2012 Modeling and Design of Modular Multilevel Converters for Grid Applications - Ilves (KTH).pdf

Modeling and Design of Modular MultilevelConverters for Grid Applications

KALLE ILVES

Licentiate ThesisStockholm, Sweden 2012

TRITA-EE 2012:060ISSN 1653-5146ISBN 978-91-7501-580-4

Electrical Energy ConversionSchool of Electrical Engineering, KTH

Teknikringen 33SE-100 44 Stockholm

SWEDEN

Akademisk avhandling som med tillstånd av KTH framlägges till offentlig granskn-ing för avläggande av teknologie licentiatexamen Mandagen den 17 december 2012klockan 10.00 i Sal H1, KTH, Teknikringen 33, Stockholm.

© Kalle Ilves, December 2012

Tryck: Universitetsservice US AB

iii

Sammanfattning

Nätanslutna högeffektomvandlare används i bland annat transmissionsnätmed högspänd liktröm (HVDC), reaktiv effektkompensering (STATCOMs),och i banmatningssystem. Sadana omvandlare bör ha en hög verkningsgrad,lag harmonisk distortion, lag kostnad och vara vara palitliga. Kaskadkoppladeomvandlare tycks vara en lovande lösning för högspända högeffektomvandlareeftersom de kan kombinera en lag harmonisk distortion med en lag switch-frekvens. De kan även göras mycket palitliga genom att inkludera redundantasubmoduler som vid behov kan ersätta defekta submoduler.

Den modulära multinivaomvandlaren (M2C) är en typ av kaskadkoppladomvandlare som har fatt ökad uppmärksamhet de senaste aren. Den häravhandlingen syftar till att bringa klarhet i dimensioneringsaspekterna ochbegränsningarna av M2C-omvandlaren. Likspänningskondensatorerna i sub-modulerna är en drivande faktor för storleken och vikten av omvandlaren.Spänningsvariationerna över dessa kondensatorer kommer att paverka ut-spänningen av omvandlaren och även generera harmoniska komponenter iströmmen som circukerar mellan fasbenen. I denna avhandling visas det attframkoppling är en möjlig metod för att styra utspänningen. Det visas ävenatt de harmoniska komponenterna i den circulerande strömmen kan styras paett sadant sätt att arbetsomradet för omvandlaren kan utökas.

Styrmetoden som används maste kunna balansera spänningarna mellansubmodulerna. Generellt leder en ökad switchfrekvens till en bättre balansmellan submodul-spänningarna. I den här avhandlingen visas det att kon-densatorspänningarna kan balanseras med programmerad modulering, ävenvid grundtonsswitchning. Detta kommer emellertid att öka spänningsrippleti kondensatorerna. För att kvantifiera kraven pa tidigare nämnda konden-satorer sa inkluderar denna avhandling även en generell analys som utgarifran antagandet att kondensatorspänningarna är väl balanserade. Slutsatsenav analysen är att vid en 50 Hz sinusformig spänningsreferens maste dentotala energilagringsförmagan i kondensatorerna vara 21 kJ per MW aktivöverförd effekt för att begränsa kondensatorspänningarna pa sadant sätt attde ej överstiger sina nominella värden med mer än 10%.

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Abstract

Grid-connected high-power converters are found in high-voltage directcurrent transmission (HVDC), static compensators (STATCOMs), and sup-plies for electric railways. Such power converters should have a high reliability,high efficiency, good harmonic performance, low cost, and a small footprint.Cascaded converters are promising solutions for high-voltage high-power con-verters since they allow the combination of excellent harmonic performanceand low switching frequencies. A high reliability can also be achieved byincluding redundant submodules in the chain of cascaded converters.

One of the emerging cascaded converter topologies is the modular multi-level converter (M2C). This thesis aims to bring clarity to the dimensioningaspects and limiting factors of M2Cs. The dc-capacitor in each submoduleis a driving factor for the size and weight of the converter. It is found thatthe voltage variations across the submodule capacitors will distort the volt-age waveforms and also induce alternating components in the current that iscirculating between the phase-legs. It is, however, shown that it is possibleto control the alternating voltage by feed-forward control. It is also shownthat if the circulating current is controlled, the injection of a second-orderharmonic component can extend the operating region of the converter. Thereason for this is that when the converter is operating close to the boundaryof overmodulation the phase and amplitude of the second-order harmonic ischosen such that the capacitors are charged prior to the time when a highvoltage should be inserted by the submodules.

The controller that is used must be able to balance the sbmodule capac-itor voltages. Typically, an increased switching frequency will enhance theperformance of the balancing control scheme. In this thesis it is shown thatthe capacitor voltages can be balanced with programmed modulation, evenif fundamental switching frequency is used. This will, however, increase thevoltage ripple across the aforementioned capacitors. In order to quantify therequirements on the dc-capacitors a general analysis is provided in this thesiswhich is based on the assumption that the capacitor voltages are well bal-anced. It is found that for active power transfer, with a 50 Hz sinusoidalvoltage reference, the capacitors must be rated for a combined energy storageof 21 kJ/MW if the capacitor voltages are allowed to increase by 10% abovetheir nominal values.

Keywords: Modular multilevel converter, feed-forward control, modulation,switching frequency, energy storage

Acknowledgements

This thesis presents the work I have carried out at the department of ElectricalEnergy Conversion at KTH since I started here in February 2010. I would like toexpress my gratitude to all of my colleagues at the aforementioned department forthe friendly working environment during the past three years. A speacial thanksshould be given to my supervisor Hans-Peter Nee, and co-supervisor Staffan Norrgafor their valuable guidance and support.

I want to thank Lennart Harnefors who is not only a member of the steeringcommitte but also a co-autor in three of the publications appended in this thesis.I would also like to express my gratitude to steering committe members GeorgiosDemetriades and Hongbo Jiang for their valuable feedback and also Elforsk for theirfinancial support. I am grateful to Oscar Wallmark for his feedback regarding mythesis. I also want to acknowledge Eva Pettersson and Celie Geira for their helpregarding administrational matters and Peter Lönn for taking care of all computerrelated problems.

