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模块化多电平逆变器的研究,模块化,电平,逆变器,研究
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毕 业 论 文（设 计）题目：模块化多电平逆变器的研究姓 名 张桐盛 学 号 201000171252 学 院 控制科学与工程学院 专 业 自动化 年 级 2010级 指导教师 张承慧 教授 2014年5月20日2山 东 大 学 本 科 生 毕 业 论 文摘 要随着人类社会的飞速发展，人们在生产和生活当中对能源的需求也在逐步增加。能源利用的转型与创新、能源网络的合理运作，也成为目前人类科学研究的一大领域。在提高能源利用率的过程中，利用现代电力电子器件代替原有传统的电气设备是当今比较热门的一个话题。本文对模块化多电平变换器展开研究，文章先介绍模块化多电平变换器的拓扑结构和工作原理。而后介绍三种调制策略，介绍载波移相调制策略，通过系统仿真可以发现在这种控制策略下系统子模块电容电压不稳定；针对这一情况介绍了平衡控制策略，这种控制策略能很好的解决系统各种不平衡的问题，但系统逆变波形不理想；最后介绍了优化后的载波移相策略，这种控制策略将传统载波移相策略与子模块电容电压选择策略相结合，解决了上下桥臂内的子模块电容电压不平衡的问题。关键词：模块化多电平变换器、调制方式、仿真波形IIABSTRACTWith the rapid development of human society, the demand of energy is gradually increased in peoples production and living. Besides rational operation of energy network, energy transformation and innovation, is becoming a major area of human science. In the process of improving energy efficiency, the use of modern power electronic devices to replace traditional electrical equipment is one of popular topics nowadays. This paper studies on Modular Multilevel Converter. The topology and the basic operating principles and are introduced. Three kinds of modulation strategy are introduced. Firstly, the carrier phase shift modulation strategy is presented. Sub-modules capacitance voltage is not stable under this control strategy. Then balance control strategy is introduced. This control strategy is a solution of system various imbalances, but system inverter waveform is not ideal. Finally, the optimized carrier phase shifting control strategy is revealed. The control strategy combined with the traditional carrier phase shifting strategy and the balanced control of capacitor, solves the sub-modules capacitance voltage imbalance problem in the bridge arm. Keywords: MMC, modulation, simulation 目 录摘 要IABSTRACTII第一章 绪论11.1课题背景及研究意义11.2研究现状21.3本文研究的主要内容2第二章 系统概述32.1 MMC拓扑结构32.2 MMC工作原理42.3 MMC等效电路52.4 本章小结6第三章 MMC控制策略73.1 CPS-SPWM调制73.1.1 MMC数学模型73.1.2 CPS-SPWM触发方式103.2 平衡控制策略113.2.1 平衡控制触发方式123.2.2 子模块电容电压排序原理133.3 优化的CPS-SPWM控制策略143.4 本章小结15第四章 系统仿真164.1 CPS-SPWM调制仿真164.1.1 系统仿真图164.1.2 系统仿真波形174.2 平衡控制策略仿真184.2.1 系统仿真图184.2.2 系统仿真波形194.3 优化CPS-SPWM调制仿真204.3.1 系统仿真图214.3.2 系统仿真波形214.4 本章小结22结 论23致谢24参考文献25ii第一章 绪论1.1课题背景及研究意义近几年随着电力电子器件在耐高压和大功率方面不断有所突破，电力电子技术应用越来越广泛。伴随着城市和工业用电的不断增加，电网容量不断扩大，而在城市供电系统中，越来越多的供电设备转到地下。传统的变压器设备由于其内部含有铁芯，在质量和体积上都不是那么理想，电力电子技术的出现改变了这一状况。通过使用电力电子器件能代替原有的传统变压器等设备，使原有的笨重、转化效率低下的设备被体积小、质量轻、使用方便、价格合理的新型现代电力电子设备逐渐代替。由于我国人口分布不均，呈现沿海地区人口密集，内陆地区人口相对较少的特点，沿海地区资源相对匮乏，而内陆地区资源丰富，所以近几年国家大量投入电网建设，将中西部的电力通过电网传输到东部地区，供东部地区城市使用。目前国内输电方式仍以高压交流输电方式为主，但是高压交流输电在有功无功、高次谐波等问题上仍难以解决，所以现在有些电网采用高压直流输电，高压直流输电必将是大势所趋。目前虽然电力电子器件的耐压值不断提高，但远远不能满足目前高压直流输电的高电压要求。为了使用电力电子器件代替原有的整流逆变环节，现实中往往使用多电平级联的方法使设备的耐压值升高，同时通过多电平的级联，采用一些调制策略，使输出电压由一个个的电平台阶累加，在逆变环节中使逆变波形更加接近正弦波，从而对交流电网和交流用电设备不产生任何影响。模块化多电平变换器(Modular Multilevel Converter-MMC)正是基于以上思想研究出来的，通过模块的级联，满足高压直流输电的要求。这种变换器通过控制策略的不同能够实现整流与逆变两功能于一体的效果。所以MMC变换器在高压直流输电中通过控制策略的变换，能够实现供电方和用电方的转换，为适应不同的供求关系做准备。而且现代光伏发电系统规模越来越庞大，所以当MMC变换器工作于逆变方式时，也能用于光伏发电并交流电网之中。1.2研究现状由于近几年直流输电越来越受到人们的广泛关注，因此与直流输电相关的电力设备应用越来越广泛。与之相关的电路拓扑也受到人们的格外关注。模块化多电平变换器（MMC）是由德国A.Lesnicar和R.Marquardt于2001年首次设计出来的1-3，从此便引起了学术界的广泛讨论。国外在这个领域的研究成果显著，各国专家学者纷纷提出不同的控制策略。西门子公司于2010年投入使用的“Trans Bay Cable Project，该工程是西门子公司基于MMC的高压直流输电的第一个工程4-6，该工程直流电压正负200kV，容量为400MW。而国内在这一方面相对落后，目前国内只有少数几所大学进行了理论方面的研究。中国电力科学研究院于2010年研制出一台电压等级为正负50kV、容量为20MW的高压直流输电的设备，并已经在上海南汇风电场成功运行7-9。1.3本文研究的主要内容本文将对模块化多电平变换器进行研究，本文将研究MMC系统的逆变功能。本篇论文的主要内容如下：第一章，绪论部分：主要介绍MMC变换器的研究背景及意义，以及目前国内外研究现状。使读者对MMC变换器有一个粗略的了解，为介绍下文做铺垫；第二章，系统概述：主要介绍MMC变换器的拓扑结构、工作原理及等效电路；第三章，控制策略：本章将会介绍针对MMC的几种不同的控制策略及其推导过程，为系统仿真做准备；第四章，系统仿真：本章将会对系统采用不同的控制方式及触发电路，将每种控制策略的优缺点通过对比一一描述。15第二章 系统概述2.1 MMC拓扑结构如图2-1所示，三相MMC逆变器主要由子模块、桥臂电感以及直流母线组成。每个模块的内部由一个电容和两个开关器件IGBT构成。其中每相上下桥臂均由N个子模块和一个桥臂电感构成，一般情况下每相上下桥臂投入子模块之和为N，由于直流母线间电压的恒为Ud，所以每个模块内电容电压始终为Ud/N，每个子模块内电容电压稳定不变。桥臂电感的作用是当投切不同的子模块时，桥臂电感能起到一个缓冲的作用，消除因为投切而造成的模块内电容电压的波动。这样的拓扑结构虽然使用开关器件数目较多，但通过特定的控制策略能使模块内电容电压趋于稳定，最终使输出电压波形更加理想。而且当级联模块数目N较多时，可以提高系统容量和电压等级，达到输出电压为级联多电平的目的10-11。图2-1 MMC拓扑结构2.2 MMC工作原理MMC的运行状态有三种，可以输出电容电压或0电压，且电流在任何情况下都能双向流动。状态1：当开关管T1、T2均关断时，正常情况下这种状态不会出现。在这种状态下，当电流的流动方向由左图所示时，电流经二极管D1给电容C0充电，电容电压上升；当电流方向如右图所示时，此时电流经D2时将电容C0切除，电容电压不变12-14。图2-2 MMC子模块工作状态1状态2：当开关管T1开通，T2关断时，此时子模块输出端电压为电容电压。当电流方向如左图所示时，电流经二极管D1给电容C0充电，电容电压上升；当子模块电流如右图所示时，电容通过开关管T1对外放电，电容电压下降。所以在这种状态下，通过电流的方向选择不同子模块投入，使电容电压在允许的范围内波动，以达到模块内电容电压稳定的要求，下文将有详细介绍12-14。 图2-3 MMC子模块工作状态2状态3：当开关管T1关断、T2开通时，此时子模块输出端电压为0。当电流方向如左图所示时，电流流经开关管T2；当电流方向如右图所示时，电流流经二极管D2，而不管电流方向如何，模块内电容总C0是相当于被“短路”，电容电压不变12-14。图2-4 MMC子模块工作状态3工作状态2和状态3是MMC系统内子模块的正常工作状态，通过控制每相上、下桥臂子模块处于状态2或状态3的数量，就能够控制输出电压，输出电压经过电感滤波之后就能形成三相正弦波。例如N=4时，每相都有2N=8个子模块，由于每相每时刻投入的子模块数量始终为N=4，所以每相上下桥臂处于投入状态的子模块数量有五种组合：4、0；3、1；2、2；1、3；0、4；设模块内电容电压为Uc这五种情况下该相输出电压分别为：4Uc、2Uc、0、-2Uc、-4Uc；通过控制这五种组合的占空比，就能使输出波形为正弦波。换句话说，MMC变换器就是通过不断移动输出点在每相相电压中所处的不同位置来最终实现逆变的效果。2.3 MMC等效电路 由于MMC每个桥臂都可看作一个受控电压源，其等效电路如图2-5所示。其中o为直流母线理想中性点。Ud交换器直流母线电压，、（i=a,b,c）分别表示变换器每相上、下桥臂上“可控电压源”电压。根据基尔霍夫定律，可以计算出MMC电压方程如下所示15-16。 其中表示变换器的i相交流输出端电压。