Pulse Width Modulation Method for Minimizing Switching Frequency and Suppressing Harmonics in Multilevel Converters

Abstract

The present invention discloses a pulse width modulation method for minimizing switching frequency and suppressing harmonics in a multilevel converter. Its main technical features include: performing equally spaced sampling on a multilevel PWM waveform within a fundamental wave period and representing it as a matrix; using a first-order difference matrix to express the switching frequency as a quadratic function with respect to this matrix; performing a Fourier series expansion on the PWM waveform and establishing constraints on the fundamental and harmonics with respect to the level vector based on a numerical integration formula; constructing a quadratic programming model with the switching frequency as the optimization objective function, converting it into a 0-1 quadratic programming model using matrix transformation, and finally solving this model to obtain a discretized multilevel PWM waveform. Compared with currently commonly used specific harmonic elimination methods, the method disclosed in the present invention significantly reduces the number of switching angles required to eliminate the same number of harmonics, effectively reducing the switching losses of the converter and improving energy conversion efficiency.

Description

Technical Field

[0001] The present invention relates to the field of power electronic systems and control methods thereof, and is a pulse width modulation method for simultaneously optimizing the switching frequency and harmonics of a multi-level converter, and is particularly suitable for application fields such as high-power inversion or rectification. Background Art

[0002] For PWM converters, power quality and conversion efficiency are, to a certain extent, contradictory. As the switching frequency increases, harmonics shift to higher frequencies, making them easier to filter out. This improves the converter's output power quality, but switching losses increase with the switching frequency, reducing conversion efficiency and increasing heat dissipation. Minimizing the switching frequency while maintaining grid power quality standards is crucial for converter optimization and has long been a research hotspot and challenge in this field.

[0003] The mathematical model used by the SHE method to solve switching angles is a set of nonlinear equations. The number of equations in this model is equal to the number of switching angles to be solved. That is, if the number of switching angles is N, then the number of harmonics that can be eliminated is N-1. In this case, if a method can be found to eliminate the same number of harmonics (N-1) but using fewer than N switching angles, the switching frequency can be significantly reduced. Recently, many researchers have found that under certain modulation ratios, the same number of switching angles can eliminate more harmonics than traditional SHE techniques, indicating that the number of switching angles required to eliminate a given number of harmonics can be smaller than the number required by SHE. In previous studies, researchers have proposed a two-level pulse width modulation method for simultaneous optimization of switching frequency and harmonics. This method cleverly converts the two-level PWM waveform into a binary vector, performs a first-order difference operation, and uses variable substitution to construct a 0-1 programming model. The resulting solution significantly reduces the switching frequency compared to the traditional SHE method. However, this model is not applicable to multi-level solutions. Based on this, the present invention proposes a multi-level solution model. Summary of the Invention

[0004] The object of the present invention is to provide a modulation method for a multi-level converter, which can reduce the switching frequency as much as possible while meeting certain harmonic requirements, thereby reducing switching losses, i.e., heat dissipation pressure, and improving the efficiency of the converter.

[0005] To achieve the above objectives, the multi-level converter switching frequency minimization and harmonic suppression pulse width modulation method of the present invention adopts the following technical means:

[0006] 1. The traditional SHE model uses switching angles to represent the PWM waveform. Once the number of switching angles is given, the switching frequency is also fixed and there is no possibility of further optimization. The present invention represents the PWM waveform as a matrix. Using the idea of ​​the optimal assignment problem model in operations research, each row in the binary matrix represents a level state, and each column represents the state of a sampling point. When the element x in the matrix is ji =1, it means that the sampling level of the i-th sampling point is the j-th level state. ji = 0, it means that the sampling level at the i-th sampling point is not the j-th level state. This representation method takes the entire PWM waveform as the solution object and does not have any restrictions on the number of jumps of the PWM waveform (corresponding to the switching frequency). It overcomes the defect of fixed switching frequency when the PWM waveform is represented by switching angle, and provides the possibility for further optimization of the switching frequency.

[0007] 2. The switching frequency is directly related to the number of transitions in the PWM waveform. During non-transition periods, the first-order difference is always 0. Only during transitions does the first-order difference result become non-zero, with the possible values ​​of 1 or -1. This paper proposes a multi-level solution model. Each row of the matrix represents whether all sampling points in a given level state transition. Therefore, it is sufficient to perform a differential operation on each row of the matrix and then sum the results. Half of the sum is taken as the switching frequency. The switching frequency is then used as the objective function for optimization.

