Minimum common-mode voltage SVM method for multilevel converters based on αβ coordinates

Abstract

The application discloses a minimum common-mode voltage SVM method of a multi-level converter based on an alpha-beta coordinate system, comprising sampling three-phase voltage reference signals, calculating reference vectors on the alpha-beta coordinate system, and rounding components of the reference vectors to determine four space vectors closest to the reference vectors to form a unit square; determining a mapping relationship between the space vectors in the alpha-beta coordinate system and three-phase output levels a, b and c of the converter; judging a sector triangle type where the reference vector is located, determining three space vectors of a synthesized reference vector, and calculating action times of the three space vectors of the synthesized reference vector according to a volt-second balance principle; respectively calculating minimum common-mode voltage switching states corresponding to the space vectors of the synthesized reference vector; and determining a switching path of the switching states according to a five-segment algorithm to complete space vector modulation. The method avoids the problem of complex calculation of switching states by using 2 / 3 conversion in a traditional space vector modulation process.

Description

Technical Field

[0001] This invention belongs to the field of multilevel converter modulation technology, and particularly relates to a method for minimizing the common-mode voltage (SVM) of multilevel converters based on the α'β' coordinate system. Background Technology

[0002] Space Vector Modulation (SVM) technology is based on the theory that a circular flux linkage trajectory in a two-dimensional coordinate system is generated by connecting three-phase symmetrical voltages to the stator windings of a motor. It converts the three-phase symmetrical reference signal into a circular reference vector trajectory in a two-dimensional Cartesian coordinate system, converts the three-phase output levels into space vectors in the same two-dimensional coordinate system, tracks the reference vector trajectory, synthesizes the reference vector using the three space vectors closest to the reference vector, calculates the duration of the space vector's action and the corresponding switching state, and finally performs switching state switching to achieve modulation of the converter. SVM algorithms have advantages such as high DC voltage utilization, low switching frequency, good output waveform quality, and ease of digital implementation, and are widely used in three-level and five-level converters. However, as the number of levels increases, the difficulty of locating the reference vector increases, the number of switching states corresponding to the space vector increases significantly, and the calculation of switching states and the selection of switching state switching sequences become very complex, making the implementation of the SVM algorithm difficult.

[0003] The common-mode voltage generated during space vector modulation by a multilevel converter poses a significant threat to the insulation of the motor. A large common-mode voltage can generate a large motor bearing current or ground current through capacitive coupling between the stator and rotor, which can lead to motor damage due to excessive bearing current or electromagnetic interference (EMI) to nearby electrical equipment, affecting the normal operation of other equipment on the power grid. Summary of the Invention

[0004] This invention provides a SVM method for minimizing the common-mode voltage of a multilevel converter based on the α'β' coordinate system. It aims to solve the problems of cumbersome calculation of the space vector modulation process of multilevel converters, the difficulty in implementing the SVM algorithm, and how to suppress the common-mode voltage of the converter output to the minimum range of variation in the existing technology.

[0005] This invention provides a method for minimizing the common-mode voltage (SVM) of a multilevel converter based on the α′β′ coordinate system, comprising:

[0006] Step 1: For the three phase voltage reference signals u ra u rb u rc Sampling and calculation yield the reference vector V in the α′β′ coordinate system. r (α′ r ,β′ rand for reference vector V r (α′ r ,β′ r The component α′ r ,β′ r Rounding is performed to determine the four space vectors V closest to the reference vector. a (α′0,β′0,V b (α′0+1,β′0,V c (α′0,β′0+1,V d (α′0+1, β′0+1) form a unit square;

[0007] Step 2: Determine the mapping relationship between the spatial vector V(α′, β′) in the α′β′ coordinate system and the three-phase output levels a, b, c of the converter as follows:

[0008]

[0009] In the formula, α′ and β′ are the coordinate components of the space vector V, α, b, c ∈ (0, ±1, ±2, …, ±n), and the switching state of the space vector V(α′, β′) is S(a, b, c), where S is the name of the switching state.

