A hybrid modulation method for minimizing common-mode voltage of cascaded multilevel converter

Abstract

The application discloses a hybrid modulation method for minimizing common-mode voltage of a cascade multi-level converter. The method obtains the nearest level switching state and three space vectors closest to a reference vector by sampling a reference signal. The switching state corresponding to the three space vectors closest to the reference vector and minimizing common-mode voltage can be directly obtained through a mapping function relationship between the space vectors and the switching state and a coordinate relationship of the three space vectors closest to the reference vector. The method obtains the nearest level switching state and three space vectors closest to a reference vector by sampling a reference signal. The switching state corresponding to the three space vectors closest to the reference vector and minimizing common-mode voltage can be directly obtained through a mapping function relationship between the space vectors and the switching state and a coordinate relationship of the three space vectors closest to the reference vector, avoiding solving of a nonlinear equation and being helpful to popularization and application of the SVPWM algorithm in n-level multi-level converters.

Description

Technical Field

[0001] This invention belongs to the field of modulation technology of cascaded multilevel converters, and particularly relates to a hybrid modulation method for minimizing the common-mode voltage of cascaded multilevel converters. Background Technology

[0002] Cascaded multilevel converters can increase the number of cascaded units to increase the number of output voltage levels, thereby improving the converter's voltage rating and capacity, and optimizing output power parameters. Cascaded converters are characterized by high modularity, ease of expansion and control, high reliability, and low harmonic content, and are widely used in high-voltage, high-power applications.

[0003] With the continuous development of cascaded multilevel converter topologies, pulse width modulation (PWM) algorithms have also evolved. Conventional modulation algorithms can be categorized into three types: Carrier Phase-Shifted PWM (CPS-PWM), Nearest Level Modulation (NLM), and Space Vector Pulse Width Modulation (SVPWM). CPS-PWM technology generates a PWM control signal by comparing a series of triangular carrier waves with a reference signal. The phase shift angle between adjacent carriers is the same. As the number of levels increases, the phase shift angle decreases, increasing the requirements for phase shift angle control accuracy and carrier synchronization, thus increasing the implementation difficulty. CPS-PWM is only suitable for cascaded converters with a relatively small number of levels. NLM technology directly calculates the two closest voltage levels and their corresponding duty cycles to the phase voltage control signal sampling point using a rounding method. It is simple to implement and has a low switching frequency. However, because the NLM output voltage lacks specific harmonics, filter design is difficult, and harmonic distortion is high at low voltage levels. Therefore, NLM is only suitable for cascaded converters with a relatively small number of voltage levels. SVPWM technology first converts the three-phase reference voltage into a reference vector on a two-dimensional rectangular coordinate plane using the Clarke transform. Then, it locates the reference vector and determines the three closest spatial vectors. Based on the volt-second balance principle, it synthesizes the reference vector using these three closest spatial vectors and calculates the duration of each spatial vector. It then calculates the corresponding switching state and determines the switching sequence. Finally, it converts the switching state into specific control signals for the switching devices, controlling the operation of each cascaded unit and achieving space vector modulation of the three-phase converter. SVPWM technology is suitable for converters with arbitrary voltage levels. Compared to traditional CPS-PWM technology, SVPWM technology reduces the number of switches by one-third, increases DC voltage utilization by 15%, and is easier to implement in digital real-time control, thus gaining widespread application. However, in the implementation of SVPWM, calculating the switching state corresponding to the space vector requires solving a non-homogeneous linear equation system. This system has infinitely many solutions. Considering the limited number of cascaded units in practical applications, only a finite number of solutions are meaningful, meaning that one space vector corresponds to multiple switching states (referred to as redundant switching states). Redundant switching states lead to problems such as large computational workload and complex switching path selection. As the number of cascaded units increases, the computational workload increases exponentially, greatly increasing the difficulty of implementing SVPWM. Summary of the Invention

[0004] This invention provides a hybrid modulation method for minimizing the common-mode voltage of a cascaded multilevel converter, which at least solves the technical problems of large computational workload and complex switching path selection caused by the aforementioned redundant switching states.

[0005] This invention provides a hybrid modulation method for minimizing the common-mode voltage of a cascaded multilevel converter, comprising:

[0006] Step 1: Determine the mapping relationship between the spatial vector V(α′, β′) in the α′β′ coordinate system and the switch state S(a, b, c);

[0007] Step 2: 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 down yields α′0 and β′0. The four spatial vectors V0(α′0, β′0), V1(α′0+1, β′0), V2(α′0, β′0+1), and V3(α′0+1, β′0+1) that are closest to the reference vector form a unit square.

[0008] For the three phase voltage reference signals u ra u rb u rc Round down to the nearest integer to obtain the nearest level switch state S. n (a n b n c n And calculate the distance reference vector V based on the mapping relationship. r (α′ r ,β′ r The nearest space vector V n (α n ,β n ), where the most recent level switch state S n (a n b n c n )for:

[0009]

[0010] In the formula, round(*) is the rounding function;

[0011] 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 (α′ r ,β′ r The three spatial vectors are used to calculate the composite reference vector V based on the second-volt balance principle. r (α′ r ,β′ r The action time of the three spatial vectors of ) is as follows, where the sector triangle type includes sector triangle B composed of spatial vectors V0(α′0,β′0), V1(α′0+1,β′0), and V2(α′0,β′0+1), and sector triangle A composed of spatial vectors V1(α′0+1,β′0), V2(α′0,β′0+1), and V3(α′0+1,β′0+1). Sector triangle A and sector triangle B form a unit square.

