Reference Vector Positioning and Common Mode Voltage Suppression Method for Cascaded H-Bridge Converters Using SVM Strategy

Abstract

The present invention discloses a reference vector positioning and common-mode voltage suppression method for a cascaded H-bridge converter SVM strategy. The method comprises sampling three phase voltage reference signals to calculate a reference vector in a traditional αβ coordinate system; positioning the reference vector using a characteristic factor; calculating the action times of three basic vectors of the synthesized reference vector based on the second-volt balance principle; calculating the maximum switching state using a correction factor, and directly obtaining the corrected switching state with the minimum common-mode voltage based on the correction factor; and applying the corrected switching state in a time-sharing manner to complete the SVM within a single cycle. The method simplifies the positioning of the reference vector in the traditional αβ coordinate system, simplifies the coordinate calculation formulas and action time calculations of the three basic vectors of the synthesized reference vector, avoids the iterative problem of using the Clark inverse transform to calculate the minimum common-mode voltage switching state in the traditional SVM process, and simplifies the calculation of the three basic vector switching states during the common-mode voltage suppression process.

Description

Technical Field

[0001] The present invention belongs to the technical field of cascaded H-bridge converter modulation, and in particular relates to a reference vector positioning and common mode voltage suppression method of a cascaded H-bridge converter SVM strategy. Background Art

[0002] Space vector modulation (SVM) technology was initially applied to three-phase motor drive systems. Its core concept is to convert three-phase symmetrical voltage signals into space vectors. By controlling the action time of the space vectors, precise control of the output voltage waveform is achieved. Specifically, SVM selects the three space vectors closest to the reference vector based on its trajectory. Based on their action time, the converter's PWM drive is adjusted to modulate the converter's output waveform. SVM technology offers high DC voltage utilization, low switching frequency, and excellent output power quality, making it widely used in three-level and five-level converters.

[0003] However, as the number of levels increases, the positioning of the reference vector in space vector modulation becomes increasingly complex. As the number of levels in a multilevel converter increases, the number of space vectors increases significantly, along with the number of switching states corresponding to these space vectors. This complicates the calculation of switching states and the selection of switching sequences. This complexity poses significant challenges to the implementation of SVM algorithms for multilevel converters, particularly when the number of levels is high, compromising both the efficiency and accuracy of the modulation algorithm.

[0004] Furthermore, multilevel converters generate common-mode voltage during the modulation process, which can pose a serious threat to the insulation performance of the motor. Large common-mode voltages, coupled through the capacitive coupling between the motor's stator and rotor, can induce large bearing currents, potentially damaging the motor's bearings and even generating electromagnetic interference (EMI) to other equipment in the power grid, impacting normal operation. Therefore, effectively controlling common-mode voltage, reducing bearing currents, and mitigating EMI are key issues in the design of cascaded H-bridge converters. Summary of the Invention

[0005] The present invention provides a reference vector positioning and common-mode voltage suppression method for the SVM strategy of a cascaded H-bridge converter, aiming to solve the problems of complex reference vector positioning, inconsistent upper and lower triangular sector calculation formulas, and difficulty in suppressing the common-mode voltage within the minimum range in the space vector modulation process of the cascaded H-bridge converter in the prior art.

[0006] The present invention provides a reference vector positioning and common mode voltage suppression method for a cascaded H-bridge converter SVM strategy, comprising:

[0007] Step 1: Let n be the number of modules of the single-phase H-bridge submodule in the three-phase cascade H-bridge, and the three phase voltage reference signals ura 、u rb 、u rc Sampling, calculating the reference vector V in the αβ coordinate system r (α r ,β r ).

[0008]

[0009] Where u ra 、u rb 、u rc is the three-phase reference voltage, α r , β r are the coordinate components of the reference vector in the αβ coordinate system.