[0010] Step 3: Spatial vector V a (α0, β0), V b (α′0+1,β′0,V c (α′0, β′0+1) form a sector triangle A, and the spatial vector V is... b (α0+1, β0), V c (α′0,β′0+1,V d (α′0+1, β′0+1) form sector triangle B, and the unit square is composed of sector triangle A and sector triangle B;

[0011] Determine the reference vector V r (α′ r ,β′ r The sector triangle type where the signal is located determines the composite reference vector V. r The three spatial vectors V1, V2, and V0 are used to calculate the composite reference vector V based on the second-volt balance principle. r The duration of action of the three spatial vectors V1, V2, and V0;

[0012] Step 4: The number of redundant switching states for any space vector V(α′, β′) in an n-stage H-bridge cascaded multilevel converter is R:

[0013] R=2n-q, (q=max||α′|, |β′|, |α′+β′|]),

[0014] Let N be the sum of the three components of any switch state S(a, b, c), i.e., N = a + b + c;

[0015] Step 4.1: If α′≥0 and β′≥0, then the space vector V(α′, β′) is located in the first quadrant, and one of the switching states of the space vector V(α′, β′) is S(a, b, c):

[0016]

[0017] At this point, the common-mode voltage of switching state S(a, b, c) is a boundary value, meaning that the value of N = a + b + c corresponding to this switching state is the largest value of N among all switching states of the space vector V(α′, β′). To calculate the switching state with the smallest common-mode voltage, it is necessary to consider the values ​​of S(α′, β′). ， b) and c) are corrected:

[0018] If (a+b+c)<0, then S(a,b,c) represents the switching state of the minimum common-mode voltage of the space vector V(α′,β′).

[0019] If (a+b+c)≥0, introduce a correction parameter K:

[0020]

[0021] In the formula, round(*) is the rounding function.

[0022] Subtracting the correction parameter K from a, b, and c simultaneously yields the switching state of the minimum common-mode voltage of the space vector V(α′, β′) as S(aK, bK, cK).

[0023] Step 4.2: If α′<0 and β′≥0, then the space vector V(α′, β′) is located in the second quadrant, and one of the switching states of V(α′, β′) is S′(a, b, c):

[0024]

[0025] If (a+b+c)≥0, then S′(a,b,c) represents the switching state of the minimum common-mode voltage of the space vector V(α′,β′).

[0026] If (a+b+c)<0, introduce a correction parameter K′:

[0027]

[0028] Subtracting the correction parameter K′ from a, b, and c simultaneously yields the switching state of the minimum common-mode voltage of the space vector V(α′, β′) as S′(aK′, bK′, cK′).

[0029] Step 4.3: If α′≤0 and β′≤0, then the space vector V(α′, β′) is located in the third quadrant, and one of the switching states of V(α′, β′) is S″(a, b, c):

[0030]

[0031] If (α+b+c)≥0, then S″(α, b, c) represents the switching state of the minimum common-mode voltage of the space vector V(α′, β′).

[0032] If (a+b+c)<0, introduce a correction parameter K″:

[0033]

[0034] Subtracting the correction parameter K″ from a, b, and c simultaneously yields the switching state of the minimum common-mode voltage of the space vector V(α′, β′) as S″(aK″, bK″, cK″).

[0035] Step 4.4: If α′>0 and β′<0, then the space vector V(α′, β′) is located in the fourth quadrant, and one of the switching states of V(α′, β′) is S″′(a, b, c):

[0036]

[0037] If (a+b+c)≥0, then S″′(a,b,c) is the switching state of the minimum common-mode voltage of the space vector V(α′,β′).

[0038] If (a+b+c)<0, introduce a correction parameter K″′:

[0039]

[0040] Subtracting the correction parameter K″′ from a, b, and c simultaneously yields the switching state of the minimum common-mode voltage of the space vector V(α′, β′) as S″′(aK″′, bK″′, cK″′).

[0041] Step 5: Determine the switching path of the switch state according to the five-segment algorithm, and proceed to the next sampling period. Repeat steps 1 to 4 to complete the space vector modulation.