[0012] Step 4: Determine the composite reference vector V r (α′ r ,β′ r Among the three spatial vectors of ), the one that is most similar to spatial vector V n (α n ,β n The nearest spatial vector and the judgment of a n +b n +c n The value is determined by whether it is 1, -1, or 0, and the synthesized reference vector V is obtained based on the mapping relationship and the optimal switching principle of the switch state. r (α′ r ,β′ r The common-mode voltage minimum switching state and the second switching state of the three space vectors of the );

[0013] Step 5: Based on the actual circuit output level range, synthesize the reference vector V. r (α′ r ,β′ r The minimum switching state of the common-mode voltage of the three space vectors is corrected;

[0014] Step 6: Determine the switching order of the three corrected space vectors and use a five-segment algorithm for hybrid modulation.

[0015] In addition, the hybrid modulation method for minimizing the common-mode voltage of a cascaded multilevel converter according to the above embodiments of the present invention may also have the following additional technical features:

[0016] Furthermore, in step 1, the mapping relationship between the spatial vector V(α′, β′) in the α′β′ coordinate system and the switch state S(a, b, c) is as follows:

[0017]

[0018] 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(a, b, c), where S is the name of the switching state.

[0019] Furthermore, step 4 specifically involves:

[0020] Case 1: When (α′ r +β′ r When α′0+β′0)≥1, the reference vector V r (α′ r ,β′ r In sector triangle A, determine the composite reference vector V. r (α′ r ,β′ r Among the three spatial vectors V1, V2, V3, which are related to spatial vector V n (α n ,β n The nearest spatial vector and the judgment of a n +b n +c n Whether the value is 1, -1, or 0, nine possible results can be obtained:

[0021] When V n =V1 and a n +b n +c n When V1 = 1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n c n S2(a) n -1, b n c n ) and S3(a n -1, b n c n -1), the second switching state is S2(a) n -1, b n c n );

[0022] When V n =V1 and a n +b n +c n When V1 = -1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n c n S2(a) n b n +1, c n+1) and S3(a n b n +1, c n The second switching state is S3(a) n b n +1, c n );

[0023] When V n =V1 and a n +b n +c n When V1 = 0, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n c n S2(a) n -1, b n c n ) and S3(a n b n +1, c n The second switching state is S1(a) n b n c n );

[0024] When V n =V2anda n +b n +c n When V1 = 1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n -1,c n -1), S2(a n b n c n ) and S3(a n b n c n -1), the second switching state is S3(a) n b n c n -1);

[0025] When V n =V2anda n +b n +c n When V1 = -1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n +1, b n c n S2(a) n b n c n ) and S3(an +1, b n +1, c n The second switching state is S1(a) n +1, b n c n );

[0026] When V n =V2anda n +b n +c n When V1 = 0, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n +1, b n c n S2(a) n b n c n ) and S3(a n b n c n -1), the second switching state is S2(a) n b n c n );

[0027] When V n =V3 and a n +b n +c n When V1 = 1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n -1,c n S2(a) n -1, b n -1,c n ) and S3(a n b n c n The second switching state is S1(a) n b n -1,c n );

[0028] When V n =V3 and a n +b n +c n When V1 = -1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n +1, b n c n +1), S2(a n b n c n +1) and S3(a nb n c n The second switching state is S2(a) n b n c n +1);

[0029] When V n =V3 and a n +b n +c n When V1 = 0, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n -1,c n S2(a) n b n c n +1) and S3(a n b n c n The second switching state is S3(a) n b n c n );

[0030] Case 2: When (α′ r +β′ r When )-(α′0+β′0)<1, the reference vector V r (α′ r ,β′ r In sector triangle B, determine the composite reference vector V. r (α′ r ,β′ r Among the three spatial vectors V0, V1, V2, and spatial vector V, the one that is most similar to the spatial vector V n (α n ,β n The nearest spatial vector and the judgment of a n +b n +c n The value can be 1, -1, or 0, resulting in 9 possible cases:

[0031] When V n =V0 and a n +b n +c n When V = 1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n S1(a) n b n c n -1) and S2(a n -1, bn c n -1), the second switching state is S1(a) n b n c n -1);

[0032] When V n =V0 and a n +b n +c n When V0, V1, and V2 are equal to -1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n S1(a) n +1, b n +1, c n ) and S2(a n b n +1, c n The second switching state is S2(a) n b n +1, c n ),

[0033] When V n =V0 and a n +b n +c n When V = 0, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n S1(a) n b n c n -1) and S2(a n b n +1, c n The second switching state is S0(a) n b n c n );

[0034] When V n =V1 and a n +b n +c n When V = 1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n -1, b n -1,c n S1(a) n b n c n ) and S2(a n -1, b nc n The second switching state is S2(a) n -1, b n c n );

[0035] When V n =V1 and a n +b n +c n When V0, V1, and V2 are equal to -1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n +1), S1(a n b n c n ) and S2(a n b n +1, c n +1), the second switch state is S0(a) n b n c n +1);

[0036] When V n =V1 and a n +b n +c n When V = 0, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n +1), S1(a n b n c n ) and S2(a n -1, b n c n The second switching state is S1(a) n b n c n );

[0037] When V n =V2anda n +b n +c n When V = 1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n -1,c n S1(a) n b n -1,c n -1) and S2(a n b n c nThe second switching state is S0(a) n b n -1,c n );

[0038] When V n =V2anda n +b n +c n When V0, V1, and V2 are equal to -1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n +1, b n c n +1), S1(a n +1, b n c n ) and S2(a n b n c n The second switching state is S1(a) n +1, b n c n );

[0039] When V n =V2anda n +b n +c n When V = 0, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n -1,c n S1(a) n +1, b n c n ) and S2(a n b n c n The second switching state is S2(a) n b n c n ).

