obtain a new carrier phase shift angle; and 3, adjusting the carrier phase shift angle to eliminate part of the output voltage harmonics caused by the DC side voltage imbalance. The application can calculate the new carrier phase shift angle by detecting the DC side voltage and the modulation degree, eliminate part of the output voltage harmonics and reduce the design requirement of the output filter under the premise of guaranteeing the superior performance of the cascade H-bridge multilevel power amplifier.

Description

Technical Field

[0001] This invention is applicable to cascaded H-bridge multilevel power amplifiers and relates to a carrier phase-shift modulation strategy for cascaded H-bridge multilevel power amplifiers. Background Technology

[0002] Power amplifiers are widely used in defense and civilian fields, such as launch systems, servo motors, sonar detection, and power electronic equipment testing systems. Traditional linear power amplifiers operate in the linear amplification region, resulting in low output signal distortion. However, they often require external bias circuits, and the power transistors in the amplification region suffer from high losses and significant heat generation, leading to low overall efficiency, especially in high-voltage, high-power applications where efficiency and heat dissipation are major issues. To adapt to high-voltage, high-power applications, some researchers have proposed using digital power amplifiers. Among them, the cascaded H-bridge multilevel power amplifier has advantages such as low dv / dt, good harmonic characteristics, and modularity for easy expansion. Compared to other digital power amplifiers, it does not require a common DC bus and does not have capacitor voltage balance control issues, leading to its widespread application.

[0003] Currently, the commonly used modulation strategies for cascaded H-bridge multilevel power amplifiers are inter-carrier stacked modulation (IPD-PWM) and carrier phase-shift modulation (CPS-PWM). Ideally, both strategies exhibit good performance, producing output voltage waveforms with high level numbers and good power quality. However, when the DC voltage on the input side of the cascaded H-bridge multilevel power amplifier is unbalanced, the output voltage waveform quality degrades. IPD-PWM modulation leads to power imbalance between cascaded units, resulting in different losses among the switching transistors and, in severe cases, current backflow. This drawback becomes more pronounced when the number of cascaded units is large, rendering IPD-PWM unsuitable. CPS-PWM modulation, on the other hand, can achieve power self-balancing between cascaded units when the DC voltage on the input side of the cascaded H-bridge multilevel power amplifier is unbalanced, but its frequency doubling effect fails, and the low-order harmonics of the output voltage increase. Existing improved CPS-PWM modulation strategies for harmonic elimination are ineffective, capable of eliminating only a limited number of harmonics, and involve complex calculations. The Homotopy algorithm, Levenberg-Marquardt algorithm, and Newton-iteration algorithm all have various shortcomings, such as insufficient accuracy of the solution results and too many iterations. They are difficult to quickly and accurately solve for the phase shift angle of the improved CPS-PWM modulation strategy and cannot effectively eliminate low-order harmonics in the output voltage caused by DC-side voltage imbalance in cascaded H-bridge multilevel power amplifiers. Summary of the Invention

[0004] To address the shortcomings of the above-mentioned improved carrier phase-shift modulation strategies, this invention proposes a carrier phase-shift modulation method for cascaded H-bridge multilevel power amplifiers. This method aims to quickly and accurately determine the appropriate carrier phase-shift angle using parameters such as the DC-side voltage and modulation index of the cascaded H-bridge multilevel power amplifier, thereby eliminating some low-order harmonics in the output voltage and improving the frequency doubling effect of the cascaded H-bridge multilevel power amplifier under DC-side voltage imbalance conditions.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] The carrier phase-shift modulation method for a cascaded H-bridge multilevel power amplifier of the present invention is characterized by comprising the following steps:

[0007] Step S1: Sequentially detect the DC-side input voltage {U} of each cascaded unit in the cascaded H-bridge multilevel power amplifier. dck |k=1,2,…,N}, and calculate the modulation index {M} of each cascaded unit. k |k=1,2,…,N};where U dck M represents the DC-side input voltage of the k-th cascaded unit; k The modulation index of the k-th cascaded unit is represented by N, and the number of cascaded units is represented by N.

[0008] Step S2: After expanding the output voltage of each cascaded unit using Fourier analysis, we obtain the Fourier analysis model of the output voltage of a single cascaded unit. Then, we combine the Fourier analysis models of the output voltage of all single cascaded units using the traditional carrier phase shift angle allocation law to obtain the Fourier analysis model of the output voltage of the cascaded H-bridge multilevel power amplifier.