[0008] In order to more clearly illustrate the specific implementation method of the model, the steps for odd-numbered multi-level and even-numbered multi-level are described here respectively.

[0009] Based on the above technical means, the odd-numbered multi-level converter switching frequency minimization harmonic suppression pulse width modulation method of the present invention includes the following steps:

[0010] Step 1: Assuming that the multi-level PWM waveform is symmetrical in half cycle and the step level value is E, perform equal-interval sampling on the multi-level PWM waveform in half cycle and express it as

[0011]

[0012] Where n is the number of sampling points in half a period, m is the number of level states, and x ji (j=1,2,…,m,i=1,2,…,n) is the jth level state of the i-th sampling point, and its value is 1 or 0. ji =1, it means that the sampling level of the i-th sampling point is the j-th level state. ji =0, it means that the sampling level of the i-th sampling point is not the j-th level state;

[0013] Step 2: Split the matrix obtained in step 1 into m row vectors according to each level state

[0014] X1=[x 11 x 12 … x 1n ]

[0015] X2=[x 21 x 22 … x 2n ]

[0016] …

[0017]

[0018] …

[0019] X m =[x m1 x m2 … x mn ]

[0020] Step 3: Express the switching frequency L as the following quadratic function of x:

[0021]

[0022] in

[0023]

[0024] Step 4: Weight each row vector in the sampling matrix X in step 1 and convert it into the actual level state of each sampling point, which is represented as a vector H;

[0025] H 1×n =M 1×m X m×n

[0026] in

[0027]

[0028] Step 5: Perform a first-order difference operation on the elements of vector H in step 4. The difference in the absolute values ​​of adjacent elements of the vector must be less than or equal to 1. This is to prevent level jumps, that is, to avoid multiple switches operating at the same time. The constraint inequality is as follows:

[0029] -I n-1 ≤(A (n-1)×n H T )≤I n-1

[0030] where I is defined n represents an n-dimensional column vector whose components are all 1 (i.e., an n×1 matrix whose elements are all 1), then

[0031] I n-1 =[1 1 … 1] n-1 T

[0032] Step 6: For the row vector in step 2 To constrain, require The number of elements in each row of the row vector with a value equal to 1 is greater than or equal to 1, that is, the level state of the PWM waveform in half a cycle is In order to ensure that the PWM waveform has m level states in one cycle, the constraint inequality is as follows

[0033]

[0034] Step 7: Constrain the matrix X in step 1. In each column of the X matrix, there can be only one value of 1 and the rest are 0, so as to ensure that each point can only correspond to one level state. The constraint equation is as follows

[0035] X m×n T I m =I n

[0036] Step 8: Expand the multi-level PWM waveform into the following Fourier series:

[0037]

[0038] Assuming that the waveform is half-cycle symmetrical and the PWM converter topology is symmetrical, that is, the ratio S between the DC voltage sources on the DC side is 1 (different constraints need to be constructed according to the waveform symmetry and the PWM topology, that is, the value of S), then it is necessary to constrain the coefficients of the Fourier transform. According to the rectangular calculation formula of numerical integration, the Fourier coefficients can be approximated as

[0039]

[0040]

[0041] in

[0042]

[0043]

[0044] Where k=1 represents the fundamental wave, k=2,3... represents the harmonic order;

[0045] Step 9: Based on the results of the above steps, construct the following 0-1 quadratic programming model

[0046]

[0047] stS1(MX) T =a1

[0048] C1(MX) T =b1

[0049] B(MX)≤E

[0050] -I n-1 ≤A(MX) T ≤I n-1

[0051]

[0052] I m T X=I n T

[0053] x ji ∈{0,1},(j=1,2,...,m, i=1,2,...,n)

[0054] Where a1 and b1 are the expected amplitudes of the fundamental sine and cosine components respectively. Since the waveform is symmetrical over half a period, the constraint matrix B is as follows:

[0055] B n×2(l-1) =[S2,…,S l ,C2,…,C l ] T

[0056] l is the highest order of harmonics to be suppressed, A is the first-order difference matrix shown in step 3, M is the level state value shown in step 4, is a column vector defined in step 5 whose only elements with different dimensions are all 1, and E is the allowable value of each harmonic component, which is defined as follows

[0057] E=[e2,e3,…,e 2(l-1) ] T

[0058] The allowable value of each harmonic component in E can be determined by referring to relevant standards (such as IEEE Standard 519, IEC61000, CIGRE WG 36-05, etc.), or it can be directly specified as a very small number according to actual requirements, for example

[0059] E=[0.01,0.01,…,0.01] T

[0060] Step 10: Solve the 0-1 quadratic programming model constructed in step 9 to obtain a discretized multi-level PWM waveform.