[0040] Furthermore, in step 5, the synthesized reference vector V is adjusted according to the actual circuit output level range. r (α′ r ,β′ r The correction of the minimum switching state of the common-mode voltage of the three space vectors includes:

[0041] If the obtained a x b x c x If ∈[±n, ±(n-1), ±(n-2), ..., ±2, ±1, 0], then the correction coefficient k = 0; if the obtained When min(a x bx c x When ) < -n, the correction coefficient k = min(a x b x c x )+n, when max(a x b x c x When ), the correction coefficient k = max(a) x b x c x )-n;

[0042] a x b x c x Simultaneously subtracting the correction factor k yields the minimum common-mode voltage switching state of the corrected space vector:

[0043]

[0044] Further, in step 6, the switching order of the three corrected space vectors is determined, and a five-segment algorithm is used for hybrid modulation, including:

[0045] Case 1: When (α′ r +β′ r When α′0+β′0)≥1, the reference vector V r (α′ r ,β′ r Given V1, V2, and V3, calculate the number of redundant switching states m1, m2, and m3 corresponding to the minimum common-mode voltage switching state of the three space vectors V1, V2, and V3. The expression for calculating the number of redundant switching states of the space vector is: m = 2n - max{a, b, c} + min{a, b, c}. Depending on the known second switching state, there are three possible results:

[0046] Given that the second switch state is S1, if m2 > m3, the switch switching sequence is S2, S1, S3; otherwise, the switch sequence is S3, S1, S2.

[0047] Given that the second switch state is S2, if m1 > m3, the switch switching sequence is S1, S2, S3; otherwise, the switch sequence is S3, S2, S1.

[0048] Given that the second switch state is S3, if m1 > m2, the switch switching sequence is S1, S3, S2; otherwise, the switch sequence is S2, S3, S1.

[0049] Based on the calculation results, there are six possible switching sequences. Using a five-segment algorithm, the switching sequence of the synthesized reference vector is as follows:

[0050] The calculated switching sequence is S1, S2, S3, and the switching sequence of the synthetic reference vector is S1→S2→S3→S2→S1, with corresponding action times of t1 / 2→t2 / 2→t3→t2 / 2→t1 / 2.

[0051] The calculated switching sequence is S1, S3, S2, and the switching sequence of the synthetic reference vector is S1→S3→S2→S3→S1, with corresponding action times of t1 / 2→t3 / 2→t2→t3 / 2→t1 / 2.

[0052] The calculated switching sequence is S2, S1, S3, and the switching sequence of the synthetic reference vector is S2→S1→S3→S1→S2, with corresponding action times of t2 / 2→t1 / 2→t3→t1 / 2→t2 / 2.

[0053] The calculated switching sequence is S2, S3, S1, and the switching sequence of the synthetic reference vector is S2→S3→S1→S3→S2, with corresponding action times of t2 / 2→t3 / 2→t1→t3 / 2→t2 / 2.

[0054] The calculated switching sequence is S3, S1, S2, and the switching sequence of the synthetic reference vector is S3→S1→S2→S1→S3, with corresponding action times of t3 / 2→t1 / 2→t2→t1 / 2→t3 / 2.

[0055] The calculated switching sequence is S3, S2, S1, and the switching sequence of the synthetic reference vector is S3→S2→S1→S2→S3, with corresponding action times of t3 / 2→t2 / 2→t1→t2 / 2→t3 / 2.

[0056] Case 2: When (α′ r +β′ r When )-(α′0+β′0)<1, the reference vector V r (α′ r ,β′ r Combined from V0, V1, and V2, calculate the corresponding number of redundant switch states m0, m1, and m2. Based on the known different switch states of the second switching, there are three possible results:

[0057] When the second switch state is S0, if m1 > m2, the switch switching sequence is S1, S0, S2; otherwise, the switch sequence is S2, S0, S1.

[0058] When the second switch state is S1, if m0 > m2, the switch switching sequence is S0, S1, S2; otherwise, the switch sequence is S2, S1, S2.

[0059] Given that the second switch state is S2, if m0 > m1, the switch switching sequence is S0, S2, S1; otherwise, the switch sequence is S1, S2, S0.

[0060] Based on the calculation results, there are six possible switching sequences. Using a five-segment algorithm, the switching sequence of the synthesized reference vector is as follows:

[0061] The calculated switching sequence is S0, S1, S2, and the switching sequence of the synthetic reference vector is S0→S1→S2→S1→S0, with corresponding action times of t0 / 2→t1 / 2→t2→t1 / 2→t0 / 2.

[0062] The calculated switching sequence is S0, S2, S1, and the switching sequence of the synthetic reference vector is S0→S2→S1→S2→S0, with corresponding action times of t0 / 2→t2 / 2→t1→t2 / 2→t0 / 2.

[0063] The calculated switching sequence is S1, S0, S2, and the switching sequence of the synthetic reference vector is S1→S0→S2→S0→S1, with corresponding action times of t1 / 2→t0 / 2→t2→t0 / 2→t1 / 2.

[0064] The calculated switching sequence is S1, S2, S0, and the switching sequence of the synthetic reference vector is S1→S2→S0→S2→S1, with corresponding action times of t1 / 2→t2 / 2→t0→t2 / 2→t1 / 2.

[0065] The calculated switching sequence is S2, S0, S1, and the switching sequence of the synthetic reference vector is S2→S0→S1→S0→S2, with corresponding action times of t2 / 2→t0 / 2→t1→t0 / 2→t2 / 2.

[0066] The calculated switching sequence is S2, S1, S0, and the switching sequence of the synthetic reference vector is S2→S1→S0→S1→S2, with corresponding action times of t2 / 2→t1 / 2→t0→t1 / 2→t2 / 2.