[0042] In addition, the SVM method for minimizing the common-mode voltage of a multilevel converter based on the α'β' coordinate system according to the above embodiments of the present invention may also have the following additional technical features:

[0043] Further, in step 1, the reference vector V r (α r ,β r The expression for ) is:

[0044]

[0045] In the formula, α′ r ,β′ r Reference vector V r The corresponding coordinate components;

[0046] For reference vector V r (α′ r ,β′ r The component α′ r ,β′ r Rounding down, we get:

[0047]

[0048] In the formula, floor(*) is the floor function.

[0049] Further, in step 3, the judgment reference vector V r (α r ,β r The sector triangle type where the signal is located determines the composite reference vector V. r The three spatial vectors V1, V2, and V0 include:

[0050] When (α′) r -α′0)+(β′ r When -β′0)≤1, the reference vector V r (α′ r ,β′ r Located in sector triangle A, the composite reference vector V r The three spatial vectors V1, V2, and V0 are respectively:

[0051]

[0052] When (α′) r -α′0)+(β′ r When -β′0)>1, the reference vector V r (α′ r ,β′ r Located in sector triangle B, the composite reference vector V r The three spatial vectors V1, V2, and V0 are respectively:

[0053]

[0054] Furthermore, in step 3, the calculation of the composite reference vector V based on the second-volt balance principle... r The durations of action of the three space vectors V1, V2, and V0 include:

[0055] When the reference vector V r (α′ r ,β′ r Located in sector triangle A:

[0056]

[0057] When the reference vector V r (α′ r ,β′ r Located in sector triangle B:

[0058]

[0059] In the formula, T s The sampling period is t1, t2, and t0, which are the durations of action of space vectors V1, V2, and V0, respectively.

[0060] This application presents a SVM method for minimizing the common-mode voltage of a multilevel converter based on the α′β′ coordinate system. By reducing the difficulty of reference vector positioning, it simplifies the calculation of the spatial vector action time of the synthesized reference vector. Furthermore, by dividing the spatial vector into quadrants and determining the quadrants, it directly obtains the common-mode voltage boundary value of the corresponding switching state of the spatial vector. Then, by introducing correction parameters to correct the switching state, the switching state of the minimum common-mode voltage of the spatial vector can be obtained. This avoids the problem of calculating the switching state using 2 / 3 conversion in the traditional spatial vector modulation process, and reduces the complexity of the SVM algorithm implementation. Attached Figure Description

[0061] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 A flowchart of a method for minimizing the common-mode voltage of a multilevel converter based on the α'β' coordinate system, provided as an embodiment of the present invention;

[0063] Figure 2 A topology diagram of a three-phase n-stage H-bridge cascaded converter provided in an embodiment of the present invention;

[0064] Figure 3 This is a triangle positioning diagram of the sector where the reference vector is located, provided in an embodiment of the present invention.

[0065] Figure 4 A timing diagram of spatial vector switching for a synthetic reference vector provided in an embodiment of the present invention;

[0066] Figure 5 The simulated output voltage waveform of a 5-stage H-bridge cascaded converter is provided for an embodiment of the present invention. Detailed Implementation

[0067] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] Please see Figure 1 The diagram illustrates a flowchart of a multilevel converter common-mode voltage minimization SVM method based on the α'β' coordinate system, as described in this application.

[0069] like Figure 1 As shown, the SVM method for minimizing the common-mode voltage of a multilevel converter based on the α'β' coordinate system specifically includes the following steps:

[0070] Step 1: For the three phase voltage reference signals u ra u rb u rc Sampling and calculation yield the reference vector V in the α'β' coordinate system. r (α′ r ,β′ r ), and for the reference vector V r (α′ r ,β′ r The component α′ r ,β′ r Rounding is performed to determine the four space vectors V closest to the reference vector. a (α′0,β′0,V b (α′0+1,β′0,V c (α′0,β′0+1,V d (α′0+1, β′0+1) form a unit square.

[0071] In this embodiment, a three-phase n-stage H-bridge cascaded converter is taken as an example. Each phase of the converter consists of n voltage-source H-bridge inverter submodules connected in series. Each H-bridge inverter submodule consists of four IGBTs and anti-parallel diodes (e.g., Figure 2 (As shown).

