WO2014135006A1 - 一种模块化多电平变换器的调制策略 - Google Patents

一种模块化多电平变换器的调制策略 Download PDF

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WO2014135006A1
WO2014135006A1 PCT/CN2014/072229 CN2014072229W WO2014135006A1 WO 2014135006 A1 WO2014135006 A1 WO 2014135006A1 CN 2014072229 W CN2014072229 W CN 2014072229W WO 2014135006 A1 WO2014135006 A1 WO 2014135006A1
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pwm
sub
module
arm
voltage
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PCT/CN2014/072229
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English (en)
French (fr)
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伍小杰
公铮
戴鹏
梁改革
耿乙文
郭全军
周娟
方蒽
赵霞
戴华夏
宗晓
刘广胜
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中国矿业大学
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Priority to US14/409,231 priority Critical patent/US9787219B2/en
Priority to AU2014225133A priority patent/AU2014225133B2/en
Publication of WO2014135006A1 publication Critical patent/WO2014135006A1/zh
Priority to ZA2014/08361A priority patent/ZA201408361B/en

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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
    • 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
    • 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
    • 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
    • H02M7/539—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 with automatic control of output wave form or frequency
    • H02M7/5395—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 with automatic control of output wave form or frequency by pulse-width modulation

Definitions

  • the present invention relates to modulation techniques in the field of multilevel power electronic converters, and in particular to carrier pulse width modulation strategies for modular multilevel converters. Background technique
  • the modular multi-level converter is a new type of voltage source converter with a strict modular design structure, which reduces the production cost in mass production; the series and sub-module, the voltage level and power level of the converter Easy to expand;
  • the multi-level output form of the converter reduces the harmonic content and total distortion of the output voltage, thereby reducing or even eliminating large-capacity AC filters; each bridge arm sub-module does not need to be turned on at the same time, reducing The rate of change of the voltage and current of the bridge arm greatly reduces the stress on the switching device.
  • the protection circuit of the modular multilevel converter is simple and easy to implement.
  • the modulation strategies of multilevel power electronic converters mainly include carrier pulse width modulation strategy and space vector pulse width modulation (SVPWM) strategy. Since the SVPWM strategy increases the number of output levels, the calculation becomes very complicated and the redundancy vector selection is difficult, and it is less used for converters above three levels.
  • the carrier pulse width modulation strategy is widely used.
  • the carrier pulse width modulation strategy for modular multilevel converters mostly adopts carrier phase shifting technology. When the carrier phase shift pulse width modulation strategy is adopted, each of the upper and lower arms of each phase needs one modulated wave and N successive phase shifted carriers, which greatly reduces the harmonic content of the output voltage without increasing the switching frequency, and is easy to module. The implementation is achieved, and the workload of the switching device is balanced.
  • the carrier phase-shifting pulse width modulation strategy increases the workload of the control system.
  • the modulation strategy needs to generate a large number of carriers, which requires high software and hardware resources of the system.
  • the modular multilevel converter modulation strategy of the present invention and the carrier phase shift pulse width modulation strategy achieve the same output power quality, and do not need to perform phase shift control on the carrier, and only need one modulated wave and N carriers per phase,
  • the number of modulated waves and carriers is reduced by half, and there is no need to design a sub-module capacitor voltage equalization closed-loop control algorithm, which greatly saves the system's hardware and software resources, facilitates engineering implementation, and is more suitable for modular multilevel converters with more levels.
  • the object of the present invention is to improve the existing carrier modulation strategy for the novel topology of the modular multilevel converter, and to reduce the requirements on the system hardware and software resources while ensuring the output power quality of the converter.
  • Each phase of the modular multilevel converter of the present invention is comprised of an upper arm, a lower arm and a reactor.
  • the modulation strategy of the modular multilevel converter of the present invention generates PWM pulses of the upper arm and the lower arm according to the carrier layer stack modulation method, and sorts the capacitor voltages of the sub-modules in the bridge arm, and combines the current direction of the bridge arms for each sub-child
