WO2021036364A1 - 任意多电平的级联h桥逆变器空间矢量脉宽调制方法 - Google Patents

任意多电平的级联h桥逆变器空间矢量脉宽调制方法 Download PDF

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WO2021036364A1
WO2021036364A1 PCT/CN2020/091726 CN2020091726W WO2021036364A1 WO 2021036364 A1 WO2021036364 A1 WO 2021036364A1 CN 2020091726 W CN2020091726 W CN 2020091726W WO 2021036364 A1 WO2021036364 A1 WO 2021036364A1
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rectangle
vector
reference vector
area
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史婷娜
姚欢
阎彦
张国政
王志强
夏长亮
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Zhejiang University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output
    • H02M7/42—Conversion of DC power input into AC power output without possibility of reversal
    • H02M7/44—Conversion of DC power input into AC power output without possibility of reversal by static converters
    • H02M7/48—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483—Converters with outputs that each can have more than two voltages levels
    • H02M7/4835—Converters with outputs that each can have more than two voltages levels comprising two or more cells, each including a switchable capacitor, the capacitors having a nominal charge voltage which corresponds to a given fraction of the input voltage, and the capacitors being selectively connected in series to determine the instantaneous output voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/0067—Converter structures employing plural converter units, other than for parallel operation of the units on a single load
    • H02M1/007—Plural converter units in cascade
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output
    • H02M7/42—Conversion of DC power input into AC power output without possibility of reversal
    • H02M7/44—Conversion of DC power input into AC power output without possibility of reversal by static converters
    • H02M7/48—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483—Converters with outputs that each can have more than two voltages levels
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output
    • H02M7/42—Conversion of DC power input into AC power output without possibility of reversal
    • H02M7/44—Conversion of DC power input into AC power output without possibility of reversal by static converters
    • H02M7/48—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/5387—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of AC power input into DC power output; Conversion of DC power input into AC power output
    • H02M7/42—Conversion of DC power input into AC power output without possibility of reversal
    • H02M7/44—Conversion of DC power input into AC power output without possibility of reversal by static converters
    • H02M7/48—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/5387—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration
    • H02M7/53871—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration with automatic control of output voltage or current
    • H02M7/53875—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration with automatic control of output voltage or current with analogue control of three-phase output
    • H02M7/53876—Conversion of DC power input into AC power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration with automatic control of output voltage or current with analogue control of three-phase output based on synthesising a desired voltage vector via the selection of appropriate fundamental voltage vectors, and corresponding dwelling times

Definitions

  • the invention relates to a modulation method of a cascaded H-bridge inverter belonging to the field of power electronic circuit control, in particular to an arbitrary multilevel cascaded H-bridge inverter space vector pulse width modulation (SVPWM) method, which is applicable
  • SVPWM space vector pulse width modulation
  • the modulation strategies for inverters mainly include carrier modulation (SPWM), recent level modulation (NVL), specific harmonic elimination modulation (SHE) and space vector modulation (SVPWM).
  • space vector modulation has greater modulation flexibility and freedom, and is easy to implement digitally, so it is an ideal modulation strategy.
  • the determination of the position of the reference vector in the space vector modulation will be very complicated, which in turn brings difficulties to determining the nearest three vector coordinates.
  • the calculation of the duty cycle of the last three vectors will become more complicated. At this time, the modulation method in the traditional two-level or three-level inverter can no longer be used.
  • the first type is based on the abc coordinate system, and this type of modulation strategy is rarely used.
  • the second type is based on a 60-degree coordinate system. Such methods usually require additional coordinate conversion.
  • the third category is based on the ⁇ coordinate system, but the implementation process of the existing methods is often more complicated. Some methods rely on the number of levels when determining the position of the reference vector, and require iterative operations. When the number of levels increases, the amount of calculation will also increase. Other methods require sector judgment and complicated trigonometric function calculations, which increase the computational complexity.
  • the present invention provides a simple, feasible, universally applicable SVPWM modulation method suitable for cascaded H-bridge inverters with any number of levels.
  • the present invention first determines the location of the reference vector, then selects the three closest voltage vectors, that is, the nearest three vector coordinates, and finally calculates the duty cycle of the action time of the three voltage vectors, and then combines the switch state to synthesize the desired reference vector , To achieve space vector pulse width modulation (SVPWM).
