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M.S. THESIS

Modeling and Control of Modular Multilevel

Voltage Source Converters for HVDC Application with

Generalized DC Bus

BY

Shenghui Cui

August 2014

Department of Electrical Engineering

College of Engineering

Seoul National University

M.S. THESIS



Generalized DC Bus

BY

Shenghui Cui

August 2014

Department of Electrical Engineering

College of Engineering

Seoul National University

공학석사학위논문

일반화된 직류단에 근거한 직류 송전용

모듈형 멀티레벨 전압형 컨버터의

모델링 및 제어



Generalized DC Bus

2014년 8월

서울대학교 대학원

전기.컴퓨터 공학부

崔盛輝

In memory of my maternal grandfather,

who inspired my love and passion in engineering.

저의 마음 속에서 항상 저를 지켜보고 계신

외할아버지께 이 논문을 바칩니다.

i

주요어: HVDC, VSC, Modular Multilevel Converter, modeling, control, balancing

학 번: 2012-23963

Abstract

Control methods of the Modular Multilevel Converter (MMC) are classified into

indirect modulation based control and direct modulation based control. In this thesis, a

modified modeling of an indirect modulated MMC is proposed for generalized DC bus of

High Voltage DC (HVDC) transmission. Based on the proposed modeling, a

comprehensive arm capacitor energy control strategy is derived, which is valid regardless

of the characteristics of the DC bus.

In addition, for the direct modulated MMC, mechanism and dynamics of the natural

balancing of the arm capacitor energy are analyzed. It is proven mathematically in this

thesis that arm capacitor energy of six arms of the MMC converges to be balanced

inherently regardless of the characteristics of the DC bus while an MMC is direct

modulated.

A novel control strategy of the MMC based Voltage Source Converter (VSC)-HVDC

transmission system is also proposed. Different from the conventional two-level converter

based transmission system or the direct modulated MMC based transmission system, the

instantaneous DC bus voltage of the MMC is fully decoupled from the energy stored in

the DC capacitors of the converter by the proposed method. The transmission line voltage

fluctuation is also suppressed during power flow variation by the proposed method.

Validity of the conducted work in this thesis is verified by both computer simulations

and experiments.

ii

iii

Contents

Abstract ................................................................................................. i

Contents ............................................................................................... iii

1. Introduction ..................................................................................... 1

1.1 Background ............................................................................... 1

1.1.1. The Era of Mercury Arc Valves ................................................................. 2

1.1.2. The Era of Power Semiconductor Valves .................................................. 3

1.2 Review of VSC-HVDC Transmission ...................................... 3

1.3 MMC, a New Era of VSC-HVDC Technology ........................ 6

1.4 Purpose of This Thesis .............................................................. 9

1.5 Thesis Outline ......................................................................... 11

2. Basic Principle and Control of the MMC ................................... 12

2.1. Operation Principle of the MMC ........................................... 12

2.2. Indirect Modulation and Direct Modulation .......................... 13

2.3. Review of the Research on Control of the MMC .................. 15

3. Indirect Modulation Based Control Strategy of MMC ............. 18

3.1 Modeling of the Indirect Modulated MMC with Stiff Voltage

Sourced DC Bus ...................................................................... 20

3.2 Control of the Indirect Modulated MMC with Stiff Voltage

Sourced DC Bus ...................................................................... 24

3.2.1 Current Control of the Indirect Modulated MMC with Stiff Voltage

Sourced DC Bus ................................................................................................ 24

3.2.2 Arm Capacitor Energy Control of the Indirect Modulated MMC with Stiff

Voltage Sourced DC Bus ................................................................................... 25

3.3 Modeling of the Indirect Modulated MMC with Generalized

DC Bus .................................................................................... 29

iv

3.3.1 Analysis of AC Grid Current of the MMC with Generalized DC Bus ..... 31

3.3.2 Analysis of DC Bus Current of the MMC with Generalized DC Bus ...... 34

3.3.3 Analysis of Circulating Current of the MMC with Generalized DC Bus 36

3.4 Control of the Indirect Modulated MMC with Generalized DC

Bus .......................................................................................... 40

3.4.1 Control of Energy Stored in the Whole Cell Capacitors of the MMC ..... 42

3.4.2 Balancing of Three Phase Leg Capacitor Energy..................................... 44

3.4.3 Balancing of Upper and Lower Arm Capacitor Energy ........................... 47

3.4.3 Overall Structure of the Proposed Method and Practical Implementation

Issues ................................................................................................................. 54

3.5 Ride Through Strategy of the AC Grid Single Line to Ground

(SLG) Short Circuit Fault ....................................................... 56

4. Direct Modulation Based Control Strategy of the MMC .......... 64

4.1 Modeling of the Direct Modulated MMC with Stiff Voltage

Sourced DC Bus ...................................................................... 65

4.1.1 Arm Output Voltage and Insertion Ratio .................................................. 65

4.1.2 Analysis of Grid Current and Leg Current ............................................... 67

4.2 Mechanism and Dynamics of Arm Capacitor Energy

Regulation of the MMC with Stiff Voltage Sourced DC Bus 70

4.2.1 Dynamics of Sum of Upper and Lower Arm Capacitor Voltages ............ 71

4.2.2 Dynamics of Difference of Upper and Lower Arm Capacitor Voltages ... 73

4.3 Modeling of the Direct Modulated MMC with Generalized DC

Bus .......................................................................................... 74


Balancing of the MMC with Generalized DC Bus ................. 77

4.4.1 Dynamics of Balancing of Leg Capacitor Voltages ................................. 77

4.4.2 Dynamics of Differences of Upper and Lower Arm Capacitor Voltages . 79

5. Control of an MMC Based Point-to-Point HVDC Transmission

System ................................................................................................. 85

5.1 Direct Modulation Based Control Strategy of the Point-to-

Point HVDC Transmission System ........................................ 85

v

5.2 Indirect Modulation Based Control Strategy of Point-to-Point

HVDC Transmission System .................................................. 88

5.2.1 Proposed Voltage-Voltage (VV) Control Strategy of VSC-HVDC

Transmission System Based on Indirect Modulated MMC .............................. 88

5.2.2 Proposed Voltage-Power (VP) Control Strategy of VSC-HVDC

Transmission System Based on Indirect Modulated MMC .............................. 89

6. Simulations and Experimental Verification ................................ 91

6.1 Simulation of an MMC under Indirect Modulation Based

Control Strategy ...................................................................... 91

6.1.1 Simulation of a 217 Level, ±200kV MMC in No Load Condition .......... 91

6.1.2 Simulation of a 217 Level, ±200kV MMC in Loaded Condition ............ 97

6.2 Experimental Verification of an MMC under Indirect

Modulation Based Control Strategy ..................................... 101

6.2.1 Experimental Verification of a 7-Level, 300V MMC in No Load

Condition ......................................................................................................... 102

6.2.2 Experimental Verification of a 7-Level, 300V MMC in Loaded Condition

......................................................................................................................... 107

6.3 Simulation of an MMC during an AC Grid SLG Fault ........ 110

6.4 Simulation of an MMC under Direct Modulation Based

Control Strategy .................................................................... 113

6.5 Simulation of a Point-to-Point HVDC Transmission System

under Direct Modulation Based Control Strategy ................ 117


under Indirect Modulation Based Control Strategy .............. 119

6.6.1 Simulation of a HVDC System Employing VV Control ........................ 120

6.6.2 Simulation of a HVDC System Employing VP Control ........................ 122

6.6.3 Simulation of a HVDC System Employing VP Control to Feed a Passive

Grid ................................................................................................................. 124

6.7 Experimental Verification of a Point-to-Point HVDC

Transmission System under Indirect Modulation Based

Control Strategy .................................................................... 126

6.7.1 Experiment of a HVDC System Employing Proposed VV Control ....... 127

vi

6.7.2 Experiment of a HVDC System Employing Proposed VP Control ....... 131

7. Conclusions .................................................................................. 134

7.1 Conclusions ........................................................................... 134

7.2 Contributions......................................................................... 136

7.3 Future Work .......................................................................... 136

Bibliography .................................................................................... 138

APPENDIX A ............................................................................. 140

APPENDIX B ............................................................................. 141

APPENDIX C ............................................................................. 142

APPENDIX D ............................................................................. 143

APPENDIX E ............................................................................. 144

APPENDIX F .............................................................................. 145

vii

Contents of Figures

Figure 1-1 Conceptual structure of the LCC-HVDC transmission system. ........................ 2

Figure 1-2 Conceptual structure of a VSC-HVDC transmission system. ........................... 4

Figure 1-3 Conceptual structure of an MMC-HVDC station. ............................................. 7

Figure 1-4 Losses of HVDC Light products for each generation [3]. ................................. 8

Figure 2-1 Operation principle of the MMC. .................................................................... 12

Figure 2-2 Simulation waveforms of the MMC under indirect modulation control and

under direct modulation control. ............................................................................... 14

Figure 2-3 Family tree of the research on control of the modular multilevel converter. .. 17

Figure 3-1 Conceptual structures of MMC stations. ......................................................... 18

Figure 3-2 Structure of an MMC analyzed in the previous works. ................................... 20

Figure 3-3 Per phase equivalent circuit of the conventional modeling with stiff DC bus

voltage source. .......................................................................................................... 22

Figure 3-4 Per phase extracted models of AC grid current and leg current in the

conventional modeling. ............................................................................................. 23

Figure 3-5 Conceptual structures of current controllers. ................................................... 24

Figure 3-6 Conceptual principle of the conventional arm capacitor energy control. ........ 27

Figure 3-7 Conceptual structures of the conventional arm capacitor energy controllers. . 27

Figure 3-8 Conventional controllers of the MMC with stiff DC bus voltage source. ....... 28

Figure 3-9 MMC model for HVDC application under the conventional control strategy. 30

Figure 3-10 Analysis of AC grid current of the MMC with generalized DC bus. ............ 31

Figure 3-11 Phase U and phase V of the MMC observed from the AC grid side. ............ 33

Figure 3-12 Three phases of the MMC observed from the AC grid side. ......................... 33

Figure 3-13 Extracted model from the MMC circuit to analyze AC grid current. ............ 34

viii

Figure 3-14 Analysis of DC bus current of the MMC with generalized DC bus. ............. 34

Figure 3-15 Extracted model from the MMC circuit to analyze DC bus current.............. 36

Figure 3-16 Analysis of circulating current of the MMC with generalized DC bus. ........ 38

Figure 3-17 Extracted model from the MMC circuit to analyze circulating currents. ...... 38

Figure 3-18 Models extracted from the MMC circuit to analyze AC grid current, DC bus

current, and circulating current. ................................................................................ 40

Figure 3-19 Principle of control of the energy stored in the whole cell capacitors of the

MMC. ........................................................................................................................ 43

Figure 3-20 Control block diagram of the proposed converter total capacitor energy

controller. .................................................................................................................. 44

Figure 3-21 Principle of balancing of three phase leg capacitor energy. .......................... 46

Figure 3-22 Control block diagram of the proposed leg capacitor energy balancing

controller. .................................................................................................................. 46

Figure 3-23 Principle of balancing of upper and lower arm capacitor energy by injecting

positive sequence circulating current. ....................................................................... 49


negative sequence circulating current. ...................................................................... 51

Figure 3-25 Control block diagram of the proposed upper and lower arm capacitor energy

balancing controller. .................................................................................................. 53

Figure 3-26 Overall control block diagram of the proposed MMC controller. ................. 54

Figure 3-27 Brief conceptual block diagram of the proposed cascade structured arm

capacitor energy balancing controller in the stationary dq reference frame. ............ 56

Figure 3-28 Schematic of the AC grid current vector controller for SLG fault ride through.