由式（2.1）可得： 由式(2.2)可知，MMC 的直流母线电压为上、下桥臂的电压和，系统输出交流电压为下桥臂与上桥臂电压差，因此，MMC 直流侧电压和交流侧电压是可以独立控制的。只要能控制上下桥臂电压，就能控制输出电压。图2-5 MMC等效电路图2.4 本章小结本章介绍了MMC变换器的基本结构及各相子模块的不同工作状态，同时简单介绍了MMC变换器的输出电压、直流母线电压与由多个子模块组成的电压源之间的关系。第三章 MMC控制策略MMC系统由于各子模块电容电压直接与系统相连，所以控制电容电压使其在一定范围内稳定是系统稳定的基础。为了解决电容电压稳定这一问题，目前有很多不同的控制策略，各种控制策略各有不同的优缺点，本文将介绍三种不同的控制策略。3.1 CPS-SPWM调制3.1.1 MMC数学模型在理想条件下，每个子模块内的电容电压恒为定值，而直流母线电压不变，所以MMC每相投入的子模块数量应为定值N。设三相中某一相上桥臂投入子模块数量为，下桥臂投入子模块数量为，且他们满足： 直流母线电压满足以下公式： 用变量表示各个模块的实时状态，可以设为： 所以每个子功率模块的电压电流关系可用如下式子表示： 从理论的角度上说，MMC上桥臂和下桥臂都可以定义为电压可控的电压源。和分别为上桥臂和下桥臂的端口输出电压。桥臂电压是所有投入子模块电容电压的总和，所以上下桥臂的端口输出电压可以表示为： 其中，j为三相中的某一相，j=a、b、c，k为每相子模块的对应编号（k=1、2、2n）。 由于三相MMC相间没有任何影响，所以只研究其中的任何一相即可应用于整个系统，以a相为例。MMC的a相等效电路如图3-1所示，iaP、iaN分别为上下桥臂的电流，Idc为直流侧电流，其参考方向按图中箭头标注方向为正，图中的o为直流母线电压Udc电压中点。图3-1 MMC的数学模型假设三相MMC的直流母线电压恒定为Udc，各相桥臂的参数都相同，设a相输出电压为ia，则ia被上下桥臂所均分。由于系统三相完全对称，所以从理论上说直流母线电流Idc分为三份，a、b、c三相分别占有其中一份；同理，流过a相上下桥臂的交流分量相同，且都为ia/2，则 由公式（3.7）、（3.8）可知，上下桥臂电流均含有直流分量和交流分量，其中交流分量只在相内流通，我们把它定义为环流，用iza表示。公式（3.7）、（3.8）相减，即可得出环流和上下桥臂电流之间的关系： 公式（3.7）、（3.8）相加，得到系统环流和上下桥臂的电流二者之间的关系： 根据电路中学习的基尔霍夫的电压定律，可以得到如下等式： 将公式（3.12）、（3.13）相加可得： 将公式（3.12）、（3.13）相减可得： 由公式（3.12）、（3.15）可以得出MMC系统桥臂电压、交流侧电压和直流侧电压之间的关系，如下图所示：图3-2 MMC系统桥臂电压、交流侧电压和直流侧电压之间的关系从交流负载侧来看，则有以下等式： 联立以上两式，即可得出交流侧输出电压方程： 定义L为等效电感，则： 从等式（3.17）可以得到MMC的a相等效电路，如下图所示，其中等效电流输出端为。图3-3 等效后的MMC数学模型3.1.2 CPS-SPWM触发方式载波移相调制技术(CPS-SPWM)是基于SPWM调制技术的一种新型控制策略，其基本思想就是通过两个甚至多个的正弦波与多个相差一定角度的三角波进行比较，最终产生所需的驱动信号。载波比和调制系数是SPWM调制的两个重要参数。载波比是指三角载波与正弦调制波的频率之比，载波比的大小关系着模块输出波形与正弦波的逼近程度；调制系数是指正弦调制波与三角载波的幅值之比。根据分析可知，MMC下桥臂端口电压之和与输出交流电压同相，而上桥臂端口电压之和与输出交流电压反相。上、下桥臂输出电压的幅值都等于交流输出电压的二分之一。因此可以采用双调制波载波移相SPWM。两个桥臂的调制波都为正弦波，幅值相等，但波形相差半个周期，即相位互差180度。三角载波的频率为fc，每个IGBT的开关频率与三角载波频率相等，周期均为T=1/fc。同相所有子模块三角载波的幅值和频率相同，同一桥臂相邻子模块相位相差T/N，上下桥臂对应的模块相位相差T/2N。如下图所示的是载波移相SPWM触发信号图，其中图3-4中的四个三角波分别为每相从上到下四个子模块的载波，四个载波之间有一定的相位差。而两个调制波都为正弦波，但二者相位相差半个周期，即180度。通过调节载波比和调制系数这两个参数即可获得理想的逆变波形。载波与调制波相比较的结果，就作为每相4个子模块的触发信号。但由于三相逆变器的每相相差120度，在时间上相差1/3个周期，所以将四个载波与调制波比较的结果延迟1/3、2/3个周期即可获得其他两相的触发信号。按照这样的思想构建的触发电路只需修改延迟时间，即可获得三相不同的触发信号，大大减少了系统的复杂程度。t(s)t(s)图3-4 CPS-SPWM触发信号发生图3.2 平衡控制策略以上介绍的CPS-SPWM触发方式虽然输出波形非常理想，但是CPS-SPWM控制策略中没有对子模块电容进行控制，所以这种控制策略势必会造成电容电压发生偏移，最终造成不平衡的问题。这种不平衡包括每相内各个模块电容电压的不平衡，而且还包括各相相间的不平衡。其实三相相间的不平衡，其原因归根究底还是每相内部模块电容电压的不平衡，只要能够控制使相内各模块的电容电压稳定在一定的范围内，就能够解决输出波形不平衡的问题。除此之外，由于使用CPS-SPWM是为了使输出波形更加理想，通常要提高载波频率，由此带来的后果是模块内IGBT的开关频率也非常高，这样造成很大的开关损耗。因此以上介绍的控制方式是需要改进的，或者是需要寻求另外一种方法已解决不平衡的问题。3.2.1 平衡控制触发方式以a相上桥臂为例，设交流输出电压为： 由公式（2-1）可得， 一个周期内投入的子模块可分两种：处于PWM状态的子模块和投切状态不变的子模块。其中投切状态不变的子模块数量为： 式（3.21）中，为n的整数部分。处于PWM状态的子模块数量为： 式（3.22）中，Mod(n)为n的小数部分。定义 式（3.23）中。Tri三角载波幅值，。则某一时刻桥臂需要投入总的子模块数量为 同理可得下桥臂某一时刻需要投入的子模块数量。这种电压平衡策略，同相上下桥臂各有一个载波。设每相有2N个子模块，上下桥臂采用同相调制时，输出电平个数为2N+1；采用反相调制时，输出电平个数为N+1。由于同相调制输出电平个数较多，谐波较小，波形理想，所以本文的平衡控制将采用同相调制方法。图3-5 平衡控制策略下投入子模块数量示意图3.2.2 子模块电容电压排序原理按照上文提到的计算方法，则可以算出各桥臂某一时刻需要投入的子模块数量，由于每个子模块内电容电压不完全相等，所以选择哪些子模块投入系统也是一个值得考虑的问题。在某一桥臂，桥臂电流的方向可以控制被投入子模块电容是充电状态还是放电状态。所以，可以检测每个桥臂子模块电容电压的值，然后根据桥臂电流方向决定投入哪个子模块。例如，当电流方向为对投入子模块充电时，检测桥臂中各模块的电容电压，选择相应电压较低的一个或几个投入到系统中，就会使这些模块的电容充电；当电流方向为对投入子模块放电时，检测桥臂中各模块的电容电压，选择相应电压较高的一个或几个投入到系统中，就会使这些模块的电容放电。例如，某一相上下桥臂各有4个子模块，某时刻各子模块电容电压和电流方向如下图所示。假设由上文中的控制策略计算出，上桥臂需要投入1个子模块，下桥臂需要投入3个子模块，此时上桥臂电流大于0，则电流对投入子模块进行充电，所以选择电容电压最低的子模块投入；下桥臂电流小于0，则电流对投入子模块进行放电，所以选择电容电压最高的3个子模块投入。图3-6 子模块电容电压排序原理3.3 优化的CPS-SPWM控制策略前面介绍的CPS-SPWM触发方式能使输出波形非常理想，但是CPS-SPWM都有一个普遍的缺点，就是不平衡的问题。这种不平衡包括每相内各个模块电容电压的不平衡，而且还包括各相相间的不平衡。其实三相相间的不平衡，其原因归根究底还是每相内部模块电容电压的不平衡，只要能够控制使相内各模块的电容电压稳定在一定的范围内，就能够解决输出波形不平衡的问题。所以将平衡控制中的模块电容电压排序策略与原始的CPS-SPWM相结合，再调节部分参数，就能进一步解决模块内电容电压不平衡的问题。3.4 本章小结本章重点介绍了MMC系统的两种不同的控制方法，从理论角度介绍了这两种方法的推导过程，同时介绍了这两种方法的优缺点。最后，根据两种方法的优点，将CPS-SPWM控制策略与平衡控制策略中的电容电压排序原理相结合，产生第三种控制策略。第四章 系统仿真4.1 CPS-SPWM调制仿真在这部分中，MMC系统将采用CPS-SPWM调制方式，系统每相共有4个子模块，换句话说，每相上、下桥臂都有2个子模块。系统a、b、c各相触发信号的载波相差120度，这样就可以使三相逆变出来的三相电压有一定的相位差。通过仿真，检验前文提到的数学模型。4.1.1 系统仿真图图4-1 CPS-SPWM调制方式仿真图4.1.2 系统仿真波形图4-2 三相电流波形图4-3 相电压波形图4-4 A相四个子模块电容电压波形从图4-2中可以看出逆变电流波形正常，三相互差120度，从图4-3相电压波形可以看出，相电压为五电平，电压经过滤波后形成正弦电流波形。但从图4-4中可以看出随着时间的推迟，A相四个子模块电容电压逐渐上升或下降，所以这种情况下，假如运行很长一段时间，系统将不稳定，最后造成逆变失败或者逆变波形不理想。4.2 平衡控制策略仿真本节将介绍平衡控制下的MMC逆变仿真。仿真电路每相有8个子模块，换句话说每相上下桥臂都有4个子模块。4.2.1 系统仿真图图4-5平衡控制下MMC系统仿真图4.2.2 系统仿真波形图4-6 三相电流波形图4-7 三相电压波形图4-8 A相上桥臂子模块电容电压波形图4-9 A相下桥臂子模块电容电压波形 从图4-6可以看出三相电流波形并非正弦波，波形不是很理想；从图4-7可以看出三相电压为9电平，经过电感滤波后形成类似正弦的电流。图4-8与图4-9可以发现A相上下桥臂8个子模块电容电压与上面的CPS-SPWM调制方式相比虽然子模块电容电压波动幅度较大，但经过一段时间后始终稳定在一定范围内，没有发生偏移，所以这种平衡控制策略是很有效的，但是逆变出来的电流波形不是很理想，仔细观察就可以发现电流波形不理想的原因在于逆变电压虽然是9电平，但是每相波形略窄，方波所占比例太少，造成每相逆变波形能量不足，因此仍需要改进。4.3 优化CPS-SPWM调制仿真本节将介绍一种优化的CPS-SPWM调制方法，这种调制方法是在前面两种控制策略的基础上建立起来的。通过仿真可以发现，原始的CPS-SPWM调制方法逆变电流波形理想，但是随着系统的运行，每相各个子模块电容电压不稳定，部分子模块电容电压上升，部分子模块电容电压下降，虽然电容电压随着时间的变化很小，但在相对较长的玩一段时间内，必会造成系统逆变波形不理想甚至逆变失败。所以，解决各相子模块电容电压的平衡问题是关键。下面将对优化CPS-SPWM调制方法仿真进行分析介绍。此次仿真每相有4个子模块，换就话说每相上下桥臂各含有两个子模块，其仿真电路在CPS-SPWM仿真的基础上增加一个模块选择环节，以实现各子模块电容电压的稳定。4.3.1 系统仿真图图4-10 优化CPS-SPWM控制策略的系统仿真图4.3.2 系统仿真波形图4-11 三相电流波形图4-12 三相电压波形图4-13 A相四个子模块电容电压波形将图4-11、图4-12分别与图4-2、图4-3比较后发现，优化CPS-SPWM效果不明显，但是从图4-13中我们可以发现，A相四个子模块电容电压经过一段时间之后电压平稳在一定范围内，而不会像使用原始CPS-SPWM调制方法时图4-4中描述的那样。所以子模块电容电压排序原理能使上下桥臂内子模块电容电压保持平衡，解决了子模块电容电压不稳定的问题。4.4 本章小结本章主要对第三章介绍的三种不同的调制方式进行仿真，并根据三相电流波形、三相电压波形及A相各子模块内电容电压波形，来研究三种调制方式的优缺点。