  • SVPWM space vector pulse width modulation
  • the voltage vector generated by the cascaded H-bridge inverter draws a multi-level space vector diagram in a rectangular coordinate system ( ⁇ coordinate system), where adjacent voltage vectors are connected to each other to form multiple triangles, one
  • the voltage vectors on the three vertices of the triangle are the nearest three vectors (NTVs), and the reference vector is in the multi-level space vector diagram; it is characterized in that the method further includes the following steps:
  • the distance between adjacent horizontal dividing dashed lines is Unit length; add 8n-1 vertical dividing dashed lines parallel to the vertical axis at equal intervals along the horizontal axis direction ( ⁇ -axis direction), the vertical dividing dashed line is parallel to the ⁇ -axis direction, and a vertical dividing dashed line in the middle Coinciding with the vertical axis ( ⁇ axis), the distance between adjacent vertical dividing dotted lines is 0.5 unit length; where n is the number of cascaded H-bridge units for each phase of the cascaded H-bridge inverter; Unit length refers to the distance from the origin to coordinates (1,0) or coordinates (0,1) in a rectangular coordinate system;
  • each rectangle has two voltage vectors at the corners At the vertex, the connection between the two voltage vectors constitutes a diagonal of the rectangle.
  • the rectangle is divided into two categories according to the difference of the diagonal of the rectangle: the angle between the diagonal and the positive direction of the ⁇ axis is 60 A rectangle with a degree of 4 degrees is regarded as a type A rectangle, and a rectangle with an angle of 120 degrees between the diagonal and the positive direction of the ⁇ axis is regarded as a type B rectangle; finally, according to the boundary of the type A rectangle/the type B rectangle, the reference vector is judged as the type A rectangle or Class B rectangle;
  • the rectangle is further divided according to the diagonal of the rectangle, the area above the diagonal in the rectangle is the type I area, and the area below the diagonal in the rectangle is the type II area, and then it is judged that the reference vector is in the type I area or Type II area; according to the division of Type A/B rectangle and Type I/Type II area, the position of the reference vector is divided into four types: AI, AII, BI and BII; AI, AII, BI and BII represent Type A respectively A type I area in a rectangle, a type II area in a type A rectangle, a type I area in a type B rectangle, and a type II area in a type B rectangle.
  • the calculation of the duty ratio of the most recent three vectors is equivalent to the duty ratio of the additional vector PS in the corresponding triangle, and the duty ratio of the most recent three vector action time when the reference vector is at different positions is obtained based on this.
  • the desired reference vector is synthesized from the switching state of the cascaded H-bridge inverter and the duty ratio of the last three vector action time, and the synthesized reference vector is used to realize SVPWM modulation.
  • step 2) after dividing the multi-level space vector diagram of the rectangular coordinate system into two types of rectangles, determining which type of rectangle the reference vector is in is specifically:
  • V ref ⁇ and V ref ⁇ are the components of the horizontal axis and vertical axis ( ⁇ and ⁇ axis) of the reference vector V ref in the Cartesian coordinate system, respectively;
  • floor( ⁇ ) represents the round-down function;
  • k rec is the rectangle determination coefficient for determining the rectangle in which the reference vector is located; when k rec is equal to 0, the reference vector is in the A-type rectangle; when k rec is equal to 1, the reference vector is in the B-type rectangle.
  • determining that the reference vector is in the type I area or the type II area is specifically:
  • the reference vector V ref is decomposed into the composition of the effective vector OP and the additional vector PS. According to the coordinates of the starting point of the additional vector PS, the additional vector PS is expressed as:
  • v s ⁇ and v s ⁇ are the horizontal axis and vertical axis ( ⁇ and ⁇ axis) components of the additional vector PS in the Cartesian coordinate system, respectively;
  • k reg is the area determination coefficient for determining the area where the reference vector is located; when k reg is greater than 0, the reference vector is in the type I area; when k reg is less than 0, the reference vector is in the type II area; when k reg is equal to 0 ,
  • the reference vector is at the boundary between type I and type II regions, and can be judged as type I region or type II region arbitrarily, and has no effect on the final result.
  • the area where the reference vector is judged is equivalent to the area where the additional vector PS is judged, and then the area where the reference vector is obtained is obtained.
  • the coordinates of the nearest three vectors in the rectangular coordinate system ( ⁇ coordinate system) are obtained according to the position of the reference vector according to the corresponding relationship in the following table:
  • v 1 , v 2, and v 3 represent the most recent three vectors, and specifically represent the first voltage vector, the second voltage vector, and the third voltage vector, respectively.
  • the processing to obtain the duty ratio of the last three vector action time when the reference vector is at different positions is specifically as follows:
  • d 1 , d 2 , and d 3 are the duty ratios of the latest three vectors v 1 , v 2 and v 3 respectively.
  • the SVPWM modulation method of the present invention suitable for cascaded H-bridge inverters at any level number realizes arbitrary multi-level modulation in the ⁇ coordinate system.
  • the nearest three vector coordinates are directly obtained from the reference vector without any iteration Calculation, and the amount of calculation has nothing to do with the number of levels.
  • the present invention only needs to determine the area where the additional vector is located in the rectangle and the duty cycle of the additional vector in the corresponding triangle, thereby simplifying the reference vector positioning and the calculation process of the duty cycle. There is no need for trigonometric function calculation, which reduces the computational complexity.