A special thanks is given to my office mate Antonios Antonopoulos who havehelped me a lot during my time at the department and is also a co-autor in fiveof the publications that are appended in this thesis. I would also like to thankDimosthenis Peftitsis, Georg Tolstoy, and former colleague Samer Shisha for all theinteresting and valuable discussions we have had. I am grateful to Andreas Krings,Naveed Malik, and Konstantin Kostov for their company during the conferencetravels and I also want to express my gratitude to the members of Roebels bar fortheir social activities.

I would like to express my deepest gratitude to my parents, my sister Emma,and my brother-in-law Shervin for their support and understanding. Finally, Iwould like to thank my beloved fiancée Liang for her love and support.

Stockholm, December 2012Kalle Ilves

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Contents

Contents ix

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Main Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Outline of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.5 Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.6 List of Appended Publications . . . . . . . . . . . . . . . . . . . . . 31.7 Related Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 The Modular Multilevel Converter 52.1 Modulation and Control . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Operating Principles and Control 113.1 Arm Currents at Direct Modulation . . . . . . . . . . . . . . . . . . 12

3.1.1 Impact of Main Circuit Filters . . . . . . . . . . . . . . . . . 153.2 Capacitor Voltage Ripple Compensation . . . . . . . . . . . . . . . . 17

4 Dimensioning Criteria 214.1 General Energy Storage Requirements . . . . . . . . . . . . . . . . . 21

4.1.1 Operating Region Extention . . . . . . . . . . . . . . . . . . . 234.2 Semiconductors Requirements . . . . . . . . . . . . . . . . . . . . . . 24

4.2.1 Minimum Switching Frequency . . . . . . . . . . . . . . . . . 254.2.2 Minimum Power Rating of Semiconductors . . . . . . . . . . 26

5 Conclusions and Future Work 315.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

ix

x CONTENTS

List of Figures 35

Bibliography 37

Publication I 41

Publication II 55

Publication III 63

Publication IV 73

Publication V 87

Publication VI 95

Publication VII 111

Chapter 1

Introduction

1.1 Background

Grid-connected high-power converters are found in high-voltage direct current trans-mission (HVDC), static compensators (STATCOMs), and supplies for electric rail-ways. Such power converters should have a high reliability, high efficiency, goodharmonic performance, low cost, and a small footprint. Cascaded converters appearto be promising for grid-connected applications since they can generate multilevelwaveforms and thus combine good harmonic performance with low switching fre-quencies. This results in a high efficiency and eliminates the need for additionalfilters. The use of cascaded building blocks (submodules or cells) also providesredundancy, which can be used to increase the reliability. One of the emergingmultilevel topologies is the modular multilevel converter (M2C) presented in [1].

This thesis considers modeling, control, and dimensioning aspects of the M2Ctopology. The aim is to provide analytical tools and a deeper understanding of thedimensioning factors in M2Cs. Not only will this make it easier to compare the M2Cwith other cascaded converter topologies, but identifying the limiting factors willalso contribute to the possible development of future improved converter topologies.

1.2 Main Objectives

• The main objective of the project is to identify suitable cascaded multileveltopologies for given target applications. The considered target applicationsare HVDC transmission, STATCOMs, and electric railway supply systems.

• The hardware requirements for the specific conversion tasks should be deter-mined. The focus should be on hardware requirements that drive the cost;installed silicon, rated power of inductors and energy storage elements.

1

2 CHAPTER 1. INTRODUCTION

• Trade-offs between different hardware requirements should be investigatedand quantified. These could, for example, be a trade off between silicon areaand capacitor requirements.

1.3 Outline of Thesis

The outline of this thesis is as follows: The modular multilevel converter, one ofthe most promising topologies for grid connected applications, is briefly describedin Chapter 2. Considerations on operating principles and control that relates tothe dimensioning criteria are presented in Chapter 3. In Chapter 4, generalizeddimensioning criteria are presented and discussed. Finally, the conclusions andfuture work are presented in Chapter 5.

1.4 Methodology

The findings in this thesis are mainly derived from theoretical models of the con-sidered converter topology. This is done by first deriving an analytical model of theconverter. The model is then analyzed with focus on a specific issue that relatesto the dimensioning criteria of the converter. The findings are then validated bysimulations and experimental results.

1.5 Main Contributions

This thesis has resulted in the following original contributions:

• An analytical model of the modular multilevel converter which can be usedto analyze the resulting currents in the converter arms for certain modulationmethods.

• A stable feed-forward voltage controller which makes it possible to controlthe ac-terminal voltage with a high accuracy and fast response without theneed of stabilizing feedback-controllers.

• A general analysis of the minimum energy storage requirements.

• A method of extending the operating region by injection of a second-orderharmonic in the current that is circulating between the phase legs.

• A modulation method that can control the relevant quantities in the converterat fundamental switching frequency.

1.6. LIST OF APPENDED PUBLICATIONS 3

1.6 List of Appended Publications

I. K. Ilves, A. Antonopoulos, S. Norrga, and H.-P. Nee, “Steady-state analysisof interaction between harmonic components of arm and line quantities ofmodular multilevel converters,” in IEEE Transactions on Power Electronics,vol. 27, no. 1, pp. 57 – 68, Jan. 2012.

II. K. Ilves, S. Norrga, L. Harnefors, and H.-P. Nee, “Analysis of arm currentharmonics in modular multilevel converters with main-circuit filters,” in Pro-cedings of International Conference on Power Electrical Systems (SSD-PES2012), Mar. 2012.

III. K. Ilves, A. Antonopoulos, S. Norrga, L. Ängquist, and H.-P. Nee, “Control-ling the ac-side voltage waveform in a modular multilevel converter with lowenergy-storage capability,” in Proceedings of European Conference on PowerElectronics and Applications (EPE 2011), pp.1-8, 30 Aug. – 1 Sept. 2011.

IV. K. Ilves, S. Norrga, L. Harnefors, and H.-P. Nee, “On energy storage re-quirements in modular multilevel converters,” Submitted for review to IEEETransactions on Power Electronics.

V. K. Ilves, A. Antonopoulos, S. Norrga, and H.-P. Nee, “Capacitor voltageripple shaping in modular multilevel converters allowing for operating regionextension,” in Procedings of 37th Annual Conference on IEEE Industrial Elec-tronics Society (IECON 2011), pp.4403 – 4408, 7 – 10 Nov. 2011.