................................................................................................................................... 57

Figure 4-1 Conceptual structure of the controller of the direct modulated MMC. ........... 67

ix

Figure 4-2 Per-phase extracted models of AC grid current and leg current of a direct

modulated MMC with stiff voltage sourced DC bus. ............................................... 69

Figure 4-3 Configuration of an MMC station in HVDC application. ............................... 74

Figure 5-1 Conceptual structure of a two-level converter based VSC-HVDC transmission

system........................................................................................................................ 86

Figure 5-2 Constant DC bus voltage controller for the rectifier........................................ 87

Figure 5-3 Constant power controller for the inverter. ...................................................... 87

Figure 5-4 Conceptual structure of VSC-HVDC transmission system based on an indirect

modulated MMC. ...................................................................................................... 88

Figure 5-5 Structure of the proposed VV controller. ......................................................... 89

Figure 5-6 Structure of the proposed VP controller. ......................................................... 90

Figure 6-1 Simulation waveforms of leg capacitor energy and differences of ................. 92

upper and lower arm capacitor energy in no load condition. ............................................ 92

Figure 6-2 Simulation waveforms of leg capacitor energy and grid current while the

converter total capacitor energy controller is activated in no load condition. ........... 93

Figure 6-3 Simulation waveforms of leg capacitor energy and circulating currents while

the leg capacitor energy balancing controller is activated in no load condition. ...... 94

Figure 6-4 Simulation waveforms of differences of upper and lower arm capacitor energy

and circulating currents while the common error eliminating module of the upper

and lower arm capacitor energy balancing controller is activated at no load condition.

................................................................................................................................... 94


and circulating currents while the differential error eliminating module of the upper

and lower arm capacitor energy balancing controller is activated at no load condition.

................................................................................................................................... 95

x

Figure 6-6 Simulation waveforms of leg capacitor energy and references of the leg

internal voltages while the leg capacitor energy balancing controller is activated in

no load condition. ...................................................................................................... 95


and references of the leg internal voltages while the common error eliminating

module is activated at no load condition. .................................................................. 96


and references of the leg internal voltage while the differential error eliminating

module is activated at no load condition. .................................................................. 96

Figure 6-9 Simulation waveforms of leg capacitor energy and DC bus current in loaded

condition. ................................................................................................................... 97

Figure 6-10 Simulation waveforms of differences of upper and lower arm capacitor

energy and DC bus current in loaded condition. ....................................................... 98

Figure 6-11 Simulation waveforms of grid current and DC bus current in loaded condition.

................................................................................................................................... 99

Figure 6-12 Simulation waveforms of DC bus voltage, converter total capacitor energy,

and grid current in loaded condition. ........................................................................ 99

Figure 6-13 Simulation waveforms of DC bus current and theoretically predicted DC bus

current by the extracted DC bus current model. ...................................................... 100

Figure 6-14 Constructed 7-level 300V experimental setup............................................. 101

Figure 6-15 Experimental waveforms of leg capacitor energy in no load condition. ..... 102

Figure 6-16 Experimental waveforms of AC grid current and converter total capacitor

energy in no load condition. .................................................................................... 102

Figure 6-17 Experimental waveforms of differences of leg capacitor energy and

circulating current in no load condition. ................................................................. 103

xi

Figure 6-18 Experimental waveforms of differences of upper and lower arm capacitor

energy in no load condition. .................................................................................... 104

Figure 6-19 Experimental waveforms of circulating current while the arm capacitor

energy differential error controller is activated in no load condition. ..................... 105


energy common error controller is activated in no load condition. ......................... 105

Figure 6-21 Experimental waveforms of references of leg internal voltage while the arm

capacitor energy differential error controller is activated in no load condition. ..... 106

Figure 6-22 Experimental waveforms of references of leg internal voltage while ......... 106

the arm capacitor energy common error controller is activated in no load condition. .... 106

Figure 6-23 Experimental waveforms of leg capacitor energy in loaded condition. ...... 107


energy in loaded condition. ..................................................................................... 107

Figure 6-25 Experimental waveforms of grid current in loaded condition. .................... 108

Figure 6-26 Experimental waveforms of instantaneous DC bus voltage, DC bus current,

converter total capacitor energy, and active current of grid side. ............................ 108


converter total capacitor energy, and active current of grid side while the DC bus

voltage command is changed from 300V to 330V. ................................................. 109







xii

Figure 6-30 Simulation waveforms of AC bus bar voltages and AC side voltages of the

MMC during the SLG fault. .................................................................................... 111

Figure 6-31 Simulation waveforms of AC grid currents, DC transmission line current, and

the DC bus voltage during the SLG fault. ............................................................... 112

Figure 6-32 Simulation waveforms of leg capacitor energy and differences of upper and

lower arm capacitor energy during the SLG fault. .................................................. 113

Figure 6-33 Simulation waveforms of differential components of leg capacitor voltage of

a direct modulated MMC. ....................................................................................... 114


voltages of a direct modulated MMC. ..................................................................... 114

Figure 6-35 Simulation waveforms of circulating currents of a direct modulated MMC.

................................................................................................................................. 116

Figure 6-36 Simulation waveforms of the transmission line current and station DC bus

voltages of the direct modulated MMC based HVDC transmission system. .......... 118

Figure 6-37 Simulation waveforms of three phase leg capacitor energy and differences of

upper and lower arm capacitor energy of the Station I of the direct modulated MMC

based HVDC transmission system. ......................................................................... 119


voltages of the indirect modulated MMC based HVDC transmission system by VV

control. .................................................................................................................... 120

Figure 6-39 Simulation waveforms of the leg capacitor energy and the differences of the

upper and lower arm capacitor energy of the Station I of the indirect modulated

MMC based HVDC transmission system by VV control. ...................................... 121



xiii

control in sudden power flow variation................................................................... 122


voltages of the indirect modulated MMC based HVDC transmission system by VP

control. .................................................................................................................... 123


upper and lower arm capacitor energy of the Station II of the indirect modulated

MMC based HVDC transmission system by VP control. ....................................... 123


voltages of the indirect modulated MMC based HVDC transmission system feeding

passive grid. ............................................................................................................ 125


upper and lower arm capacitor energy of the Station II of the indirect modulated

MMC based HVDC transmission system feeding a passive grid. .......................... 125

Figure 6-45 Constructed 300V down scale experimental setup of a point-to-point HVDC

transmission system. ............................................................................................... 127

Figure 6-46 Experimental waveforms of the DC bus voltages of the Station I and Station

II, transmission line current, and the active current of Grid I during starting

procedure. ................................................................................................................ 128

Figure 6-47 Experimental waveforms of the DC bus current and the leg capacitor energy

of the Station I during power flow variation in VV control. ................................... 129

Figure 6-48 Experimental waveforms of the DC bus current and the differences of upper

and lower arm capacitor energy during power flow variation in VV control. ........ 129

Figure 6-49 Experimental waveforms of the DC bus voltages of two stations, converter

total capacitor energy of the Station I, and the DC bus current in VV control. ...... 130

Figure 6-50 Experimental waveforms of the grid currents of the Grid I and the DC bus

xiv

current during power flow variation in VV control. ............................................... 130

Figure 6-51 Experimental waveforms of the active current of Grid I and the leg capacitor

energy of the Station I during power flow variation in VP control. ........................ 131

Figure 6-52 Experimental waveforms of the active current of Grid I and the differences of

upper and lower arm capacitor energy during power flow variation in VP control. 132


total capacitor energy of the Station I, and the DC bus current in VP control. ....... 132


current during power flow variation VP control. .................................................... 133

xv

Contents of Tables

Table 1.1 Lists of VSC-HVDC projects before emergence of the MMC. ........................... 5

Table 1.2 Lists of VSC-HVDC projects based on the MMC. ............................................. 8

Table 2.1 Characteristics of the indirect modulation and the direct modulation. .............. 13

1

1. Introduction

1.1 Background

With the development of the human society, explosive growth of demands for energy is

being a crucial issue. Because electricity is one of the most popular and efficient fashion

of energy delivery, high power long distance electricity transmission becomes more and

more important.

Currently, high voltage is the unique solution for high power long distance electricity

transmission. An Ultra High Voltage Alternating Current (UHVAC) transmission system

with voltage up to 1150kV has ever been built up in Soviet Union in 1980s for 907km

long distance power transmission, and several UHVAC transmission systems with voltage

over 1000kV have been constructed in Japan, Italy, and China.

One of the main advantages of the AC transmission is feasibility to step up and step

down voltage by transformers. However, since its operation is associated with issues such

as synchronization, stability, and power flow calculation and control, control of an AC

grid is highly complex. Moreover, since considerable series inductance and shunt

capacitance exist in long distance transmission line, much of AC voltage is applied to

overcome the voltage across the inductance and much of AC current is to charge and

discharge the capacitance of transmission line itself. For long distance HVAC, Flexible

Alternating Current Transmission System (FACTS) devices are usually employed to

enhance capacity and reliability of the transmission system. The effective transmission

capacity of the HVAC transmission system is highly limited by the length of the distance

and cannot be improved merely by improving the voltage level.

A High Voltage Direct Current (HVDC) transmission is an alternate solution for long

2

distance high power transmission. Since no effective series inductance and shunt

conductance appear in a DC system, voltage drop across the transmission line is

negligible compared to the rated line voltage and no current is needed to charge and

discharge the line capacitance alternately. Compared to the HVAC transmission system,

the HVDC transmission system presents several advantages such as long distance

transmission (up to 2375km, so far), high power capacity (up to 7200MW at present), no

synchronization issue, fast power flow control, possibility to use underground and

undersea cables, and lower losses. A 500kV HVAC transmission system can only transmit

800~1000MW electricity, a 750kV HVAC transmission system can transmit

2000~2500MW, and an 1150kV UHVAC system can deliver 4000~5000MW. However, a

±500kV HVDC transmission system can transmit 3000~3500MW electricity, and a

±800kV UHVDC transmission system can transmit up to 4800~7200MW electricity.

Since the classic HVDC system consists of thyristor based converters, it was named as

the Line Commutated Converter HVDC (LCC-HVDC) system.

Figure 1-1 Conceptual structure of the LCC-HVDC transmission system.

1.1.1. The Era of Mercury Arc Valves

The mercury arc valve was invented by Peter Cooper Hewitt in 1902 and was used as

rectifier at the beginning of the application. In 1928 the mercury arc valve which could

operate in inverter mode was invented and initiated development of HVDC technology.

AC Grid AC Grid

3

The world’s first commercial HVDC transmission system was built up in 1954 to

transmit electricity from Island Gotland to Swedish Mainland through a 100km undersea

cable. The mercury arc valve based HVDC transmission system with highest capacity is

the Pacific DC Intertie Project in United States which transmits 1440MW power over a

1372km long distance. The mercury arc valve based HVDC transmission system with

highest voltage is the Nelson River Bipol Project which transmits 1620MW power

through a ±450kV transmission line.