[0061] The pulse width modulation method for minimizing switching frequency of an even-numbered multi-level converter and suppressing harmonics of the present invention comprises the following steps:

[0062] Step 1: Assuming that the even multi-level PWM waveform has a symmetrical half-cycle and the step level value is E, perform equal-interval sampling on the half-cycle multi-level PWM waveform and express it as

[0063]

[0064] Where n is the number of sampling points in half a period, m is the number of level states, and x ji (j=1,2,…,m,i=1,2,…,n) is the jth level state of the i-th sampling point, and its value is 1 or 0. ji =1, it means that the sampling level of the i-th sampling point is the j-th level state. ji = 0, it means that the sampling level of the i-th sampling point is not the j-th level state. At this time, the left column vector (1,…,m) T Indicates the jth level state, not the actual value of the level state.

[0065] Step 2: Split the matrix obtained in step 1 into m row vectors according to each level state

[0066] X1=[x 11 x 12 … x 1n ]

[0067] …

[0068]

[0069] …

[0070] X m =[x m1 x m2 … x mn ]

[0071] Step 3: Express the switching frequency L as the following quadratic function of x:

[0072]

[0073] in

[0074]

[0075] Step 4: Weight each row vector in the sampling matrix X in step 1 and convert it into the actual level state of each sampling point, which is represented as a vector H;

[0076] H 1×n =M 1×m X m×n

[0077] Where M is a specific numerical matrix of m actual level states.

[0078]

[0079] Step 5: Perform a first-order difference operation on the elements of vector H in step 4. The difference in the absolute values ​​of adjacent elements of the vector must be less than or equal to 1. This is to prevent level jumps, that is, to avoid multiple switches operating at the same time. The constraint inequality is as follows:

[0080] -I n-1 ≤(A (n-1)×n H T )≤I n-1

[0081] where I is defined n represents an n-dimensional column vector whose components are all 1 (i.e., an n×1 matrix whose elements are all 1), then

[0082] I n-1 =[1 1 … 1] n-1 T

[0083] Directly perform subtraction constraints on the first and last elements of vector H to ensure that there is no waveform jump at the connection of each half cycle. The constraint inequality is as follows

[0084] -1≤H(1)-H(n)≤1

[0085] Step 7: For the row vector X1,…,X in step 2 m To constrain, require The number of elements in each row of the row vector with a value equal to 1 is greater than or equal to 1, that is, the level state of the PWM waveform in half a cycle is In order to ensure that the PWM waveform has m level states within one cycle, the constraint inequality is as follows

[0086]

[0087] Step 8. Constrain the matrix X in step 1. In each column of the X matrix, there can be only one value of 1 and the rest are 0, so as to ensure that each point can only correspond to one level state. The constraint equation is as follows

[0088] X m×nT I m =I n

[0089] Step 9: Expand the multi-level PWM waveform into the following Fourier series:

[0090]

[0091] Assuming that the waveform is half-cycle symmetrical and the PWM converter topology is symmetrical, that is, the ratio S between the DC voltage sources on the DC side is 1 (different constraints need to be constructed according to the waveform symmetry and the PWM topology, that is, the value of S), then it is necessary to constrain the coefficients of the Fourier transform. According to the rectangular calculation formula of numerical integration, the Fourier coefficients can be approximated as

[0092]

[0093]

[0094] in

[0095]

[0096]

[0097] Where k=1 represents the fundamental wave, k=2,3... represents the harmonic order;

[0098] Step 10: Based on the results of the above steps, construct the following 0-1 quadratic programming model

[0099]

[0100] stS1(MX) T =a1

[0101] C1(MX) T =b1

[0102] B(MX)≤E

[0103] -I n-1 ≤A(MX) T ≤I n-1

[0104]

[0105] -1≤(MX) (1) -(MX) (n) ≤1

[0106] I m T X=I n T

[0107] x ji ∈{0,1},(j=1,2,...,m, i=1,2,...,n)