[0009] Step S3: Divide the Fourier analysis model into a fundamental frequency component and a harmonic frequency component, and make the sum of all relevant terms for each harmonic frequency zero, thereby obtaining a set of parameters related to the carrier phase shift angle {θ}. k A nonlinear transcendental system of equations for |k=1,2,…,N}, where θ k This represents the carrier phase shift angle of the k-th cascaded unit;

[0010] Step S4: Select the DC-side input voltage {U} of each cascaded unit. dck |k=1,2,…,N} and modulation {M} k Substituting |k=1,2,…,N} into the nonlinear transcendental equations and using a neural network-genetic hybrid algorithm to solve the nonlinear transcendental equations, we can obtain the carrier phase shift angle modulated under DC-side voltage imbalance, thereby realizing carrier phase shift modulation of the cascaded H-bridge multilevel power amplifier.

[0011] The carrier phase-shift modulation method for the cascaded H-bridge multilevel power amplifier described in this invention is also characterized in that step S4 includes the following steps:

[0012] Step S4.1: Use equation (8) to obtain the carrier phase shift angle θ of the kth cascaded unit. k The nonlinear transcendental equation system F(θ) k );

[0013]

[0014] In equation (8), H mk Let represent the coefficient of the m-th harmonic component of the k-th cascaded unit, and m represents the harmonic order relative to the carrier frequency, m = 1, 2, ..., M, where M is the highest harmonic;

[0015] Step S4.2: Adjust the modulation index {M} k |k=1,2,…,N} and DC side input voltage {U dck The input |k=1,2,…,N} is used to input the pre-trained BP neural network, and the output is N carrier phase shift angle ambiguity solutions {θ′}. k |k=1,2,...,N}, where θ k ′ represents the ambiguous solution of the phase shift angle of the k-th carrier;

[0016] Step S4.3: Define the generation counter as t, and the maximum number of generations as T;

[0017] Initialize t = 1, define the population of generation t. in, Describes the population X of generation t. (t) The a-th individual; and initialized. n is the population size; P is defined as... s To select the probability threshold, define P. c Let P be the threshold for the crossover probability. m This is the threshold for the probability of mutation;

[0018] Step S4.4: Initialize a = 1;

[0019] Step S4.5: Construct the a-th individual using equation (9) fitness function

[0020]

[0021] In equation (9), Represents the a-th individual The sum of the m-th harmonic cosine components of the N cascaded units, and Represents the a-th individual The sum of the m-th harmonic sinusoidal components of the N units, and

[0022] Step S4.6: Selection of the optimal population:

[0023] Calculate the a-th individual Survival probability like Greater than P s If so, then directly retain the a-th individual. And as the t+1 generation population X (t) If the individuals are in the sequence, proceed to step S4.7; otherwise, proceed to step S4.7.

[0024] Step S4.7: Individual crossover operation:

[0025] Generate the a-th individual random crossover probability And judge Greater than P c Does it hold true? If it does, then the a-th individual... Partial fuzzy solutions and the (a+1)th individual The fuzzy solutions in the equation are swapped to obtain the updated a-th individual. And assign to Otherwise, keep constant;

[0026] Step S4.8: Individual variation operation:

[0027] Generate the a-th individual It is the probability of random mutation. judge Less than P m Does it hold true? If it does, then for the a-th individual... The partial fuzzy solutions in the model are mutated to obtain the updated a-th individual. And assign to Otherwise, keep constant;

[0028] Step S4.9: Transfer the a-th individual And as the t+1 generation population X (t) Individuals within;

[0029] Step S4.10: After assigning a+1 to a, if a>n, it means that the (t+1)th generation population X has been obtained. (t+1) Otherwise, return to step S4.5 and execute sequentially;

[0030] Step S4.11: Determine whether t = T holds true. If it does, it means that the population X of generation T has been obtained. (T)and X (T) The individual with the highest fitness is used as the final precise phase shift angle {θ}. k * If |k=1,2,…,N}, otherwise, assign t+1 to t and proceed to step S4.4.

[0031] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the carrier phase shift modulation method, and the processor is configured to execute the program stored in the memory.

[0032] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program is executed by a processor to perform the steps of the carrier phase-shift modulation method.

[0033] Compared with existing technologies, the beneficial effects of this invention are reflected in:

[0034] 1. This invention overcomes the problem that the harmonic elimination frequency is limited to twice the carrier frequency by improving the algorithm for solving the nonlinear equation system of carrier phase shift angle, thus enabling the elimination of higher harmonic numbers in the output voltage.