  • the method of the present invention can be applied to the fields of motor speed regulation, renewable energy power generation and the like.
  • Figure 1 is a topological structure diagram of the cascaded H-bridge inverter
  • Figure 2 is the space vector diagram and rectangular division diagram in the ⁇ coordinate system
  • Figure 3 is a schematic diagram of a reference vector positioning method
  • Figure 4a is the line voltage waveform diagram when there is one H-bridge unit in each phase of the inverter (three-level);
  • Figure 4b is a line voltage waveform diagram when there are 2 H-bridge units per phase of the inverter (five-level);
  • Figure 4c is the line voltage waveform diagram when the inverter has 3 H-bridge units per phase (seven levels);
  • Figure 4d is the line voltage waveform diagram when the inverter has 4 H-bridge units per phase (nine levels).
  • the topology of the cascaded H-bridge inverter is shown in Figure 1. Taking each phase of the cascaded H-bridge inverter with only one H-bridge unit (three-level) as an example, it should be noted that the present invention is applicable to any multi-level. At this time, the three-level space vector diagram formed by the voltage vector is shown in Fig. 2 in the ⁇ coordinate system.
  • the specific implementation is carried out under the three-level inverter output.
  • the voltage vector generated by the cascaded H-bridge inverter constitutes a multi-level space vector diagram, in which adjacent voltage vectors are connected to each other to form multiple triangles, and the voltage vectors on the three vertices of a triangle These are called the nearest three vectors (NTVs).
  • NTVs nearest three vectors
  • n is the number of H-bridge units cascaded for each phase of the cascaded H-bridge inverter; unit length refers to the distance from the origin to the coordinate (1,0) or the coordinate (0,1) in the rectangular coordinate system The distance between
  • the horizontal and vertical dotted lines divide the multi-level space vector diagram into multiple rectangles. On each rectangle, there are two voltage vectors at the vertices of the rectangle. The connection between the two voltage vectors forms a rectangle. A diagonal line. Rectangles are divided into two categories according to their diagonals: a rectangle with an angle of 60 degrees between the diagonal and the positive direction of the ⁇ axis is defined as a type A rectangle, between the diagonal and the positive direction of the ⁇ axis A rectangle with an angle of 120 degrees is defined as a type B rectangle. In Figure 2, the dark color represents the A-type rectangle, and the light color represents the B-type rectangle to distinguish. According to the boundary of the rectangle, the horizontal axis quantization factor q ⁇ and the vertical axis quantization factor q ⁇ are:
  • V ref ⁇ and V ref ⁇ are the horizontal and vertical axis components of the reference vector V ref in the Cartesian coordinate system, respectively;
  • floor( ⁇ ) represents the round-down function;
  • k rec is the rectangle judgment coefficient of the rectangle where the reference vector is judged.
  • the judgment conditions are shown in Table 1. When k rec is equal to 0 or 1, the reference vector is in the A rectangle or the B rectangle, respectively.
  • the rectangle can be further divided into type I area and type II area.
  • the area above the diagonal is the type I area
  • the area below the diagonal is the type II area
  • the type I area and the type II area is combined into an upper triangle and a lower triangle, as shown in Figure 3.
  • the determination of the area can be achieved by the following methods.
  • the reference vector V ref is decomposed into an effective vector OP and an additional vector PS:
  • V ref OP+PS (3)
  • the area where the judgment reference vector is located can be equivalent to the area where the judgment additional vector PS is located.
  • the coordinates of its lower left end point are expressed as In a type A rectangle, as shown in the left picture of Fig. 3, the coordinates are the coordinates of point P; while in a type B rectangle, as shown in the right picture of Fig. 3, the coordinates of point P should be Therefore, according to the coordinates of point P, the additional vector PS can be expressed as:
  • v s ⁇ and v s ⁇ are the horizontal axis and vertical axis ( ⁇ and ⁇ axis) components of the additional vector PS in the Cartesian coordinate system, respectively.
  • k A and k B are the coefficients for judging the type I area and the type II area in the type A rectangle and the type B rectangle, respectively.
  • k A and k B are greater than 0 or less than 0, the reference vector is in the type I region or the type II region, respectively.
  • Equations (5) and (6) can be further integrated to calculate the regional determination coefficient:
  • k reg is the area determination coefficient of the area where the reference vector is determined.
  • the judgment conditions are as shown in Table 1.
  • k reg is equal to 0
  • the reference vector is at the boundary between the type I area and the type II area, and it is arbitrarily judged as the type I area or the type II area, which has no effect on the final result.
  • the position of any point in the space of the reference vector can be located in the A/B rectangle and I/II area by formulas (2) and (7) in.