[0108] Where a1 and b1 are the expected amplitudes of the fundamental sine and cosine components respectively. Since the waveform is symmetrical over half a period, the constraint matrix B is as follows:

[0109] B n×2(l-1) =[S2,…,S l ,C2,…,C l ] T

[0110] l is the highest order of harmonics to be suppressed, A is the first-order difference matrix shown in step 3, M is the level state value shown in step 4, I m ,I n ,I n-1 is a column vector defined in step 5 whose only elements with different dimensions are all 1, and E is the allowable value of each harmonic component, which is defined as follows

[0111] E=[e2,e3,…,e 2(l-1) ] T

[0112] The allowable value of each harmonic component in E can be determined by referring to relevant standards (such as IEEE Standard 519, IEC61000, CIGRE WG 36-05, etc.), or it can be directly specified as a very small number according to actual requirements, for example

[0113] E=[0.01,0.01,…,0.01] T

[0114] Step 10: Solve the 0-1 quadratic programming model constructed in step 9 to obtain a discretized multi-level PWM waveform. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] Attachment Figure 1 This is the correspondence diagram between matrix elements and five-level PWM waveform.

[0116] Attachment Figure 2 It is the three-level PWM phase voltage waveform.

[0117] Attachment Figure 3 It is the four-level PWM phase voltage waveform. DETAILED DESCRIPTION

[0118] Two specific embodiments of the technical solution adopted by the present invention are given below. It should be pointed out that the specific embodiments described are only for facilitating the understanding of the present invention and do not serve as a limitation. Applications made by technicians based on these embodiments without creative mental effort also fall within the scope of protection of the present invention. Specific embodiment one:

[0120] Assuming that the three-level PWM waveform is symmetrical in half cycle and the number of sampling points in half cycle is 360, the variable matrix is

[0121]

[0122] Corresponding to the three level states, the variable matrix is ​​split into three row vectors as follows

[0123] X1=[x 11 x 12 … x 1 360 ]

[0124] X2=[x 21 x 22 … x 2 360 ]

[0125] X3=[x 31 x 32 … x 3 360 ]

[0126] The switching frequency L is expressed as the following quadratic function of x

[0127]

[0128] in

[0129]

[0130] Convert the sampling matrix X into the actual level state of each sampling point, represented as a vector H

[0131]

[0132] The anti-jump constraint on vector H is as follows

[0133]

[0134] Constrain the matrix X to ensure that each point can only correspond to one level state

[0135]

[0136] For row vectors X1, X2, …, X mConstraints are required to require that the number of elements with a value of 1 in each row of m row vectors is greater than or equal to 1, ensuring that the level state of the PWM waveform is constant within half a cycle. At this time, the PWM waveform has m level states in one cycle.

[0137]

[0138] Assuming that the harmonics to be eliminated are the 5th, 7th, 11th, 13th, 17th, 19th, and 23rd harmonics, and taking k as {1, 5, 7, 11, 13, 17, 19, 23}, the following quadratic programming model is constructed:

[0139]

[0140] stS1(MX)=a1

[0141] C1(MX)=b1

[0142] B(MX)≤E

[0143] -I 359 ≤A 359×360 (MX) T ≤I 359

[0144] I 360 T (X 2×360 ) T ≥I2 T

[0145] I3 T X=I 360 T

[0146] x ji ∈{0,1},(j=1,2,3,i=1,2,...,360)

[0147] in

[0148]

[0149]

[0150] B 360×14 =[S5,S7,S 11 ,S 13 ,S 17 ,S 19 ,S 23 ,C5,C7,C 11 ,C 13 ,C 17 ,C 19 ,C 23] T

[0151] Take a1=0.6,b1=0,E=[0.01,0.01,…,0.01] T By calling the Gurobi toolbox in MATLAB, we can find the solution matrix X of the quadratic programming model. Using matrix transformation, we can get the actual level value within half a period of the three-level half-period symmetrical PWM waveform, that is, the vector H as follows:

[0152] [0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1 ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1]

[0153] The corresponding three-level PWM waveform is shown in the attached figure. Figure 2 shown. Specific embodiment two:

[0155] Assuming that the four-level PWM waveform is symmetrical in half cycle and the number of sampling points in half cycle is 360, the variable matrix is

[0156]

[0157] Corresponding to the three level states, the variable matrix is ​​split into three row vectors as follows

[0158] X1=[x 11 x 12 … x 1 360 ]