25结 论 经仿真可以看出，CPS-SPWM的逆变波形理想，但有不平衡问题的出现，这种不平衡包括三相相间的不平衡、各相上下桥臂之间的不平衡，还包括各上下桥臂桥臂内子模块间电容电压的不平衡。所以这种调制方式应该做进一步改进。而通过平衡控制下的仿真结果，可以看出之前提到的各种不平衡都消失了，这种控制策略解决了MMC变换器所有的不平衡的问题，但新的问题也出现了，波形不理想，和正弦波相差很大，所以这种控制策略可圈可点。当然，其中的子模块电容电压排序原理还是很不错的思想，值得借鉴。通过将原始CPS-SPWM调制方式与子模块电容电压排序原理相结合，就产生了本文中的第三种调制方式。这种调制方式解决了上下各桥臂子模块电容电压不平衡的问题。致谢本次毕业设计在进行过程当中受到来自各方人员的关心和帮助，在此向他们表示衷心的感谢！首先要对张承慧教授及杜春水副教授表示感谢，感谢他们的指导。和其他同学一样，在这半年多的学习过程当中，每当遇到不懂的问题，我都是先去找老师，老师对此都会给予全力的帮助，并叮嘱同一个实验室的研究生学长学姐们对我加以指导。另外，对于我的这次毕业设计，老师提出过不少宝贵的建议和意见，这一点使得我的设计更加完善。其次，感谢设计过程当中帮助过我的学长学姐们，毕业设计期间他们把自己往年的各种经验毫无保留地分享给我们，并给了我们很多技术上的指导。这里特别提出要感谢石秀岩和邢相洋学长。在与他们相处的这段日子里，学长对我进行过许多手把手的指导，包括文献的检索和下载、开题报告演示文稿的制作、论文的书写等等，每一次都是有问必答，为我的设计提供了不可或缺的帮助。参考文献1熊焘. 基于模块组合多电平变换器的高压直流输电系统研究D.北京交通大学,2012.2董文杰. 模块化多电平变换器电压平衡策略研究D.合肥工业大学,2012.3管敏渊,徐政. MMC型VSC-HVDC系统电容电压的优化平衡控制J. 中国电机工程学报,2011,12:9-14.4韦延方,卫志农,孙国强,孙永辉,滕德红. 适用于电压源换流器型高压直流输电的模块化多电平换流器最新研究进展J. 高电压技术,2012,05:1243-1252.5杨晓峰,林智钦,郑琼林,游小杰. 模块组合多电平变换器的研究综述J. 中国电机工程学报,2013,06:1-15.6孙浩. 模块组合多电平变换器（MMC）的控制策略研究D.北京交通大学,2010.7杨晓峰. 模块组合多电平变换器（MMC）研究D.北京交通大学,2012.8李彩霞. 级联型多电平变流器在有源电力滤波器中的应用研究D.浙江大学,2006.9查申森,郑建勇,苏麟,吴恒荣,陈军. 基于IGBT串联运行的动态均压研究J. 电力自动化设备,2005,05:20-23.10张晓丽,石新春,王毅. 多电平变换器拓扑结构和控制方法研究J. 电源技术应用,2003,07:330-334+343.11汤广福,贺之渊,滕乐天,易荣,何维国. 电压源换流器高压直流输电技术最新研究进展J. 电网技术,2008,22:39-44+89.12李永东,饶建业. 大容量多电平变换器拓扑现状与进展J. 电气技术,2008,09:7-12.13丁冠军,汤广福,丁明,贺之渊. 新型多电平电压源换流器模块的拓扑机制与调制策略J. 中国电机工程学报,2009,36:1-8.14屠卿瑞,徐政,郑翔,管敏渊. 模块化多电平换流器型直流输电内部环流机理分析J. 高电压技术,2010,02:547-552.15管敏渊,徐政,屠卿瑞,潘伟勇. 模块化多电平换流器型直流输电的调制策略J. 电力系统自动化,2010,02:48-52.16刘钟淇,宋强,刘文华. 基于模块化多电平变流器的轻型直流输电系统J. 电力系统自动化,2010,02:53-58.IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 24, NO. 7, JULY 20091737Control and Experiment of Pulsewidth-ModulatedModular Multilevel ConvertersMakoto Hagiwara, Member, IEEE, and Hirofumi Akagi, Fellow, IEEEAbstractA modular multilevel converter (MMC) is one ofthe next-generation multilevel converters intended for high- ormedium-voltage power conversion without transformers. TheMMC is based on cascade connection of multiple bidirectionalchopper-cells per leg, thus requiring voltage-balancing control ofthe multiple floating dc capacitors. However, no paper has madean explicit discussion on voltage-balancing control with theoreticaland experimental verifications. This paper deals with two typesof pulsewidth-modulated modular multilevel converters (PWM-MMCs) with focus on their circuit configurations and voltage-balancing control. Combination of averaging and balancing con-trolsenablesthePWM-MMCstoachievevoltagebalancingwithoutany external circuit. The viability of the PWM-MMCs, as well asthe effectiveness of the voltage-balancing control, is confirmed bysimulation and experiment.Index TermsMedium-voltage power conversion, multilevelconverters, voltage-balancing control.I. INTRODUCTIONHIGH-POWER converters for utility applications requireline-frequency transformers for the purpose of enhanc-ing their voltage or current rating 14. The 80-MVA Staticsynchronous Compensator (STATCOM) commissioned in 2004consists of 18 neutral-point-clamped (NPC) converter legs 4,where each of the ac sides is connected in series by the corre-sponding transformer. The use of line-frequency transformers,however, not only makes the converter heavy and bulky, butalso induces the so-called dc magnetic flux deviation when asingle-line-to-ground fault occurs 5.Recently, many scientists and engineers of power systemsand power electronics have been involved in multilevel convert-ers intended for achieving medium-voltage power conversionwithout transformers 68. Two of the representatives are:1) the diode-clamped multilevel converter (DCMC) 6, 7;2) the flying-capacitor multilevel converter (FCMC) 8.The three-level DCMC, or a NPC converter 9 has been putinto practical use 10. If a voltage-level number is more thanthree in the DCMC, inherent voltage imbalance occurs in theseries-connected dc capacitors, thus resulting in requiring anexternal balancing circuit (such as a buckboost chopper) for apair of dc capacitors 11. Furthermore, a significant increasein the clamping diodes required renders assembling and build-ing of each leg more complex and difficult. Thus, a reasonablevoltage-level number would be up to five from a practical pointManuscriptreceivedJuly16,2008;revisedOctober16,2008.Currentversionpublished July 22, 2009. Recommended for publication by Associate EditorS. Bhattacharya.TheauthorsarewiththeDepartmentofElectricalandElectronicEngineering,Tokyo Institute of Technology, 152-8552 Tokyo, Japan (e-mail: mhagiakg.ee.titech.ac.jp; akagiee.titech.ac.jp).Digital Object Identifier 10.1109/TPEL.2009.2014236Fig. 1.Circuit configuration of a chopper-cell-type modular multilevel in-verter:(a)Powercircuit,and(b)BidirectionalPWMchopper-cellwithafloatingdc capacitor.ofview.AsfortheFCMC,thefour-levelpulsewidthmodulation(PWM)inverteriscurrentlyproducedbyonemanufactureofin-dustrialmedium-voltagedrives12.However,thehighexpenseof flying capacitors at low carrier frequencies (say, lower than1 kHz) is the major