1.1.2. The Era of Power Semiconductor Valves

The thyristor was proposed by Whilliam Shockley in 1950 and was commercialized by

General Electric as a product named Silicon Controlled Rectifier (SCR). Compared to the

mercury arc valve, the thyristor has merits such as lower cost and higher reliability. The

world’s first thyristor based HVDC transmission system was the Eel River Crossing

Project built by General Electric in 1972.

1.2 Review of VSC-HVDC Transmission

The concept of Voltage Sourced Converter based HVDC (VSC-HVDC) was proposed

by Boon-Teck Ooi in 1990. The main characteristic of the VSC-HVDC transmission

system was based on self-commutated power semiconductors such as IGBTs instead of

line-commutated thyristor.

The world’s first VSC-HVDC transmission system was the Hallsjon Project built up by

ABB corporation in 1997 with ±10kV voltage level and 3MW capacity. The world’s first

commercial VSC-HVDC transmission was the Gotland Project that taken into service in

1999 with ±80kV voltage level and 50MW capacity.

Before the emergence of the Modular Multilevel Converter (MMC) topology, all of the

4

VSC-HVDC transmission systems are constructed by ABB corporation, and the product

name was registered as the HVDC Light. The VSC-HVDC systems were based on two-

level or three-level diode neutral point clamed voltage sourced converters as shown in Fig.

1-2. Similar to the LCC-HVDC converter, the VSC-HVDC converter calls for series

connection of power semiconductors as shown in Fig. 1-2 where hundreds of IGBTs were

connected in series for a transmission system with voltage up to hundreds of kV.

Figure 1-2 Conceptual structure of a VSC-HVDC transmission system.

Compared to the classic LCC-HVDC system, the VSC-HVDC system presents many

merits such as black start capability, finer reactive power control, compact station size,

lower AC gird current harmonics, and applicability of conventional symmetrical AC

transformers. But it also presents several disadvantages such as higher cost, higher

stations losses, and difficulty of series connection of IGBTs.

The first generation of the HVDC Light was based on the two-level converter topology

and the switching frequency was up to 1950Hz, the transmission line voltage was up to

±80kV. The second generation of the HVDC Light was based on diode neutral point

5

clamped three-level converter topology and the switching frequency was reduced to

1260Hz. For the second generation products, the transmission line voltage was up to

±150kV and the power capacities were up to 330MW. The third generation of HVDC

Light was based on two-level converter topology for simple structure but an Optimized

Pulse Width Modulation (OPWM) technology was developed to reduce switching

frequency to (1150Hz) improve efficiency. Table 1.1 shows the list of VSC-HVDC

projects before emergence of the MMC (http://new.abb.com/systems/hvdc/hvdc-light).

Table 1.1 Lists of VSC-HVDC projects before emergence of the MMC.

Project Country Capacity Voltage Level Application

Caprivi Link Namibia 300MW 350kV Grid Interconnection

DolWin 2 Germany 900MW ±320kV Offshore Wind

Connections

East West

Innerconnector

UK 500MW ±200kV Grid Interconnection

Aland Aland Islands 100MW ±80kV Grid Interconnection

BorWin 1 Germany 400MW ±150kV Offshore Wind

Connections

Skagerrak Norway 700MW 500kV Grid Interconnection

Gotland Sweden 50MW ±80kV Grid Interconnection

Estlink Finland 350MW ±150kV Grid Interconnection

Tjaereborg Denmark 7.2MW ±9kV Offshore Wind

Connections

Hallsjon Sweden 3MW ±10kV Connecting Remote

Generation

Troll A Norway 188 ±60kV Offshore Platform

6

Dorwin 1 Germany 800MW ±320kV Offshore Wind

Connections

NordBalt Lithuania 700MW ±320kV Grid Interconnection

Valhall Norway 78MW 150kV Offshore Platform

Murraylink Australia 220MW ±150kV Grid Interconnection

Terranora

Interconnector

Australia 180MW ±80kV Grid Interconnection

Mackinac United States 200MW 71kV Back-to-Back Grid

Connection

Cross Sound

Cable

United States 330MW ±150kV City Center Infeed

Eagle Pass United States 36MW ±15.9kV Grid Interconnection

Nord E.ON 1 Germany 400MW ±150kV Offshore Wind

Connections

1.3 MMC, a New Era of VSC-HVDC Technology

The Modular Multilevel Converter was first proposed by R. Marquadt in 2001 [1] and

was first commercialized by Siemens Corporation in the Trans Bay Cable Project located

in California, United States [2]. The MMC-based VSC-HVDC technology, which was

named as HVDC Plus by Siemens, 4th Generation HVDC Light by ABB, HVDC

MaxSine by Alstom, and HVDC Flexible by C-EPRI, initiated a new era of VSC-HVDC

application. Compared to the conventional two-level or three-level converter based

HVDC transmission systems, the MMC converter for HVDC application presented

several significant advantages such as modularity and simple voltage scaling, very low

dv/dt and harmonics, no necessity of series connection of power semiconductors,

7

possibility of use of conventional AC transformers, elimination of high voltage DC bus

capacitor, and redundancy in case of cell failure.

Figure 1-3 Conceptual structure of an MMC-HVDC station.

A conceptual structure of an MMC-HVDC station is shown in Fig. 1-3. An MMC

converter contains three legs for three phases, and each leg contains two arms,

respectively the upper arm and the lower arm. Each arm consists of an arm inductor and

up to hundreds of half-bridge chopper cells. The AC side of the MMC is usually

connected to the AC grid through a wye-delta conventional commercial transformer, and

smoothing reactors are usually installed in the DC bus of the MMC to eliminate current

harmonics and to suppress inrush current in case of a HVDC transmission line short

circuit fault.

Thanks to the multilevel nature of the MMC, it can generate almost pure sinusoidal

waveform voltage in the AC side and contributes almost no harmonics to AC grid.

AC gridConverter transformer

Arm inductors

Smoothing reactor HVDC transmission line

Voltage divider

8

Moreover, the switching frequency can be reduced to around line frequency and the

losses are reduced significantly compared to the two-level and three-level converters. As

shown in Fig. 1-4 denoted as Generation 4, the losses of the MMC-based HVDC system

are reduced to less than 1% and the efficiency of the MMC-based HVDC is even

competitive compared to the classic LCC-HVDC.

Figure 1-4 Losses of HVDC Light products for each generation [3].

The MMC seems to be the most promising solution for future wide applications of

VSC-HVDC transmission. Currently, several MMC based VSC-HVDC transmission

projects are ongoing or in service as listed in Table 1.2.

Table 1.2 Lists of VSC-HVDC projects based on the MMC.

Project Country Capacity Voltage

Level

Status

Trans Bay Cable United States 400MW ±200kV In service

9

Shanghai Wind

Farm Integration

China 18MW ±30kV In service

Nan’ao Multi-

terminal

China 50/100/200MW ±160kV In service

Zhoushan Multi-

terminal

China 400/300/100/100

/100 MW

±200kV Ongoing

Dalian City Infeed China 1000MW ±320kV Postponed

INELFE France, Spain 1000×2MW ±320kV Ongoing

Tres Amigas (Ph-I) United States 750MW ±300kV Ongoing

South-West Link Sweden, Norway 700×2MW ±300kV Ongoing

1.4 Purpose of This Thesis

Control methods of the MMC are classified into indirect modulation based control

method and direct modulation based control. For the indirect modulation based control

method, modulation index is calculated by on-line sensed cell capacitor voltage. However,

for the direct modulation based control method, modulation index is calculated by rated

cell capacitor voltage in an open-loop manner.

For the direct modulated MMC since the modulation index is calculated by rated cell

capacitor voltage, a twice line frequency voltage synthesization error is introduced

inherently. The voltage synthesization error induces considerable twice line frequency

circulating current which flows inside the converter and leads to additional losses. The

circulating current is usually suppressed by improving reactance of the arm inductor or by

employing Circulating Current Suppressing Controller (CCSC). For the indirect

modulated MMC since the modulation index is calculated by sensed cell capacitor

10

voltage, output voltage is modulated correctly and the circulating current caused by

voltage synthesization error is inherently avoided.

For the direct modulated MMC, six arm capacitor energy are balanced naturally

without employing additional controller. Its natural balancing characteristic has been

reported by several articles by both simulation and experiment. However, currently the

mechanism of the natural balancing is not revealed analytically. For the indirect

modulated MMC, six arm capacitor energy balancing is marginally stable and additional

arm capacitor energy balancing controller should be employed. State-of-the-art arm

capacitor energy balancing method is valid only for the stiff DC bus case but is not valid

for the HVDC application in which the DC bus is not a stiff voltage source.

In this thesis, a modified modeling of the MMC is proposed for the generalized DC bus.

Based on the modified modeling, a comprehensive arm capacitor energy control strategy

is proposed which is valid regardless of characteristics of the DC bus. By the proposed

control strategy, the AC grid side, the DC bus side, and the arm capacitor energy are fully

decoupled. Based on the proposed MMC control method, a novel concept of the control

of the MMC-based HVDC system is proposed by which the transmission line voltage

fluctuation during fast power flow variation can be fully suppressed. A fault ride through

method is proposed for single line to ground fault by which the AC grid side and the DC

bus side is fully decoupled and the twice line frequency fluctuation in the DC

transmission line voltage is inherently avoided.

In this thesis, the mechanism of the arm capacitor energy natural balancing of the direct

modulated MMC is analyzed analytically. It is revealed in this thesis that unbalance of the

six arm capacitor energy would induce circulating current inside the converter and the

circulating current transfers energy between arms to balance six arm capacitor energy

inherently. Dynamics of the arm capacitor energy natural balancing are analyzed

11

mathematically.

1.5 Thesis Outline

The remaining parts of this thesis are organized as follows.

In Chapter 2, basic operation principle of the MMC is described and the concept and

characteristics of the indirect modulation and the direct modulation are introduced. A

literature review of the research on control of the MMC is given.

In Chapter 3, indirect modulation based control strategy is discussed. The

conventional indirect modulation based control strategy for the MMC with stiff voltage

sourced DC bus is reviewed. The proposed indirect modulation based control strategy for

the MMC with generalized DC bus is presented.

In Chapter 4, mechanism of the arm capacitor energy natural balancing of the direct

modulated MMC is revealed and its dynamics are analyzed mathematically.

In Chapter 5, the proposed novel concept of the MMC based HVDC system control is

introduced.

In Chapter 6, results of simulation and experiment are presented.

In Chapter 7, conclusions, contributions, and future work are summarized.

12

2. Basic Principle and Control of the MMC

2.1. Operation Principle of the MMC

Figure 2-1 Operation principle of the MMC.

The basic operation principle of the MMC is shown in Fig. 2-1. Both the upper arm

and the lower arm generate DC voltage plus AC voltage. The DC voltages generated by

both arms are with the same amplitude, which is equal to the half of the DC bus voltage.

The AC voltages generated by both arms are with opposite polarity and with the same

amplitude, which is equal to the amplitude of the AC side output voltage generated by the

MMC.

Basically, as shown in Fig. 2-1, the DC bus voltage is determined by the sum of the

upper arm output voltage and the lower arm output voltage. And the AC grid side output

voltage of the MMC is determined by the difference of the upper arm output voltage and

the lower arm output voltage.