  • the module assigns a PWM pulse to determine the operating status of the submodule.
  • the modulation strategy of a modular multilevel converter of the present invention has the advantages of: only one modulated wave and N carriers per phase (N is a modular multilevel converter
  • N is a modular multilevel converter
  • the number of sub-modules of the upper or lower arm of the phase) can make the phase voltage of the modular multilevel converter output N+1 without carrier phase shifting.
  • the control algorithm has high precision, easy to implement, save software. And hardware resources; can ensure that the number of sub-modules input per phase at any time is N, the sub-module capacitor voltage can realize voltage equalization control without closed-loop control strategy; at the same time, it is convenient for the voltage and power level of the modular multi-level converter Adjustment, not limited by the number of levels.
  • Figure 1 is the main circuit topology of a modular multilevel converter
  • Figure 2 is a sub-module circuit topology of a modular multilevel converter
  • 3 is a schematic diagram of carrier layer modulation modulation.
  • a modulation strategy for a modular multilevel converter characterized in that: based on a carrier stacking method, combining the current direction of each bridge arm and the sub-module capacitor voltage sequence, the switching state of each sub-module is determined.
  • Figure 1 is a main circuit topology of a modular multilevel converter, each phase consisting of an upper arm, a lower arm and a series reactor, the upper arm comprising N submodules (SM ⁇ -SM ⁇ ), the lower arm includes N submodules (SM dl -SMdN).
  • the circuit structure of all submodules is the same, as shown in Figure 2.
  • the modular multilevel converter is composed of 2N internal circuit identical submodules, and the submodule circuit structure is shown in FIG. 2.
  • VT1 and VT2 represent high-power controllable power electronic switches such as insulated gate bipolar transistors (IGBT) and integrated gate commutated thyristors (IGCT); Dl and D2 represent anti-parallel diodes of VT1 and VT2 respectively; C represents DC capacitors.
  • the voltage is ⁇ , each sub-module is a half-bridge structure, and the power switches VT1 and VT2 are connected in series and connected in parallel with the DC capacitor C.
  • a and B are the input and output ends of the sub-module. As shown in FIG.
  • the upper arm and the lower arm are each connected in series by N sub-modules, that is, the output B of the previous sub-module is connected to the input A of the next sub-module.
  • the input end A of the uppermost sub-module SM ul of the upper arm is connected to the positive pole of the DC power supply, and the output end B of the lower sub-module SM dN of the lower arm is connected to the negative pole of the DC power supply.
  • the submodules of the modular multilevel converter contain separate control units.
  • each sub-module requires only one trigger pulse.
  • the trigger pulse is inverted to obtain a complementary trigger pulse, and the dead zone is set as the trigger signal of VT1 and VT2 in the sub-module.
  • the modulation strategy of the present invention can be implemented in the following four steps:
  • the capacitor voltages of the upper arm and the lower arm submodule measured in step (2) are respectively sorted from small to large, and the sorting result remains unchanged during a voltage equalization control period.
  • the sub-module serial number corresponding to the capacitor voltage sequence of the upper arm sub-module is placed in the array t u [i]
  • the sub-module serial number corresponding to the capacitor voltage sequence of the lower-arm sub-module is placed in the array t d [i].
  • the PWM pulses are assigned to the sub-modules of the upper arm and the lower arm according to the sub-module capacitor voltage sequencing result and the bridge arm current direction.
  • the N-way PWM pulse obtained in step (1) is PWM ⁇ PWM 2 , . .., PWMJ times assigned to submodule SM(t u [l]), SM(t u [2]), ..., SM(t u [N]) ; if upper arm current au ⁇ 0, current Discharge the capacitor in the input state sub-module, reduce the capacitor voltage, and assign the N-channel PWM pulses PWM l 7 PWM 2 , ..., PWM N obtained in step (1) to the sub-module SM(t u [N]). SM(t u [Nl]), ..., SM(t u [l]).
  • the lower arm For the lower arm, if the lower arm current du > 0, the current is charged in the capacitor of the input state sub-module, the capacitor voltage rises, and the N-way PWM pulse PWM, PWM 2 ' obtained in step (1), ..., PWM N ' is assigned to submodule SM(t d [N]), SM(t d [Nl]), ..., SM(t d [l]) in sequence ; if the lower arm current is du ⁇ 0, the current is discharged in the capacitor of the input state sub-module, the capacitor voltage is lowered, and the N-way PWM pulses PWM, PWM 2 ', ..., PWM N ' obtained in step (1) are sequentially assigned to the sub-module SM (t d [ l]), SM(t d [2]), ..., SM(t d [N]).