  • the position of the reference vector has four categories: AI, AII, BI and BII.
  • the coordinates of point P can be expressed as I.e., v coordinates of endpoints 3.
  • the coordinates of the endpoints of v 1 and v 2 can be obtained according to the position relationship of the nearest three vectors, and the nearest three vectors of the other positions can be obtained in the same way.
  • the coordinates of the latest three vectors in the ⁇ coordinate system are shown in Table 2.
  • the switching state of the cascaded H-bridge inverter After obtaining the latest three vector coordinates, by selecting the zero-sequence component and performing coordinate transformation, the switching state of the cascaded H-bridge inverter can be obtained.
  • V ref d 1 OQ+d 2 OR+(1-d 1 -d 2 )OP (8)
  • equation (8) can be expressed as:
  • d 1 , d 2 , and d 3 are the duty ratios of v 1 , v 2 and v 3 respectively.
  • Embodiment In order to verify the feasibility of the proposed SVPWM algorithm, simulation verification is performed on the Matlab/Simulink platform.
  • the sampling frequency is 2.5kHz
  • the resistive load impedance is 10 ⁇ .
  • the modulation degree is 0.9
  • the simulated waveforms of the line voltage V AB under different numbers of H-bridge units are shown in Fig. 4.
  • the output level of the cascaded H-bridge inverter also rises from three-level to nine-level, and each H-bridge unit
  • the required DC voltage has also dropped to 200V, 100V, 66V and 50V.
  • the method of the present invention is suitable for any level and any modulation degree, and has good effects even when the number of levels is large, and has good universality.

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Abstract

一种任意多电平的级联H桥逆变器空间矢量脉宽调制方法。将多电平空间矢量图进行重新划分，并通过判断参考矢量所处位置直接得到最近三矢量的坐标，将参考矢量等效为附加矢量计算得到最近三矢量的占空比；并且通过零序分量和坐标变换得到开关状态，合成所期望的参考矢量，进行SVPWM调制。实现了在直角坐标系下的任意多电平调制，不需任何迭代计算，且计算量与电平数无关；简化了参考矢量定位以及占空比的计算过程，降低了计算复杂度。

Description

任意多电平的级联H桥逆变器空间矢量脉宽调制方法 技术领域
本发明涉及属于电力电子电路控制领域的一种级联H桥逆变器的调制方法，尤其是一种任意多电平的级联H桥逆变器空间矢量脉宽调制(SVPWM)方法，适用于级联H桥逆变器在电机调速、可再生能源发电等领域。
背景技术