13

2.2. Indirect Modulation and Direct Modulation

Several efforts have been pursued on control of the modular multilevel converter. The

control strategies of the MMC can be classified into indirect modulation based control

strategies and the direct modulation based control strategies. The main difference between

the indirect modulation based and the direct modulation based control strategies is the

calculation method of the modulation index as shown in Table 2.1.

Table 2.1 Characteristics of the indirect modulation and the direct modulation.

Indirect Modulation Direct Modulation

Modulation Index

Calculation

* *

, ,

1 1

,xu xlxu xlN N

xu i xl i

i i

v vn n

v v

* *

, ,

,xu xlxu xl

dc rated dc rated

v vn n

V V

Number of Inserted Cells xu xl armN N N xu xl armN N N

Synthesized Voltage * *,xu xu xl xlv v v v * *,xu xu xl xlv v v v

For the indirect modulation based control strategy, the modulation index is calculated

by the reference of the arm output voltage and the sum of sensed voltages of the

capacitors in the arm. The sum of numbers of instantaneous inserted cells of the upper

arm and the lower arm is time varying, and the arm output voltage can be synthesized

correctly as its reference value.

For the direct modulation based control strategy, the modulation index is calculated by

the reference of the arm output voltage and the rated DC bus voltage which is a constant

value. The sum of numbers of instantaneous inserted cells of the upper arm and the lower

arm is always fixed to the number of cells in each arm. Obviously, the arm output voltage

cannot track its reference correctly.

14

Figure 2-2 Simulation waveforms of the MMC under indirect modulation control and

under direct modulation control.

(a) Direct modulation based control. (b) Indirect modulation based control.

The simulation waveforms of the MMC under indirect modulation control and under

direct modulation control are presented in Fig. 2-2 to show the differences of the two

modulation methods.

For the direct modulated MMC, since a twice line frequency fluctuation in the cell

capacitor voltage is induced in loaded condition, a considerable twice line frequency

voltage synthesization error exists. The twice line frequency voltage synthesization error

induces a considerable twice line frequency circulating current into the leg current, which

should be suppressed by increasing reactance of the arm inductors or by closed loop

circulating current suppressing control. One of the main benefits of the direct modulation

control method is that the sums of capacitor voltages of six different arms can be

balanced naturally and it simplifies the control remarkably.

0

100000

200000

300000

400000VuP_ref+200000 VuP

0

100000

200000

300000

400000VuN_ref+200000 VuN

2.26 2.28 2.3 2.32 2.34

Time (s)

0K

-10K

-20K

10K

20KVuP_ref+200000-VuP VuN_ref+200000-VuN

* ( )uuv kV ( )uuv kV

* ( )ulv kV ( )ulv kV

* ( )uu uuv v kV* ( )ul ulv v kV

400

0400

020

-20Time(s)

2.26 2.28 2.30 2.32 2.34

0

-500

-1000

500

1000Iuu-Iul

0

-500

-1000

500

1000(Iul+Iuu)/2

2.26 2.28 2.3 2.32 2.34

Time (s)

0

-100

-200

-300

-400

-500

Idc

( )usi A

( )uoi A

( )dci A

1000

-10001000

-1000

-500

Time(s)2.26 2.28 2.30 2.32 2.34

0

0

100000

200000

300000

400000VuP_ref VuP

0

100000

200000

300000

400000VuN_ref VuN

2.26 2.28 2.3 2.32 2.34

Time (s)

0K

-10K

-20K

10K

20KVuP_ref-VuP VuN_ref-VuN

400

0400

020

-20

Time(s)

2.26 2.28 2.30 2.32 2.34

0

-500

-1000

500

1000Iuu-Iul

0

-500

-1000

500

1000(Iuu+Iul)/2

2.26 2.28 2.3 2.32 2.34

Time (s)

0

-100

-200

-300

-400

-500

Idc

1000

-10001000

-1000

-500

Time(s)2.26 2.28 2.30 2.32 2.34

0

Upper arm output voltage and its reference

Lower arm output voltage and its reference

Voltage synthesization error

AC grid current

Leg Current

DC bus current

( )usi A

( )uoi A

( )dci A

AC grid current

Leg Current

DC bus current

* ( )uuv kV ( )uuv kV

* ( )ulv kV ( )ulv kV

* ( )uu uuv v kV* ( )ul ulv v kV

Upper arm output voltage and its reference

Lower arm output voltage and its reference

Voltage synthesization error

(a) (b)

15

For the indirect modulated MMC, the arm output voltage can be synthesized correctly

as its reference value and no twice line frequency current circulates inside the converter.

However, the balancing of capacitor voltages between different arms is marginally stable

and a closed loop arm capacitor energy (or voltage) balancing controller should be

employed.

2.3. Review of the Research on Control of the MMC

Fig. 2-3 shows the family tree of the research on control of the MMC. For the direct

modulation based control strategy, in [4] the impact of sampling frequency on harmonics

of AC side output voltage had been investigated by Z. Xu, et al from Zhejiang University.

In [5] a closed loop circulating current suppressing controller constructed in twice line

frequency synchronous reference frame was proposed to suppress the twice line

frequency circulating current introduced inherently by the direct modulation. Circulating

current suppressing controllers based on Proportional Integral Resonant (PIR) regulator in

stationary reference frame and repetitive regulator were reported in [6-8]. In [9], the

operation characteristics of the MMC in unbalanced AC grid condition had been analyzed,

and it revealed that a twice line frequency fluctuation would exist in the DC bus voltage if

the AC grid is severely unbalanced, for example in the AC grid short circuit fault. A

control method to suppress the fluctuation in the DC bus had been proposed in [10]. The

terminal electromechanical transient of the MMC was analyzed in [11] for Multi Terminal

DC (MTDC) grid, and it had revealed that the terminal behavior of the direct modulated

MMC is similar to that of the two-level converter.

Investigation of an MMC based Back-to-Back (BTB) system was firstly published by

M. Saeedifard, et al from Purdue University [12]. And predictive control of the BTB

system was discussed in [13-15].

16

Steady state analysis was conducted in [16] and [17] to investigate interaction between

harmonic components of different variables and parameters. In [18] and [19], the

capacitor voltage oscillation reduction methods by current injection in twice line

frequency synchronous rotating reference frame and in stationary reference frame had

been proposed.

For the indirect modulation based control strategy, level shift carrier modulation based

control strategy and phase shift carrier modulation based control strategy were developed.

As the first approach on closed loop control of level shift carrier modulation based

control strategy, the internal dynamics of the MMC and relationship between arm

capacitor energy and current of the MMC were analyzed in detail in [20]. Based on the

work pursued by [20], a double closed loop controller had been proposed to improve

dynamics of arm capacitor energy control [21]. An open-loop control strategy of level

shift carrier modulation based control strategy was firstly proposed by A. Antonopoulos,

et al from Royal Institute of Technology (KTH) [22]. And its global asymptotic stability

were analyzed and proven in [23-25]. The phase shift carrier modulation based control

strategies were developed by [26-28]. The phase shift carrier modulation calls for

synchronized phase shifted carrier signals and it is not practical for the high voltage

applications in which hundreds of cells are contained in each arm. The phase shift carrier

modulation based control strategies were developed for medium voltage motor drive and

BTB systems in medium voltage grids.

17

Modulation

Direct Indirect

Closed-loop Open-loop

Impact of sampling

frequency [4], ZJU[2

01

1J]

Circulating current

suppression [5], ZJU

[20

11

J]

Control under

unbalanced condition

[9], ZJU[20

12

J]

Suppressing DC

voltage ripple under

unbalanced condition

[10], ZJU

[20

12

J]

Terminal

electromechanical

transient, MTDC

[11], ZJU

[20

14

J]BTB system, normal

and fault condition

[12], Purdue[20

10

J]

BTB system,

predictive control

[13], Purdue[20

12

J]

Reduced switching

frequency [14],

Purdue[20

13

J]

Predictive control,

fast algorithm [15],

Xi＇an JTU[20

14

C]

Interaction between

harmonic components

[16], KTH[20

12

J]

Simple steady state

model [17], Tsinghua

[20

13

J]

Deep suppressing

[6], NCSU

[20

12

C]

Deep suppressing

[7], C.A.S.

[20

13

J]

Deep suppressing,

repetitive controller

[8], ZJU[20

14J]

Voltage Oscillation

Reduction, double

synchronous ref., PTP

system [18], NTNU

[20

13

J]

Optimization in ABC

frame, PTP system

[19], NTNU[20

14

J]

First approach [20],

KTH

[20

12

J]

Double closed loop

approach [21], HUST

[20

14J]

Improved method for

generalized DC bus

Mechanism of self-

balancing First approach [22],

KTH

[20

11

J]

Analysis of balancing

mechanism [23], KTH

[20

13

J]

Global asymptotic

stability [24], KTH

[20

14

J]

Global asymptotic

stability, current

controlled, [25], KTH[20

14

J]

Generalized D

C

bus situation

Stiff DC bus situation

Two reference

(Level shift carrier)

Multi-reference

(Phase shift carrier)

First approach, no arm

balancing [26], TIT

[20

09

J]

Improved control, arm

balancing by voltage

injection [27], TIT[20

11

J]

Improved control, arm

balancing by current

injection [28], TIT[20

14

J]

Poor

per

form

ance

of

cir

cula

ting c

urr

ent

regula

tion.

Clo

sed-l

oop

Figure 2-3 Family tree of the research on control of the modular multilevel converter.

18

3. Indirect Modulation Based Control Strategy of

MMC

Currently many efforts have been made on development of indirect modulation based

control strategy of the MMC. In previous work, a stiff DC bus voltage source was

presumed. Under such assumption, internal dynamics of each phase could be analyzed

independently and energy stored in cell capacitors of each arm can be controlled

independently for each phase [20].

However, different from the conventional two-level converter or three-level converter

based VSC-HVDC system, there is no capacitor in the DC bus. Moreover, usually a

smoothing reactor is installed in series in the DC bus.

Figure 3-1 Conceptual structures of MMC stations.

(a) Structure of an MMC station in previous work. (b) Structure of an MMC station in

real application.

No c

ap

aci

tors

in

DC

bu

s!

(a) (b)

19

If the DC bus is connected with a capacitor in parallel, the DC bus presents voltage

source characteristics, as shown in Fig. 3-1. However, if the DC bus is connected with a

reactor in series, the DC bus reveals more current source characteristics, as shown in Fig.

3-1. Then in the real application, the basic assumption of the conventional indirect

modulation based control strategy, namely, the stiff DC bus voltage source is not

reasonable. The model of the MMC based on such assumption is not valid, and the

corresponding control strategy leads to poor dynamics and can even make the system be

unstable.

In this chapter, at first the conventional modeling and control strategy of the indirect

modulated MMC are reviewed. A generalized model of the MMC is proposed for

generalized DC bus without any pre-assumption of DC bus. Based on the proposed

modeling a comprehensive arm capacitor energy control strategy is proposed, which is

valid for generalized DC bus.

20

3.1 Modeling of the Indirect Modulated MMC with Stiff Voltage

Sourced DC Bus

Figure 3-2 Structure of an MMC analyzed in the previous works.