disadvantage of the FCMC 13.A modular multilevel converter (MMC) has been proposedin1420,intendedforhigh-powerapplications.Fig.1showsabasiccircuitconfiguration ofathree-phasemodularmultilevelinverter.Eachlegconsistsoftwostacksofmultiplebidirectionalcascaded chopper-cells and two noncoupled buffer inductors.The MMC is suitable for high- or medium-voltage power con-version due to easy construction/assembling and flexibility inconverter design. Siemens has a plan of putting it into practicalusewiththetradenameof“high-voltagedirectcurrent(HVDC)-plus.” It is reported in 19 that a system configuration of theHVDC-plus has a power rating of 400 MVA, a dc-link voltageof 200 kV, and 200 cascaded chopper cells per leg. The au-thors of 1420, however, have made no detailed descriptionof staircase modulation, especially about a crucial issue of howto achieve voltage balancing of 200 floating dc capacitors perleg. Moreover, no experimental result has been reported yet.0885-8993/$26.00 2009 IEEE1738IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 24, NO. 7, JULY 2009Fig. 2.Classification of modular multilevel converters.This paper focuses on voltage-balancing control and oper-ating performance of a pulsewidth-modulated MMC (PWM-MMC) equipped with either two noncoupled buffer inductorsor a single coupled buffer inductor per leg. The final aim of thispaper is to apply the PWM-MMC to medium-voltage powerconverters in a power rating of 110 MVA, a dc-link voltage of1030 kV,and aswitchingfrequency of 2002000 Hz.Combin-ing averaging control with balancing control enables achieve-ment of voltage balancing of multiple floating dc capacitorswithout any external circuit. In addition, this paper proposesthe dual MMC for low-voltage large-current power conversion.Each dc side of positive and negative chopper-cells possesses acommon dc capacitor, whereas its ac side is connected in par-allel via multiple buffer inductors. The similarity between thetwo MMCs exists in terms of circuit configuration and controlmethod. The validity of the two MMCs is confirmed not onlyby simulated results, but also by experimental results.II. TOPOLOGIES OFMMCSA. Classification From the TopologiesFig. 2 shows a classification of MMCs based on single-phasehalf-bridgeorfull-bridgeconverter-cells.Fromtheirtopologies,MMCs can be classified into:1) double-star-configured MMCs;2) a star-configured MMC Fig. 3(a);3) a delta-configured MMC Fig. 3(b); and4) the dual MMC (Fig. 14).Moreover, the double-star-configured MMCs can be classi-fied into:1) a chopper-cell-type MMC (Fig. 1); and2) a bridge-cell-type MMC.B. Comparisons in Function and ApplicationThe double-star-configured MMC topology possesses thecommon dc-link terminals as shown in Fig. 1(a), which en-able dc-to-ac and ac-to-dc power conversion. However, thestar/delta-configured MMC topology has no common dc-linkterminals as shown in Fig. 3. As a result, it has no capabilityof achieving dc-to-ac and ac-to-dc power conversion althoughit can control active power back and forth between the three-phase ac terminals and the floating dc capacitors. This meansFig. 3.Circuit configuration of MMCs: (a) Star-configured MMC, and(b) Delta-configured MMC.that the star/delta-configured MMC topology is not applicableto industrial motor drives, but it is suitable for STATCOMs andenergy storage systems 2123. This consideration is one ofthe most significant differences in function and application be-tween the double-star-configured MMC topology in Fig. 1 andthe star/delta-configured MMC topology in Fig. 3.The bridge-cell-type MMC replaces the chopper cell inFig. 1(b) with single-phase full-bridge converter cells. Hence,the dc-voltage source E can be replaced with a single-phaseac-voltage source 16. The detail of the dual MMC is discussedin Section V. In this paper, the chopper-cell-type MMC isreferred to simply as “the MMC” because attention is paid toit exclusively.C. Definition of DC Loop CurrentsFig. 1 shows a three-phase inverter based on the MMC.Each leg of the circuit consists of two stacks of four bidirec-tional chopper-cells and two noncoupled buffer inductors. Eachchopper-cell consists of a floating dc capacitor and twoinsulated-gate bipolar transistors that form a bidirectional chop-per. Attention is paid to the u-phase chopper-cells because theoperating principle is identical among the three legs.The following circuit equation exists in Fig. 1(a)1:E =8?j=1vju+ lddt(iP u+ iN u).(1)Here, E is a supply dc voltage, vjuis an output voltage of the u-phasechopper-cellnumberedj,l isabufferinductance,andiP uand iN uare positive- and negative-arm currents, respectively.TheKirchhoffsvoltagelaw(KVL)loopgivenby(1)isreferredto as the “dc loop,” which is independent of the load. The circu-lating current along the u-phase dc loop, iZucan be defined asiZu= iP uiu2= iN u+iu2=12(iP u+ iN u).