[0159] X2=[x 21 x 22 … x 2 360 ]

[0160] X3=[x 31 x 32 … x 3 360 ]

[0161] X4=[x 41 x 42 … x 4 360 ]

[0162] The switching frequency L is expressed as the following quadratic function of x

[0163]

[0164] in

[0165]

[0166] Convert the sampling matrix X into the actual level state of each sampling point, represented as a vector H

[0167]

[0168] The anti-jump constraint on vector H is as follows

[0169]

[0170] Constrain the matrix X to ensure that each point can only correspond to one level state

[0171]

[0172] For row vectors X1, X2, …, X m To constrain, require The number of elements with a value of 1 in each row of the row vector is greater than or equal to 1, ensuring that the level state of the PWM waveform is constant within half a cycle. At this time, the PWM waveform has m level states in one cycle.

[0173]

[0174] Directly perform subtraction constraints on the first two elements of vector H to ensure that there is no waveform jump at the junction of the half-cycle waveform. The constraint inequality is as follows

[0175] -1≤H(1)-H(360)≤1

[0176] Assuming that the harmonics to be eliminated are the 5th, 7th, 11th, 13th, 17th, and 19th harmonics, and taking k as {1, 5, 7, 11, 13, 17, 19}, the following quadratic programming model is constructed:

[0177]

[0178] stS1(MX)=a1

[0179] C1(MX)=b1

[0180] B(MX)≤E

[0181] -I 359 ≤A 359×360 (MX) T ≤I 359

[0182] I 360 T (X 2×360 ) T ≥I2 T

[0183] -1≤(MX) (1) -(MX) (360) ≤1

[0184] I4 T X=I 360 T

[0185] x ji ∈{0,1},(j=1,2,3,4; i=1,2,...,360.)

[0186] in

[0187]

[0188]

[0189] B 360×12 =[S5,S7,S 11 ,S 13 ,S 17,S 19 ,C5,C7,C 11 ,C 13 ,C 17 ,C 19 ] T

[0190] Take a1=0.65, b1=0, E=[0.01,0.01,…,0.01] T By calling the Gurobi toolbox in MATLAB, we can find the solution matrix X of the quadratic programming model. Using matrix transformation, we can get the actual level value within half a period of the three-level half-period symmetrical PWM waveform, that is, the vector H as follows:

[0191] [-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,1.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1 .5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,- ...

[0192] The corresponding four-level PWM waveform is shown in the attached figure. Figure 3 shown.

[0193] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person familiar with the technology can understand and think of any changes or replacements within the technical scope disclosed by the present invention, which should be included in the scope of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A pulse width modulation method for minimizing switching frequency harmonic suppression of an odd-numbered multilevel converter, characterized in that The steps include: Step 1: Sample the odd-numbered multi-level PWM waveform at equal intervals. Assume that the number of level states is m and the number of sampling points is n. The value at each sampling point is recorded as a binary variable. In this case, m is an odd number, and the PWM waveform is represented by the following matrix X. In this case, the left column vector is Indicates the actual level state value; FIG1 is an example of the corresponding diagram of the matrix elements and the five-level PWM waveform for explanation; Step 2: Split the matrix obtained in step 1 into m row vectors according to each level state Step 3: Perform a first-order difference operation on each row vector in step 2, add the number of non-zero items in the calculated results, and then take the coefficient r1 to express it as the switching frequency L L=r1(X1A T AX1 T +X2A T AX2 T +…+X m A T AX m T ) Where A is the first-order difference matrix; Step 4: Calculate the level state of each sampling point according to the matrix in step 1, and express the actual level state of n points as a vector H; Step 5: Perform a skip-jump constraint on the vector H in step 4, i.e., avoid simultaneous operation of multiple switches. Step 6: Constrain the row vector in step 2 to ensure that it works in m level states at this time; Step 7: Constrain the matrix in step 1 to ensure that only one level state can be sampled at each point; Step 8: Perform Fourier series expansion on the PWM waveform to calculate the functional relationship between the amplitude of the fundamental wave and each harmonic sine and cosine component and the level state sequence; Step 9: Based on the functional relationship obtained in step 8, the amplitudes of the fundamental sine and cosine components to be controlled are set to the desired values, and the amplitudes of the harmonic sine and cosine components to be suppressed are set to 0 or less than a specified constant. With these as constraints, a mathematical model is established with the switching frequency in step 3 as the optimization objective function. Step 10: Solve the mathematical model in step 9 to obtain the values ​​of the actual level states of n points, which are the desired PWM waveforms.