Structure of an MMC analyzed in the previous works is shown in Fig. 3-2. Without

loss of generality, phase U is analyzed. According to Kirchhoff’s law, two independent

equations can be derived from Path I and Path II in Fig. 3-2 to describe upper and lower

arm current of the phase U as (3.1) and (3.2).

( ) ( )( ) 0.2

dcuu o o uu s s uu ul ug

Vv sL R i sL R i i v (3.1)

( ) ( )( ) 0.2

dcul o o ul s s uu ul ug

Vv sL R i sL R i i v (3.2)

Leg current of the phase x, xoi is defined as the average value of the upper arm

current and the lower arm current of the phase U, as (3.3). Then the grid current xsi and

the leg current xoi of phase x can be used to fully describe the upper arm current and

vvg

vwg+-

+-

+-

vuu

vul

iuu

iul

ius

U V W

iuo

ivu iwu

ivl iwl

+

-

+

-

+

-

+

-

+

-

+

-

ivo

iwo

ivs

iws

vvu vwu

vvl vwl

sLs+RssLo+Ro

sLo+Ro

2

dcV

2

dcV

vug

Path I

Path II

21

lower arm current of phase x.

.2

xu xlxo

i ii

(3.3)

By adding (3.1) and (3.2), dynamics of the grid current of phase U can be derived as

(3.4).

( )

.2 2

uu ul o oug us s s us

v v sL Rv i sL R i

(3.4)

By subtracting (3.2) from (3.1), dynamics of the leg current of phase U can be

derived as (3.5).

.2

dc uu ulo o uo

V v vsL R i

(3.5)

In (3.4), the term in the left hand side can independently affects the grid current. It is

defined as output EMF of the MMC and is denoted as usv .

.2

uu ulus

v vv

(3.6)

In (3.5), the term in the left hand side can independently affects the leg current. It is

defined as leg internal voltage of the MMC and is denoted as uov .

.2

dc uu uluo

V v vv

(3.7)

Substituting (3.6) and (3.7) into (3.4) and (3.5), (3.8) and (3.9) can be deduced.

.2

o ous ug us s s us

sL Rv v i sL R i

(3.8)

.uo o o uov sL R i (3.9)

From (3.8) and (3.9), if the output EMF and the leg internal voltage can be controlled

independently, then both the grid current usi and the leg current uoi can be

22

independently regulated, which means that the upper arm current and the lower arm

current are fully controllable. In above analysis, it can be observed that the grid current

and the leg current of phase U are only affected by the output EMF and the leg internal

voltage of phase U, then dynamics of currents of each phase can be analyzed and

controlled independently if the DC bus of the MMC is a stiff voltage source.

From (3.6) and (3.7), the upper arm output voltage and the lower arm output voltage

can be described as (3.10) and (3.11).

.2

dcuu xs uo

Vv v v (3.10)

.2

dcul xs uo

Vv v v (3.11)

According to (3.10) and (3.11), per phase equivalent circuit of the conventional

modeling with stiff DC bus voltage source is shown in Fig 3-3. And according to (3.4)

and (3.5), the grid current model and the leg current model can be extracted from Fig 3-3,

as shown in Fig. 3-4.

Figure 3-3 Per phase equivalent circuit of the conventional modeling with stiff DC bus

voltage source.

vxu

vxl

ixu

ixl

ixo

+

+-

-+

-

+

+-

-+

-

-vxs

-vxo

vxs

-vxo

ixs

+

+

+

-

-

-vxg

1

2Vdc

1

2Vdc

1

2Vdc

1

2Vdc

s ssL R

o osL R

o osL R

23

Figure 3-4 Per phase extracted models of AC grid current and leg current in the

conventional modeling.

(a) Per phase extracted model of AC grid current. (b) Per phase extracted model of leg

current.

vxsixs+-

vxg + -

s ssL R2

o osL R

MMC

+

- dcV

+-

-2vxo +

- dcV

AC Grid

2 o osL R

(a)

(b)

ixo

MMC DC Bus

24

3.2 Control of the Indirect Modulated MMC with Stiff Voltage

Sourced DC Bus

3.2.1 Current Control of the Indirect Modulated MMC with Stiff Voltage Sourced

DC Bus

Figure 3-5 Conceptual structures of current controllers.

(a) Structure of grid current controller. (b) Structure of leg current controller.

Fig. 3-5 shows the conceptual structures of current controllers. Since the grid current

and the leg current are independently affected by the output EMF and the leg internal

voltage respectively, the outputs of the controllers are correspondingly the references of

the output EMF and the leg internal voltage. Since for the indirect modulated MMC

(3.12) and (3.13) are valid for each phase, then the references of upper arm output

voltage and lower arm output voltage should be (3.14) and (3.15).

* .xu xuv v (3.12)

* .xl xlv v (3.13)

+-

*xsi

xsi

Controller

*xsv

+-

*xoi

xoi

Controller

*xov

(a)

+-

gsv

1

1

2s s o osL R sL R

xsi

Plant

(b)

1

o osL R

xoi

Plant

25

* * * .

2

dcuu us uo

Vv v v (3.14)

* * * .

2

dcul us uo

Vv v v (3.15)

3.2.2 Arm Capacitor Energy Control of the Indirect Modulated MMC with Stiff

Voltage Sourced DC Bus

Control of arm capacitor energy is one of the main concerns of the control of the MMC.

The objective of the control of arm capacitor energy is to regulate the energy stored in the

arm capacitors to its rated reference value, which can be expressed mathematically as

(3.16) and (3.17). The energy stored in upper arm capacitors and lower arm capacitors of

phase x are denoted as xuE and xlE respectively.

* .xu armE E (3.16)

* .xl armE E (3.17)

To control the arm capacitor energy, the power flow into each arm in a leg should be

considered. Power that flow into the upper and lower arms of the phase x can be deduced

as (3.18) and (3.19) neglecting the losses.

*

* * * 1( )( ).

2 2

xu dcxu xu xu xs xo xo xs

dE VP v i v v i i

dt (3.18)

*

* * * 1( )( ).

2 2

xl dcxl xl xl xs xo xo xs

dE VP v i v v i i

dt (3.19)

It should be noticed that regulating the upper arm capacitor energy and the lower arm

capacitor energy to their rated references is mathematically equal to regulating their sum

to twice the rated references and their difference to null, which can be described by (3.20)

and (3.21).

26

*2 .xu xl armE E E (3.20)

0.xu xlE E (3.21)

Sum and difference of power that flow into the upper arm and the lower arm of phase x

can be deduced from (3.18) and (3.19) as (3.22) and (3.23).

* * *( )2 .x xu xl

x xu xl dc xo xs xs xo xo

dE d E EP P P V i v i v i

dt dt

(3.22)

* * *( ) 12 .

2

x xu xlx xu xl dc xs xs xo xo xs

dE d E EP P P V i v i v i

dt dt

(3.23)

For VSC-HVDC application, the third terms in the right hand sides of both (3.22) and

(3.23) can be neglected [20]. In (3.22), sum of the power flow into upper arm capacitors

and lower arm capacitors can be regulated by a DC component of leg current. It means

that a DC component of leg current can be drawn from the infinite DC bus to charge or

discharge the energy of upper and lower arm capacitors, namely, the leg capacitor energy

as shown in Fig. 3-6(a). In (3.23), difference of the power flow into upper arm capacitors

and lower arm capacitors can be regulated by a line frequency component of the leg

current. It means that a line frequency component of the leg current can be drawn from

the infinite DC bus to redistribute the energy charged in the upper arm capacitors and the

lower arm capacitors of phase x as shown in Fig. 3-6(b).

In the steady state, DC components of both xP and xP should be null. Then in the

steady state, there should be no line frequency component in the leg current, and the

magnitude of the DC component of the leg current should be (3.24).

*

, .xs xs

DCxo DC

dc

v ii

V (3.24)

27

Figure 3-6 Conceptual principle of the conventional arm capacitor energy control.

(a) Principle of control of sum of upper and lower arm capacitor energy. (b) Principle of

control of difference of upper and lower arm capacitor energy.

Figure 3-7 Conceptual structures of the conventional arm capacitor energy controllers.

(a) Structure of controller of sum of upper and lower arm capacitor energy. (b) Structure

of controller of difference of upper and lower arm capacitor energy.

ixu

ixl

ixo,DC

+

+-

-+

-

+

+-

-+

-

-vxs

-vxo

vxs

-vxo

ixs+-vxg

1

2Vdc

1

2Vdc

s ssL R

o osL R

o osL R

ixu

ixl

ixo,AC

+-

+

-

+

+-

-+

-

-vxs

-vxo

vxs

-vxo

ixs+-vxg

s ssL R

o osL R

o osL R

1

2dcV

+

-

1

2dcV

(a) (b)

+-

*2 armE

xE

Controller

*xP

(a)

xE

Plant

Leg Current

ControllerxP

1

s

+-

0

xE

Controller

*xP

(b)

xE

Plant

Leg Current

ControllerxP

1

s

28

Fig. 3-7 shows conceptual structures of arm capacitor energy controllers. Both xP and

xP are controlled by regulating the leg current. Since the dynamics of current control

are much faster than the dynamics of capacitor energy control, (3.25) and (3.26) can be

assumed.

*.x xP P (3.25)

*.x xP P (3.26)

Figure 3-8 Conventional controllers of the MMC with stiff DC bus voltage source.

(a) Conventional grid current controller of the MMC. (b) Conventional arm capacitor

energy controller of the MMC.

Fig. 3-8 shows the conventional controller of the MMC. Arm capacitor energy

Twice Line Frequency

Notch Filter

xuE

xlE,x fltE

PI dcV*

xP

Line Frequency

Notch Filter

,x fltE

msV

*xP

+

+

+

-

*xs

ms

v

V

+

+

*,xo DCi

*,xo ACi

PIR+

-

xoi

*xov

+

*xs xsv i


Notch Filter

, ffxP

xuE

xlE PI

AC Current

Vector

Controller

* *,ds qsi i

, ,us vs wsi i i , ,ug vg wgv v v

* * *, ,us vs wsv v v

(a) AC grid current vector controller

(b) Arm capacitor energy controller

+-

-

*xE

+

0

*xoi

29

controller is in cascaded structure, with a leg current controller as the inner loop and an

arm capacitor energy controller as the outer loop. It should be noticed that since there is a

twice line frequency fluctuation in xE and a line frequency fluctuation in xE , notch

filters with center frequencies at twice line frequency and line frequency are employed.

3.3 Modeling of the Indirect Modulated MMC with Generalized

DC Bus

The conventional control strategy presents good dynamics while the DC bus is a stiff

voltage source, and its validity was verified by both simulation and experiment and was

reported by several publications [20, 21].

However, in practical HVDC application since the DC bus of the MMC is connected in

series with a smoothing reactor to filter current harmonics out and to suppress inrush

current in case of the DC transmission line short circuit fault, modeling the DC bus of the

MMC as a stiff voltage source would be invalid.

30

Figure 3-9 MMC model for HVDC application under the conventional control strategy.