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Inverter Devices (AREA)

Abstract

一种模块化多电平变换器的调制策略，基于载波层叠方法，结合各桥臂电流方向和子模块电容电压顺序，确定各子模块的投切状态。该调制策略的有益效果是：每相仅需要一个调制波和N个载波，N为模块化多电平变换器各相上桥臂或下桥臂的子模块个数，无需载波移相即可使模块化多电平变换器输出N+1个电平，控制算法精确度高，易于工程实现，节省软件和硬件资源；可以保证任意时刻每相投入的子模块个数为N，子模块电容电压无需闭环控制策略即可实现电压均衡控制；同时，便于对模块化多电平变换器电压和功率等级的调整，不受电平数量的限制。

Description

一种模块化多电平变换器的调制策略 技术领域
本发明涉及多电平电力电子变换器领域的调制技术， 具体涉及模块化多电平变换器 的载波脉宽调制策略。 背景技术
在高压大功率领域，多电平电力电子变换器以其独特的优势得到越来越广泛的应用。 模块化多电平变换器是一种新型电压源型变换器， 其采用严格的模块化设计结构， 在大 规模生产时降低了生产成本； 通过子模块的串联， 变换器的电压等级和功率等级易于扩 展； 变换器多电平的输出形式降低了输出电压的谐波含量和总畸变率， 从而可以减小甚 至省去大容量的交流滤波器； 各桥臂子模块不需同时开通， 降低了桥臂电压、 电流的变 化率， 使得开关器件承受的应力大大降低； 同时， 模块化多电平变换器保护电路简单， 易于实现。
多电平电力电子变换器的调制策略主要有载波脉宽调制策略和空间矢量脉宽调制 (SVPWM)策略等。 由于 SVPWM策略在输出电平数增加时， 计算变得非常复杂且冗余矢 量选择较为困难， 较少用于三电平以上的变换器。 载波脉宽调制策略的应用较为广泛， 目前用于模块化多电平变换器的载波脉宽调制策略大都采用了载波移相技术。 采用载波 移相脉宽调制策略时， 每相上、 下桥臂各需要一个调制波和 N个依次移相的载波， 在不 提高开关频率的前提下大大降低输出电压的谐波含量， 易于模块化实现， 并且使得开关 器件的工作负荷均衡一致。 但是， 由于每个移相所得的载波都需要单独生成并且要求彼 此进行同步， 采用载波移相脉宽调制策略时会增加控制系统的工作负荷。 特别是当变换 器电平数较高， 子模块数量较多时， 采用该调制策略需要生成大量载波， 对系统的软硬 件资源要求较高。 本发明模块化多电平变换器调制策略与载波移相脉宽调制策略取得相 同输出电能质量的同时， 不需要对载波进行移相控制， 并且每相仅需要一个调制波和 N 个载波， 将调制波和载波数量减少一半， 也无需设计子模块电容电压均衡闭环控制算法， 大幅度节省系统的软硬件资源， 便于工程实现， 更适用于电平数较多的模块化多电平变 换器。 发明内容
本发明的目的是针对模块化多电平变换器这种新型拓扑结构， 对现有的载波调制策 略进行改进， 在保证变换器输出电能质量的前提下降低对系统软硬件资源的要求。
本发明所述模块化多电平变换器的每相由上桥臂、 下桥臂和电抗器构成。 本发明模 块化多电平变换器的调制策略根据载波层叠调制方法生成上桥臂和下桥臂的 PWM脉冲， 通过对桥臂中子模块电容电压进行排序， 结合桥臂电流方向， 为各个子模块分配 PWM 脉冲， 确定子模块的工作状态。 与已有的技术相比， 本发明一种模块化多电平变换器的调制策略所具有的优点是： 每相仅需要一个调制波和 N个载波 （N为模块化多电平变换器各相上桥臂或下桥臂的子 模块个数）， 无需载波移相即可使模块化多电平变换器输出相电压为 N+1 电平， 控制算 法精确度高， 易于工程实现， 节省软件和硬件资源； 可以保证任意时刻每相投入的子模 块个数为 N， 子模块电容电压无需闭环控制策略即可实现电压均衡控制； 同时， 便于对 模块化多电平变换器电压和功率等级的调整， 不受电平数量的限制。 附图说明
图 1是模块化多电平变换器的主电路拓扑
图 2是模块化多电平变换器的子模块电路拓扑
图 3是载波层叠调制原理图 具体实施方式
一种模块化多电平变换器的调制策略， 其特征是： 基于载波层叠方法， 结合各桥臂 电流方向和子模块电容电压顺序， 确定各子模块的投切状态。
下面结合附图对本发明作进一步的描述- 图 1为模块化多电平变换器的主电路拓扑，各相由上桥臂、下桥臂和串联的电抗器 构成， 上桥臂包括 N个子模块 （SM^-SM^), 下桥臂包括 N个子模块 （SMdl-SMdN)。 所有子模块的电路结构均相同， 如图 2所示。