[0067] This application presents a hybrid modulation method for minimizing the common-mode voltage of a cascaded multilevel converter. This method allows for the direct acquisition of the switching state with the minimum common-mode voltage among all switching states corresponding to the space vector. It avoids solving nonlinear equations and can be implemented using only simple arithmetic transformations. This method avoids complex trigonometric function and irrational number calculations and can be applied to any series converter. It is also easy to implement on a computer. Attached Figure Description

[0068] 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.

[0069] Figure 1 A flowchart illustrating a hybrid modulation method for minimizing the common-mode voltage of a cascaded multilevel converter, as provided in an embodiment of the present invention;

[0070] Figure 2 This is a triangle positioning diagram of the sector where the reference vector is located, provided as an embodiment of the present invention. Detailed Implementation

[0071] 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.

[0072] Please see Figure 1 The flowchart illustrates a hybrid modulation method for minimizing the common-mode voltage of a cascaded multilevel converter according to this application.

[0073] like Figure 1 As shown, the hybrid modulation method for minimizing the common-mode voltage of a cascaded multilevel converter specifically includes the following steps:

[0074] Step 1: Determine the mapping relationship between the spatial vector V(α′, β′) in the α′β′ coordinate system and the switch state S(a, b, c).

[0075] In this embodiment, 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 is determined as follows:

[0076]

[0077] In the formula, α′ and β′ are the coordinate components of the space vector V. For an n-stage H-bridge cascaded multilevel converter, a, b, c ∈ [±n, ±(n-1), ±(n-2), ..., ±2, ±1, 0], then α′, β′ ∈ [±2n, ±(2n-1), ±(2n-2), ..., ±2, ±1, 0]. The switching state of the space vector V(α′, β′) is S(a, b, c), where S is the name of the switching state.

[0078] Step 2: 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 down yields α′0 and β′0. The four spatial vectors V0(α′0, β′0), V1(α′0+1, β′0), V2(α′0, β′0+1), and V3(α′0+1, β′0+1) that are closest to the reference vector form a unit square.

[0079] For the three phase voltage reference signals u ra u rb u rc Round down to the nearest integer to obtain the nearest level switch state S. n (a n b n c n And calculate the distance reference vector V based on the mapping relationship. r (α′ r ,β′ r The nearest space vector V n (α n ,β n ).

[0080] In this embodiment, the reference vector V r (α′ r ,β′ r The expression for ) is:

[0081]

[0082] In the formula, α′ r ,β′ r Reference vector V r The corresponding coordinate components;

[0083] For reference vector V r (α′ r ,β′ r The component α′ r ,β′ r Rounding down, we get:

[0084]

[0085] In the formula, floor(*) is the floor function.

[0086] Among them, the most recent level switch state S n (a n b n c n )for:

[0087]

[0088] In the formula, round(*) is the rounding function.

[0089] 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 (α′ r ,β′ r The three spatial vectors are used to calculate the composite reference vector V based on the second-volt balance principle. r (α′ r ,β′ r The three spatial vectors of the sector triangle are: the sector triangle B composed of spatial vectors V0(α′0,β′0), V1(α′0+1,β′0), and V2(α′0,β′0+1), and the sector triangle A composed of spatial vectors V1(α′0+1,β′0), V2(α′0,β′0+1), and V3(α′0+1,β′0+1). Sector triangle A and sector triangle B form a unit square.

[0090] In this embodiment, when (α′ r -α′0)+(β′ r When -β′0)≤1, the reference vector V r (α′ r ,β′ r ) is located in sector triangle B, when (α′ r -α′0)+(β′ r When -β′0)>1, the reference vector V r (α′ r ,β′ r In sector triangle A (e.g.) Figure 2 (As shown).

[0091] Step 4: Determine the composite reference vector V r (α′ r ,β′ r Among the three spatial vectors of ), the one that is most similar to spatial vector V n (α n ,β nThe nearest spatial vector and the judgment of a n +b n +c n The value is determined by whether it is 1, -1, or 0, and the synthesized reference vector V is obtained based on the mapping relationship and the optimal switching principle of the switch state. r (α′ r ,β′ r The three space vectors of the common-mode voltage minimum switching state and the second switching state.

[0092] In this embodiment, the synthesized reference vector V is obtained based on the mapping relationship and the optimal switching principle (i.e., space vectors with more redundant switching states take priority and the switching states change by only one unit level before and after switching). r (α′ r ,β′ r The minimum common-mode voltage switching state and the second switching state of the three space vectors are as follows:

[0093] Case 1: When (α′ r +β′ r When α′0+β′0)≥1, the reference vector V r (α′ r ,β′ r In sector triangle A, determine the composite reference vector V. r (α′ r ,β′ r Among the three spatial vectors V1, V2, V3, which are related to spatial vector V n (α n ,β n The nearest spatial vector and the judgment of a n +b n +c n Whether the value is 1, -1, or 0, nine possible results can be obtained:

[0094] When V n =V1 and a n +b n +c n When V1 = 1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n c n S2(a) n -1, b n c n ) and S3(a n -1, b n c n -1), the second switching state is S2(a) n -1, b n cn );

[0095] When V n =V1 and a n +b n +c n When V1 = -1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n c n S2(a) n b n +1, c n +1) and S3(a n b n +1, c n The second switching state is S3(a) n b n +1, c n );

[0096] When V n =V1 and a n +b n +c n When V1 = 0, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n c n S2(a) n -1, b n c n ) and S3(a n b n +1, c n The second switching state is S1(a) n b n c n );

[0097] When V n =V2anda n +b n +c n When V1 = 1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n -1,c n -1), S2(a n b n c n ) and S3(a n b n c n -1), the second switching state is S3(a) n b n c n -1);

[0098] When V n =V2anda n +b n +c n When V1 = -1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n +1, b n c n S2(a) n b n c n ) and S3(a n +1, b n +1, c n The second switching state is S1(a) n +1, b n c n );