[0072] The converter's three-phase voltage reference signal u ra u rb u rc for:

[0073]

[0074] In the formula, n is the number of H-bridge inverter sub-modules connected in series in each phase of the converter, m is the modulation coefficient, 0 < m ≤ 1, and ω is the angular frequency of the reference voltage signal.

[0075] Reference vector V r (α′ r ,β′ r The expression for ) is:

[0076]

[0077] In the formula, α′ r ,β′ r Reference vector V r The corresponding coordinate components;

[0078] For reference vector V r (α′ r ,β′ r The component α′ r ,β′ r Rounding down, we get:

[0079]

[0080] In the formula, floor(*) is the floor function.

[0081] Step 2: Determine the mapping relationship between the spatial vector V(α′, β′) in the α′β′ coordinate system and the three-phase output levels a, b, c of the converter as follows:

[0082]

[0083] In the formula, α′ and β′ are the coordinate components of the space vector V, a, b, c ∈ (0, ±1, ±2, …, ±n), and the switching state of the space vector V(α′, β′) is S(α, b, c), where S is the name of the switching state.

[0084] Step 3: Determine the reference vector V r (α′ r ,β′ r The sector triangle type where the signal is located determines the composite reference vector V. r The three spatial vectors V1, V2, and V0 are used to calculate the composite reference vector V based on the second-volt balance principle. r The duration of action of the three spatial vectors V1, V2, and V0, where the sector triangle type includes the spatial vector V a (α′0,β′0,V b (α′0+1,β′0,V cThe sector triangle A composed of (α0, β0+1), and the space vector V b (α′0+1,β′0,V c (α′0,β′0+1,V d (α′0+1, β′0+1) form sector triangle B, and sector triangle A and sector triangle B form a unit square (e.g., Figure 3 (As shown).

[0085] In this embodiment, when (α′ r -α′0)+(β′ r When -β′0)≤1, the reference vector V r (α′ r ,β′ r Located in sector triangle A, the composite reference vector V r The three spatial vectors V1, V2, and V0 are respectively:

[0086]

[0087] When (α′) r -α′0)+(β′ r When -β′0)>1, the reference vector V r (α′ r ,β′ r Located in sector triangle B, the composite reference vector V r The three spatial vectors V1, V2, and V0 are respectively:

[0088]

[0089] When the reference vector V r (α′ r ,β′ r Located in sector triangle A, the composite reference vector V r The durations of action of the three space vectors V1, V2, and V0 are as follows:

[0090]

[0091] When the reference vector V r (α′ r ,β′ r Located in sector triangle B, the composite reference vector V r The durations of action of the three space vectors V1, V2, and V0 are as follows:

[0092]

[0093] In the formula, T sThe sampling period is t1, t2, and t0, which are the durations of action of space vectors V1, V2, and V0, respectively.

[0094] Step 4: Calculate the composite reference vector V separately. r The minimum common-mode voltage switching states S1, S2, and S0 corresponding to the space vectors V1, V2, and V0.

[0095] In this embodiment, for a multilevel converter, a space vector may correspond to multiple switching states with different common-mode voltages. The following algorithm, requiring only a finite number of comparisons and arithmetic operations, can quickly determine the switching state with the minimum common-mode voltage corresponding to the space vector.

[0096] Specifically, this includes: the number of redundant switching states of any space vector V(α′, β′) in an n-stage H-bridge cascaded multilevel converter is R:

[0097] R=2n-q, (q=max[|α′|, |β′|, |α′+β′|]), (9)

[0098] Let N be the sum of the three components of any switch state S(a, b, c), i.e., N = a + b + c; (10)

[0099] Step 4.1: If α′≥0 and β′≥0, then the space vector V(α′, β′) is located in the first quadrant, and one of the switching states of the space vector V(α′, β′) is S(a, b, c):

[0100]

[0101] At this point, the common-mode voltage of switching state S(a, b, c) is a boundary value, meaning that the value of N = a + b + c corresponding to this switching state is the largest value of N among all switching states of the space vector V(α′, β′). To calculate the switching state with the smallest common-mode voltage, S(a, b, c) needs to be corrected:

[0102] If (a+b+c)<0, then S(a,b,c) represents the switching state of the minimum common-mode voltage of the space vector V(α′,β′).