Fig. 3-9 shows the MMC circuit for HVDC application. The DC bus voltage dcV is

not stiff and it would vary in accordance with operation of the MMC.

iuu

iul

+

-+

-

+

-+

-

*1

2dcV

ivu

ivl

+

-+

-

+

-+

-

iwu

iwl

+

-+

-

+

-+

-

*usv *

vsv *wsv

*uov *

vov *wov

*usv *

vsv *wsv

*uov *

vov *wov

ius

ivs

iws

vug

vvg

vwg

dcv

+-

+-

+-

*1

2dcV *1

2dcV

*1

2dcV

*1

2dcV *1

2dcV

sLs+Rs

sLo+Ro

sLo+Ro

dci

dci

+-

+-

+-

+-

+-

+-

31

3.3.1 Analysis of AC Grid Current of the MMC with Generalized DC Bus

Figure 3-10 Analysis of AC grid current of the MMC with generalized DC bus.

AC grid current should be analyzed regardless of the DC bus. As shown in Fig. 3-10,

without loss of generality, phase U and phase V are considered. According to Kirchhoff’s,

two independent equations can be derived to describe currents flow in phase U and phase

V as (3.27) and (3.28).

* * *

* * *

( / 2 ) ( ) ( )

( / 2 ) ( ) ( ) 0.

us dc uo o o uu s s us ug

vs dc vo o o vu s s vs vg

d dv V v L R i L R i v

dt dt


dt dt

(3.27)

* * *

* * *

( / 2 ) ( ) ( )

( / 2 ) ( ) ( ) 0.

us dc uo o o ul s s us ug

vs dc vo o o vl s s vs vg


dt dt


dt dt

(3.28)

iuu

iul

+

-+

-

+

-+

-

*1

2dcV

ivu

ivl

+

-+

-

+

-+

-

iwu

iwl

+

-+

-

+

-+

-

*usv *

vsv *wsv

*uov *

vov *wov

*usv *

vsv *wsv

*uov *

vov *wov

ius

ivs

iws

vug

vvg

vwg

dcv

+-

+-

+-

*1

2dcV *1

2dcV

*1

2dcV

*1

2dcV *1

2dcV

sLs+Rs

sLo+Ro

sLo+Ro

dci

dci

+-

+-

+-

+-

+-

+-

Loop I

Loop II

32

From (3.27) and (3.28), the following equations can be deduced to describe AC grid

current of phase U and phase V.

*

*

( )( / 2) ( )

( ) ( )( / 2) ( ) 0.

us o o us s s us ug

vs o o vs s s vs vg

d dv L R i L R i v

dt dt

d dv L R i L R i v

dt dt

(3.29)

*

*

( )( / 2) ( )

( ) ( )( / 2) ( ) 0.

us o o us s s us ug

vs o o vs s s vs vg

d dv L R i L R i v

dt dt

d dv L R i L R i v

dt dt

(3.30)

According to (3.29) and (3.30), it is found that the DC bus voltage reference term

*dcV and the leg internal voltage reference term *

xov are cancelled in dynamic equations

of the AC grid current of phase U and phase V. From the AC grid side, phase U and phase

V of the MMC look like output EMFs behind the arm inductors and the grid currents split

equally into upper arms and lower arms, as shown in Fig . 3-11.

This conclusion can be extended to three phases, as shown in Fig. 3-12. From the AC

grid side, the MMC consists of two symmetric sets of three phase output EMFs behind

arm inductors and the three phase currents split equally into the upper sets and the lower

sets. Then a model can be extracted from the MMC model shown in Fig. 3-9 to describe

the AC grid current, as shown in Fig. 3-13(a) and it can be further simplified as Fig. 3-

13(b).

33

Figure 3-11 Phase U and phase V of the MMC observed from the AC grid side.

Figure 3-12 Three phases of the MMC observed from the AC grid side.

+-

+-

ius/2

+

-+

-

+

-+

-

*1

2dcV

+

-+

-

+

-+

-

iwl

+

-+

-

+

-+

-

*usv *

vsv *wsv

*uov *

vov *wov

*usv *

vsv *wsv

*uov *

vov *wov

ius

ivs

iws

vug

vvg

vwg

dcv

+-

+-

+-

*1

2dcV *1

2dcV

*1

2dcV

*1

2dcV *1

2dcV

sLs+Rs

sLo+Ro

sLo+Ro

dci

dci

+-

+-

+-

+-

ivs/2

-ius/2 -ivs/2

+-

+-

ius/2

-ius/2

+

-+

-

+

-+

-

*1

2dcV

+

-+

-

+

-+

-

+

-+

-

+

-+

-

*usv *

vsv *wsv

*uov *

vov *wov

*usv *

vsv *wsv

*uov *

vov *wov

ius

ivs

iws

vug

vvg

vwg

dcv

+-

+-

+-

*1

2dcV *1

2dcV

*1

2dcV

*1

2dcV *1

2dcV

sLs+Rs

sLo+Ro

sLo+Ro

dci

dci

+-

+-

+-

+-

ivs/2 iws/2

-ivs/2 -iws/2

34

Figure 3-13 Extracted model from the MMC circuit to analyze AC grid current.

(a) Extracted model of AC grid current. (b) Simplified equivalent model of AC grid

current.

3.3.2 Analysis of DC Bus Current of the MMC with Generalized DC Bus

Figure 3-14 Analysis of DC bus current of the MMC with generalized DC bus.

ius

ivs

iws

vug

vvg

vwg

*usv

*vsv

*wsv

+ -

+ -

+ -+-

+-

+-

ius/2

+

-

+

-

+

-

*usv *

vsv *wsv

*usv *

vsv *wsv

ius

ivs

iws

S SsL R

vug

vvg

vwg

+

-

+

-

+

-

+-

+-

+-

sLo+Ro

sLo+Ro

ivs/2 iws/2

-ius/2 -ivs/2 -iws/2

(a) (b)

s ssL R2

o osL R

iuo

iuo

+

-+

-

+

-+

-

*1

2dcV

ivo

ivo

+

-+

-

+

-+

-

iwo

iwo

+

-+

-

+

-+

-

*usv *

vsv *wsv

*uov *

vov *wov

*usv *

vsv *wsv

*uov *

vov *wov

ius

ivs

iwsdcv

+-

+-

+-

*1

2dcV *1

2dcV

*1

2dcV

*1

2dcV *1

2dcV

sLs+Rs

sLo+Ro

sLo+Ro

dci

dci

+-

+-

+-

+-

+-

+-

+

-

Loop I Loop II Loop III

35

DC bus current should be analyzed regardless of the AC grid side. According to Loop I,

Loop II, and Loop III shown in Fig. 3-14, the instantaneous value of the DC bus voltage

can be calculated as (3.31), (3.32), and (3.33).

* *

* * * *( ) ( )( ) ( ) .2 2

dc dcus uo o o uu ul us uo dc

V Vdv v L R i i v v v

dt (3.31)

* *

* * * *( ) ( )( ) ( ) .2 2

dc dcvs vo o o vu vl vs vo dc


dt (3.32)

* *

* * * *( ) ( )( ) ( ) .2 2

dc dcws wo o o wu wl ws wo dc


dt (3.33)

By adding (3.31), (3.32), and (3.33), the instantaneous DC bus voltage can be

deduced as (3.34).

* * * *2

2( )( ) ( ).3 3

dcdc dc o o uo vo wo

idv V R L v v v

dt (3.34)

It is observed in (3.34) that the instantaneous DC bus voltage is determined by the DC

bus voltage reference, the DC bus current, and the common mode component of the three

phase leg internal voltages.

36

Figure 3-15 Extracted model from the MMC circuit to analyze DC bus current.

(a) Extracted model of DC bus current. (b) Simplified equivalent model of DC bus

current.

According to (3.34), a model can be extracted from the conventional model to describe

the DC bus current as shown in Fig. 3-15(a). In the extracted model, the DC bus current

flows equally into three phases. The extracted circuit in Fig. 3-15(a) can be further

simplified as Fig. 3-15(b). It can be observed in the simplified DC bus current model that,

if a control strategy can naturally promise nullification of the common mode component

of the leg internal voltages, then from the DC bus side the MMC looks like a high speed

controlled voltage source behind an inductor.

3.3.3 Analysis of Circulating Current of the MMC with Generalized DC Bus

By substituting (3.34) into (3.31), (3.32), and (3.33), dynamics of three phase leg

currents can be deduced as (3.35), (3.36), and (3.37).

* * *

*2( )( ) 2( ).3 3

dc uo vo woo o uo uo

i v v vdL R i v

dt

(3.35)

* * *

*2( )( ) 2( ).3 3

dc uo vo woo o vo vo

i v v vdL R i v

dt

(3.36)

+

-

+

-

+

-

+

-

+

-

+

-

*1

2dcV *1

2dcV *1

2dcV

3

dci

3

dci

3

dci

* * *2( )

3uo vo wov v v

dcv

dci

sLo+Ro

sLo+Ro

*1

2dcV *1

2dcV *1

2dcV

+-

+

-

* * *2( )

3uo vo wov v v

*dcV dcv

2(sLo+Ro)/3

+-

(a) (b)

dci

37

* * *

*2( )( ) 2( ).3 3

dc uo vo woo o wo wo

i v v vdL R i v

dt

(3.37)

In the conventional modeling, if the DC bus is a stiff voltage source, leg current xoi

of phase x is only affected by its leg internal voltage xov as (3.9). However, if the DC

bus is not a stiff voltage source, dynamics of the leg currents are affected not only by the

corresponding phase leg internal voltage but also by the DC bus current and the common

mode component of three phase leg internal voltages. It means that contrast to the stiff

DC bus voltage source case, there is a strong coupling of leg currents between different

phases.

A circulating current of phase x, is defined as difference between the leg current and

the averaged current of the DC bus current that equally flows into each phase, and is

denoted by ,xo ciri .

, .3

dcxo cir xo

ii i (3.38)

Then (3.35), (3.36), and (3.37) can be represented by following equations.

* * *

*,2( ) 2( ).

3

uo vo woo o uo cir uo

v v vdL R i v

dt

(3.39)

* * *

*,2( ) 2( ).

3

uo vo woo o vo cir vo

v v vdL R i v

dt

(3.40)

* * *

*,2( ) 2( ).

3

uo vo woo o wo cir wo

v v vdL R i v

dt

(3.41)

For the three phase MMC, sum of three phase leg currents is equal to the DC bus

current. Then a basic characteristic of the circulating current can be deduced as (3.42).

, , , 0.uo cir vo cir wo ciri i i (3.42)

Eq.(3.42) means that the circulating currents only flow inside the converter without

38

being leaked to neither the AC grid side nor the DC bus side as shown in Fig. 3-16.

Figure 3-16 Analysis of circulating current of the MMC with generalized DC bus.

Figure 3-17 Extracted model from the MMC circuit to analyze circulating currents.

(a) Extracted model of circulating currents. (b) Simplified equivalent model of circulating

currents.

Since in the HVDC application the DC bus current is determined by power flow,

iuo,cir

iuo,cir

-+

-

*1

2dcV

ivo,cir

ivo,cir

-+

-

iwo,cir

iwo,cir

-+

-

*usv *

vsv *wsv

*uov *

vov *wov

*usv *

vsv *wsv

*uov *

vov *wov

ius

ivs

iws

vug

vvg

vwg

dcV

+-

+-

+-

*1

2dcV *1

2dcV

*1

2dcV

*1

2dcV *1

2dcV

sLs+Rs

sLo+Ro

sLo+Ro

dci

dci+-

+-

+-

+

-

+

-+

-

+

+-

+

-+

-

+

+-

+

-+

-

+

+-

iuo,cir

*uov *

vov *wov

ivo,cir iwo,cir

sLo+Ro

sLo+Ro

+-

+-

+-

+-

+-

+-

*uov *

vov *wov

*uov *

vov*wov

iuo,cir ivo,cir iwo,cir * * *

3

uo vo wov v v

+-

+-

+-

+-

(a) (b)

39

regulating three phase leg currents is equal to regulating three phase circulating currents.