[0099] When V n =V2anda n +b n +c n When V1 = 0, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n +1, b n c n S2(a) n b n c n ) and S3(a n b n c n -1), the second switching state is S2(a) n b n c n );

[0100] When V n =V3 and a n +b n +c n When V1 = 1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n -1,c n S2(a) n -1, b n -1,c n ) and S3(a n b n c n The second switching state is S1(a) n b n -1,c n );

[0101] When V n =V3 and a n +b n +c n When V1 = -1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n +1, b n c n +1), S2(a n b n c n +1) and S3(a n b n c n The second switching state is S2(a) n b n c n +1);

[0102] When V n =V3 and a n +b n +c n When V1 = 0, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n -1,c n S2(a) n b n c n +1) and S3(a n b n c n The second switching state is S3(a) n b n c n );

[0103] Case 2: When (α′ r +β′ r When )-(α′0+β′0)<1, the reference vector V r (α′ r ,β′ r In sector triangle B, determine the composite reference vector V. r (α′ r ,β′ r Among the three spatial vectors V0, V1, V2, and spatial vector V, the one that is most similar to the spatial vector V n (α n ,β n The nearest spatial vector and the judgment of a n +b n +c n The value can be 1, -1, or 0, resulting in 9 possible cases:

[0104] When V n =V0 and a n +b n +c n When V = 1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n S1(a) n b n c n -1) and S2(a n -1, b n c n -1), the second switching state is S1(a) n b n c n -1);

[0105] When V n =V0 and a n +b n +c n When V0, V1, and V2 are equal to -1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n S1(a) n +1, b n +1, c n ) and S2(a n b n +1, c n The second switching state is S2(a) n b n +1, c n );

[0106] When V n =V0 and a n +b n +c n When V = 0, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n S1(a) n b n c n -1) and S2(a n b n +1, c n The second switching state is S0(a) n b n c n );

[0107] When Vn =V1 and a n +b n +c n When V = 1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n -1, b n -1,c n S1(a) n b n c n ) and S2(a n -1, b n c n The second switching state is S2(a) n -1, b n c n );

[0108] When V n =V1 and a n +b n +c n When V0, V1, and V2 are equal to -1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n +1), S1(a n b n c n ) and S2(a n b n +1, c n +1), the second switch state is S0(a) n b n c n +1);

[0109] When V n =V1 and a n +b n +c n When V = 0, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n +1), S1(a n b n c n ) and S2(a n -1, b n c n The second switching state is S1(a) n b n c n );

[0110] When V n=V2anda n +b n +c n When V = 1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n -1,c n S1(a) n b n -1,c n -1) and S2(a n b n c n The second switching state is S0(a) n b n -1,c n );

[0111] When V n =V2anda n +b n +c n When V0, V1, and V2 are equal to -1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n +1, b n c n +1), S1(a n +1, b n c n ) and S2(a n b n c n The second switching state is S1(a) n +1, b n c n );

[0112] When V n =V2anda n +b n +c n When V = 0, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n -1,c n S1(a) n +1, b n c n ) and S2(a n b n c n The second switching state is S2(a) n b n c n ).

[0113] Step 5: Based on the actual circuit output level range, synthesize the reference vector V.r (α′ r ,β′ r The minimum switching state of the common-mode voltage of the three space vectors is corrected.

[0114] In this embodiment, if the obtained a x b x c x If ∈[±n, ±(n-1), ±(n-2), ..., ±2, ±1, 0], then the correction coefficient k = 0; if the obtained When min(a x b x c x When ) < -n, the correction coefficient k = min(a x b x c x )+n, when max(a x b x c x When ), the correction coefficient k = max(a) x b x c x )-n;

[0115] a x b x c x Simultaneously subtracting the correction factor k yields the minimum common-mode voltage switching state of the corrected space vector:

[0116]

[0117] S(a x ′,b x ′, c x ′) is the spatial vector V x (α x ,β x The corresponding actual circuit can achieve the switching state with the minimum common-mode voltage. S0, S1, S2 (S1, S2, S3) are corrected according to formula (5).

[0118] Step 6: Determine the switching order of the three corrected space vectors and use a five-segment algorithm for hybrid modulation.

[0119] In this embodiment, determining the switching order of the three corrected space vectors and performing hybrid modulation using a five-segment algorithm includes:

[0120] Case 1: When (α′ r +β′ r When α′0+β′0)≥1, the reference vector V r (α′ r ,β′r Given V1, V2, and V3, calculate the number of redundant switching states m1, m2, and m3 corresponding to the minimum common-mode voltage switching state of the three space vectors V1, V2, and V3. The expression for calculating the number of redundant switching states of the space vector is: m = 2n - max{a, b, c} + min{a, b, c}. Depending on the known second switching state, there are three possible results:

[0121] Given that the second switch state is S1, if m2 > m3, the switch switching sequence is S2, S1, S3; otherwise, the switch sequence is S3, S1, S2.

[0122] Given that the second switch state is S2, if m1 > m3, the switch switching sequence is S1, S2, S3; otherwise, the switch sequence is S3, S2, S1.

[0123] Given that the second switch state is S3, if m1 > m2, the switch switching sequence is S1, S3, S2; otherwise, the switch sequence is S2, S3, S1.

[0124] Based on the calculation results, there are six possible switching sequences. Using a five-segment algorithm, the switching sequence of the synthesized reference vector is as follows:

[0125] The calculated switching sequence is S1, S2, S3, and the switching sequence of the synthetic reference vector is S1→S2→S3→S2→S1, with corresponding action times of t1 / 2→t2 / 2→t3→t2 / 2→t1 / 2.