[0035] 2. This invention employs a neural network-genetic hybrid algorithm. Due to its strong global optimization search capability, it can accurately solve high-dimensional nonlinear equations, enabling this invention to be applied to cascaded H-bridge multilevel power amplifiers with a larger number of cascaded units.

[0036] 3. This invention uses a neural network-genetic hybrid algorithm to solve nonlinear transcendental equations. It solves the problems of multi-input multi-output neural networks being too complex and traditional genetic algorithms being prone to getting trapped in local optima. The solution obtained is more accurate and stable, thus requiring less storage space in practical applications. It also makes the solution process more reliable and the carrier phase shift angle more accurate. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of a traditional CPS-PWM modulation strategy;

[0038] Figure 2 This is a flowchart of the improved carrier phase shift modulation strategy based on a neural network-genetic hybrid algorithm used in this invention;

[0039] Figure 3a The output voltage THD of a 6-unit cascaded H-bridge multilevel power amplifier under traditional CPS-PWM is shown in the figure.

[0040] Figure 3bTo improve the THD analysis diagram of the output voltage of a 6-unit cascaded H-bridge multilevel power amplifier under CPS-PWM;

[0041] Figure 4a THD analysis diagram of the output voltage of a 10-unit cascaded H-bridge multilevel power amplifier under traditional CPS-PWM;

[0042] Figure 4b Analysis of the output voltage THD of a 10-unit cascaded H-bridge multilevel power amplifier under CPS-PWM. Detailed Implementation

[0043] In this embodiment, as Figure 1 As shown, a carrier phase-shift modulation method for a cascaded H-bridge multilevel power amplifier is described. This method focuses on a cascaded H-bridge multilevel power amplifier operating under unbalanced DC-side input voltage conditions. By detecting the DC-side voltage and modulation depth of each cascaded unit, a neural network-genetic hybrid algorithm is used to solve the harmonic elimination nonlinear transcendental equations to obtain a new carrier phase-shift angle. The modulation strategy is then adjusted based on this new carrier phase-shift angle to eliminate some output voltage harmonics. Specifically, the method includes:

[0044] Step S1: Sequentially detect the DC-side input voltage {U} of each cascaded unit in the cascaded H-bridge multilevel power amplifier. dck |k=1,2,…,N}, and calculate the modulation index {M} of each cascaded unit. k |k=1,2,…,N};where U dck M represents the DC-side input voltage of the k-th cascaded unit; k The modulation index of the k-th cascaded unit is represented by N, and the number of cascaded units is represented by N.

[0045] Step S2: After expanding the output voltage of each cascaded unit using Fourier analysis, the Fourier analysis model of the output voltage of a single cascaded unit is obtained. The Fourier analysis expression of a single cascaded unit is shown in Equation (1):

[0046]

[0047] In equation (1), the expressions for each coefficient are:

[0048]

[0049] In equation (2), m is the m-th harmonic, ω is the triangular carrier angular frequency, and U dck M is the DC-side input voltage of the k-th unit. k Let k be the modulation index of the k-th unit.

[0050] Then, the Fourier analysis models of the output voltage of all individual cascaded units are combined using the traditional carrier phase shift angle allocation law to obtain the Fourier analysis model of the output voltage of the cascaded H-bridge multilevel power amplifier, as shown in equation (4).

[0051] For traditional CPS-PWM modulation strategies, such as Figure 1 As shown, the coefficients of the Fourier decomposition expressions of each unit of the cascaded H-bridge multilevel power amplifier are the same, the difference lies in their phase shift angles. Based on this characteristic, the results of the Fourier analysis expansion of the output voltage of all cascaded H-bridge units are combined, and the traditional carrier phase shift angle formula is shown in equation (3):

[0052]

[0053] The Fourier expression for the output voltage of the N-module cascaded H-bridge multilevel power amplifier can be obtained as follows:

[0054]

[0055] Step S3: Divide the Fourier analysis model into a fundamental part and a harmonic part, as shown in equation (6), and make the sum of all relevant terms of each harmonic zero, thereby obtaining a set of information about the carrier phase shift angle {θ}. k A nonlinear transcendental system of equations for |k=1,2,…,N}, where θ k This represents the carrier phase shift angle of the k-th cascaded unit;

[0056] According to equation (4), the Fourier model of the output voltage of the N-module cascaded H-bridge multilevel power amplifier, the expression for the m-th harmonic is shown in equation (5):