[0010] Step 2: In the αβ coordinate system, the reference vector V is calculated based on the characteristic factor. r (α r ,β r ) for vector positioning. First, calculate the two characteristic factors J and K. These two characteristic factors determine the unique diamond sector where the reference vector is located; then use these two characteristic factors to calculate the coordinates V of the midpoint of the diamond sector in the αβ coordinate system. z (α z ,β z ); Finally, use the midpoint coordinates to calculate the coordinates of the three basic vectors adjacent to the reference vector in the αβ coordinate system V4(α4,β4), V3(α3,β3), and V0(α0,β0). The specific steps are as follows:

[0011] Step 2.1: According to the coordinate component α of the reference vector in the αβ coordinate system r , β r Calculate the two characteristic factors J and K of the diamond sector.

[0012]

[0013] Where, α r , β r are the coordinate components of the reference vector, J and K are the two characteristic factors of the diamond sector, and floor(*) is the floor rounding function.

[0014] Step 2.2: According to the two characteristic factors α of the diamond sector r , β r Calculate the coordinates V of the midpoint of the diamond sector z (α z ,β z ).

[0015]

[0016] Where J and K are the two characteristic factors of the diamond sector, α z , β z are the coordinate components of the midpoint of the diamond sector.

[0017] Step 2.3: According to the coordinate component α of the midpoint of the diamond sector z , β z Calculate three basic vectors V4(α4, β4), V3(α3, β3), and V0(α0, β0).

[0018]

[0019] Where, α z , β z are the midpoint coordinates of the diamond sector, V4, V3, and V0 are three basic vectors, and sign(*) is the sign function.

[0020] Step 3: Calculate the action times t4, t3, and t0 of the three basic vectors V4, V3, and V0 based on the volt-second balance principle.

[0021]

[0022] Where, T s is the sampling period, α z , β z is the coordinate component of the midpoint of the diamond sector, α r , β r are the coordinate components of the reference vector, t4, t3, and t0 are the action times of the three basic vectors V4, V3, and V0, and abs(*) is the absolute value function.

[0023] Step 4: Calculate the switching state with the minimum common-mode voltage corresponding to the basic vector based on the correction coefficient. First, calculate the correction factors of the three basic vectors V4 (α4, β4), V3 (α3, β3), and V0 (α0, β0) based on the characteristic factors, and calculate the maximum switching state S4 (a4, b4, c4), S3 (a3, b3, c3), and S0 (a0, b0, c0) of the three basic vectors based on the correction factors; then calculate the common-mode voltage of the maximum switching state and the number of redundant switching states of the basic space vector, and use this to determine the correction coefficients of the three basic vectors; finally, use the correction coefficients to calculate the corrected switching state S of the three basic vectors 44 (a 44 ,b 44 ,c 44 ), S 33 (a 33 ,b 33 ,c 33 ), S 00 (a 00 ,b 00,c 00 The specific steps are as follows:

[0024] Step 4.1: Calculate the correction factors of V4, V3, and V0 based on the two characteristic factors of the diamond sector.

[0025] For the basic vector V4, the correction factors p4 and q4 are calculated as follows:

[0026]

[0027] For the basic vector V3, the correction factors p3 and q3 are calculated as follows:

[0028]

[0029] For the basic vector V0, the correction factors p0 and q0 are calculated as follows:

[0030]

[0031] Step 4.2: Calculate the maximum switching state of V4, V3, and V0 based on the correction factor.

[0032] For the basic vector V4, the correction factors are p4 and q4, and the maximum switching state is S4 (a4, b4, c4).

[0033] If p4≥0 and q4≥0, then w 41 =1,w 42 =0,w 43 =0.

[0034] If p4<0 and (q4-p4)≥0, then w 41 =0,w 42 =1,w 43 =0.

[0035] If q4<0 and (q4-p4)<0, then w 41 =0,w 42 =0,w 43 =1.

[0036] The maximum switching state S4(a4,b4,c4) is calculated as follows:

[0037]

[0038] For the basic vector V3, the correction factors are p3 and q3, and the maximum switching state is S3 (a3, b3, c3).

[0039] If p3≥0 and q3≥0, then w 31 =1,w 32 =0,w 33 =0.

[0040] If p3<0 and (q3-p3)≥0, then w 31 =0,w 32 =1,w 33 =0.

[0041] If q3<0 and (q3-p3)<0, then w 31 =0,w 32 =0,w 33 =1.