[0126] The calculated switching sequence is S1, S3, S2, and the switching sequence of the synthetic reference vector is S1→S3→S2→S3→S1, with corresponding action times of t1 / 2→t3 / 2→t2→t3 / 2→t1 / 2.

[0127] The calculated switching sequence is S2, S1, S3, and the switching sequence of the synthetic reference vector is S2→S1→S3→S1→S2, with corresponding action times of t2 / 2→t1 / 2→t3→t1 / 2→t2 / 2.

[0128] The calculated switching sequence is S2, S3, S1, and the switching sequence of the synthetic reference vector is S2→S3→S1→S3→S2, with corresponding action times of t2 / 2→t3 / 2→t1→t3 / 2→t2 / 2.

[0129] The calculated switching sequence is S3, S1, S2, and the switching sequence of the synthetic reference vector is S3→S1→S2→S1→S3, with corresponding action times of t3 / 2→t1 / 2→t2→t1 / 2→t3 / 2.

[0130] The calculated switching sequence is S3, S2, S1, and the switching sequence of the synthetic reference vector is S3→S2→S1→S2→S3, with corresponding action times of t3 / 2→t2 / 2→t1→t2 / 2→t3 / 2.

[0131] Case 2: When (α′ r +β′ r When )-(α′0+β′0)<1, the reference vector V r (α′ r ,β′ r Combined from V0, V1, and V2, calculate the corresponding number of redundant switch states m0, m1, and m2. Based on the known different switch states of the second switching, there are three possible results:

[0132] When the second switch state is S0, if m1 > m2, the switch switching sequence is S1, S0, S2; otherwise, the switch sequence is S2, S0, S1.

[0133] When the second switch state is S1, if m0 > m2, the switch switching sequence is S0, S1, S2; otherwise, the switch sequence is S2, S1, S2.

[0134] Given that the second switch state is S2, if m0 > m1, the switch switching sequence is S0, S2, S1; otherwise, the switch sequence is S1, S2, S0.

[0135] Based on the calculation results, there are six possible switching sequences. Using a five-segment algorithm, the switching sequence of the synthesized reference vector is as follows:

[0136] The calculated switching sequence is S0, S1, S2, and the switching sequence of the synthetic reference vector is S0→S1→S2→S1→S0, with corresponding action times of t0 / 2→t1 / 2→t2→t1 / 2→t0 / 2.

[0137] The calculated switching sequence is S0, S2, S1, and the switching sequence of the synthetic reference vector is S0→S2→S1→S2→S0, with corresponding action times of t0 / 2→t2 / 2→t1→t2 / 2→t0 / 2.

[0138] The calculated switching sequence is S1, S0, S2, and the switching sequence of the synthetic reference vector is S1→S0→S2→S0→S1, with corresponding action times of t1 / 2→t0 / 2→t2→t0 / 2→t1 / 2.

[0139] The calculated switching sequence is S1, S2, S0, and the switching sequence of the synthetic reference vector is S1→S2→S0→S2→S1, with corresponding action times of t1 / 2→t2 / 2→t0→t2 / 2→t1 / 2.

[0140] The calculated switching sequence is S2, S0, S1, and the switching sequence of the synthetic reference vector is S2→S0→S1→S0→S2, with corresponding action times of t2 / 2→t0 / 2→t1→t0 / 2→t2 / 2.

[0141] The calculated switching sequence is S2, S1, S0, and the switching sequence of the synthetic reference vector is S2→S1→S0→S1→S2, with corresponding action times of t2 / 2→t1 / 2→t0→r1 / 2→t2 / 2.

[0142] In summary, the method of this application calculates a reference vector and the spatial vectors corresponding to the three vertices of a sector triangle containing the reference vector using a three-phase phase voltage reference signal. Then, the three-phase phase voltage reference signal is rounded to the nearest integer to obtain the switching state with the minimum common-mode voltage corresponding to the spatial vector closest to the reference vector in the sector triangle. Based on the positional relationship of the spatial vectors corresponding to the three vertices of the sector triangle and the mapping function between the spatial vectors and the switching states, the switching states with the minimum common-mode voltage corresponding to the other two spatial vectors are directly obtained. Finally, the spatial vectors determine the switching order of the switching states corresponding to the three vertices of the sector triangle. This method directly obtains the switching state with the minimum common-mode voltage among all switching states corresponding to the spatial vectors, avoiding the need for solving nonlinear equations. The algorithm can be implemented using only simple arithmetic transformations, avoiding complex trigonometric function and irrational number calculations. It can be applied to arbitrary series converters and is easy to implement on a computer.

[0143] 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 hybrid modulation method for minimizing the common-mode voltage of a cascaded multilevel converter, characterized in that, include: Step 1: Determine the mapping relationship between the spatial vector V(α′, β′) in the α′β′ coordinate system and the switch state S(a, b, c); Step 2: 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 up yields α′0 and β′0. The four spatial vectors V0(α′0, β′0), V1(α′0+1, β′0), V2(α′0, β′0+1), and V3(α′0+1, β′0+1) that are closest to the reference vector form a unit square. For the three phase voltage reference signals u ra u rb u rc Round down to the nearest integer to obtain the nearest level switch state S. n (a n b n c n And calculate the distance reference vector V based on the mapping relationship. r (α′ r ,β′ r The nearest space vector V n (α′ n ,β′ n ), where the most recent level switch state S n (a n b n c n )for: In the formula, round(*) is the rounding function; 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 (α′ r ,β′ r The three spatial vectors are used to calculate the composite reference vector V based on the second-volt balance principle. r (α′ r ,β′ r The action time of the three spatial vectors of ) is as follows, where the sector triangle type includes sector triangle B composed of spatial vectors V0(α′0,β′0), V1(α′0+1,β′0), and V2(α′0,β′0+1), and sector triangle A composed of spatial vectors V1(α′0+1,β′0), V2(α′0,β′0+1), and V3(α′0+1,β′0+1). Sector triangle A and sector triangle B form a unit square. Step 4: Determine the composite reference vector V r (α′ r ,β′ r Among the three spatial vectors of ), the one that is most similar to spatial vector V n (α′ n ,β′ n The nearest spatial vector and the judgment of a n +b n +c n The value is determined by whether it is 1, -1, or 0, and the synthesized reference vector V is obtained based on the mapping relationship and the optimal switching principle of the switch state. r (α′ r ,β′ r The common-mode voltage minimum switching state and the second switching state of the three space vectors of the ); Step 5: Based on the actual circuit output level range, synthesize the reference vector V. r (α′ r ,β′ r The minimum switching state of the common-mode voltage of the three space vectors is corrected; Step 6: Determine the switching order of the three corrected space vectors and use a five-segment algorithm for hybrid modulation.