According to (3.39), (3.40), (3.41), and (3.42) a model can be extracted from the

MMC circuit to describe circulating current as shown in Fig. 3-17(a), and it can be further

simplified as Fig. 3-17(b).

In the conventional arm capacitor energy control strategy, the arm capacitor energy was

controlled independently for each phase, which means that the leg current of each phase

was controlled independently. In this case a common mode component defined as (3.43)

would exist in three phase leg internal voltages if arm capacitor energy control and leg

current regulation are implemented independently for each phase.

* * *

*, .

3

uo vo woxo com

v v vv

(3.43)

It is noticed in Fig. 3-15(b) that the common mode leg internal voltage *

,xo comv would

affect instantaneous DC bus voltage. Moreover, it would also affect the circulating

current as shown in Fig. 3-17(b). It may accumulate a large DC component in *

,xo comv

and make the system unstable. Contrast to motor-drive application, the DC bus in the

HVDC transmission system is not anymore a stiff DC voltage source, and reveals rather

current source characteristics, and the common mode leg internal voltage *

,xo comv should

be controlled as null. If an arm capacitor energy control strategy can nullify *

,xo comv

inherently, then the AC grid current control, the DC bus current control, and the arm

capacitor energy control can be completely decoupled. And, the MMC for HVDC may

have better dynamic performance compared to the conventional arm capacitor energy

control strategy.

40

Figure 3-18 Models extracted from the MMC circuit to analyze AC grid current, DC bus

current, and circulating current.

(a) Extracted model of AC grid current. (b) Extracted model of DC bus current.

(c) Extracted model of circulating current.

In summary, for the MMC with generalized DC bus, the circuit can be divided into

three extracted models to describe the AC grid current, the DC bus current, and the

circulating current as shown in Fig. 3-18. The objective of the control of the MMC with

generalized DC bus is to control the MMC with a strategy which inherently nullifies the

common mode component of leg internal voltages. Then AC grid current control, DC bus

current control, and arm capacitor energy control (which is implemented by circulating

current in the proposed method in this thesis) can be fully decoupled regardless of the

characteristic of the DC bus.

3.4 Control of the Indirect Modulated MMC with Generalized DC

Bus

Arm capacitor energy control of the MMC is one of the main concerns of the control of

the MMC. The principle of the conventional arm capacitor energy control strategy is to

draw a DC leg current from the infinite DC bus to charge or discharge the leg capacitor

energy, and to draw a line frequency AC leg current from the infinite DC bus to transfer

energy between the upper arm capacitors and the lower arm capacitors.

ius

ivs

iws

vug

vvg

vwg

*usv

*vsv

*wsv

*uov *

vov*wov

iuo,cir ivo,cir iwo,cir * * *

3

uo vo wov v v +

-

* * *2( )

3uo vo wov v v

*dcV dcV

(sLo+Ro)/2sLs+Rs

sLo+Ro

2(sLo+Ro)/3+ -

+ -

+ -

+-

+-

+-

(a) (b) (c)

+-

+-

+-

+-

+-

41

While, the principle of the proposed arm capacitor energy control strategy is to draw

active power from the AC grid or the DC bus into the whole converter capacitors and

redistribute the energy stored in capacitors of six different arms by the circulating

currents which flow only inside the converter.

The main objective of arm capacitor energy control is controlling energy stored in

capacitors of six arms as rated reference, namely as (3.44).

*

*

*

*

*

*

.

uu arm

ul arm

vu arm

vl arm

wu arm

wl arm

E E

E E

E E

E E

E E

E E

(3.44)

The six independent equations in (3.44) is mathematically equivalent to the following

six independent equations.

*

, ,

6 .total xu xl arm

x u v w

E E E E

(3.45)

.u uu ul v vu vlE E E E E E (3.46)

.v vu vl w wu wlE E E E E E (3.47)

0.u uu ulE E E (3.48)

0.v vu vlE E E (3.49)

0.w wu wlE E E (3.50)

It should be noticed that (3.45) means controlling energy stored in the whole cell

capacitors of the MMC, (3.46) and (3.47) mean inter-leg capacitor energy balancing,

and (3.48), (3.49), and (3.50) mean upper and lower arm capacitor energy balancing for

42

each phase.

3.4.1 Control of Energy Stored in the Whole Cell Capacitors of the MMC

Power flows into cell capacitors of each phase can be described as (3.51), (3.52), and

(3.53).

* * * * *2 .uu dc uo us us uo uo dc uo us us

dEP V i v i v i V i v i

dt

(3.51)

* * * * *2 .vv dc vo vs vs vo vo dc vo vs vs


dt

(3.52)

* * * * *2 .ww dc wo ws ws wo wo dc wo ws ws


dt

(3.53)

By adding (3.51), (3.52), and (3.53), power flows into whole cell capacitors of the

MMC can be calculated as (3.54).

* * * *, , .u v w dc dc us us vs vs ws wsP V i v i v i v i (3.54)

According to (3.54), difference of the power flows from the DC bus and the power

flows into the AC grid side would charge or discharge the whole cell capacitors of the

MMC.

43

Figure 3-19 Principle of control of the energy stored in the whole cell capacitors of the

MMC.

(a) Rectifier mode. (b) Inverter mode.

If an MMC operates in rectifier mode to control DC bus voltage, the capacitive energy

stored in the MMC should be regulated by controlling AC grid side active power flows

into the MMC, namely by controlling active current as shown in Fig. 3-19 (a). On the

other hand, for an MMC operates in inverter mode, the energy stored in the whole cell

capacitors of the MMC should be regulated by controlling DC bus side power flows into

the MMC, namely by controlling the DC bus current as shown in Fig. 3-19 (b).

vuu

vul

iuu

iul

ius

UiDC

V W

iuo

ivu iwu

ivl iwl

+

-

+

-

ivo

iwo

ivs

iws

vvu vwu

vvl vwl

AC Grid

sLs+RssLo+Ro

sLo+Ro

+

-

+

-

+

-

+

-

vuu

vul

iuu

iul

ius

UiDC

V W

iuo

ivu iwu

ivl iwl

+

-

+

-

ivo

iwo

ivs

iws

vvu vwu

vvl vwl

AC Grid

sLs+RssLo+Ro

sLo+Ro

+

-

+

-

+

-

+

-

dcv dcv

(a) (b)

Higher Power

Lower Power

44

Figure 3-20 Control block diagram of the proposed converter total capacitor energy

controller.

(a) Converter total capacitor energy controller for rectifier mode. (b) Converter total

capacitor energy controller for inverter mode.

The control block diagram of the proposed converter total capacitor energy controller

is shown in Fig. 3-20, for both rectifier mode and inverter mode. It should be mentioned

that in this thesis it is assumed that grid voltage vector is oriented to synchronously

rotating q-axis, which means that d-axis current stands for reactive current and q-axis

current stands for active current.

As analyzed in section 3.3.1, regulating the AC grid currents or the DC bus current

would not generate the common mode component of leg internal voltages.

3.4.2 Balancing of Three Phase Leg Capacitor Energy

For an MMC connected with a generalized DC bus, balancing of three phase leg

capacitor energy and balancing of upper and lower arm capacitor energy should not affect

neither AC grid nor DC bus current regulation. In this case, the balancing should be

implemented not by the common mode voltage injection which is usually employed for

(a)

IP

KK

s

*totalE

totalE

(b)

IP

KK

s

*totalE

totalE

*ACP

ff dc dcP V i 3

2gV

Grid Current

Vector

Controller

*qgi

*dgi

*, ,us vs wsv

3

2ff g qgP V i ,dc ratedV

*DCP

*dci DC Bus

Current

Regulator

*dcV

45

phase capacitor energy balancing in cascade full-bridge based STATCOMs, but by the

power flowing only inside the converter. The circulating current defined in section 3.3.3

that flows only inside the converter can transfer energy between different arms without

affecting neither AC grid current nor DC bus current and it is employed in the proposed

control strategy for arm capacitor energy balancing.

The power flow into three different legs expressed in (3.51), (3.52), and (3.53) can

also be represented as (3.55), (3.56), and (3.57).

* * *, .

3

u dcu dc us us dc uo cir

dE iP V v i V i

dt

(3.55)

* * *, .

3

v dcv dc vs vs dc vo cir

dE iP V v i V i

dt

(3.56)

* * *, .

3

w dcw dc ws ws dc wo cir

dE iP V v i V i

dt

(3.57)

The first two terms in the right hand sides of (3.55), (3.56), and (3.57) are

determined by power flow and the converter total capacitor energy controller in section

3.4.1. In the steady state, the first two terms in the right hand side would be cancelled if

the AC grid is balanced. Since the sum of the circulating currents is inherently null as

(3.42), if a DC component is injected in the circulating currents, sum of the last terms in

the right hand sides of (3.55), (3.56), and (3.57) is inherently null as (3.58).

* * *

, , , 0.dc uo cirDC dc vo cirDC dc wo cirDCV i V i V i (3.58)

Eq.(3.55), (3.56), (3.57), and (3.58) indicate that a DC component of the circulating

currents can transfer energy between three legs without affecting neither the AC grid side

nor the DC bus side as shown in Fig. 3-21.

46

Figure 3-21 Principle of balancing of three phase leg capacitor energy.

Figure 3-22 Control block diagram of the proposed leg capacitor energy balancing

controller.

(a) Leg capacitor energy reference updating module. (b) Inter-leg capacitor energy

balancing module.

The control block diagram of the proposed leg capacitor energy balancing controller is

iuo,cirDC

iuo,cirDC

-+

-

*1

2dcV

ivo,cirDC

ivo,cirDC

-+

-

iwo,cirDC

iwo,cirDC

-+

-

*usv *

vsv *wsv

*uov *

vov *wov

*usv *

vsv *wsv

*uov *

vov *wov

ius

ivs

iws

vug

vvg

vwg

dcv

+-

+-

+-

*1

2dcV *1

2dcV

*1

2dcV

*1

2dcV *1

2dcV

sLs+Rs

sLo+Ro

sLo+Ro

dci

dci+-

+-

+-

+

-

+

-+

-

+

+-

+

-+

-

+

+-

+

-+

-

+

+-

Energy exchange

PI

+++

(b)


Notch Filters

,u fltE

uE

3

,u fltE

,v fltE

,w fltEvE

wE

*dcV

*,uo cirDCi

,v fltE

*,vo cirDCi

,w fltE

*,wo cirDCi

*dcV

*dcV

PI

PI

*legE

*legE

*legE

*legE

47

shown in Fig. 3-22. Contrast to the conventional leg capacitor energy control method, the

most important point of the proposed strategy is that the leg capacitor energy reference is

updated at every sampling period as the average capacitor energy of three legs, instead of

a constant reference value which is usually set as rated leg capacitor energy in the

conventional method. The principle of the conventional leg capacitor energy control

method was drawing power from the infinite DC bus into each leg independently, while

the principle of the proposed method is drawing power from the AC grid or DC bus into

the whole capacitors of the converter and balancing leg capacitor energy by DC

circulating currents which flow only inside the converter. Since the reference of leg

capacitor energy is updated online as the three leg average capacitor energy, sum of errors

of the controllers in Fig. 3-22(b) can always be kept as null.