[0057]

[0058] In equation (5), Using the basic trigonometric product-to-sum formulas, equation (5) is transformed into equation (6):

[0059]

[0060] Making the sum of the coefficients in equation (6) equal to 0, we obtain the information about the carrier phase shift angle {θ}. k The nonlinear transcendental equations system of |k=1,2,…,N} is shown in equation (7):

[0061]

[0062] Step S4: Select the DC-side input voltage {U} of each cascaded unit. dck |k=1,2,…,N} and modulation {M} kSubstituting |k=1,2,…,N} into the nonlinear transcendental equations and using a neural network-genetic hybrid algorithm to solve the nonlinear transcendental equations, we can obtain the carrier phase shift angle modulated under DC-side voltage imbalance, thereby realizing carrier phase shift modulation of the cascaded H-bridge multilevel power amplifier.

[0063] The specific implementation steps are as follows:

[0064] Step S4.1: Use equation (8) to obtain the carrier phase shift angle θ of the kth cascaded unit. k The nonlinear transcendental equation system F(θ) k );

[0065]

[0066] In equation (8), H mk Let represent the coefficient of the m-th harmonic component of the k-th cascaded unit, and m represents the harmonic order relative to the carrier frequency, m = 1, 2, ..., M, where M is the highest harmonic;

[0067] Step S4.2: Construct a single-layer BP neural network with the following topology: the input layer is 2N, i.e., the modulation density is {M}. k |k=1,2,…,N} and DC side input voltage {U dck |k=1,2,…,N}, with 5 hidden layers and N output layers, which is equivalent to N carrier phase shift angle ambiguity solutions {θ}. k '|k=1,2,…,N}. Using 300 sets of data as training samples for the neural network, with 150 sets as the training set and 150 sets as the test set, a simple single-layer BP neural network model is trained.

[0068] Adjustment system {M k |k=1,2,…,N} and DC side input voltage {U dck The input |k=1,2,…,N} is used to input the pre-trained BP neural network, and the output is N carrier phase shift angle ambiguity solutions {θ′}. k |k=1,2,...,N}, where θ′ k This represents the ambiguous solution for the phase shift angle of the k-th carrier.

[0069] Step S4.3: Define the generation counter as t, and the maximum number of generations as T;

[0070] Initialize t = 1, define the population of generation t. in, Describes the population X of generation t. (t) The a-th individual; and initialized. n is the population size; P is defined as...s To select the probability threshold, define P. c Let P be the threshold for the crossover probability. m This is the threshold for the probability of mutation;

[0071] Step S4.4: Initialize a = 1;

[0072] Step S4.5: Construct the a-th individual using equation (9) fitness function

[0073]

[0074] In equation (9), Represents the a-th individual The sum of the m-th harmonic cosine components of the N cascaded units, and Represents the a-th individual The sum of the m-th harmonic sinusoidal components of the N units, and

[0075] The optimization objective of the neural network-genetic hybrid algorithm is to minimize the value of the nonlinear equation system in equation (8), i.e. and If the value of is minimized, then the fitness function The closer the value is to 1, the better the optimization effect of the neural network-genetic hybrid algorithm is judged;

[0076] Step S4.6: Selection of the optimal population:

[0077] Calculate the a-th individual Survival probability like Greater than P s If so, then directly retain the a-th individual. And as the t+1 generation population X (t) If the individuals are in the sequence, proceed to step S4.7; otherwise, proceed to step S4.7.

[0078] Step S4.7: Individual crossover operation:

[0079] Generate the a-th individual random crossover probability And judge Greater than P c Does it hold true? If it does, then the a-th individual... Partial fuzzy solutions and the (a+1)th individual The fuzzy solutions in the equation are swapped to obtain the updated a-th individual. And assign to Otherwise, keep constant;

[0080] Step S4.8: Individual variation operation:

[0081] Generate the a-th individual It is the probability of random mutation. judge Less than P m Does it hold true? If it does, then for the a-th individual... The partial fuzzy solutions in the model are mutated to obtain the updated a-th individual. And assign to Otherwise, keep constant;

[0082] Step S4.9: Transfer the a-th individual And as the t+1 generation population X (t) Individuals within;

[0083] Step S4.10: After assigning a+1 to a, if a>n, it means that the (t+1)th generation population X has been obtained. (t+1) Otherwise, return to step S4.5 and execute sequentially;

[0084] Step S4.11: Determine whether t = T holds true. If it does, it means that the population X of generation T has been obtained. (T) and X (T) The individual with the highest fitness is used as the final precise phase shift angle {θ}. k * If |k=1,2,…,N}, otherwise, assign t+1 to t and proceed to step S4.4.