随着电力电子技术在中高压、大功率场合的不断发展，传统两电平逆变器已难以适用。因此多电平逆变器在中、大功率电能变换领域得到了越来越广泛的关注与研究。其中，级联H桥逆变器具有模块化的特点，所需功率器件少，不存在直流侧电容均压的问题，而且非常易于电平数的扩展，这些优势使得该逆变器在工业场合广泛应用。针对逆变器的调制策略主要有载波调制(SPWM)，最近电平调制(NVL)，特定谐波消除调制(SHE)和空间矢量调制(SVPWM)。其中空间矢量调制具有更大的调制灵活性和自由度，且易于数字化实现，因而是一种理想的调制策略。但是，随着电平数的增加，空间矢量调制中对于参考矢量位置的判定会非常复杂，进而对确定最近三矢量坐标带来困难。此外，对最近三矢量的占空比计算也会愈发繁复。此时，传统两电平或三电平逆变器中的调制方法已无法使用。
现有多电平逆变器的调制方法根据坐标系的不同主要有三类。第一类基于abc坐标系，这类调制策略应用较少。第二类基于60度坐标系，此类方法通常需要额外的坐标转换。第三类则基于αβ坐标系，但现有方法的实现过程往往较为复杂。一些方法在判定参考矢量位置时依赖于电平数，需要进行迭代运算，当电平数增加时，计算量也会随之增加。另一些方法则需要扇区判断以及复杂的三角函数运算，从而增加了计算复杂度。
发明内容
为了解决背景技术中存在的技术问题，本发明提供了一种简单可行、普适性好的适用于任意电平数下级联H桥逆变器的SVPWM调制方法。本发明首先判定参考矢量所在位置，然后选择出距离它最近的三个电压矢量，即最近三矢量坐标，最后计算三个电压矢量作用时间的占空比，进而结合开关状态合成所期望的参考矢量，实现空间矢量脉宽调制(SVPWM)。
本发明所采用的技术方案是：
1)由级联H桥逆变器所生成的电压矢量绘制直角坐标系(αβ坐标系)下的多电平空间矢量图，其中相邻电压矢量之间相互连线构成了多个三角形，一个三角形的三个顶点上的电压矢量为最近三矢量(NTVs)，参考矢量处于多电平空间矢量图中；其特征在于，方法还包括如下步骤：
2)将直角坐标系(如图2的αβ坐标系)的多电平空间矢量图进行划分两类矩形，并判断参考矢量处于哪类矩形中：
沿竖直轴方向(β轴方向)等间隔添加4n+1条平行于水平轴方向的水平分割虚线，水平分割虚线平行于α轴方向，且中间的一条水平分割虚线与水平轴(α轴)重合，相邻水平分割虚线之间间距为
Figure PCTCN2020091726-appb-000001
个单位长度；沿水平轴方向(α轴方向)等间隔添加8n-1条平行于竖直轴方向的竖直分割虚线，竖直分割虚线平行于β轴方向，且中间的一条竖直分割虚线与竖直轴(β轴)重合，相邻竖直分割虚线之间间距为0.5个单位长度；其中，n为级联H桥逆变器每一相所级联的H桥单元的个数；单位长度是指直角坐标系中从原点到坐标(1,0)或坐标(0,1)之间的距离；
通过水平分割虚线与竖直分割虚线把多电平空间矢量图划分多个矩形(将位于边缘的直角三角形也补充看作是一个矩形。)，在每个矩形上均有两个电压矢量位于角顶点，该两个电压矢量之间的连线构成了矩形的一条对角线，根据矩形对角线的不同将矩形分为两类：对角线与α轴正向方向之间夹角为60度的矩形作为A类矩形，对角线与α轴正向方向之间夹角为120度的矩形作为B类矩形；最后根据A类矩形/B类矩形的边界判断参考矢量处于A类矩形或B类矩形中；
3)根据矩形的对角线将矩形进一步划分，将矩形中对角线上方的区域为I型区域，将矩形中对角线下方的区域为II型区域，然后判断参考矢量处于I型区域或II型区域；再根据A类/B类矩形和I型/II型区域的划分，参考矢量所处的位置有AI、AII、BI和BII四类；AI、AII、BI和BII分别表示A类矩形中的I型区域、A类矩形中的II型区域、B类矩形中的I型区域、B类矩形中的II型区域。
4)根据参考矢量所处的位置得到最近三矢量在直角坐标系(αβ坐标系)下的坐标，之后通过选择零序分量并进行坐标变换得到级联H桥逆变器的开关状态；
5)将参考矢量分解为有效矢量OP和附加矢量PS，处理获得参考矢量在不同位置时最近三矢量作用时间的占空比；
本发明将最近三矢量占空比的求解等效于求解附加矢量PS在对应三角形中 的占空比，据此求得参考矢量在不同位置时最近三矢量作用时间的占空比。
6)由级联H桥逆变器的开关状态和最近三矢量作用时间的占空比合成所期望的参考矢量，利用合成的参考矢量实现SVPWM调制。
所述步骤2)中，在将直角坐标系的多电平空间矢量图进行划分两类矩形后，判断参考矢量处于哪类矩形中具体为：
首先采用以下公式计算水平轴量化因子q α和竖直轴量化因子q β分别为：
Figure PCTCN2020091726-appb-000002
式中，V refα和V refβ分别为参考矢量V ref在直角坐标系的水平轴和竖直轴(α和β轴)分量；floor(·)表示向下取整函数；
接着通过以下公式判断获得参考矢量所处于的A类矩形还是B类矩形：
Figure PCTCN2020091726-appb-000003
式中，k rec为判定参考矢量所处矩形的矩形判定系数；当k rec等于0时，参考矢量处于A类矩形中；当k rec等于1时，参考矢量处于B类矩形中。
所述步骤3)中，判断参考矢量处于I型区域或II型区域具体为：