VI. K. Ilves, A. Antonopoulos, S. Norrga, and H.-P. Nee, “A new modulationmethod for the modular multilevel converter allowing fundamental switchingfrequency,” in IEEE Transactions on Power Electronics, vol. 27, no. 8, pp.3482 – 3494, Aug. 2012.

VII. K. Ilves, A. Antonopoulos, L. Harnefors, S. Norrga, and H.-P. Nee, “Cir-culating current control in modular multilevel converters with fundamentalswitching frequency,” in Procedings of International Power Electronics andMotion Control Conference (IPEMC 2012), Jun. 2012.

1.7 Related Publications

• K. Ilves, A. Antonopoulos, S. Norrga, and H.-P. Nee, “A new modulationmethod for the modular multilevel converter allowing fundamental switchingfrequency,” in Procedings of International Conference on Power Electronics(ICPE 2011), pp. 991 – 998, May – Jun. 2011.

4 CHAPTER 1. INTRODUCTION

• L. Ängquist, A. Antonopoulos, D. Siemaszko, K. Ilves, M. Vasiladiotis, M,and H.-P. Nee, “Open-loop control of modular multilevel converters usingestimation of stored energy,” in IEEE Transactions on Industry Applications,vol. 47, no. 6, pp. 2516 – 2524, Nov. – Dec. 2011.

• D. Siemaszko, A. Antonopoulos, K. Ilves, M. Vasiladiotis, L. Ängquist, andH.-P. Nee, “Evaluation of control and modulation methods for modular multi-level converters,” in Procedings of International Power Electronics Conference(IPEC 2010), pp. 746 – 753, 21 – 24 Jun. 2010.

• A. Antonopoulos, K. Ilves, L. Ängquist, and H.-P. Nee, “On interaction be-tween internal converter dynamics and current control of high-performancehigh-power ac motor drives with modular multilevel converters,” in Proced-ings of Energy Conversion Congress and Exposition (ECCE 2010), pp. 4293– 4298, 12-16 Sept. 2010.

• L. Ängquist, A. Antonopoulos, D. Siemaszko, K. Ilves, M. Vasiladiotis, andH.-P. Nee, “Inner control of modular multilevel converters - an approach usingopen-loop estimation of stored energy,” in Procedings of International PowerElectronics Conference (IPEC 2010), pp.1579 – 1585, 21 – 24 Jun. 2010.

• S. Norrga, L. Ängquist, K. Ilves, L. Harnefors, and H.-P. Nee, “Decoupledsteady-state model of the modular multilevel converter with half-bridge cells,”in 6th IET International Conference on Power Electronics, Machines andDrives (PEMD 2012), pp.1 – 6, 27 – 29 Mar. 2012.

Chapter 2

The Modular Multilevel Converter

In order to find the dimensioning factors of a Modular Multilevel Converter (M2C),an understanding of its basic operating principles is essential. The schematic of onephase leg of the modular multilevel converter is shown in Fig. 2.1. Each phase legconsits of two arms, one upper arm and one lower arm, connected in series between

Figure 2.1: One phase leg of the modular multilevel converter.

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6 CHAPTER 2. THE MODULAR MULTILEVEL CONVERTER

the dc terminals. The ac terminal is located at the midpoint between the twoarms as shown in Fig. 2.1. Each arm consists of one arm inductor and N seriesconnected half-bridges with dc capacitors, termed submodules. The resistive lossesin the converter are modeled as resistors with the resistance R connected in serieswith each arm inductor. The purpose of the arm inductors is to limit parasiticcurrents and fault currents [2]. In order to limit the parasitic current, the requiredarm inductors are typically very small [3]. However, in grid applications, the arminductors may be in the range of 0.1 p.u. in order to limit fault currents [4].

The arm currents can be expressed as the sum of one common mode componentand one differential mode component. The common mode component is flowingbetween the dc terminals and the differential mode component is flowing to theac-side. Accordingly, the upper and lower arm currents iu and il in Fig. 2.1 aregiven by

iu = ic + idif (2.1a)il = ic − idif, (2.1b)

where ic is the common mode component and idif is the differential mode compo-nent, corresponding to half of the ac-side current. The common mode componentwill hereafter be referred to as the circulating current. In order for any active powertransfer to take place, the circulating current must have a dc-offset idc. The circu-lating current can, however, also have any number of harmonic components. Thismeans that ic and idif can be expressed as

ic =∞∑n=1

in + 12 iac (2.2a)

idif = 12 iac, (2.2b)

where iac is the ac-side current, and in is the nth-order harmonic in the circulatingcurrent. If the converter is assumed to be lossless, the time average of the inputpower must be equal to the time average of the output power. Accordingly,

Vdcidc = vaciac

2 cos(ϕ), (2.3)

where Vdc is the pole-to-pole voltage of the dc-link, vac is the amplitude of thealternating voltage, iac is the amplitude of the alternating current, and ϕ is thepower angle. Solving (2.3) for idc gives that

idc = iac

4 m cos(φ), (2.4)

2.1. MODULATION AND CONTROL 7

where m is the modulation index, defined as

m = 2vac

Vdc. (2.5)

The converter is controlled in such a way that the voltages across the submodulecapacitors are kept approximately constant. In this way the capacitors act asvoltage sources that can be inserted and bypassed in the chain of series connectedsubmodules. Consequently, each arm can generate a N + 1 level voltage waveform.The voltage across each chain of series connected submodules is referred to asinserted voltage. Ideally, each arm inserts an alternating voltage with a dc offset.The alternating component is in antiphase between the upper and the lower arm.In this way, a direct voltage will be imposed between the dc terminals and analternating voltage is generated at the ac terminal.

Assuming that the voltage across each submodule capacitor is constant, the av-erage duty-ratio of the submodules in each arm is varying sinusoidally with time.The average duty-ratio in each arm is referred to as as the insertion index. Ac-cordingly, the insertion indices nl and nu for the lower and upper arms are givenby

nu = 1 − m cos(ω1t)2 (2.6a)

nl = 1 + m cos(ω1t)2 , (2.6b)

where m is the modulation index. This type of modulation when the insertionindices are not compensating for the voltage variations in the submodule capacitorswill be referred to as direct modulation.