(2)1The subscript symbol j means numbering of each chopper cell.HAGIWARA AND AKAGI: CONTROL AND EXPERIMENT OF PULSEWIDTH-MODULATED MODULAR MULTILEVEL CONVERTERS1739Fig. 4.Block diagram of dc-capacitor voltage control: (a) Averaging control,and (b) Balancing control.Note that iP u, iN u, iu, and idare branch currents whereas iZuis a loop current that is impossible to measure directly.III. CONTROLMETHOD OF THEMMCThe voltage-balancing control of eight floating dc capacitorsper leg in Fig. 1 can be divided into:1) averaging control; and2) balancing control.A. Averaging ControlFig. 4(a) shows a block diagram of the averaging control. Itforces the u-phase average voltage vCuto follow its commandvC, where vCuis given by vCu=188?j=1vCju.(3)Let a dc-loop current command of iZube iZu, as shown inFig. 4(a). It is given byiZu= K1(vC vCu) + K2?(vC vCu)dt.(4)Thevoltagecommandobtainedfromtheaveragingcontrol,vAuis given byvAu= K3(iZu iZu) + K4?(iZu iZu)dt.(5)When vC vCu, iZuincreases. The function of the currentminor loop in Fig. 4(a) forces the actual dc-loop current iZuto follow its command iZu. As a result, this feedback controlof iZuenables vCuto follow its command vCwithout beingaffected by the load current iu.B. Balancing ControlThe use of the balancing control described in 21 forces theindividualdcvoltagetofollowitscommandvC.Fig.4(b)showsablockdiagramoftheu-phasebalancingcontrol,wherevBjuisthevoltagecommandobtainedfromthebalancingcontrol.Sincethe balancing control is based on either iP uor iN u, the polarityFig. 5.Voltage command of each arm: (a) Positive arm, and (b) Negative arm.of vBjushould be changed according to that of iP uor iN u.When vC vCju(j : 1 4) in the positive arm of Fig. 1(a), apositive active power should be taken from the dc power supplyinto the four chopper-cells. When iP uis positive, the product ofvBju(= vBju) and iP uforms the positive active power. WheniP uisnegative,thepolarityofvBjushouldgetinversetotakethepositiveactivepower.Finally,vBjuforj = 1 4isrepresentedasvBju=?K5(vC vCju)(iP u 0)K5(vC vCju)(iP u 0)K5(vC vCju)(iN u 0).(7)Fig. 5 shows a voltage command of each chopper-cell vju.The positive-arm and negative-arm commands are obtained as:vju= vAu+ vBjuvu4+E8(j : 1 4)(8)vju= vAu+ vBju+vu4+E8(j : 5 8)(9)where vuis an ac-voltage command for the u-phase load. Notethat Fig. 5 includes the feedforward control of the dc supplyvoltage E. The voltage command vjuis normalized by eachdc-capacitor voltage vCju, followed by comparison with a tri-angular waveform having a maximal value of unity and a min-imal value of zero with a carrier frequency of fC. The actualswitchingfrequencyofeachchopper-cell,fSisequaltofC.Theeightchopper-cellshavetheeighttriangularwaveformswiththesamefrequencybutaphasedifferenceof45(= 360/8)toeachother for achieving harmonic cancellation and enhancing cur-rent controllability. As a result, the line-to-neutral voltage is anine-level voltage waveform, and a line-to-line voltage is a 17-level voltage waveform with an equivalent switching frequencyof 8fC.C. Simulated ResultsFig.6showssimulatedwaveformsfromFig.1.TablesIandIIsummarize circuit parameters and control gains used for simu-lation using a software package of the “PSCAD/EMTDC” 24.The dc supply voltage E and the rated active power P are setas E = 9 kV and P = 1 MW, and therefore, the nominal ratedline-to-line rms voltage of the MMC is 5.5 kV. An intrinsic1740IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 24, NO. 7, JULY 2009Fig. 6.Simulated waveforms obtained from Fig. 1, where f = 50 Hz, vC=2.25 kV, and E = 9 kV.TABLE ICIRCUITPARAMETERSUSED FORSIMULATIONTABLE IICONTROLGAINSUSED FORSIMULATIONone-sampling delay occurs due to digital control. The dc-capacitor voltage command of each chopper-cell is vC=2.25 kV (= 9 kV/4), while three-phase load voltage commandsof each phase are given asvu= 0.5E sin2ftvv= 0.5E sin?2ft 23?vw= 0.5E sin?2ft 43?E = 9 kVf = 50 Hz.(10)Note that vu, vv, and vware the three-phase line-to-neutral volt-ages.InFig.6,eachchoppercellisoperatedatunitymodulationindex.In Table I, a unit capacitance constant H is defined asH =3 8 12CV2CP=12 1.9 103 2.252 106106= 0.115(11)where VCis the rated dc voltage of each chopper cell. Note thatH is defined as a ratio of all electrostatic energy stored in dccapacitors with respect to rated active power 25. Therefore, Hhas a unit of second.2Fig. 6 indicates that vuvis a 17-level line-to-line voltage,achieving voltage balancing of all the dc capacitors. The dcinput power pdis represented aspd= E id(12)where idis a dc input current. The waveform of pdincludes thefollowing two frequency components: one is a 6th-frequency(300 Hz) component stemming from a three-phase full-bridgeconverter, and the other is a fundamental frequency (50 Hz)component stemming from an output frequency of 50 Hz. Thedetailed analysis of each waveform will be carried out in thenext section.IV. EXPERIMENTALRESULTSA. System Configuration Used for ExperimentFig. 