所述模块化多电平变换器每相由 2N个内部电路相同的子模块构成，子模块电路结构 如图 2所示。 VT1和 VT2代表绝缘栅双极型晶体管 (IGBT)、 集成门极换流晶闸管 (IGCT) 等大功率可控电力电子开关； Dl、 D2分别代表 VT1、 VT2的反并联二极管； C代表直 流电容， 其电压为^， 每个子模块为半桥结构， 功率开关 VT1和 VT2串联后与直流电容 C并联， A、 B为子模块的输入输出端。 如图 1所示， 上桥臂和下桥臂均由 N个子模块 串联构成， 即上一子模块的输出端 B与下一子模块的输入端 A相连。 上桥臂最上方子模 块 SMul的输入端 A接到直流电源正极，下桥臂最下方子模块 SMdN的输出端 B接到直流 电源负极。 同时， 模块化多电平变换器的子模块含有独立的控制单元。
为了便于描述，首先说明模块化多电平变换器中子模块正常运行时的两个工作状态。 如图 2所示， 当 VT1开通而 VT2关断时， 电流通过 D1向电容充电， 或者通过 VT1对电 容进行放电，称为子模块投入状态； 当 VT1关断而 VT2开通时， 电流通过 VT2或者 D2， 电容始终处在旁路状态， 其电压不会变化， 称为子模块切除状态。
由于各子模块 VT1与 VT2的开关状态互补这一特殊性，每个子模块仅需要一路触发 脉冲。 在子模块控制单元中对触发脉冲进行取反运算得到互补的触发脉冲， 设置死区后 作为子模块中 VT1与 VT2的触发信号。
以模块化多电平变换器 a相为例说明桥臂电流方向对子模块电容电压的影响。如图 1 所示， 上桥臂电流 au和下桥臂电流 ad的正方向均为向下。 当 au和 ^的值大于 0时， 为 充电电流， 处于投入状态的子模块电容将充电， 电容电压升高； 当 ^和 ^的值小于 0 时， 为放电电流， 处于投入状态的子模块电容将放电， 电容电压降低。
本发明的调制策略可以分为以下四个步骤实施：
(1)如图 3所示，采用 N个具有相同幅值 Ac=2/N，相同频率 ，相同相位的三角载波， 层叠于图中纵坐标为 -1到 1的区间内， 自底向上依次为第 1， 2， ...， N个载波。 将调制 波与这 N个载波进行比较， 当调制波的值大于三角载波的值时， 比较结果的输出为 1 ; 反之，当调制波的值小于三角载波的值时，比较结果的输出为 0。通过比较得到 N路 PWM 脉冲， 与各三角载波——对应， 分别为 PWM PWM2, ...， PWMN。 对这 N路 PWM脉 冲进行取反， 得到 N路 PWM脉冲 PWM , PWM2% ...， PWMN'。
(2)在每个电压均衡控制周期起始时刻测量各相上桥臂电流 au和下桥臂电流 ad，同时 测量上桥臂子模块电容电压 以及下桥臂子模块电容电压
WcdNo
(3)分别对步骤 (2)测量的上桥臂、 下桥臂子模块电容电压由小到大进行排序， 并使排 序结果在一个电压均衡控制周期内保持不变。 把上桥臂子模块电容电压顺序对应的子模 块序号放入数组 tu[i]中， 把下桥臂子模块电容电压顺序对应的子模块序号放入数组 td[i] 中。
(4)根据子模块电容电压排序结果和桥臂电流方向为上桥臂和下桥臂的各个子模块分 配 PWM脉冲。
对于上桥臂而言， 若上桥臂电流 au>0， 电流为处于投入状态子模块的电容充电， 电 容电压升高， 把步骤 (1)中所得的 N路 PWM脉冲 PWM^ PWM2， ...， PWMJ 次分配 给子模块 SM(tu[l])， SM(tu[2]), ...， SM(tu[N]); 若上桥臂电流 au<0， 电流为处于投入状 态子模块的电容放电， 电容电压降低， 把步骤 (1)中所得的 N 路 PWM 脉冲 PWMl 7 PWM2, …， PWMN依次分配给子模块 SM(tu[N])， SM(tu[N-l])， …， SM(tu[l])。
对于下桥臂而言， 若下桥臂电流 du>0， 电流为处于投入状态子模块的电容充电， 电 容电压升高， 把步骤 (1)中所得的 N路 PWM脉冲 PWM , PWM2'， ...， PWMN '依次分配 给子模块 SM(td[N])， SM(td[N-l]), ...， SM(td[l]); 若下桥臂电流 du<0， 电流为处于投入 状态子模块的电容放电， 电容电压降低， 把步骤 (1)中所得的 N路 PWM脉冲 PWM , PWM2'， …， PWMN'依次分配给子模块 SM(td[l])， SM(td[2])， …， SM(td[N])。