[0085] Step S5: Based on the solution result of step S4.11, modify the carrier phase shift angle in the carrier phase shift modulation strategy to achieve the effect of eliminating some output voltage harmonics. For a cascaded H-bridge multilevel power amplifier with N cascaded units, it can eliminate at most m times the carrier frequency harmonics, where m = (N-1) / 2, N is an odd number; m = (N-2) / 2, N is an even number.

[0086] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0087] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0088] The flowchart of the implementation of this invention is as follows: Figure 2As shown, based on the analysis in steps S1 to S5, the effectiveness of the carrier phase-shifting modulation strategy used in this invention is further verified by using a 6-module cascaded H-bridge multilevel power amplifier and a 10-module cascaded H-bridge multilevel power amplifier. In the simulation example of this invention, frequency-doubled unipolar carrier phase-shifting SPWM modulation is used.

[0089] For a 6-module cascaded H-bridge multilevel power amplifier, the DC-side voltage parameter is: U dc1 =100V, U dc2 =90V, U dc3 =75V, U dc4 =80V, U dc5 =85V, U dc6 =85V, modulation index M k All values ​​are taken as 0.8, carrier frequency f c =10kHz, the output voltage of the cascaded H-bridge multilevel power amplifier and its Fourier analysis results are as follows Figure 3a and Figure 3b As shown, where Figure 3a The Fourier analysis results of the output voltage when using the traditional CPS-PWM modulation strategy are shown. Figure 3b The Fourier analysis results of the output voltage when using the improved CPS-PWM modulation strategy based on a neural network-genetic hybrid algorithm are shown. It can be seen that due to the DC-side voltage imbalance, integer multiples of carrier harmonics such as 20kHz, 40kHz, and 60kHz appear in the output voltage when using the traditional CPS-PWM modulation strategy, rendering the frequency doubling effect of the traditional CPS-PWM modulation strategy ineffective. However, after adopting the improved CPS-PWM modulation strategy based on a neural network-genetic hybrid algorithm proposed in this invention, the harmonics at 20kHz and 40kHz are effectively eliminated.

[0090] Similarly, this invention is also applicable to cascaded H-bridge multilevel power amplifiers with a larger number of cascaded units. The neural network-genetic hybrid algorithm can solve more complex nonlinear transcendental equations. The DC-side voltage parameters of the 10-module cascaded H-bridge multilevel power amplifier are: U dc1 =100V, U dc2 =90V, U dc3 =75V, U dc4 =80V, U dc5 =85V, U dc6 =85V, U dc7 =75V, U dc8 =70V, U dc9 =80V, U dc10 =85V, modulation index M k All values ​​are taken as 0.8, carrier frequency f c=10kHz, the simulated power amplifier output voltage and its Fourier analysis results are as follows Figure 4a and Figure 4b As shown. Under DC-side voltage imbalance, Figure 4a When the traditional CPS-PWM modulation strategy is used, harmonics of frequencies such as 20kHz, 40kHz, 60kHz, 80kHz, and 100kHz appear in the output voltage. Figure 4b After adopting the improved CPS-PWM modulation strategy based on the neural network-genetic hybrid algorithm proposed in this invention, harmonics at 20kHz, 40kHz, 60kHz and 80kHz are effectively eliminated.

[0091] The carrier phase-shift modulation strategy of the cascaded H-bridge multilevel power amplifier described in this invention provides a methodological guide for eliminating some output voltage harmonics in the cascaded H-bridge multilevel power amplifier under DC-side voltage imbalance conditions. The above description is only an embodiment of this invention and is not intended to limit the invention. Any modifications, synonymous substitutions, and improvements made within the precision and principles of this invention should be included within the protection scope of this invention.