[0103] If (a+b+c)≥0, introduce a correction parameter K:

[0104]

[0105] In the formula, round(*) is the rounding function.

[0106] Subtracting the correction parameter K from a, b, and c simultaneously yields the switching state of the minimum common-mode voltage of the space vector V(α′, β′) as S(aK, bK, cK).

[0107] Step 4.2: If α′<0 and β′≥0, then the space vector V(α′, β′) is located in the second quadrant, and one of the switching states of V(α′, β′) is S(a, b, c):

[0108]

[0109] If (α+b+c)≥0, then S(a,b,c) represents the switching state of the minimum common-mode voltage of the space vector V(α′,β′).

[0110] If (a+b+c)<0, introduce a correction parameter K′:

[0111]

[0112] Subtracting the correction parameter K′ from a, b, and c simultaneously yields the switching state of the minimum common-mode voltage of the space vector V(α′, β′) as S′(aK′, bK′, cK′).

[0113] Step 4.3: If α′≤0 and β′≤0, then the space vector V(α′, β′) is located in the third quadrant, and one of the switching states of V(α′, β′) is S″(a, b, c):

[0114]

[0115] If (α+b+c)≥0, then S″(a,b,c) represents the switching state of the minimum common-mode voltage of the space vector V(α′,β′).

[0116] If (a+b+c)<0, introduce a correction parameter K″:

[0117]

[0118] Subtracting the correction parameter K″ from a, b, and c simultaneously yields the switching state of the minimum common-mode voltage of the space vector V(α′, β′) as S″(aK″, bK″, cK″).

[0119] Step 4.4: If α′>0 and β′<0, then the space vector V(α′, β′) is located in the fourth quadrant, and one of the switching states of V(α′, β′) is S″′(a, b, c):

[0120]

[0121] If (a+b+c)≥0, then S″′(a,b,c) is the switching state of the minimum common-mode voltage of the space vector V(α′,β′).

[0122] If (a+b+c)<0, introduce a correction parameter K″′:

[0123]

[0124] Subtracting the correction parameter K″′ from a, b, and c simultaneously yields the switching state of the minimum common-mode voltage of the space vector V(α′, β′) as S″′(aK″′, bK″′, cK″′).

[0125] Step 5: Determine the switching path of the switch state according to the five-segment algorithm, and proceed to the next sampling period. Repeat steps 1 to 4 to complete the space vector modulation.

[0126] In this embodiment, a five-segment algorithm is used to determine the switching path of the switch state. Taking V1 as the starting point and V0 as the ending point as an example, the switching path is S1→S2→S0→S2→S1, and the switching state action times are t1 / 2→t2 / 2→t0→t2 / 2→t1 / 2 respectively (e.g., Figure 4 (As shown). Proceed to the next sampling cycle and repeat steps 1 to 4 to complete space vector modulation.

[0127] In summary, the method of this application simplifies the calculation of the spatial vector action time of the synthesized reference vector by reducing the difficulty of reference vector positioning. Furthermore, by dividing the spatial vector into quadrants and determining the quadrants, the common-mode voltage boundary value of the corresponding switching state of the spatial vector is directly obtained. Then, by introducing correction parameters to correct the switching state, the switching state of the minimum common-mode voltage of the spatial vector can be obtained. This avoids the problem of calculating the switching state using 2 / 3 conversion in the traditional spatial vector modulation process and reduces the complexity of SVM algorithm implementation.

[0128] In one specific embodiment, taking a 5-stage H-bridge cascaded converter as an example, let the modulation coefficient m = 0.92, n = 5, the reference voltage signal angular frequency ω be 100π, and the sampling period T be... s =0.2ms, and the reference voltage signal is sampled at t=2.8ms to obtain u. ra =3.386, u rb =1.851, u rc = -5.237. α is calculated using formula (2). r =8.623, b r = -1.535, meaning the reference vector is V r (8.623, -1.535).

[0129] According to formula (3), rounding down the coordinate components of the reference vector yields α0 = 8 and β0 = -2;

[0130] Distance reference vector V r The four most recent space vectors V (8.623, -1.535) a (8, -2), V b (9, -2), V c(8, -1), V d (9, -1) form a unit square.