参考矢量V ref分解为有效矢量OP和附加矢量PS的合成，根据附加矢量PS起始点的坐标，附加矢量PS表示为：
Figure PCTCN2020091726-appb-000004
式中，v sα、v sβ分别为附加矢量PS在直角坐标系的水平轴和竖直轴(α和β轴)分量；
接着通过以下公式判断获得参考矢量所处于矩形中的I型区域还是II型区域：
Figure PCTCN2020091726-appb-000005
式中，k reg为判定参考矢量所处区域的区域判定系数；当k reg大于0时，参考矢量处于I型区域；当k reg小于0时，参考矢量处于II型区域；k reg等于0时，参考矢量处于I型和II型区域的边界，可任意判定为I型区域或II型区域，对最后结果没有影响。
本发明在任一矩形中，判断参考矢量所处的区域等效为判断附加矢量PS所处的区域，进而获得参考矢量所处的区域。
所述步骤4)中，按照如下表的对应关系，根据参考矢量所处的位置获得最近三矢量在直角坐标系(αβ坐标系)下的坐标：
Figure PCTCN2020091726-appb-000006
其中，v 1、v 2和v 3表示最近三矢量，具体分别表示第一电压矢量、第二电压矢量、第三电压矢量。
所述步骤5)中，处理获得参考矢量在不同位置时最近三矢量作用时间的占空比，具体为：
当参考矢量位于AI区域或BI区域的位置时，采用以下公式获得最近三矢量的占空比：
Figure PCTCN2020091726-appb-000007
当参考矢量位于AII区域或BII区域的位置时，采用以下公式获得最近三矢量的占空比：
Figure PCTCN2020091726-appb-000008
式中，d 1、d 2、d 3分别为最近三矢量v 1、v 2和v 3的占空比。
本发明的有益效果是：
本发明的适用于任意电平数下级联H桥逆变器的SVPWM调制方法，实现了在αβ坐标系下的任意多电平调制，最近三矢量坐标由参考矢量直接获得，不需任何迭代计算，且计算量与电平数无关。
本发明通过将参考矢量等效为附加矢量，只需判断附加矢量在矩形中所处的区域以及附加矢量在相应三角形中的占空比，从而简化了参考矢量定位以及占空比的计算过程，不需要三角函数计算，降低了计算复杂度。
本发明的方法可应用于电机调速、可再生能源发电等领域。
附图说明
图1是级联H桥逆变器的拓扑结构图；
图2是αβ坐标系下的空间矢量图以及矩形划分图；
图3是参考矢量定位方法示意图；
图4a是当逆变器每一相有1个H桥单元时(三电平)的线电压波形图；
图4b是当逆变器每一相有2个H桥单元时(五电平)的线电压波形图；
图4c是当逆变器每一相有3个H桥单元时(七电平)的线电压波形图；
图4d是当逆变器每一相有4个H桥单元时(九电平)的线电压波形图。
具体实施方式
下面结合实例和附图对本发明的适用于任意电平数下级联H桥的SVPWM调制方法做出详细说明。
级联H桥逆变器的拓扑结构如图1所示。以级联H桥逆变器每一相仅有1个H桥单元(三电平)为例进行说明，需要说明的是本发明适用于任意多电平。此时由电压矢量构成的三电平空间矢量图在αβ坐标系下如图2所示。
本发明的实施例的SVPWM调制过程，包括如下步骤：
具体实施是在逆变器输出三电平下实施进行。
1)级联H桥逆变器所生成的电压矢量构成了多电平空间矢量图，其中相邻电压矢量之间相互连线，构成了多个三角形，一个三角形的三个顶点上的电压矢量被称作最近三矢量(NTVs)。将直角坐标系(αβ坐标系)形式下的三电平空间矢量图按照图2中虚线所示进行划分：
沿竖直轴方向(β轴方向)等间隔添加4n+1条平行于水平轴方向的水平分割虚线，水平分割虚线平行于α轴方向，且中间的一条水平分割虚线与水平轴(α轴)重合，相邻水平分割虚线之间间距为
Figure PCTCN2020091726-appb-000009
个单位长度；沿水平轴方向(α轴方向)等间隔添加8n-1条平行于竖直轴方向的竖直分割虚线，竖直分割 虚线平行于β轴方向，且中间的一条竖直分割虚线与竖直轴(β轴)重合，相邻竖直分割虚线之间间距为0.5个单位长度。
其中，n为级联H桥逆变器每一相所级联的H桥单元的个数；单位长度是指直角坐标系中从原点到坐标(1,0)或坐标(0,1)之间的距离；
水平分割虚线与竖直分割虚线把多电平空间矢量图划分为多个矩形，在每个矩形上都有两个电压矢量位于矩形顶点，这两个电压矢量之间的连线构成了矩形的一条对角线。根据矩形的对角线的不同将矩形分为两类：对角线与α轴正向方向之间夹角为60度的矩形定义为A类矩形，对角线与α轴正向方向之间夹角为120度的矩形定义为B类矩形。在图2中以深色代表A类矩形，浅色代表B类矩形，以示区分。根据矩形的边界，分别为水平轴量化因子q α和竖直轴量化因子q β分别为：
Figure PCTCN2020091726-appb-000010
式中，V refα和V refβ分别为参考矢量V ref在直角坐标系的水平轴和竖直轴分量；floor(·)表示向下取整函数；
接着通过以下公式的矩形判定系数判断获得参考矢量所处于的A类矩形还是B类矩形：
Figure PCTCN2020091726-appb-000011