Claims

1. A carrier phase-shift modulation method for a cascaded H-bridge multilevel power amplifier, characterized in that, Includes the following steps: Step S1: Sequentially detect the DC-side input voltage {U} of each cascaded unit in the cascaded H-bridge multilevel power amplifier. dck |k=1,2,…,N}, and calculate the modulation index {M} of each cascaded unit. k |k=1,2,…,N}; Among them, U dck M represents the DC-side input voltage of the k-th cascaded unit; k The modulation index of the k-th cascaded unit is represented by N, and the number of cascaded units is represented by N. Step S2: After expanding the output voltage of each cascaded unit using Fourier analysis, we obtain the Fourier analysis model of the output voltage of a single cascaded unit. Then, we combine the Fourier analysis models of the output voltage of all single cascaded units using the traditional carrier phase shift angle allocation law to obtain the Fourier analysis model of the output voltage of the cascaded H-bridge multilevel power amplifier. Step S3: Divide the Fourier analysis model into a fundamental frequency component and a harmonic frequency component, and make the sum of all relevant terms for each harmonic frequency zero, thereby obtaining a set of parameters related to the carrier phase shift angle {θ}. k A nonlinear transcendental system of equations for |k=1,2,…,N}, where θ k This represents the carrier phase shift angle of the k-th cascaded unit; Step S4: Select the DC-side input voltage {U} of each cascaded unit. dck |k=1,2,…,N} and modulation {M} k Substituting |k=1,2,…,N} into the nonlinear transcendental equations and using a neural network-genetic hybrid algorithm to solve the nonlinear transcendental equations, we can obtain the carrier phase shift angle modulated under DC-side voltage imbalance, thereby realizing carrier phase shift modulation of the cascaded H-bridge multilevel power amplifier.

2. The carrier phase-shift modulation method for a cascaded H-bridge multilevel power amplifier according to claim 1, characterized in that, Step S4 includes the following steps: Step S4.1: Use equation (8) to obtain the carrier phase shift angle θ of the kth cascaded unit. k The nonlinear transcendental equation system F(θ) k ); In equation (8), H mk Let represent the coefficient of the m-th harmonic component of the k-th cascaded unit, and m represents the harmonic order relative to the carrier frequency, m = 1, 2, ..., M, where M is the highest harmonic; Step S4.2: Adjust the modulation index {M} k |k=1,2,…,N} and DC side input voltage {U dck The input |k=1,2,…,N} is used to input the pre-trained BP neural network, and the output is N carrier phase shift angle ambiguity solutions {θ′}. k |k=1,2,...,N}, where θ′ k This represents the ambiguous solution for the phase shift angle of the k-th carrier. Step S4.3: Define the generation counter as t, and the maximum number of generations as T; Initialize t=1, define the population of generation t. in, Describes the population X of generation t. (t) The a-th individual; and initialized. n is the population size; P is defined as... s To select the probability threshold, define P. c Let P be the threshold for the crossover probability. m This is the threshold for the probability of mutation; Step S4.4: Initialize a = 1; Step S4.5: Construct the a-th individual using equation (9) fitness function In equation (9), Represents the a-th individual The sum of the m-th harmonic cosine components of the N cascaded units, and Represents the a-th individual The sum of the m-th harmonic sinusoidal components of the N units, and Step S4.6: Selection of the optimal population: Calculate the a-th individual Survival probability like Greater than P s If so, then directly retain the a-th individual. And as the t+1 generation population X (t) If the individuals are in the sequence, proceed to step S4.7; otherwise, proceed to step S4.

7. Step S4.7: Individual crossover operation: Generate the a-th individual random crossover probability And judge Greater than P c Does it hold true? If it does, then the a-th individual... Partial fuzzy solutions and the (a+1)th individual The fuzzy solutions in the equation are swapped to obtain the updated a-th individual. And assign to Otherwise, keep constant; Step S4.8: Individual variation operation: Generate the a-th individual It is the probability of random mutation. judge Less than P m Does it hold true? If it does, then for the a-th individual... The partial fuzzy solutions in the model are mutated to obtain the updated a-th individual. And assign to Otherwise, keep constant; Step S4.9: Transfer the a-th individual And as the t+1 generation population X (t) Individuals within; Step S4.10: After assigning a+1 to a, if a>n, it means that the (t+1)th generation population X has been obtained. (t+1) Otherwise, return to step S4.5 and execute sequentially; Step S4.11: Determine whether t = T holds true. If it does, it means that the population X of generation T has been obtained. (T) and X (T) The individual with the highest fitness is used as the final precise phase shift angle {θ}. k * If |k=1,2,…,N}, otherwise, assign t+1 to t and proceed to step S4.

4.

3. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the carrier phase-shift modulation method of claim 1 or 2, and the processor is configured to execute the program stored in the memory.

4. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program, when run by the processor, executes the steps of the carrier phase-shift modulation method according to claim 1 or 2.

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