7(a) shows a half-bridge circuit based on the MMC,wherethestacknumberofchoppercellswasselectedasfourperleg to confirm the basic operating principle, although the stack2H can be defined in the traditional two-level converters as well. An opti-mization of H is left for the future work.HAGIWARA AND AKAGI: CONTROL AND EXPERIMENT OF PULSEWIDTH-MODULATED MODULAR MULTILEVEL CONVERTERS1741Fig. 7.Experimental circuit: (a) Half-bridge circuit, and (b) Systemconfiguration.Fig. 8.Digital control system used for experiment.number of chopper cells was eight in Fig. 1. Fig. 7(b) showsa system configuration used for experiment. The midpoint ofthe two dc input series-connected capacitors is connected backto the neutral point of the star winding of the transformer, thusmaking the midpoint voltage stable. The dc supply voltage E isregulated at 140 V, and the capacitance value of Cdis chosen as20 mF.Fig. 8 shows the digital control system used for experiment.Thesystemdetectseachdc-capacitorvoltagevCj,bothpositive-and negative-arm currents iPand iN, and a dc supply voltageE as input signals to the A/D unit. The A/D unit consisting ofseven A/D converters takes in the analog signals, and then itconverts them into seven 12-bits digital signals. A digital signalprocessor (DSP) unit using a 16-bit DSP (ADSP-2105) takesin the digital signals, and produces the voltage commands vjafter completing the digital processing shown in Figs. 4 and 5.A field-programmable gate array (FPGA) unit has the followingmultifunctions:TABLE IIICIRCUITPARAMETERSUSED FOREXPERIMENTTABLE IVCONTROLGAINSUSED FOREXPERIMENT1) generating carrier signals with appropriate phase differ-ences;2) comparing vjwith the corresponding triangular carriersignal; and3) producing gate signals with a dead time of 2 s.The FPGA unit produces 8-bit (= 2 4) gate signals in to-tal, because each chopper cell possesses two semiconductorswitches. Furthermore, the FPGA unit sends back sampling sig-nals to the DSP unit for realizing the so-called “synchronoussampling.”Attentionispaidtoaone-samplingdelayoccurringintheDSPunit. The experiment selected the carrier frequency as fC=8 kHz, while each triangular carrier had a phase differenceof 90(= 360/4). If a conventional synchronous samplingwas adopted, the DSP unit would yield a time delay of 63 s=1/(2 fC) because its sampling and command renewal wouldbe conducted at the peak value of each carrier waveform. Thesampling delay can be reduced with the following samplingmethod for improving controllability of output voltages: As forchopper-cell 1, for instance, the sampling is conducted at thepeak value of carrier signal 4, and then vjis changed at the peakvalue of carrier signal 1. As a consequence, the time delay isminimized to be 31 s = 1 / (4 fC). A three-phase MMC canreduce the time delay further by phase-shifting of each leg by120.B. Operating Performance Under a Steady-State ConditionTables III and IV summarize the circuit parameters and con-trol gains used for experiment.3An R-L load with a powerfactor of 0.9 at 50 Hz was utilized. The experiment was carriedout under the condition P = 250 W.3The experimental conditions are the same in H and l (per unit) as those inFig. 6.1742IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 24, NO. 7, JULY 2009Fig. 9.Experimental waveforms obtained from Fig. 7, where f = 50 Hz,vC= 70 V, and E = 140 V.Fig.9showstheexperimentalwaveformswhenthedc-voltagecommand of each chopper-cell was set as vC= 70 V. The acvoltage command for the load was given byv0=2V0sin2ftV0= 50 Vf = 50 Hz.(13)Fig. 7(a) yields the following equation:v0=12?4?j=3vj2?j=1vj?l2ddti0(14)v0=?R + Lddt?i0.(15)The waveform of v0is slightly different from that in a DCMCandanFCMC,duetotheexistenceofthesecondtermoftherighthand in (14). Note that both DCMC and FCMC have a completestaircase waveform with a constant (not curved) voltage level.Substituting (14) into (15) yields12?4?j=3vj2?j=1vj?= Ri0+?L +l2?ddti0.(16)Hence, harmonic voltages included in the left hand in (16) ap-pearacrossbothLandl/2.Ifl/2isdominantoverL(L ? l/2),most of the harmonic voltages appear across l/2, bringing lessharmonic voltages to v0. If L is dominant over l/2 (L ? l/2),most of the harmonic voltages appear across L to the contrary.Although the load current i0is sinusoidal with a fundamentalcomponent of 50 Hz, the arm currents iPand iNcontain non-negligible low-order harmonic currents. This interesting phe-nomenonoccursduetotheeffectofthebalancingcontrol.Fig.9indicates that the voltage command from the balancing control,vB1is a discontinuous sawtooth waveform as expected from(6) and (7). As a result, vB1brings a discontinuous circulatingcurrent to the dc loop, producing low-order harmonic currentsin iPand iN. It is obvious that the fluctuations in iPand iNare accompanied by those in vB1. The switching ripple currentscontained in iPand iNare determined by the inductance valueof the buffer inductors and the harmonic voltages resulting fromthe four chopper-cells. Note that switching-frequency compo-nents of 16 kHz are dominant in iPand iN. In other words,the ripple currents can be reduced by increasing the carrier fre-quency and the buffer inductance value. Carefully looking intovB1and iPin Fig. 9 reveals that a subtle difference