式中，k rec为判定参考矢量所处矩形的矩形判定系数。判定条件如表1所示，当k rec等于0或1时，参考矢量分别处于A类矩形或B类矩形中。
表1
Figure PCTCN2020091726-appb-000012
2)根据矩形的对角线可将矩形进一步划分为I型区域和II型区域，对角线上方的区域为I型区域，对角线下方的区域为II型区域，且I型区域和II型区域分别组合成了上三角形与下三角形，如图3所示。对区域的判定可以通过下述方法实现。
在两类矩形中，将参考矢量V ref分解为有效矢量OP和附加矢量PS：
V ref＝OP+PS    (3)
因此，由图3可知，在任一矩形中，判断参考矢量所处的区域可以等效为判断附加矢量PS所处的区域。并且在任一矩形中，其左下角端点的坐标表示为
Figure PCTCN2020091726-appb-000013
在A类矩形中，如图3左图所示，该坐标即为P点坐标；而在B类矩形中，如图3右图所示，P点坐标应为
Figure PCTCN2020091726-appb-000014
因此，根据P点坐标，附加矢量PS可表示为：
Figure PCTCN2020091726-appb-000015
式中，v sα、v sβ分别为附加矢量PS在直角坐标系的水平轴和竖直轴(α和β轴)分量。
对于A类矩形和B类矩形，分别计算系数：
Figure PCTCN2020091726-appb-000016
Figure PCTCN2020091726-appb-000017
式中，k A、k B分别是A类矩形和B类矩形中判断I型区域和II型区域的系数。当k A、k B大于0或小于0时，参考矢量分别处于I型区域或II型区域。
式(5)和式(6)可进一步整合计算区域判定系数：
Figure PCTCN2020091726-appb-000018
式中，k reg为判定参考矢量所处区域的区域判定系数。判定条件如表1所示，k reg等于0时，参考矢量处于I型区域和II型区域的边界，任意判定为I型区域或II型区域，对最后结果没有影响。
通过将多电平空间矢量图进行矩形划分，并根据上述位置判定方法，参考矢量在空间上任一点的位置都可以通过式(2)与式(7)定位在A/B矩形和I/II区域中。根据上述划分，参考矢量所处的位置有AI、AII、BI和BII四类。
3)以参考矢量处于AI位置为例，如图3左图所示，P点的坐标可表示为
Figure PCTCN2020091726-appb-000019
Figure PCTCN2020091726-appb-000020
即v 3的端点坐标。此时，根据最近三矢量位置关系就可求出v 1和v 2的端点坐标，其余位置的最近三矢量同理可求得。据此得到最近三矢量在αβ坐标系下的坐标如表2所示。
表2
Figure PCTCN2020091726-appb-000021
Figure PCTCN2020091726-appb-000022
在得到了最近三矢量坐标之后，通过选择零序分量并进行坐标变换，就可得到级联H桥逆变器的开关状态。
以上所有计算过程无迭代算法，因此计算量与电平数或调制度无关。
4)根据伏秒平衡原则，在图3中的参考矢量V ref可表示为
V ref＝d 1OQ+d 2OR+(1-d 1-d 2)OP    (8)
式中，d 1为矢量OQ对应的占空比；d 2为矢量OR对应的占空比。
由图3中矢量位置的关系，式(8)可表示为：
Figure PCTCN2020091726-appb-000023
由式(3)和式(9)得到最近三矢量占空比与附加矢量在相应三角形中占空比的等效性，进而求解附加矢量PS在相应三角形中的占空比。因此，参考矢量位于AI区域或BI区域位置时，最近三矢量占空比可表示为：
Figure PCTCN2020091726-appb-000024
式中，d 1、d 2、d 3分别为v 1、v 2和v 3的占空比。
同理，参考矢量位于AII区域或BII区域位置时，最近三矢量占空比表示为：
Figure PCTCN2020091726-appb-000025
以上所有计算只涉及代数运算，而没有复杂的三角函数运算与扇区判断， 从而极大地减少了运算量。
实施例为了验证所提SVPWM算法的可行性，在Matlab/Simulink平台上进行仿真验证。仿真中，采样频率为2.5kHz，阻感负载阻抗为10Ω。调制度为0.9时，不同H桥单元个数下的线电压V AB仿真波形如图4所示。当级联H桥逆变器每一相级联1到4个H桥单元时，级联H桥逆变器的输出电平也从三电平上升到九电平，并且每个H桥单元所需直流电压也有所下降，分别为200V、100V、66V以及50V。本发明中的方法适用于任意电平、任意调制度，即使电平数很多时依然具有良好的效果，具有很好的普适性。

Claims (5)

  1. 一种任意多电平的级联H桥逆变器空间矢量脉宽调制方法，方法包括：
    1)由级联H桥逆变器所生成的电压矢量绘制直角坐标系下的多电平空间矢量图，其中相邻电压矢量之间相互连线构成了多个三角形，参考矢量处于多电平空间矢量图中；其特征在于，方法还包括如下步骤：