2.1 Modulation and Control

Numerous control strategies have been proposed since the M2C was introducedin [1]. These control strategies may be based on phase-shifted carriers as presentedin [5], [6], or based on the sorting algorithm that was presented in [1], such as thecontrollers in [7–9]. In these control strategies the capacitor voltages are controlledeither by feedback control or by actively choosing which submodule to insert orbypass based on the measured capacitor voltages. It is also possible to controlthe converter by programmed modulation. This means that by a proper choice ofswitching angles the harmonic performance of the M2C can be further improved byusing harmonic elimination methods [10–14].

As the capacitor voltages are varying with time additional harmonic componentsmay appear in the arm voltages and the circulating current. In fact, if the circu-lating current is not controlled, a second-order harmonic component will appear in

8 CHAPTER 2. THE MODULAR MULTILEVEL CONVERTER

the circulating current [15, 16]. Not only does this component increase the lossesbut it also affects the capacitor voltage ripple and the loss distribution betweenthe semiconductors [16]. Due to these adverse effects, it is important to controlthe circulating current in M2Cs. Several different methods for suppressing thesecond-order harmonic in the circulating current have been developed [7, 8, 14,17].

2.2 Experimental Setup

For experimental validation of the theoretical findings, a laboratory prototype ofan M2C is used. The prototype is a three-phase converter rated for 10 kVA andhas five submodules per arm. The nominal voltage of each submodule is 100Vand the capacitance of each submodule capacitor is 3.33mF. The converter can beconnected to either a controllable dc source or an autotransformer connected to thegrid. It is thus possible to operate the converter in both inverter and rectifier mode.The nominal dc-link voltage is 500V, although it is possible to reduce the dc-linkvoltage if necessary. This is done in [Publication VI] where one submodule ineach arm is permanently bypassed and the dc-link voltage is reduced to 400V.

The inductance of the arm inductors can be varied by mechanically reconnectingthe windings. In most of the experiments, however, the inductors are connected suchthat the arm inductance L is 4.67mH. The combined resistance of the arm inductorsand submodules is estimated in [Publication I] to be 0.9Ω. The aforementionedlaboratory prototype is shown in Fig. 2.2. A more detailed description of thehardware and control system is described in [18] and [19].

2.2. EXPERIMENTAL SETUP 9

Figure 2.2: A laboratory prototype of a three-phase modular multilevel converterwith five submodules per arm.

Chapter 3

Operating Principles and Control

When the converter is transferring active power from the dc link to the ac side,a direct current is flowing between the dc terminals. This current is charging thesubmodule capacitors and moves energy from the dc link into the converter. Thealternating current is split evenly between the arms and is in phase with the alter-nating component of the inserted voltage when active power is transferred. Thismeans that the alternating current is able to discharge the submodule capacitorsand thus it is possible to transfer active power through the converter.

The voltage across the submodule capacitors will vary as they are charged anddischarged by the direct and alternating currents. Using a simplified model, theresulting capacitor voltage ripple in each arm can be estimated by integrating theproduct of the insertion index and the arm current [Publication I]. Ideally, thearm currents are given by the sum of the direct component idc and half of thealternating component iac. If direct modulation is used, the insertion indices aregiven by (2.6).

The idealized model can be compared with experimental data from the proto-type described in Section 2.2. The measured and estimated peak-to-peak voltageripple at active power transfer in inverter mode with the modulation index 0.9 isshown in Fig. 3.1. It is observed that there is a significant discrepancy between themeasured and estimated capacitor voltage ripple. In fact, the measured capacitorvoltage ripple is close to 30% larger than the estimated values. The reason for thisis that the arm currents are not accurately described by the sum of the direct com-ponent and half of the alternating component. In fact, experimental data indicatethat in addition to the direct component, there is also a second-order harmoniccirculating between the dc terminals.

The discrepancy between the simplified model and the experimentally obtaineddata indicates that parasitic components in the arm currents can have a significant

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12 CHAPTER 3. OPERATING PRINCIPLES AND CONTROL

Figure 3.1: Estimated and measured capacitor voltage ripple at active power trans-fer using a simplified model.

impact on the capacitor voltages. It is concluded that the observed second-orderharmonic component originates from the variations in the capacitor voltages asthe capacitors are charged and discharged by the arm currents. This means thatnot only is the capacitor voltage ripple increased by the the parasitic components,but the parasitic components themselves may also be influenced by the size of theenergy storage elements. Therefore, it is important to analyze the dynamics of thearm currents in order to understand how the system is affected by the size of thesubmodule capacitors.

3.1 Arm Currents at Direct Modulation

A detailed analysis relating the ac-side quantities to the arm currents is providedin [Publication I]. The analysis focuses on steady-state operation with a highswitching frequency. It is found that a second-order harmonic is induced as a directresult of the power transfer through the converter. It could also be concluded thathigher-order harmonics are also induced in the circulating current as a consequenceof the second-order harmonic component.

The dynamic equations governing even-order and odd-order harmonics in thecirculating current can be decoupled. It is then found that there is no excitation ofodd-order harmonics during nominal operation. This is an interesting result since itmeans that the first zero-sequence component in the inserted voltage of each phaseleg is the sixth-order harmonic. This means that the dc link voltage is, generally, notaffected by the capacitor voltage variations as the sixth-order harmonc componentis, in most cases, comparably small.

3.1. ARM CURRENTS AT DIRECT MODULATION 13

The magnitude of each harmonic component in the circulating current is closelyrelated to the value of the submodule capacitance C and arm inductance L. It isfound that there exist a resonant peak for each harmonic component at which itsamplitude takes its maximum value. In order to avoid the resonant peak of thesecond-order harmonic, the product LC should be chosen such that

LC >5N

12ω21. (3.1)

The value of the product LC related to the resonant peak is always lower for higher-order harmonics and lower modulation indices. This means that if the product LCis chosen such that (3.1) is satisfied, the resonant peak can be avoided for at allmodulation indices and all harmonic-orders.