exists atthe times of polarity change between the waveforms of vB1andiP. The reason is that the 16-kHz switching ripple componentcontained in iPis not taken into the control circuit precisely,because the sampling frequency of DSP is set as 16 kHz. Thisphenomenon produces no effect on the balancing control be-cause the harmonic current makes no contribution to formingany active power.Applying the averaging control forces the average voltage vCto follow its command vC(= 70 V). The calculation of (3)has a function of reducing ac components in vC. From Fig. 9,vC1and vC3contain 50-Hz components caused by i0. This accomponentisinverseproportionaltothefundamentalfrequencyof i0. This is similar to flying capacitors in the FCMC.The dc voltage of each chopper-cell is kept balanced by thebalancingcontrol.Makingreferenceto(8)simplifiesthevoltagecommands of chopper-cells 1 and 2, v1and v2, as follows:v1= v2? v02+E4(17)whereareasonableapproximationofvB1= vB2= vA? 0wasmade. Equation (17) implies that chopper-cells 1 and 2 wereoperated under the same modulation index. As a result, vC1wasequal to vC2in Fig. 9 because the chopper-cells 1 and 2 utilize acommon arm current iP, and (17) leads to a relation of v1= v2.In a similar way, vC3was equal to vC4in Fig. 9. Experimentalwaveforms of iZand iZshow that no steady-state error, even ina small control gain, existed between iZand iZin terms of theirdc components because of an extremely low resistance alongthe dc loop.C. Operating Performance Under a Transient-State ConditionFig.10showsexperimentalwaveformsoftheMMCwhenthevoltagecommandwasreducedtohalf,butthecircuitparametersand the control gains were not changed. The transient voltageHAGIWARA AND AKAGI: CONTROL AND EXPERIMENT OF PULSEWIDTH-MODULATED MODULAR MULTILEVEL CONVERTERS1743Fig. 10.Experimental waveforms when the voltage command was changedfrom 50 to 25 V.Fig. 11.Experimental waveforms when only the balancing control wasdisabled.Fig. 12.Coupled inductor used for experiment.fluctuations in vC1and vC3were suppressed to less than 5%with respect to its rated voltage of 70 V.Fig. 11 shows experimental waveforms before and after thebalancing control was disabled intentionally but the averagingcontrol was enabled. The voltage imbalance was gradually ex-panding with the passage of time. Hence, the balancing controlis indispensable for stable operation.D. Operating Performance Using a Coupled Buffer InductorThetwononcoupledbufferinductorsinFig.7canbereplacedwith a single coupled buffer inductor intended for a size reduc-tion in the magnetic components. Fig. 12 shows specificationsof the inductor used for experiment. The terminals “a” and “b”are connected to the positive- and negative-arms, respectively,Fig. 13.Experimental waveforms when a coupled buffer inductor was used.while the terminal “c,” or the midpoint is directly connectedto the load. The relation of lab= 4lac= 4lbcexists in Fig. 12.It should be noted that the inductor presents no inductance toi0because the magnetic fluxes produced by the fundamentalfrequency components in iPand iNcancel out each other. Asa consequence, the inductor presents the inductance of labonlyto the circulating current iZ. The use of the coupled inductorresults in bringing considerable reductions in size, weight, andcost to the magnetic core.4Fig. 13 shows experimental waveforms when the coupledinductor was utilized. In Fig. 13, each chopper cell was oper-ated at a modulation index of 0.83, while the balancing controlusing the load current was utilized (see the Appendix.). Sincethe inductor produces no effect on i0, (14) can be rewritten asfollows:v0=12?4?j=3vj2?j=1vj?.(18)Hence, v0is a staircase waveform with a constant voltage levelas shown in Fig. 13. In other words, the MMC operates as amultilevel voltage source that is independent of i0. ComparisonbetweenFigs.9and13revealsthatbothhavesimilarwaveformsexcept for v0.4An optimization of the inductor is left for the future work.1744IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 24, NO. 7, JULY 2009Fig. 14.Half-bridge circuit using the dual MMC.V. DUALMMCFig. 14 shows a half-bridge circuit of the other MMC witha dual relation to Fig. 7. Each dc side of positive and negativechopper-cells possesses a common dc capacitor, whereas its acside is connected in parallel via two buffer inductors.5A. Control MethodThe control method of the dual MMC is basically the sameas that of Fig. 1 except for the following: although Fig. 1 hasa common dc loop to cascaded chopper-cells per leg, the dualMMC has multiple dc loops because the multiple chopper-cellsforming an arm are connected in parallel. This means that themultiple current minor loops should be provided for the aver-aging control. Chopper-cell 1 in Fig. 14, for instance, shouldcontrol a circulating current iZ1included in iP 1. Here, iZ1isobtained asiZ1= iP 1i04.(19)B. Operating Performance Under a Steady-State ConditionFig.15showsexperimentalwaveformsobtainedfromFig.14.Here, the dc supply voltage was E = 70 V, and the dc voltagecommand of each chopper cell was vC= 70 V. The ac voltagecommand of the load was given byv0=2V0sin2ftV0= 25 Vf = 50 Hz.