[0131] (α′ r -α′0)+(β′ r -β′0)=(8.623-8)+[-1.535-(-2)]=1.088>1, V r Located in sector triangle B, the composite reference vector V r The spatial vectors V1, V2, and V0 are respectively: V1(9, -2), V2(8, -1), and V0(9, -1).

[0132] The durations t1, t2, and t0 of the spatial vectors V1, V2, and V0 are calculated according to formula (8), and we get t1 = 0.0754 ms, t2 = 0.107 ms, and t0 = 0.0176 ms.

[0133] Based on step 4, calculate the switching state with the minimum common-mode voltage of V1, V2, and V0:

[0134] V1(9, -2) is located in the fourth quadrant. One of the switching states of V1 is S1(a1, b1, c1). According to formulas (17) and (18), we can calculate a1 = 5, b1 = 3, c1 = -4, and K″′ = 1. After correcting S1, we get the switching state S1(4, 2, -5) with the minimum common-mode voltage of V1.

[0135] V2(8, -1) is located in the fourth quadrant. One of the switching states of V2 is S2(a2, b2, c2). According to formulas (17) and (18), we can calculate a2 = 5, b2 = 4, c2 = -3, and K″′ = 2. After correcting S2, we get the switching state S2(3, 2, -5) with the minimum common-mode voltage of V2.

[0136] V0(9, -1) is located in the fourth quadrant. One of the switching states of V0 is S0(a0, b0, c0). According to formulas (17) and (18), we can calculate a0 = 5, b0 = 4, c0 = -4, and K″′ = 2. After correcting S0, we can obtain the switching state S0(4, 3, -5) with the minimum common-mode voltage of V0.

[0137] Using a five-segment algorithm, the switching path of the switch state is determined, with V2 as the starting point and V0 as the ending point, the switching path is S″. ′ 2→S″′1→S″′0→S″′1→S″′2, the switching state action times are t2 / 2→t1 / 2→t0→t1 / 2→t2 / 2 respectively, and the switching sequence is as follows: Figure 5 As shown.