2. The hybrid modulation method for minimizing the common-mode voltage of a cascaded multilevel converter according to claim 1, characterized in that, In step 1, the mapping relationship between the spatial vector V(α′, β′) in the α′β′ coordinate system and the switch state S(a, b, c) is as follows: 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(a, b, c), where S is the name of the switching state.

3. The hybrid modulation method for minimizing the common-mode voltage of a cascaded multilevel converter according to claim 1, characterized in that, Step 4 is as follows: Case 1: When (α′ r +β′ r When α′0+β′0)≥1, the reference vector V r (α′ r ,β′ r In sector triangle A, determine the composite reference vector V. r (α′ r ,β′ r Among the three spatial vectors V1, V2, V3, which are related to spatial vector V n (α′ n ,β′ n The nearest spatial vector and the judgment of a n +b n +c n Whether the value is 1, -1, or 0, nine possible results can be obtained: When V n =V1 and a n +b n +c n When V1 = 1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n c n S2(a) n -1, b n c n ) and S3(a n -1, b n c n -1), the second switching state is S2(a) n -1, b n c n ); When V n =V1 and a n +b n +c n When V1 = -1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n c n S2(a) n b n +1, c n +1) and S3(a n b n +1, c n The second switching state is S3(a) n b n +1, c n ); When V n =V1 and a n +b n +c n When V1 = 0, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n c n S2(a) n -1, b n c n ) and S3(a n b n +1, c n The second switching state is S1(a) n b n c n ); When V n =V2anda n +b n +c n When V1 = 1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n -1,c n -1), S2(a n b n c n ) and S3(a n b n c n -1), the second switching state is S3(a) n b n c n -1); When V n =V2anda n +b n +c n When V1 = -1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n +1, b n c n S2(a) n b n c n ) and S3(a n +1, b n +1, c n The second switching state is S1(a) n +1, b n c n ); When V n =V2anda n +b n +c n When V1 = 0, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n +1, b n c n S2(a) n b n c n ) and S3(a n b n c n -1), the second switching state is S2(a) n b n c n ); When V n =V3 and a n +b n +c n When V1 = 1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n -1,c n S2(a) n -1, b n -1,c n ) and S3(a n b n c n The second switching state is S1(a) n b n -1,c n ); When V n =V3 and a n +b n +c n When V1 = -1, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n +1, b n c n +1), S2(a n b n c n +1) and S3(a n b n c n The second switching state is S2(a) n b n c n +1); When V n =V3 and a n +b n +c n When V1 = 0, the switching state with the minimum common-mode voltage corresponding to V1, V2, and V3 is S1(a n b n -1,c n S2(a) n b n c n +1) and S3(a n b n c n The second switching state is S3(a) n b n c n ); Case 2: When (α′ r +β′ r When )-(α′0+β′0)<1, the reference vector V r (α′ r ,β′ r In sector triangle B, determine the composite reference vector V. r (α′ r ,β′ r Among the three spatial vectors V0, V1, V2, and spatial vector V, the one that is most similar to the spatial vector V n (α n ,β n The nearest spatial vector and the judgment of a n +b n +c n The value can be 1, -1, or 0, resulting in 9 possibilities: When V n =V0 and a n +b n +c n When V = 1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n S1(a) n b n c n -1) and S2(a n -1, b n c n -1), the second switching state is S1(a) n b n c n -1); When V n =V0 and a n +b n +c n When V0, V1, and V2 are equal to -1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n S1(a) n +1, b n +1, c n ) and S2(a n b n +1, c n The second switching state is S2(a) n b n +1, c n ); When V n =V0 and a n +b n +c n When V = 0, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n S1(a) n b n c n -1) and S2(a n b n +1, c n The second switching state is S0(a) n b n c n ); When V n =V1 and a n +b n +c n When V = 1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n -1, b n -1,c n S1(a) n b n c n ) and S2(a n -1, b n c n The second switching state is S2(a) n -1, b n c n ); When V n =V1 and a n +b n +c n When V0, V1, and V2 are equal to -1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n +1), S1(a n b n c n ) and S2(a n b n +1, c n +1), the second switch state is S0(a) n b n c n +1); When V n =V1 and a n +b n +c n When V = 0, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n c n +1), S1(a n b n c n ) and S2(a n -1, b n c n The second switching state is S1(a) n b n c n ); When V n =V2anda n +b n +c n When V = 1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n -1,c n S1(a) n b n -1,c n -1) and S2(a n b n c n The second switching state is S0(a) n b n -1,c n ); When V n =V2anda n +b n +c n When V0, V1, and V2 are equal to -1, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n +1, b n c n +1), S1(a n +1, b n c n ) and S2(a n b n c n The second switching state is S1(a) n +1, b n c n ); When V n =V2anda n +b n +c n When V = 0, the switching state with the minimum common-mode voltage corresponding to V0, V1, and V2 is S0(a n b n -1,c n S1(a) n +1, b n c n ) and S2(a n b n c n The second switching state is S2(a) n b n c n ).