The theoretical findings in [Publication I] show that the amplitude of thehigher-order harmonics in the circulating current is strictly decreasing for certainvalues of L and C. It can be shown that this is the case if (3.1) is satisfied. Infact, if (3.1) is satisfied, the amplitude of the fourth-order harmonic is at least tentimes smaller than the amplitude of the second-order harmonic. This means thatalthough higher-order harmonics may exist in the circulating current, the harmoniccontent is most often dominated by the second-order harmonic. Therefore, as anapproximation, the arm currents in (2.2) can be simplified to

iu ≈ idc + i2 + 12 iac (3.2a)

il ≈ idc + i2 − 12 iac. (3.2b)

In high-power applications, the arm resistance R can be considered to be verysmall. By neglecting the resistance R and assuming that (3.1) is satisfied, thesecond-order harmonic component in the circulating current can be expressed as

i2 ≈ Re

3m[3ejφa1 − m2 cos(φ)]

12 + 8m2 − 48σ ej2ω1t

iac, (3.3)

whereσ = ω2

1LC

N. (3.4)

The theoretical findings in [Publication I] were verified experimentally usingthe converter described in Section 2.2. Fig. 3.2 shows the measured amplitudesof the second-order harmonic component when the converterer is operating attdifferent frequencies. The solid line in Fig. 3.2 is a fitted curve where the valuesof the arm resistance R and submodule capacitance C were extracted from themeasured values by least square fitting of the analytical expressions to the measured


Figure 3.2: Measured amplitudes of the second-order harmonic in the circulatingcurrent and a fitted curve calculated using the analytical expressions.

Figure 3.3: Measured peak-to-peak capacitor voltage ripple as function of the loadcurrent (rms).

values. The estimated value of R in Section 2.2 is the value that was extracted bythe least square fitting.

As the arm current can be described by (3.2) and (3.3) it should be possibleto obtain an improved estimation of the capacitor voltage ripple in Fig. 3.1. Theestimated capacitor voltage ripple when the second-order harmonic is included inthe model is shown in Fig. 3.3. It is concluded that the theoretical model in[Publication I] can be used to obtain an accurate estimation of the resultingcapacitor voltage ripple.

3.1. ARM CURRENTS AT DIRECT MODULATION 15

3.1.1 Impact of Main Circuit Filters

Since the harmonic components in the circulating current are often dominated bythe second-order harmonic it appears appropriate to use a main circuit filter in orderto eliminate this harmonic component in the circulating current [2]. An illustrationof how such a main circuit filter can be implemented is shown in Fig. 3.4. The filterconsists of one filter capacitancce, Cf , in parallel with one filter inductance Lf .The filter is tuned to block the second-order harmonic in the circulating current.Consequently, the capacitance Cf can be expressed as

Cf = 14ω2

1Lf. (3.5)

The impact of a main circuit filter is analyzed in [Publication II]. It is con-cluded that not only can the main circuit filter block the second-order harmonic,but it also prevents the excitation of higher-order harmonics. Consequently, thecirculating current will be a direct component wih a high-frequency ripple origi-nating from the insertion and bypassing of the submodules. It is, however, foundthat this is not true for the case when third-order harmonic injection is used. Thereason for this is that the third-order harmonic injection will induce a fourth-orderand a sixth-order harmonic component in the circulating current.

The analysis in [Publication II] indicates that there exist resonant peaks wherethe amplitudes of the harmonic components in the circulating current take theirmaximum values. This means that with an inappropriate filter design, large har-monic components may appear in the circulating current. The theoretical findingswere validated by computer simulations of a converter with a main circuit filter.

Figure 3.4: Implementation of a main circuit filter tuned to block the second-orderharmonic in the circulating current.


Figure 3.5: Simulated insertion indices (upper), arm currents, and circulating cur-rent (lower) with a main circuit filter.

Fig. 3.5 shows the simulated insertion indices, arm currents, and circulating current.It is observed that the circulating current is, initially, a direct current. The reasonfor this is that there is no excitation of the fourth order harmonic. However, af-ter 0.04 seconds when third-order harmonic injection is activated, an unacceptablylarge fourth-order harmonic component appear in the circulating current.

The findings in [Publication II] indicate that the filter design can have a sig-nificant impact on the resulting harmonic components in the circulating current.It is possible to design the filter in such a way that all harmonic components arewell damped in steady-state operation, even when third-order harmonic injectionis used. However, it is concluded that in real systems with transients and powerflow controllers the main circuit filter cannot guarantee that large harmonic com-ponents are not induced in the circulating current. Therefore, it is concluded thatthe implementation of a circulating current controller is inevitable.

3.2. CAPACITOR VOLTAGE RIPPLE COMPENSATION 17

3.2 Capacitor Voltage Ripple Compensation

The analysis in [Publication I] and [Publication II] consider the harmonic com-ponents that are imposed between the dc terminals as a result of the capacitorvoltage variations. The varying capacitor voltages will, however, also affect the ac-side voltage waveform. The distortion of the ac-side voltage waveform is analyzedin [Publication III].

It is known that it is possible to compensate for the capacitor voltage rip-ple by measuring the capacitor voltages [7]. This will, however, render the sys-tem unstable which means that stabilizing feedback controllers are required. In[Publication III] it is shown that it is possible to control the ac-side voltage witha stable feed-forward controller. This is done by adjusting the insertion indices as

n∗u = 12vcu

(vi − 2vac − L

diacdt

−Riac

)(3.6a)

n∗l = 12vcl

(vi + 2vac + L

diacdt

+Riac

), (3.6b)

where nu and nl are given by (2.6), vac is the requested ac-side voltage, vcu andvcl are the sum of all the capacitor voltages in the upper and lower arms, and viis the voltage that should be imposed between the dc terminals. If vi is chosen asa constant value, the system will become unstable and require stabilizing freebackcontroller as it was concluded in [7]. In [Publication III] it is proposed that thevoltage vi can be chosen as

vi = nlvcl + nuvcu. (3.7)

In this way, the ac-terminal voltage can be controlled by means of a feed-forwardcontroller without the need for a stabilizing feedback controller.