[0042] The maximum switching state S3(a3,b3,c3) is calculated as follows:

[0043]

[0044] For the basic vector V0, the correction factors are p0 and q0, and the maximum switching state is S0 (a0, b0, c0).

[0045] If p0≥0 and q0≥0, then w 01 =1,w 02 =0,w 03 =0.

[0046] If p0<0 and (q0-p0)≥0, then w 01 =0,w 02 =1,w 03 =0.

[0047] If q0<0 and (q0-p0)<0, then w 01 =0,w 02 =0,w 03 =1.

[0048] The maximum switching state S0(a0, b0, c0) is calculated as follows:

[0049]

[0050] Step 4.3: Calculate the number of redundant switch states R4, R3, and R0 of V4, V3, and V0.

[0051] For the basic vector V4, the number of redundant switch states R4 is calculated as follows:

[0052]

[0053] For the basic vector V3, the number of redundant switch states R3 is calculated as follows:

[0054]

[0055] For the basic vector V0, the number of redundant switch states R0 is calculated as follows:

[0056]

[0057] Step 4.4: Calculate the common-mode voltages N4, N3, and N0 of the maximum switching states S4 (a4, b4, c4), S3 (a3, b3, c3), and S0 (a0, b0, c0) based on the definition of common-mode voltage.

[0058]

[0059] Step 4.5: Calculate the correction coefficients H4, H3, and H0 for V4, V3, and V0.

[0060] For the basic vector V4, the correction coefficient H4 is determined as follows:

[0061] If the common mode voltage N4≤0, then H4=0.

[0062] If the common-mode voltage N4>0, then H4=min(round(N4),(R4-1)).

[0063] For the basic vector V3, the correction coefficient H3 is determined as follows:

[0064] If the common mode voltage N3≤0, then H3=0.

[0065] If the common-mode voltage N3>0, then H3=min(round(N3),(R3-1)).

[0066] For the basic vector V0, the correction coefficient H0 is determined as follows:

[0067] If the common mode voltage N0≤0, then H0=0.

[0068] If the common-mode voltage N0>0, then H0=min(round(N0),(R0-1)).

[0069] Step 4.6: Calculate the corrected switch state based on the correction coefficient.

[0070] For the basic vector V4, the correction coefficient is H4, and the corrected switching state is S 44 (a 44 ,b 44 ,c 44 ) is calculated as follows:

[0071]

[0072] For the basic vector V3, its correction coefficient is H3, and the corrected switching state is S 33 (a 33 ,b 33 ,c 33) is calculated as follows:

[0073]

[0074] For the basic vector V0, its correction coefficient H0, the corrected switching state is S 00 (a 00 ,b 00 ,c 00 ) is calculated as follows:

[0075]

[0076] Step 5: Use the corrected switch state to determine the switching path of the switch state in a time-sharing manner, and enter the next sampling period. Repeat the steps to complete the space vector modulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following is a brief introduction to the drawings involved in the description of the embodiments. The drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0078] Figure 1 A flowchart of a reference vector positioning and common mode voltage suppression method for a cascaded H-bridge converter SVM strategy provided by one embodiment of the present invention;

[0079] Figure 2 A topology diagram of a three-phase n-stage H-bridge cascade converter provided in one embodiment of the present invention;

[0080] Figure 3 A diamond-shaped sector positioning diagram of a reference vector provided in an embodiment of the present invention;

[0081] Figure 4 A timing diagram of space vector switching of a synthetic reference vector provided by an embodiment of the present invention;

[0082] Figure 5 This is a simulated output voltage waveform diagram of a 5-level H-bridge cascade converter provided by an embodiment of the present invention. Specific implementation methods

[0083] To make the purpose, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0084] See also Figure 1 , which shows a flow chart of a reference vector positioning and common-mode voltage suppression method of a cascaded H-bridge converter SVM strategy of the present application.

[0085] like Figure 1 As shown, the reference vector positioning and common mode voltage suppression method of the cascaded H-bridge converter SVM strategy specifically includes the following steps:

[0086] In this embodiment, a three-phase n-stage H-bridge cascade converter is taken as an example. Each phase of the converter is composed of n voltage-type H-bridge inverter modules connected in series. Each H-bridge inverter module is composed of four IGBTs and anti-parallel diodes (such as Figure 2 shown).