4. The hybrid modulation method for minimizing the common-mode voltage of a cascaded multilevel converter according to claim 1, characterized in that, In step 5, the synthesized reference vector V is adjusted according to the actual circuit output level range. r (α′ r ,β′ r The correction of the minimum switching state of the common-mode voltage of the three space vectors includes: If the obtained a x b x c x If ∈[±n, ±(n-1), ±(n-2), ..., ±2, ±1, 0], then the correction coefficient k = 0; if the obtained When min(a x b x c x When ) < -n, the correction coefficient k = min(a x b x c x )+n, when max(a x b x c x When ), the correction coefficient k = max(a) x b x c x )-n; a x b x c x Simultaneously subtracting the correction factor k yields the minimum common-mode voltage switching state of the corrected space vector:

5. The hybrid modulation method for minimizing the common-mode voltage of a cascaded multilevel converter according to claim 1, characterized in that, In step 6, the switching order of the three corrected space vectors is determined, and a five-segment algorithm is used for hybrid modulation, including: Case 1: When (α′ r +β′ r When α′0+β′0)≥1, the reference vector V r (α′ r ,β′ r Given V1, V2, and V3, calculate the number of redundant switching states m1, m2, and m3 corresponding to the minimum common-mode voltage switching state of the three space vectors V1, V2, and V3. The expression for calculating the number of redundant switching states of the space vector is: m = 2n - max{a, b, c} + min{a, b, c}. Depending on the known second switching state, there are three possible results: Given that the second switch state is S1, if m2 > m3, the switch switching sequence is S2, S1, S3; otherwise, the switch sequence is S3, S1, S2. Given that the second switch state is S2, if m1 > m3, the switch switching sequence is S1, S2, S3; otherwise, the switch sequence is S3, S2, S1. Given that the second switch state is S3, if m1 > m2, the switch switching sequence is S1, S3, S2; otherwise, the switch sequence is S2, S3, S1. Based on the calculation results, there are six possible switching sequences. Using a five-segment algorithm, the switching sequence of the synthesized reference vector is as follows: The calculated switching sequence is S1, S2, S3, and the switching sequence of the synthetic reference vector is S1→S2→S3→S2→S1, with corresponding action times of t1 / 2→t2 / 2→t3→t2 / 2→t1 / 2. The calculated switching sequence is S1, S3, S2, and the switching sequence of the synthetic reference vector is S1→S3→S2→S3→S1, with corresponding action times of t1 / 2→t3 / 2→t2→t3 / 2→t1 / 2. The calculated switching sequence is S2, S1, S3, and the switching sequence of the synthetic reference vector is S2→S1→S3→S1→S2, with corresponding action times of t2 / 2→t1 / 2→t3→t1 / 2→t2 / 2. The calculated switching sequence is S2, S3, S1, and the switching sequence of the synthetic reference vector is S2→S3→S1→S3→S2, with corresponding action times of t2 / 2→t3 / 2→t1→t3 / 2→t2 / 2. The calculated switching sequence is S3, S1, S2, and the switching sequence of the synthetic reference vector is S3→S1→S2→S1→S3, with corresponding action times of t3 / 2→t1 / 2→t2→t1 / 2→t3 / 2. The calculated switching sequence is S3, S2, S1, and the switching sequence of the synthetic reference vector is S3→S2→S1→S2→S3, with corresponding action times of t3 / 2→t2 / 2→t1→t2 / 2→t3 / 2. Case 2: When (α′ r +β′ r When )-(α′0+β′0)<1, the reference vector V r (α′ r ,β′ r Combined from V0, V1, and V2, calculate the corresponding number of redundant switch states m0, m1, and m2. Based on the known different switch states of the second switching, there are three possible results: When the second switch state is S0, if m1 > m2, the switch switching sequence is S1, S0, S2; otherwise, the switch sequence is S2, S0, S1. When the second switch state is S1, if m0 > m2, the switch switching sequence is S0, S1, S2; otherwise, the switch sequence is S2, S1, S2. Given that the second switch state is S2, if m0 > m1, the switch switching sequence is S0, S2, S1; otherwise, the switch sequence is S1, S2, S0. Based on the calculation results, there are six possible switching sequences. Using a five-segment algorithm, the switching sequence of the synthesized reference vector is as follows: The calculated switching sequence is S0, S1, S2, and the switching sequence of the synthetic reference vector is S0→S1→S2→S1→S0, with corresponding action times of t0 / 2→t1 / 2→t2→t1 / 2→t0 / 2. The calculated switching sequence is S0, S2, S1, and the switching sequence of the synthetic reference vector is S0→S2→S1→S2→S0, with corresponding action times of t0 / 2→t2 / 2→t1→t2 / 2→t0 / 2. The calculated switching sequence is S1, S0, S2, and the switching sequence of the synthetic reference vector is S1→S0→S2→S0→S1, with corresponding action times of t1 / 2→t0 / 2→t2→t0 / 2→t1 / 2. The calculated switching sequence is S1, S2, S0, and the switching sequence of the synthetic reference vector is S1→S2→S0→S2→S1, with corresponding action times of t1 / 2→t2 / 2→t0→t2 / 2→t1 / 2. The calculated switching sequence is S2, S0, S1, and the switching sequence of the synthetic reference vector is S2→S0→S1→S0→S2, with corresponding action times of t2 / 2→t0 / 2→t1→t0 / 2→t2 / 2. The calculated switching sequence is S2, S1, S0, and the switching sequence of the synthetic reference vector is S2→S1→S0→S1→S2, with corresponding action times of t2 / 2→t1 / 2→t0→t12→t2 / 2.

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