It is evident that the inserted voltage in (3.7) will not be a direct voltage sincevcl and vcu are varying with time. This will only affect the voltage that is imposedbetween the dc terminals and will not influence the voltage waveform at the ac ter-minal. The presented control method can, however, be combined with a circulatingcurrent controller that will adjust vi such that vi becomes a direct voltage. Thiscould for example be done by using an open-loop approach as presented in [8, 9].The ac-side voltage would then be controlled with a high bandwidth and precisionusing a feed-forward controller whereas the dc-side voltage would be controlled withan open-loop controller derived from the steady-state representation of the system.In order to avoid problems during transients, an additional controller that dampsoscillations in the circulating current can be added.

The proposed feed-forward controller was implemented on the prototype de-scribed in Section 2.2. The circulating current was controlled by adjusting vi usingan open-loop controller in combination with a damping controller that counteracts


Figure 3.6: Measured ac-side voltage and current waveforms during a step transient.

Figure 3.7: Measured arm currents and circulating current during a step transient.

changes in the circulating current. The converter was then set to operate in in-verter mode, supplying a passive load with the modulation index 0.4. The currentsand voltages were then recorded as the modulation index was increased to 0.9 inone step. The recorded ac-side voltage and and current waveforms are shown inFig. 3.6. By analyzing the recorded data it could be verified that the amplitude ofthe ac-side voltage waveform was, in fact, equal to the requested value.

The arm currents were recorded during the transient in order to verify thatthe circulating current controller could function properly at the same time as thefeed-forward controller is acting on the ac-side voltage. The recorded arm currentsand the circulating current are shown in Fig. 3.7. It is observed that the circulating

3.2. CAPACITOR VOLTAGE RIPPLE COMPENSATION 19

current is, in fact, a direct current both before and after the step change.

Chapter 4

Dimensioning Criteria

4.1 General Energy Storage Requirements

It has been shown that it is possible to compensate for the variations in the capacitorvoltages in order to avoid distorted voltage waveforms and harmonic componentsin the circulating current. The power transfer capability is, however, still limitedby the size of the capacitors. The reason for this is that the capacitor voltage ripplemust be limited. The peak voltage across the submodule capacitors is limited bythe voltage rating of the submodules. There is also a lower limit for the capacitorvoltages below which the voltage variations cannot be compensated for which resultsin overmodulation. The relation between the size of the submodule capacitors andthe power transfer capability is analyzed in [Publication IV].

The fingings in [Publication IV] indicate that the power transfer capability isdirectly related to the total energy storage in the converter and is not affected bythe number of submodules. The required energy storage per MVA can be calculatedfrom the desired modulation index, voltage limit, and grid frequency. The voltagelimit is given by the factor kmax and defines the relation between the upper voltagelimit and the nominal submodule voltage. That is, if kmax is equal to 1.1 this meansthat the capacitor voltages are allowed to increase by 10% above their nominalvalues.

It is found that the energy storage requirements are directly proportional tothe apparent power transfer of the submodules, inversely proportional to the gridfrequency, and has a nonlinear dependency on kmax. Fig. 4.1 shows the requiredenergy storage capability per transferred MVA for different values of kmax with andwithout third-order harmonic injection. The calculated values in Fig. 4.1 indicatethat the energy storage requirements are significantly higher for reactive power con-sumption, compared to active power transfer and reactive power generation. The

21

22 CHAPTER 4. DIMENSIONING CRITERIA

Figure 4.1: Required energy storage capability per transferred MVA for differentvalues of kmax with (red) and without (blue) third-order harmonic injection.

required energy storage for reactive power consumption is, however, significantlyreduced when third-order harmonic injection is used.

In [Publication IV] it is concluded that the energy storage requirements arealso affected by the modulation index. Fig. 4.2 shows an example of how the energystorage requirements vary with the modulation index at active power transfer whenthe capacitor voltages are limited such that they do not exceed their nominal valuesby more than 10%. It is observed that for active power transfer it is advantageousto operate the converter with third-order harmonic injection at a modulation indexthat is close to unity. However, the modulation index that results in the highestpower transfer capability is not only affected by the power angle but also the up-per limit of the capacitor voltages. The required energy storage in Fig. 4.2 wascalculated with the same voltage limit as for Fig. 4.1.

4.1. GENERAL ENERGY STORAGE REQUIREMENTS 23

Figure 4.2: Required energy storage capability per transferred MW for differentmodulation indices and values of kmax with (red) and without (blue) third-orderharmonic injection.

4.1.1 Operating Region Extention

In [Publication IV] it was concluded that the size of the submodule capacitorscan be related to the power transfer capability of the converter. This limitation canbe illustrated by the experimentally obtained waveforms in Fig 4.3. The waveformsin Fig. 4.3 are obtained in inverter operation with a passive, mainly resistive load.The requested voltage in Fig. 4.3 is well below the peak value of the availablevoltage. However, the peak of the requested voltage does not coincide with thepeak of the available voltage. As a consequence, if the peak of the available voltageis to be limited to 510 V, the power transfer cannot be increased without enteringthe region of overmodulation. This is the main reason for why the power transfercapability is limited by the size of the capacitors at capacitive power angles. Thepossibility of injecting a second-order harmonic in the circulating current in orderto alleviate this problem is investigated in [Publication V]. The purpose of theinjected second-order harmonic is to alter the capacitor voltage waveform in such away that the peak of the available voltage coincides with the peak of the requested


Figure 4.3: Requested voltage and available voltage in the upper and lower arms.

voltage.The impact of injecting a second-order harmonic in the circulating current is

analysed analytically in [Publication V]. The expressions are then used to find asuitable value of the phase and amplitude of a second order harmonic that will givethe desired results. The method of injecting a second-order harmonic componentin the circulating current was also tested on the laboratory prototype decribed inSection 2.2 with the same load conditions as for the waveforms in Fig. 4.3. Thephase and amplitude of the second-order harmonic that would give the desired effectwas then calculated. The measured available and requested voltages are shown inFig. 4.4 as the converter is controlled in such a way that the calculated second-orderharmonic component is obtained in the circulating current. It is observed that thepeak of the requested voltage coincides with the peak of the available voltage. Inthis way overmodulation can be avoided, and the peak voltage of the submodulecapacitors can be reduced at the same time.