[0087] Converter three phase voltage reference signal u ra 、u rb 、u rc for:

[0088]

[0089] Where n is the number of H-bridge inverter 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.

[0090] Step 1: Three phase voltage reference signals u ra 、u rb 、u rc Sampling, calculating the reference vector V in the αβ coordinate system r (α r ,β r ), V r (α r ,β r ) location as Figure 3 As shown, the calculation formula is as follows:

[0091]

[0092] Where u ra 、u rb 、u rc is the three-phase reference voltage, α r , β r are the coordinate components of the reference vector in the αβ coordinate system.

[0093] Step 2.1: According to the coordinate component α of the reference vector in the αβ coordinate system r , β r Calculate the two characteristic factors J and K of the diamond sector. The diamond sector is as follows Figure 3 As shown, the calculation formula is as follows:

[0094]

[0095] Where, α r , β r are the coordinate components of the reference vector, J and K are the two characteristic factors of the diamond sector, and floor(*) is the floor rounding function.

[0096] Step 2.2: According to the two characteristic factors α of the diamond sector r , β r Calculate the coordinates V of the midpoint of the diamond sector z (α z ,β z ), V z (α z ,β z ) location as Figure 3 As shown, the calculation formula is as follows:

[0097]

[0098] Where J and K are the two characteristic factors of the diamond sector, α z , β z are the coordinate components of the midpoint of the diamond sector.

[0099] Step 2.3: According to the coordinate component α of the midpoint of the diamond sector z , β z Calculate the three basic vectors V4(α4,β4), V3(α3,β3), and V0(α0,β0), whose positions are as follows Figure 3 As shown, even though the reference vector may fall in the upper or lower triangular sector of the diamond sector, Figure 3 As shown in the left and right figures, this method can use the same formula to calculate the coordinates of the three basic vectors. The calculation formula is as follows:

[0100]

[0101] Where, α z , β z are the midpoint coordinates of the diamond sector, V4, V3, and V0 are three basic vectors, and sign(*) is the sign function.

[0102] Step 3: Calculate the action times t4, t3, and t0 of the three basic vectors V4, V3, and V0 based on the volt-second balance principle.

[0103]

[0104] Where, T s is the sampling period, α z , β z is the coordinate component of the midpoint of the diamond sector, α r, β r are the coordinate components of the reference vector, t4, t3, and t0 are the action times of the three basic vectors V4, V3, and V0, and abs(*) is the absolute value function.

[0105] In this embodiment, for a cascaded H-bridge converter, a single base vector may correspond to multiple switching states with different common-mode voltages. The following algorithm, using only a limited number of comparisons and arithmetic operations, can quickly determine the switching state corresponding to the base vector with the lowest common-mode voltage.

[0106] Since the reference vector is synthesized by three adjacent basic vectors, each of the following calculation steps has three parts. However, the method of the present invention unifies the formulas for calculating the switch state of the three basic vectors, and the same calculation formula is used regardless of which basic vector is used to calculate the switch state.

[0107] Step 4.1: Calculate the correction factors of V4, V3, and V0 based on the two characteristic factors of the diamond sector.

[0108] For the basic vector V4, the correction factors p4 and q4 are calculated as follows:

[0109]

[0110] For the basic vector V3, the correction factors p3 and q3 are calculated as follows:

[0111]

[0112] For the basic vector V0, the correction factors p0 and q0 are calculated as follows:

[0113]

[0114] Step 4.2: Calculate the maximum switching state of V4, V3, and V0 based on the correction factor.

[0115] For the basic vector V4, the correction factors are p4 and q4, and the maximum switching state is S4 (a4, b4, c4).

[0116] If p4≥0 and q4≥0, then w 41 =1,w 42 =0,w 43 =0.

[0117] If p4<0 and (q4-p4)≥0, then w 41 =0,w 42 =1,w 43 =0.

[0118] If q4<0 and (q4-p4)<0, then w 41 =0,w42 =0,w 43 =1.

[0119] The maximum switching state S4(a4,b4,c4) is calculated as follows:

[0120]

[0121] For the basic vector V3, the correction factors are p3 and q3, and the maximum switching state is S3 (a3, b3, c3).