    2)将直角坐标系的多电平空间矢量图进行划分两类矩形，并判断参考矢量处于哪类矩形中：
    沿竖直轴方向等间隔添加4n+1条平行于水平轴方向的水平分割虚线，水平分割虚线平行于α轴方向，且中间的一条水平分割虚线与水平轴重合，相邻水平分割虚线之间间距为
    Figure PCTCN2020091726-appb-100001
    个单位长度；沿水平轴方向等间隔添加8n-1条平行于竖直轴方向的竖直分割虚线，竖直分割虚线平行于β轴方向，且中间的一条竖直分割虚线与竖直轴重合，相邻竖直分割虚线之间间距为0.5个单位长度；其中，n为级联H桥逆变器每一相所级联的H桥单元的个数；单位长度是指直角坐标系中从原点到坐标(1,0)或坐标(0,1)之间的距离；
    通过水平分割虚线与竖直分割虚线把多电平空间矢量图划分多个矩形，在每个矩形上均有两个电压矢量位于角顶点，该两个电压矢量之间的连线构成了矩形的一条对角线，根据矩形对角线的不同将矩形分为两类：对角线与α轴正向方向之间夹角为60度的矩形作为A类矩形，对角线与α轴正向方向之间夹角为120度的矩形作为B类矩形；最后根据A类矩形/B类矩形的边界判断参考矢量处于A类矩形或B类矩形中；
    3)根据矩形的对角线将矩形进一步划分，将矩形中对角线上方的区域为I型区域，将矩形中对角线下方的区域为II型区域，然后判断参考矢量处于I型区域或II型区域；再根据A类/B类矩形和I型/II型区域的划分，参考矢量所处的位置有AI、AII、BI和BII四类；
    4)根据参考矢量所处的位置得到最近三矢量在直角坐标系下的坐标，之后通过选择零序分量并进行坐标变换得到级联H桥逆变器的开关状态；
    5)将参考矢量分解为有效矢量OP和附加矢量PS，处理获得参考矢量在不同位置时最近三矢量作用时间的占空比；
    6)由级联H桥逆变器的开关状态和最近三矢量作用时间的占空比合成所期望的参考矢量，利用合成的参考矢量实现SVPWM调制。
  2. 根据权利要求1所述的任意多电平的级联H桥逆变器空间矢量脉宽调制方法，其特征在于：所述步骤2)中，在将直角坐标系的多电平空间矢量图进 行划分两类矩形后，判断参考矢量处于哪类矩形中具体为：
    首先采用以下公式计算水平轴量化因子q α和竖直轴量化因子q β分别为：
    Figure PCTCN2020091726-appb-100002
    式中，V refα和V refβ分别为参考矢量V ref在直角坐标系的水平轴和竖直轴分量；floor(·)表示向下取整函数；
    接着通过以下公式判断获得参考矢量所处于的A类矩形还是B类矩形：
    Figure PCTCN2020091726-appb-100003
    式中，k rec为判定参考矢量所处矩形的矩形判定系数；当k rec等于0时，参考矢量处于A类矩形中；当k rec等于1时，参考矢量处于B类矩形中。
  3. 根据权利要求1所述的任意多电平的级联H桥逆变器空间矢量脉宽调制方法，其特征在于：所述步骤3)中，判断参考矢量处于I型区域或II型区域具体为：
    参考矢量V ref分解为有效矢量OP和附加矢量PS的合成，附加矢量PS表示为：
    Figure PCTCN2020091726-appb-100004
    式中，v sα、v sβ分别为附加矢量PS在直角坐标系的水平轴和竖直轴分量；
    接着通过以下公式判断获得参考矢量所处于矩形中的I型区域还是II型区域：
    Figure PCTCN2020091726-appb-100005
    式中，k reg为判定参考矢量所处区域的区域判定系数；当k reg大于0时，参考矢量处于I型区域；当k reg小于0时，参考矢量处于II型区域；k reg等于0时，参考矢量处于I型和II型区域的边界，可任意判定为I型区域或II型区域。
  4. 根据权利要求1所述的任意多电平的级联H桥逆变器空间矢量脉宽调制方法，其特征在于：所述步骤4)中，按照如下表的对应关系，根据参考矢量所处的位置获得最近三矢量在直角坐标系下的坐标：
    Figure PCTCN2020091726-appb-100006
    其中，v 1、v 2和v 3表示最近三矢量。
  5. 根据权利要求1所述的任意多电平的级联H桥逆变器空间矢量脉宽调制方法，其特征在于：所述步骤5)中，处理获得参考矢量在不同位置时最近三矢量作用时间的占空比，具体为：
    当参考矢量位于AI区域或BI区域的位置时，采用以下公式获得最近三矢量的占空比：
    Figure PCTCN2020091726-appb-100007
    当参考矢量位于AII区域或BII区域的位置时，采用以下公式获得最近三矢量的占空比：
    Figure PCTCN2020091726-appb-100008
    式中，d 1、d 2、d 3分别为最近三矢量v 1、v 2和v 3的占空比。
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