Claims

权利要求书
1. 一种模块化多电平变换器的调制策略， 其特征在于： 基于载波层叠方法， 结合各 桥臂电流方向和子模块电容电压顺序， 确定各子模块的投切状态， 包括以下步骤：
(1)采用 N个幅值、 频率、 相位均相同的三角载波， 层叠于纵坐标为 -1 到 1 的区间 内， 自底向上依次为第 1， 2， ...， N个载波； 将调制波与这 N个载波进行比较， 当调制 波的值大于三角载波的值时， 比较结果输出为 1， 反之， 当调制波的值小于三角载波的值 时， 比较结果输出为 0; 通过比较得到 N路 PWM脉冲， 与各三角载波一一对应， 分别为 PWMi , PWM2, ...， PWMN; 对这 N 路 PWM 脉冲进行取反， 得到 N 路 PWM 脉冲 PWMi' , PWM2'， …， PWMN' ;
(2)在每个电压均衡控制周期起始时刻测量各相上桥臂电流 au和下桥臂电流 ad， 同时 测量上桥臂各子模块电容电压 ^， ucu2 , ...， McuN以及下桥臂各子模块电容电压 Mcdl，
(3)分别对步骤 (2)测量的上桥臂、 下桥臂子模块电容电压由小到大进行排序， 并使排 序结果在一个电压均衡控制周期内保持不变； 把上桥臂子模块电容电压顺序对应的子模 块序号放入数组 tu[i]中， 把下桥臂子模块电容电压顺序对应的子模块序号放入数组 td[i] 中；
(4)根据子模块电容电压排序结果和桥臂电流方向为上桥臂和下桥臂的各个子模块分 配 PWM脉冲：
对于上桥臂而言， 若上桥臂电流 au>0， 把步骤 (1)中所得的 N路 PWM脉冲 PWMl 7 PWM2, ...， PWMN依次分配给子模块 SM(tu[l])， SM(tu[2])， ...， SM(tu[N]); 若上桥臂电 流 au<0， 把步骤 (1)中所得的 N路 PWM脉冲 PWMi， PWM2， ...， PWMN依次分配给子 模块 SM(tu[N])， SM(tu[N-l])， …， SM(tu[l]);
对于下桥臂而言， 若下桥臂电流 du > 0， 把步骤 (1)中所得的 N 路 PWM 脉冲 PWMi'， PWM2'， ...， PWMN'依次分配给子模块 SM(td[N])， SM(td[N-l])， ...， SM(td[l]) ; 若下桥臂电流 du < 0， 把步骤（I)中所得的 N 路 PWM 脉冲 PWM ， PWM2'， ...， PWMN'依次分配给子模块 SM(td[l])， SM(td[2])， ...， SM(td[N])。
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