[0122] If p3≥0 and q3≥0, then w 31 =1,w 32 =0,w 33 =0.

[0123] If p3<0 and (q3-p3)≥0, then w 31 =0,w 32 =1,w 33 =0.

[0124] If q3<0 and (q3-p3)<0, then w 31 =0,w 32 =0,w 33 =1.

[0125] The maximum switching state S3(a3,b3,c3) is calculated as follows:

[0126]

[0127] For the basic vector V0, the correction factors are p0 and q0, and the maximum switching state is S0 (a0, b0, c0).

[0128] If p0≥0 and q0≥0, then w 01 =1,w 02 =0,w 03 =0.

[0129] If p0<0 and (q0-p0)≥0, then w 01 =0,w 02 =1,w 03 =0.

[0130] If q0<0 and (q0-p0)<0, then w 01 =0,w 02 =0,w 03 =1.

[0131] The maximum switching state S0(a0, b0, c0) is calculated as follows:

[0132]

[0133] Step 4.3: Calculate the number of redundant switch states R4, R3, and R0 of V4, V3, and V0.

[0134] For the basic vector V4, the number of redundant switch states R4 is calculated as follows:

[0135]

[0136] For the basic vector V3, the number of redundant switch states R3 is calculated as follows:

[0137]

[0138] For the basic vector V0, the number of redundant switch states R0 is calculated as follows:

[0139]

[0140] Step 4.4: Calculate the common-mode voltages N4, N3, and N0 for the maximum switching states S4 (a4, b4, c4), S3 (a3, b3, c3), and S0 (a0, b0, c0) based on the definition of common-mode voltage.

[0141]

[0142] Step 4.5: Calculate the correction coefficients H4, H3, and H0 for V4, V3, and V0.

[0143] For the basic vector V4, the correction coefficient H4 is determined as follows:

[0144] If the common mode voltage N4≤0, then H4=0.

[0145] If the common-mode voltage N4>0, then H4=min(round(N4),(R4-1)).

[0146] For the basic vector V3, the correction coefficient H3 is determined as follows:

[0147] If the common mode voltage N3≤0, then H3=0.

[0148] If the common-mode voltage N3>0, then H3=min(round(N3),(R3-1)).

[0149] For the basic vector V0, the correction coefficient H0 is determined as follows:

[0150] If the common mode voltage N0≤0, then H0=0.

[0151] If the common-mode voltage N0>0, then H0=min(round(N0),(R0-1)).

[0152] Step 4.6: Calculate the corrected switch state based on the correction coefficient.

[0153] For the basic vector V4, the correction coefficient is H4, and the switching state after correction is S 44 (a 44 ,b 44 ,c 44 ) is calculated as follows:

[0154]

[0155] For the basic vector V3, its correction coefficient is H3, and the corrected switching state is S 33 (a 33 ,b 33 ,c 33 ) is calculated as follows:

[0156]

[0157] For the basic vector V0, its correction coefficient H0, the corrected switching state is S 00 (a 00 ,b 00 ,c 00 ) is calculated as follows:

[0158]

[0159] Step 5: The modified switch state is time-shared to determine its switching path, and the next sampling cycle is performed, and steps 1 to 4 are repeated to complete the space vector modulation. In this embodiment, a five-segment algorithm is used to determine the switching path of the switch state. Taking V3 as the starting point and V0 as the end point as an example, the switching path is S3→S4→S0→S4→S3, and the switch state action time is t3 / 2→t4 / 2→t0→t4 / 2→t3 / 2 (as shown in FIG. Figure 4 Then, the next sampling cycle is performed and steps 1 to 4 are repeated to complete the space vector modulation.

[0160] In summary, the method of the present invention simplifies the positioning of the reference vector and the calculation of the basic vector action time in the traditional αβ coordinate system, unifies the calculation formulas for the coordinates of the three adjacent basic vectors in the upper triangular sector and the lower triangular sector and the calculation formula for the basic vector action time, and directly obtains the maximum switching state corresponding to the basic vector based on the conditional judgment of the correction factor, and then introduces the correction coefficient to correct the maximum switching state, so as to obtain the switching state corresponding to the minimum common-mode voltage of the basic vector, thereby avoiding the iterative problem of using Clark inverse transform to calculate the switching state in the traditional space vector modulation process, and reducing the complexity of the SVM algorithm implementation.