4.2 Semiconductors Requirements

In a conventional two-level converter, there is a trade-off between switching fre-quency and harmonic performance which increases the switching losses in the con-verter. In fact, in a conventional two-level converter, the switching losses may be

4.2. SEMICONDUCTORS REQUIREMENTS 25

Figure 4.4: Available voltage and requested voltage in the upper and lower armsusing the proposed second-order harmonic injection method.

as high as 50% of the overall converter losses [20]. The cascaded structure of amodular multilevel converter allows the combination of excellent harmonic perfor-mance and very low switching frequency. This is one of the key features that leadsto the very high efficiency of the M2C. However, this also means that the choice ofswitching frequency will have a noticable impact on the overall losses in the con-verter. In fact, it has been shown that the submodule losses can increase by 20-40%when the switching frequency is increased from two to four times the fundamentalfrequency [21].

4.2.1 Minimum Switching Frequency

When the switching frequency is reduced, deviations in the capacitor voltages be-come inevitable. Although a temporary unbalance in the capacitor voltages may beacceped, the capacitor voltages must be kept balanced over time. The lower limitof the switching frequency where the capacitor voltages can be kept balanced overtime is considered in [Puiblication VI].

In [Publication VI] it is shown that the capacitor voltages can be kept bal-anced even at fundamental switching frequecny. This is done by a round-robinsystem in which the pulse pattern to the N submodules in each arm is cycled


among the submodules. It is also found that the order in which the pulse patternis cycled can have a significant impact on the resulting capacitor voltage ripple.Although the capacitor voltage ripple is affected by the order in which the pulsesare cycled, a significant increase of the capacitor voltage ripple compared to higherswitching frequencies cannot be avoided.

By using the proposed round-robin system the capacitor voltages can be keptbalanced without any form of feedback controller. Fig. 4.6 shows the capacitorvoltages in three submodules of a simulated system with 12 submodules per arm.After approximately 0.2 seconds, a disturbance is introduced in three of the twelvesubmodules in one arm. The first submodule is discharged such that its voltage is40% less than the nominal value, the second submodule is charged to a voltage 20%higher than the nominal value and the third submodule is discharged to a voltagethat is 20% less than the nominal value. It is observed that all of the capacitorvoltages are slowly converging back to their nominal values. Although the capacitorvoltages can be balanced without any feedback controllers, an active control of thecapacitor voltages may be required in order to ensure that the capacitor voltagesremain balanced when the dynamics of the grid and external power flow controllersare considered. The implementation of such a feedback controller could be donewithout increasing the switching frequency.

Circulating Current Control

A control method that can eliminate the second-order harmonic in the circulatingcurrent at fundamental switching frequency is presented in [Publication VII].The proposed method introduces small deviations in the width of the square pulsesthat are imposed by each submodule.

The functionality of the proposed control schem was validated experimentallyusing the prototype described in Section 2.2. In this experiment, the converter wasconnected to the grid and set to operate in rectifier mode, supplying a passive 5.5 kWresistive load connected to the dc terminals. At the same time, the converter wasinjecting 0.8 kVAr reactive power to the grid. The recorded arm currents and thecirculating current in one of the phases are shown in Fig. 4.6. It is concluded thatno second-order harmonic component can be observed in the circulating currentwhen the proposed control scheme is used.

4.2.2 Minimum Power Rating of Semiconductors

As a consequence of the low switching frequency of the devices in modular multi-level converters the thermal limitation of the semiconductors is not the dimensioningfactor. Instead, the dimensioning factor is the power rating of the semiconductors.


Figure 4.5: Simulated capacitor voltages in three of the twelve submodules in onearm.


Figure 4.6: Measured arm currents and the circulating current with fundamentalswitching frequency operating in rectifier mode.

That is, the product of the rated voltage and the rated current. The semiconductordevices must be able to withstand the voltage of one submodule capacitor. Forsafety purposes, the actual voltage rating of the semiconductors would be cho-sen higher than the maximum expected operating voltage in any real application.However, in order to quantify the semiconductor requirements in such a way thatdifferent topologies can be compared, the power rating is assumed to be equal tothe product of the maximum expected operating voltage and the expected peakcurrent.

The maximum expected operating voltage of each semiconductor device, Vrated,is found by multiplying the nominal submodule voltage with the allowed increasein the capacitor voltages, defined by kmax [Publication V]. Accordingly,

Vrated = Vdc

Nkmax, (4.1)

where Vdc is the pole-to-pole voltage of the dc link. The current rating, Irated, ofthe devices is defined by the peak-value of the arm currents at the rated operatingpoint. Since the alternating current is divided evenly between the upper and lowerarms, Irated can be expressed as

Irated = idc + 12 iac. (4.2)

Substituting idc in(4.2) with (2.4) yields

Irated = iac

(12 + 1

4m cos(φ)). (4.3)


The power rating of each semiconductor is then given by the product of (4.1) and(4.3),

Prated = Vdc

N

(12 + 1

4m cos(φ))kmaxiac. (4.4)

Solving (2.5) for Vdc gives that

Vdc = 2vac

m. (4.5)

Substituting Vdc in (4.4) with (4.5) yields

Prated = 2vac

mN

(12 + 1

4m cos(φ))ksmiac. (4.6)

The combined power rating of all semiconductors in the converter is obtained bymultiplying (4.6) with the number of switches in the converter. As each submodulehas 2 switches and there are six arms with N submodules in each arm, the totalnumber of switches in the converter is 12N . This gives that the combined powerrating, PSM, of the semiconductor devices is given by

PSM = 16Sm

(12 + 1

4m cos(φ))ksm, (4.7)

where

S = 3(vaciac

2

). (4.8)

Chapter 5

Conclusions and Future Work

In the initial analysis of the arm currents it was found that only even-order har-monics are induced in the circulating current. Consequently, there is no third-orderharmonic in the circulating current that will cause a voltage and current ripple onthe dc link. The first zero-sequence component is the sixth-order harmonic, whichin most cases is negligible. This means that the capacitor voltage ripple will notcause any significant disturbances on the dc link. The second-order harmonic can,however, be significant and cause increased losses and capacitor voltage ripple.Therefore, a previously presented main-circuit filter is able to block this harmoniccomponent without any additional control actions was analyzed. It was found thatwhen third-order harmonic injection is used, the design of the filter becomes in-creasingly important for high-power converters with high efficiencies. The reasonfor this is that third-order harmonic injection may induce a fourth-order harmonicin the circulating current. If this is not taken into consideration when designingthe filter, resonance may occur.