(20)The circuit parameters and control gains were the same as thosein Fig. 9. It should be noted that the experiment was carried outusing four noncoupled buffer inductors.Figs.9and15showthatbothMMCshavesimilarwaveforms.However, comparison reveals that the two waveforms of v0are different in harmonic voltage. The reason is that the buffer5The dc capacitor of each chopper cell can be floated as in Fig. 7.Fig. 15.Experimental waveforms obtained from Fig. 14, where f = 50 Hz,vC= 70 V, and E = 70 V.inductance in the dual MMC is smaller than that in Fig. 7 due toparallel connection of the two buffer inductors. Fig. 15 showsthatiP 1andiN 1arehalvesofiPandiN,respectively.Therefore,the dual MMC is suitable for low-voltage large-current powerconversion.VI. CONCLUSIONThis paper has dealt with two types of PWM-MMCs, propos-ing their control method and verifying their operating principle.Computer simulation using the “PSCAD/EMTDC” softwarepackage has confirmed the proper operation of the three-phasePWM-MMC. Experiments using a laboratory system have ver-ified the viability and effectiveness of the single-phase PWM-MMC. The MMC is showing considerable promise as a powerconverter for medium-voltage motor-drives, high-voltage di-rect current (HVDC) systems, STATCOMs, and back-to-backsystems.APPENDIXA. Another Averaging Control MethodThis section describes another averaging control method dif-ferent from Fig. 4(a), which is characterized by controlling in-dependent average voltages of positive and negative chopperHAGIWARA AND AKAGI: CONTROL AND EXPERIMENT OF PULSEWIDTH-MODULATED MODULAR MULTILEVEL CONVERTERS1745cells vCupand vCun, which are given as follows: vCup=144?j=1vCju(21) vCun=148?j=5vCju.(22)The current command of the positive chopper-cells, iZupisrepresented asiZup= K1(vC vCup) + K2?(vC vCup)dt(23)while that of the negative chopper-cells, iZunis represented asiZun= K1(vC vCun) + K2?(vC vCun)dt.(24)Here, the voltage command of the positive chopper-cells vAupis given byvAup= K3(iZu iZup) + K4?(iZu iZup)dt(25)while that of the negative chopper-cells, vAunis given byvAun= K3(iZu iZun) + K4?(iZu iZun)dt.(26)B. Other Balancing Control MethodsThe balancing control forms an active power between theoutput voltage of each chopper-cell vBjuand the correspond-ing arm current. The following describes two other balancingcontrol methods different from Fig. 4(b).1) The method using the arm currents iP uand iN u: For thepositive chopper-cells numbered 1 to 4, vBjuis given byvBju= K5(vC vCju)iP u.(27)For the negative chopper-cells numbered 58, vBjuis given byvBju= K5(vC vCju)iN u.(28)Equations(27)and(28)indicatethatvBju(= vBju)containsthesamefrequencycomponentsasiP uoriN u,iftheaccomponentsincluded in vCjucan be eliminated. Hence, vBjucontains dcand 50-Hz components. The dc component of vBjuforms anactive power with that of iP uor iN u, and the 50-Hz componentof vBjuwith that of iP uor iN u. To avoid an undesirable effecton the control system, ac components included in vCjushouldbe eliminated fully by a low-pass filter.2) The method using the load current iu: For the positivechopper cells numbered 14, vBjuis given byvBju= K5(vC vCju)iu.(29)For the negative chopper cells numbered 58, vBjuis given byvBju= K5(vC vCju)iu.(30)Equations (29) and (30) indicate that vBju(= vBju) containsthe same frequency components as iuor iu. Note that iuis inphase with iP u, whereas iuis in phase with iN u. The 50-Hzcomponent included in vBjuforms an active power with that ofiP uor iN u.REFERENCES1 S. Mori, K. Matsuno, T. Hasegawa, S. Ohnishi, M. Takeda, M. Seto,S.Murakami,andF.Ishiguro,“Developmentofalargestaticvargeneratorusing self-commutated inverters for improving power system stability,”IEEE Trans. Power Syst., vol. 8, no. 1, pp. 371377, Feb. 1993.2 K. Kunomura, K. Yoshida, K. Ito, N. Nagayama, M. Otsuki, T. Ishizuka,F. Aoyama, and T. Yoshino, “Electronic frequency converter,” in Proc.IEEJ IPEC, 2005, pp. 21872191.3 T.Uzuka,S.Ikedo,andK.Ueda,“Astaticvoltagefluctuationcompensatorfor ac electric railway,” in Conf. Rec. IEEE PESC, 2005, pp. 18691873.4 T. Fujii, S. Funahashi, N. Morishima, M. Azuma, H. Teramoto, N. Iio,H.Yonezawa,D.Takayama,andY.Shinki,“A80MVAGCTSTATCOMfor the Kanzaki substation,” in Proc. IEEJ IPEC, 2005, pp. 12991306.5 M. Hagiwara, P. V. Pham, and H. Akagi, “Calculation of dc magneticflux deviation in the converter-transformer of a self-commutated BTBsystemduringsingle-line-to-groundfaults,” IEEETrans.PowerElectron.,vol. 23, no. 2, pp. 698706, Mar. 2008.6 F. Z. Peng, “A generalized multilevel inverter topology with self voltagebalancing,” IEEETrans.Ind.Appl.,vol.37,no.2,pp.611618,Mar./Apr.2001.7 J. Rodriguez, J. S. Lai, and F. Z. Peng, “Multilevel inverters: A surveyof topologies, controls, and applications,” IEEE Trans. Ind. Electron.,vol. 49, no. 4, pp. 724738, Aug. 2002.8 T. A. Meynard and H. 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