[0161] In a specific embodiment, taking a 5-level H-bridge cascade converter as an example, it is assumed that the modulation coefficient m=0.92, n=5, the reference voltage signal angular frequency ω=100π, and the sampling period T s =0.1ms, and the reference voltage signal is sampled at t=2.4ms to obtain u ra =3.872,u rb =1.213,u rc =-5.085. According to formula (2), the reference vector V is calculated. r (α r ,β r )=(3.872,3.636), calculate the characteristic factors according to formula (3) and get J=2, K=8, calculate the coordinates of the midpoint of the diamond sector according to formula (4) and get V z (α z ,β z )=(3.668,3.464), and the three adjacent basic vectors of the synthetic reference vector are calculated according to formula (5) to obtain V4(α4,β4)=(4.000,3.464), V3(α3,β3)=(3.333,3.464), and V0(α0,β0)=(3.668,4.041). According to formula (6), the action time of the three basic vectors is calculated to be t4=65.91us, t3=4.30 7us, t0 = 29.78us, according to formula (7), the correction factor of basic vector V4 is calculated as p4 = 3, q4 = 9, according to formula (8), the correction factor of basic vector V3 is calculated as p3 = 2, q3 = 8, according to formula (9), the correction factor of basic vector V0 is calculated as p0 = 2, q0 = 9, according to formula (10), the maximum switching state of basic vector V4 is calculated as S4(a4, b4, c4) = (5, 2, -4) According to formula (11), the maximum switching state of basic vector V3 is calculated as S3(a3, b3, c3) = (5, 3, -3). According to formula (12), the maximum switching state of basic vector V0 is calculated as S0(a0, b0, c0) = (5, 3, -4). According to formula (13), the number of redundant switching states of basic vector V4 is calculated as R4 = 2. According to formula (14), the number of redundant switching states of basic vector V3 is calculated as R3 = 3. According to formula (15), the number of redundant switching states of basic vector V0 is calculated as R0 = 2. According to formula (16), the common mode voltages of the maximum switching states of the three basic vectors are calculated as N4 = 1, N3 = 1.667, and N0 = 1.333. According to step 4.5, the correction coefficients of the three basic vectors are determined as H4 = 1, H3 = 2, and H0 = 1. According to formula (17), the switching state with the minimum common mode voltage after correction of basic vector V4 is calculated as S 44 (a 44 ,b 44 ,c 44)=(4,1,-5), and calculate the switching state with the minimum common-mode voltage after the basic vector V3 is corrected according to formula (18) to obtain S 33 (a 33 ,b 33 ,c 33 )=(3,1,-5), and calculate the switching state with the minimum common-mode voltage after the basic vector V0 is corrected according to formula (19) to obtain S 00 (a 00 ,b 00 ,c 00 )=(4,2,-5), and finally use the five-segment algorithm to determine the switching path of the switch state. Taking V3 as the starting point and V0 as the end point as an example, the switching path is S3→S4→S0→S4→S3, and the switching state action time is t3 / 2→t4 / 2→t0→t4 / 2→t3 / 2 (such as Figure 5 shown).