2. A pulse width modulation method for minimizing switching frequency harmonic suppression in an even-numbered multilevel converter, characterized in that The steps include: Step 1: Sample the even-numbered multi-level PWM waveform at equal intervals. Assume that the number of level states is m and the number of sampling points is n. The value at each sampling point is recorded as a binary variable. In this case, m is an even number. The PWM waveform is represented by the following matrix X. In this case, the left column vector (1,…,n) T Indicates the jth level state, not the actual value of the level state; Step 2: Split the matrix obtained in step 1 into m row vectors according to each level state Step 3: Perform a first-order difference operation on each row vector in step 2, add the number of non-zero items in the calculated results, and then take the coefficient r2 to represent the switching frequency L L=r2(X1A T AX1 T +X2A T AX2 T +…+X m A T AX m T ) Where A is the first-order difference matrix; Step 4: Calculate the level state of each sampling point according to the matrix in step 1, and express the actual level state of n points as a vector H; Step 5: Perform a skip-jump constraint on the vector H in step 4, i.e., avoid simultaneous operation of multiple switches. Step 6: Constrain the row vector in step 2 to ensure that it works in m level states at this time; Step 7: Constrain the matrix in step 1 to ensure that only one level state can be sampled at each point; Step 8: Perform Fourier series expansion on the PWM waveform to calculate the functional relationship between the amplitude of the fundamental wave and each harmonic sine and cosine component and the level state sequence; Step 9: Based on the functional relationship obtained in step 8, the amplitudes of the fundamental sine and cosine components to be controlled are set to the desired values, and the amplitudes of the harmonic sine and cosine components to be suppressed are set to 0 or less than a specified constant. With these as constraints, a mathematical model is established with the switching frequency in step 3 as the optimization objective function. Step 10: Solve the mathematical model in step 9 to obtain the values ​​of the actual level states of n points, which are the desired PWM waveforms.

3. The pulse width modulation method according to claim 1 and claim 2, characterized in that: The multi-level PWM waveform in step 1 of the odd-numbered multi-level model is a PWM waveform with half-cycle symmetry or quarter-cycle symmetry, wherein the topology structure for generating the PWM waveform can be a symmetrical or asymmetrical structure.

4. The pulse width modulation method according to claim 1, wherein: The switching frequency L in step 2 of the odd-numbered multi-level model is a quadratic function of X as follows: L=r1(X1A T AX1 T +X2A T AX2 T +…+X m A T AX m T ) Where A is the first-order difference matrix.

5. The pulse width modulation method according to claim 1, wherein: In step 8 of the odd-numbered multi-level model, the amplitudes of the fundamental wave and the sine and cosine components of each harmonic are linear combinations of the level state sequence.

6. The pulse width modulation method according to claim 2, characterized in that: The multi-level PWM waveform in step 1 of the even-numbered multi-level model is a PWM waveform with half-cycle symmetry or quarter-cycle symmetry, wherein the topology structure for generating the PWM waveform can be a symmetrical or asymmetrical structure.

7. The pulse width modulation method according to claim 2, characterized in that: The switching frequency L in step 2 of the even multi-level model is a quadratic function of X as follows: L=r2(X1A T AX1 T +X2A T AX2 T +…+X m A T AX m T ) Where A is the first-order difference matrix.

8. The pulse width modulation method according to claim 2, characterized in that: In step 8 of the even-numbered multi-level model, the amplitudes of the fundamental wave and the sine and cosine components of each harmonic are linear combinations of the level state sequence.

9. The pulse width modulation method according to claim 4 or 5, characterized in that: The model established in step 9 of the odd-numbered multi-level model is a quadratic programming model.

10. The pulse width modulation method according to claim 5, characterized in that: In step 4 of the odd-numbered multi-level model, matrix variable substitution is used to transform the quadratic programming model into a 0-1 quadratic programming model.

11. The pulse width modulation method according to claim 4 or 5, characterized in that: The model established in step 9 of the even-numbered multi-level model is a quadratic programming model.

12. The pulse width modulation method according to claim 5, characterized in that: In step 4 of the even-numbered multi-level model, matrix variable substitution is used to transform the quadratic programming model into a 0-1 quadratic programming model.

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