The analysis indicates that there will always exist resonant frequencies evenif they are not excited in nominal steady state operation. In real applications,however, the dynamics of the grid and external power flow controllers may beunpredictable and therefore a circulating current controller may be required evenwhen main circuit filters are used in order to avoid unacceptably large harmoniccomponents in the circulating current.

If left uncompensated, the voltage variations in the submodule capacitors willdistort the ac-side voltage waveform. Previously presented feed-forward controllerscan compensate for these variations but will require stabilizing feedback controllersin order to ensure stability. It was, however, found that a form of stable feed-forwardcontrol of the ac-terminal voltage is possible without the need of stabilizing feedbackcontrollers. This means that the distortion of the ac-side voltage waveform can be

31

32 CHAPTER 5. CONCLUSIONS AND FUTURE WORK

compensated for even with high demands on accuracy and bandwidth. It was alsoshown that the aforementioned feed-forward controller can be combined with anactive control of the circulating current. Consequently, the limiting factors of thesize of the submodule capacitors are mainly the operating range the and voltagerating of the submodules whereas the harmonic disturbances on both the dc-sideand ac-side can be compensated for by control actions.

In order to compensate for the capacitor voltage ripple, the requested voltagethat is to be inserted must be available in the arms at all times in order to avoidovermodulation. The capacitor voltage ripple must also be limited such that thepeak voltage does not exceed the voltage rating of the submodules. The generalizedanalysis of the energy storage requirements indicates that the relation between theoperating range and the size of the submodule capacitors is directly related to thetotal energy that is stored in the converter. Since the size and cost of of high voltagecapacitors is proportional to their rated energy storage capability, this means thatthe overall size and cost of the energy storage elements cannot be affected by simplychanging the number of submodules per arm. Therefore, when considering theoverall size and cost of the energy storage elements it is reasonable to strictly speakin terms of stored energy per power transfer capability.

The generalized analysis of the energy storage requirements indicated that therequired energy storage per transferred MVA varies with the power angle. Typi-cally, reactive power generation has lower requirements on the energy storage thanreactive power consumption. In fact, the active power transfer capability can evenin some cases be increased by injecting reactive power into the grid. The energystorage requirements can in some cases also be reduced by third-order harmonic in-jection. When the converter is consuming reactive power from the grid, third-orderharmonic injection results in a significant reduction of the energy storage require-ments. For active power transfer and reactive power generation the relation is theopposite. At active power transfer and reactive power generation the difference is,however, less significant.

It was discovered that if the circulating current is controlled, the shape of thecapacitor voltage waveforms can be altered by injecting a second-order harmonic.In this way the operating region can be extended by shaping the capacitor voltagesin such a way that the point in time where the capacitor voltages reach theirmaximum values occur at the same time as when the voltage reference is at itsmaximum value. This method for extending the operating region will, however,increase the losses due to the injected second-order harmonic and also increase thecomplexity of the control system.

When the operating region, circulating currents, dc-side quantities, and ac-sidequantities are analyzed, the capacitor voltages are often assumed to be well balancedwhich is equivalent to assuming an infinite switching frequency. However, one of

5.1. FUTURE WORK 33

the key features of the modular multilevel converter is the possibility to operateat low switching frequencies. Therefore, the lower limit of the switching frequencywas investigated. It was found that it is possible to control all relevant quantities,including the circulating current, even at fundamental switching frequency. Thiswill, however, increase the capacitor voltage ripple meaning that there is a trade-offbetween the switching frequency and the capacitor voltage ripple.

5.1 Future Work

This thesis presents an extensive analysis of the operating principles and dimen-sioning factors of modular multilevel converters. The analytical tools that havebeen derived can be adapted and applied to other topologies as well. In this way, adetailed comparison can be made between various converter topologies for specificconversion tasks.

Although the modular multilevel converter is an interesting and promising topol-ogy, other promising topologies that are still undiscovered may exist. Therefore,the future work should not only be limited to comparing existing topologies but aneffort should be made to find new alternatives for high-power applications.

List of Figures

2.1 One phase leg of the modular multilevel converter. . . . . . . . . . . . . 52.2 A laboratory prototype of a three-phase modular multilevel converter

with five submodules per arm. . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 Estimated and measured capacitor voltage ripple at active power trans-fer using a simplified model. . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Measured amplitudes of the second-order harmonic in the circulatingcurrent and a fitted curve calculated using the analytical expressions. . 14

3.3 Measured peak-to-peak capacitor voltage ripple as function of the loadcurrent (rms). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.4 Implementation of a main circuit filter tuned to block the second-orderharmonic in the circulating current. . . . . . . . . . . . . . . . . . . . . 15

3.5 Simulated insertion indices (upper), arm currents, and circulating cur-rent (lower) with a main circuit filter. . . . . . . . . . . . . . . . . . . . 16

3.6 Measured ac-side voltage and current waveforms during a step transient. 183.7 Measured arm currents and circulating current during a step transient. . 18

4.1 Required energy storage capability per transferred MVA for differentvalues of kmax with (red) and without (blue) third-order harmonic in-jection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2 Required energy storage capability per transferred MW for differentmodulation indices and values of kmax with (red) and without (blue)third-order harmonic injection. . . . . . . . . . . . . . . . . . . . . . . . 23

4.3 Requested voltage and available voltage in the upper and lower arms. . 244.4 Available voltage and requested voltage in the upper and lower arms

using the proposed second-order harmonic injection method. . . . . . . 254.5 Simulated capacitor voltages in three of the twelve submodules in one

arm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

35

36 List of Figures

4.6 Measured arm currents and the circulating current with fundamentalswitching frequency operating in rectifier mode. . . . . . . . . . . . . . . 28

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38 BIBLIOGRAPHY

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Documents

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