[0162] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A reference vector positioning and common mode voltage suppression method for a cascaded H-bridge converter SVM strategy, characterized in that: include: Step 1: Let n be the number of modules of the single-phase H-bridge submodule in the three-phase cascade H-bridge, and the three phase voltage reference signals u ra 、u rb 、u rc Sampling, calculating the reference vector V in the αβ coordinate system r (α r ,β r ); Where, α r , β r are the coordinate components of the reference vector in the αβ coordinate system; Step 2: In the αβ coordinate system, the reference vector V is calculated based on the characteristic factor. r (α r ,β r ) for vector positioning; first calculate the two characteristic factors J and K, which determine the unique diamond sector where the reference vector is located; then use these two characteristic factors to calculate the coordinates V of the midpoint of the diamond sector in the αβ coordinate system z (α z ,β z ); Finally, the coordinates of the three basic vectors adjacent to the reference vector in the αβ coordinate system are calculated using the midpoint coordinates V4(α4,β4), V3(α3,β3), and V0(α0,β0); Step 2.1: According to the coordinate component α of the reference vector in the αβ coordinate system r , β r Calculate the two characteristic factors J and K of the diamond sector; Where J and K are the two characteristic factors of the diamond sector, and floor(*) is the floor rounding function; Step 2.2: According to the two characteristic factors α of the diamond sector r , β r Calculate the coordinates V of the midpoint of the diamond sector z (α z ,β z ); Where, α z , β z are the coordinate components of the midpoint of the rhombus sector; Step 2.3: According to the coordinate component α of the midpoint of the diamond sector z , β z Calculate three basic vectors V4(α4,β4), V3(α3,β3), and V0(α0,β0); Where V4, V3, and V0 are three basic vectors, and sign(*) is the sign function; Step 3: Calculate the action time t4, t3, and t0 of the three basic vectors V4, V3, and V0 according to the volt-second balance principle; Where, T s is the sampling period, t4, t3, t0 are the action times of the three basic vectors V4, V3, V0, abs(*) is the absolute value function; Step 4: Calculate the switching state with the minimum common-mode voltage corresponding to the basic vector based on the correction coefficient; first, calculate the correction factors of the three basic vectors V4 (α4, β4), V3 (α3, β3), and V0 (α0, β0) based on the characteristic factors, and calculate the maximum switching state S4 (a4, b4, c4), S3 (a3, b3, c3), and S0 (a0, b0, c0) of the three basic vectors based on the correction factors; then calculate the common-mode voltage of the maximum switching state and the number of redundant switching states of the basic space vector, and use this to determine the correction coefficients of the three basic vectors; finally, use the correction coefficients to calculate the corrected switching state S of the three basic vectors 44 (a 44 ,b 44 ,c 44 ), S 33 (a 33 ,b 33 ,c 33 ), S 00 (a 00 ,b 00 ,c 00 ); Step 4.1: Calculate the correction factors of V4, V3, and V0 based on the two characteristic factors of the diamond sector; For the basic vector V4, the correction factors p4 and q4 are calculated as follows: For the basic vector V3, the correction factors p3 and q3 are calculated as follows: For the basic vector V0, the correction factors p0 and q0 are calculated as follows: Step 4.2: Calculate the maximum switching states of V4, V3, and V0 based on the correction factors; where i = 4, 3, 0; For the basic vector V i The correction factor is p i ,q i , the maximum switching state is S i (a i ,b i ,c i ); If p i ≥0 and q i ≥0, then w i1 =1,w i2 =0,w i3 =0; If p i <0 and (q i -p i )≥0, then w i1 =0,w i2 =1,w i3 =0; If q i <0 and (q i -p i )<0, then w i1 =0,w i2 =0,w i3 =1; Maximum switching state S i (a i ,b i ,c i ) is calculated as follows: Step 4.3: Calculate the number of redundant switch states R4, R3, and R0 of V4, V3, and V0; where i = 4, 3, and 0; For the basic vector V i The number of redundant switch states R i The calculation is as follows: Step 4.4: Calculate the common-mode voltages N4, N3, and N0 for the maximum switching states S4 (a4, b4, c4), S3 (a3, b3, c3), and S0 (a0, b0, c0) based on the definition of common-mode voltage; where i = 4, 3, 0. Step 4.5: Calculate the correction coefficients H4, H3, and H0 for V4, V3, and V0; where i = 4, 3, and 0; For the basic vector V i Its correction coefficient H i Determine as follows: If the common mode voltage N i ≤0, then H i =0; If the common mode voltage N i >0, then H i =min(round(N i ),(R i -1); Step 4.6: Calculate the corrected switch state based on the correction coefficient; where i = 4, 3, 0; For the basic vector V i The correction factor is H i , the corrected switch state is S ii (a ii ,b ii ,c ii ) is calculated as follows: Step 5: Use the corrected switch state to determine the switching path of the switch state in a time-sharing manner, and enter the next sampling period. Repeat the steps to complete the space vector modulation.

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