[0138] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for minimizing the common-mode voltage of a multilevel converter using a coordinate system based on the α′β′ coordinate system, characterized in that, include: Step 1: For the three phase voltage reference signals u ra u rb u rc Sampling and calculation yield the reference vector V in the α′β′ coordinate system. r (α′ r ,β′ r ), and for the reference vector V r (α′ r ,β′ r The component α′ r ,β′ r Rounding is performed to determine the four space vectors V closest to the reference vector. a (α′0,β′0,V b (α′0+1,β′0,V c (α′0,β′0+1,V d (α′0+1, β′0+1) form a unit square, where the reference vector V r (α′ r ,β′ r The expression for ) is: In the formula, α′ r ,β′ r Reference vector V r The corresponding coordinate components; For reference vector V r (α′ r ,β′ r The component α′ r ,β′ r Rounding down, we get: In the formula, floor(*) is the floor function; Step 2: Determine the mapping relationship between the spatial vector V(α′, β′) in the α′β′ coordinate system and the three-phase output levels a, b, c of the converter as follows: In the formula, α′ and β′ are the coordinate components of the space vector V, α, b, c ∈ (0, ±1, ±2, …, ±n′), and the switching state of the space vector V(α′, β′) is S(α, b, c), where S is the name of the switching state. Step 3: Determine the reference vector V r (α′ r ,β′ r The sector triangle type where the signal is located determines the composite reference vector V. r The three spatial vectors V1, V2, and V0 are used to calculate the composite reference vector V based on the volt-second balance principle. r The duration of action of the three spatial vectors V1, V2, and V0, where the sector triangle type includes the spatial vector V a (α′0,β′0,V b (α′0+1,β′0,V c The sector triangle A composed of (α′0, β′0+1), and the spatial vector V b (α′0+1,β′0,V c (α′0,β′0+1,V d (α′0+1, β′0+1) form sector triangle B, sector triangle A and sector triangle B form a unit square, and in step 3, the judgment reference vector V r (α′ r ,β′ r The sector triangle type where the signal is located determines the composite reference vector V. r The three space vectors V1, V2, and V0 include: When (α′) r -α′0)+(β′ r When -β′0)≤1, the reference vector V r (α r ,β r Located in sector triangle A, the composite reference vector V r The three spatial vectors V1, V2, and V0 are respectively: When (α′) r -α′0)+(β′ r When -β′0)>1, the reference vector V r (α′ r ,β′ r Located in sector triangle B, the composite reference vector V r The three spatial vectors V1, V2, and V0 are respectively: Step 4: Calculate the composite reference vector V separately. r The minimum common-mode voltage switching states S1, S2, and S0 corresponding to the space vectors V1, V2, and V0 specifically include: the number of redundant switching states existing in any space vector V(α′, β′) of an n-stage H-bridge cascaded multilevel converter is R: R=2n-q, (q=max[|α′|, |β′|, |α′+β′|]), Let N be the sum of the three components of any switch state S(α, b, c), i.e., N = a + b + c; Step 4.1: If α′≥0 and β′≥0, then the space vector V(α′, β′) is located in the first quadrant, and one of the switching states of the space vector V(α′, β′) is S(a, b, c): At this point, the common-mode voltage of the switching state S(α, b, c) is a boundary value, meaning that the value of N = a + b + c corresponding to this switching state is the largest value of N among all switching states of the space vector V(α′, β′). To calculate the switching state with the smallest common-mode voltage, S(α, b, c) needs to be corrected: If (a+b+c)<0, then S(α,b,c) represents the switching state of the minimum common-mode voltage of the space vector V(α′,β′). If (a+b+c)≥0, introduce a correction parameter K: In the formula, round(*) is the rounding function. Subtracting the correction parameter K from a, b, and c simultaneously yields the switching state of the minimum common-mode voltage of the space vector V(α′, β′) as S(aK, bK, cK). Step 4.2: If α′<0 and β′≥0, then the space vector V(α′, β′) is located in the second quadrant, and one of the switching states of V(α′, β′) is S′(a, b, c): If (a+b+c)≥0, then S′(a,b,c) represents the switching state of the minimum common-mode voltage of the space vector V(α′,β′). If (a+b+c)<0, introduce a correction parameter K′: Subtracting the correction parameter K′ from a, b, and c simultaneously yields the switching state of the minimum common-mode voltage of the space vector V(α′, β′) as S′(aK′, bK′, cK′). Step 4.3: If α′≤0 and β′≤0, then the space vector V(α′, β′) is located in the third quadrant, and one of the switching states of V(α′, β′) is S″(a, b, c): If (a+b+c)≥0, then S″(a,b,c) represents the switching state of the minimum common-mode voltage of the space vector V(α′,β′). If (α+b+c)<0, introduce a correction parameter K″: Subtracting the correction parameter K″ from a, b, and c simultaneously yields the switching state of the minimum common-mode voltage of the space vector V(α′, β′) as S″(aK″, bK″, cK″). Step 4.4: If α′>0 and β′<0, then the space vector V(α′, β′) is located in the fourth quadrant, and one of the switching states of V(α′, β′) is S″′(a, b, c): If (α+b+c)≥0, then S″′(a,b,c) represents the switching state of the minimum common-mode voltage of the space vector V(α′,β′). If (a+b+c)<0, introduce a correction parameter K″′: Subtracting the correction parameter K″′ from a, b, and c simultaneously yields the switching state of the minimum common-mode voltage of the space vector V(α′, β′) as S″′(aK″′, bK″′, cK″′). Step 5: Determine the switching path of the switch state according to the five-segment algorithm, and proceed to the next sampling period. Repeat steps 1 to 4 to complete the space vector modulation. In step 3, the composite reference vector V is calculated based on the volt-second balance principle. r The durations of action of the three space vectors V1, V2, and V0 include: When the reference vector V r (α′ r ,β′ r Located in sector triangle A: When the reference vector V r (α′ r ,β′ r Located in sector triangle B: In the formula, T s The sampling period is t1, t2, and t0, which are the durations of action of space vectors V1, V2, and V0, respectively.

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