* * *, , , 0.leg u flt leg v flt leg w fltE E E E E E (3.59)

Eq.(3.59) indicates that sum of references of DC components of three phase

circulating currents generated by the leg capacitor energy balancing controller in Fig. 3-

22(b) is inherently nullified, which means that nullification of common mode component

of leg internal voltages is guaranteed inherently as (3.60). In addition, problems caused

by *

,xo comv such as poor dynamics and system stability issues can be inherently

prevented. Since there is a considerable twice line frequency fluctuation in the leg

capacitor energy, notch filters with a center frequency at twice line frequency should be

employed.

* *, ,

, , , ,

0 0.xo cirDC xo DC

x u v w x u v w

i v

(3.60)

3.4.3 Balancing of Upper and Lower Arm Capacitor Energy

Differences of power that flow into upper arms and lower arms can be derived as

48

(3.61), (3.62), and (3.63).

* * * * * *,

1 12 2 2 .

2 2 3

u dcu dc us us uo uo us dc us us us uo cir

dE iP V i v i v i V i v v i

dt

(3.61)

* * * * * *,

1 12 2 2 .

2 2 3

v dcv dc vs vs vo vo vs dc vs vs vs vo cir


dt

(3.62)

* * * * * *,

1 12 2 2 .

2 2 3

w dcw dc ws ws wo wo ws dc ws ws ws wo cir


dt

(3.63)

Since the first two terms in the right hand sides of (3.61), (3.62), and (3.63) do not

generate DC components , only the last terms in the right hand sides should be considered.

Since the upper and lower arm capacitor energy should be balanced for three legs

independently, three Degree of Freedoms (DOFs) are necessary to regulate uP , vP ,

and wP independently. In the proposed method, a positive sequence circulating current

and a negative sequence circulating current are employed. If the three phase output EMFs

are defined as (3.64), then its corresponding space vector can be denoted by (3.65).

*

*

*

cos( )

cos( 2 / 3) .

cos( 2 / 3)

us ms o

vs ms o

ws ms o

v V t

v V t

v V t

(3.64)

( )

.oj tmsV e

sV (3.65)

If a positive sequence circulating current is injected inside the MMC as (3.66), then

according to (3.61), (3.62), and (3.63), differences of power that flow into upper and

lower arm capacitors caused by the injected positive sequence circulating current can be

deduced as (3.67).

49

*, , ,

*, , ,

*, , ,

cos( )

cos( 2 / 3) .

cos( 2 / 3)

uo cirAC pos cirAC pos o pos

vo cirAC pos cirAC pos o pos

wo cirAC pos cirAC pos o pos

i I t

i I t

i I t

(3.66)

, ,

, ,

, ,

cos( )

cos( ) .

cos( )

u pos ms cirAC pos pos

v pos ms cirAC pos pos

w pos ms cirAC pos pos

P V I

P V I

P V I

(3.67)

In (3.67), the injected positive sequence circulating current only contributes to

common components of uP , vP , and wP , which means that it can be injected to

eliminate only common errors of upper and lower arm capacitor energy of three phases as

shown in Fig. 3-23.


positive sequence circulating current.

iuo,cirAC,pos

-+

-

*1

2dcV

-+

-

-+

-

*usv *

vsv *wsv

*uov *

vov *wov

*usv *

vsv *wsv

*uov *

vov *wov

ius

ivs

iws

vug

vvg

vwg

dcV

+-

+-

+-

*1

2dcV *1

2dcV

*1

2dcV

*1

2dcV *1

2dcV

sLs+Rs

sLo+Ro

sLo+Ro

dci

dci+-

+-

+-

+

-

+

-+

-

+

+-

+

-

+

+-

+

-+

-

+

+-

+

-

iwo,cirAC,posivo,cirAC,pos

50

If a negative sequence circulating current is injected inside the MMC as (3.68), then

according to (3.61), (3.62), and (3.63), differences of power that flow into upper and

lower arm capacitors caused by the injected negative sequence circulating current can be

deduced as (3.69).

*, , ,

*, , ,

*, , ,

cos( )

cos( 2 / 3) .

cos( 2 / 3)

uo cirAC neg cirAC neg o neg

vo cirAC neg cirAC neg o neg

wo cirAC neg cirAC neg o neg

i I t

i I t

i I t

(3.68)

, ,

, ,

, ,

cos( )

cos( 2 / 3) .

cos( 2 / 3)

u neg ms cirAC neg neg

v neg ms cirAC neg neg

w neg ms cirAC neg neg

P V I

P V I

P V I

(3.69)

In (3.69), the injected negative sequence circulating current only contributes to

differential components of uP , vP , and wP , which means that it can be injected to

eliminate only differential errors of upper and lower arm capacitor energy of three phases


51


negative sequence circulating current.

In summary, the positive and negative sequence circulating current can be injected to

eliminate both common and differential errors of upper and lower arm capacitor energy of

three phases. In (3.67) and (3.69), if the injected positive sequence circulating current is

in phase with the output EMF, namely pos , then , ,, ,cirAC pos cirAC neg negI I

provides three DOFs for upper and lower arm capacitor energy balancing. Then the

positive sequence circulating current can be injected to eliminate the common error comE

of upper and lower arm capacitor energy, and the negative sequence circulating current

can be injected to eliminate the differential errors dE and qE of upper and lower arm

capacitor energy as represented by (3.70).

iuo,cirAC,neg

-+

-

*1

2dcV

-+

-

-+

-

*usv *

vsv *wsv

*uov *

vov *wov

*usv *

vsv *wsv

*uov *

vov *wov

ius

ivs

iws

vug

vvg

vwg

dcV

+-

+-

+-

*1

2dcV *1

2dcV

*1

2dcV

*1

2dcV *1

2dcV

sLs+Rs

sLo+Ro

sLo+Ro

dci

dci+-

+-

+-

+

-

+

-+

-

+

+-

+

-

+

+-

+

-+

-

+

+-

+

-

iwo,cirAC,negivo,cirAC,neg

52

,

,

,

1{ ( )}3

2 1 1( ) cos( ).3 3 3

3 3( ) sin( )

3 3

comcom u v w ms cirAC pos

dd u v w ms cirAC neg neg

qq v w ms cirAC neg neg

dE dP E E E V I

dt dt

dE dP E E E V I

dt dt

dE dP E E V I

dt dt

(3.70)

Since for upper and lower arm capacitor energy balancing references of line frequency

circulating currents only include positive and negative sequence components, inherent

nullification of common mode component of leg internal voltages is guaranteed as (3.71).

* *, ,

, , , ,

0 0.xo cirAC xo AC

x u v w x u v w

i v

(3.71)

Then in accordance with (3.60) and (3.71), inherent nullification of the common

mode component of the leg internal voltages can be confirmed. It means that the proposed

arm capacitor energy balancing control strategy, including the inter-leg capacitor energy

balancing and upper and lower arm capacitor energy balancing, inherently prevents

common mode component of leg internal voltages and promises good performance of

current regulation and arm capacitor energy balancing. Moreover, the proposed control

strategy fully decouples AC grid current control, DC bus current control, and control of

circulating currents which play a crucial role in arm capacitor energy balancing inside the

converter in the proposed method.

53

Figure 3-25 Control block diagram of the proposed upper and lower arm capacitor energy

balancing controller.

(a) Common error eliminating module. (b) Differential error eliminating module.

Control block diagram of the proposed upper and lower arm capacitor energy

balancing controller is shown in Fig. 3-25. The line frequency notch filters, which should

be employed to filter the energy fluctuation out are omitted in the Fig. 3-25. To make the

reference of the negative sequence circulating current, (3.72) and (3.73) are used in the

Reference Making block and the Transformation block in the Fig. 3-25(b), respectively.

* * * *( )* *

, , , , 2.o

d q d qj tdo cirAC neg qo cirAC neg

ms ms

P jP P jPi ji e

V V

sV (3.72)

1/ 3comE

0 +-

*comP

msV

*

,cir posI

*xs

ms

v

V

*, ,xo cirAC posi

+

-,u fltE

comE

+

-,v fltE

+-,w fltE

*dP

*qP

Ref.

Making

*, ,do cir negi

Tra

nsf

orm

atio

n

*usv *

vsv*wsv

*, ,uo cirAC negi

*, ,vo cirAC negi

*, ,wo cirAC negi

comE

comE

uvw

dq*

, ,qo cir negi

,uvw fltE

PI

(a)

(b)

+-

0

+-

0

+-

0

PI

PI

PI

*uP

*vP

*wP

54

*, , *

, ,*, , *

, ,*, ,

1 0

1 3.

2 2

1 3

2 2

uo cirAC neg

do cirAC neg

vo cirAC neg

qo cirAC neg

wo cirAC neg

ii

ii

i

(3.73)

3.4.3 Overall Structure of the Proposed Method and Practical Implementation

Issues

Figure 3-26 Overall control block diagram of the proposed MMC controller.

Fig. 3-26 shows the overall control block diagram of the proposed controller of the

MMC operates in rectifier mode. The MMC total capacitor energy are controlled by the

active and reactive power controller and the references of output EMFs generated in this

module are transmitted to the upper and lower arm balancing controller to generate

references of injected line frequency circulating currents. The references of AC

*totalE

totalE

*ACP

ff dc dcP V i 3

2gV

Grid Current

Vector

Controller

*qgi

*dgi

*, ,us vs wsv

3

2gV

*ACQ

+

-,u fltE

comE

+

-,v fltE

+-,w fltE

*dP

*qP

Making

Ref.

*, ,do cirAC negi

*usv *

vsv*wsv

*, ,uo cirAC negi

*, ,vo cirAC negi

*, ,wo cirAC negi

comE

comE

uvw

dq*

, ,qo cirAC negi

+-

0

+-

0

+-

0

PI

PI

PI

*uP

*vP

*wP

1/ 3comE

0 +-

*comP

msV

*,cirAC posI

*xs

ms

v

V

*, ,xo cirAC posi

,uvw fltE

PI

IP

KK

s

Active and reactive power controller.

Upper and lower arm balancing controller – Differential error

Upper and lower arm balancing controller – Common error

*, ,us vs wsv

PI

+++

(b) Inter-leg energy balancing module.(a) Leg Energy Reference updating module.


Notch Filters

,u fltE

uE

*

legE

*legE

3

,u fltE

,v fltE

,w fltEvE

wE

*dcV

*,uo cirDCi

,v fltE

*legE

*,vo cirDCi

,w fltE

*legE

*,wo cirDCi

*dcV

*dcV

PI

PI

Leg balancing controller.

+

+

*,xo cirDCi

+-

,xo ciri

2 2CI CR

CP

o

K K sK

s s

*,xo cirACi

*,xo ciri *

xov

+

-

+

-*xov

*

2

dcV+

-

++

*xsv

*xuv

*xlv

Circulating current regulator.

*,xo cirDCi

*,xo cirACi

Arm output voltage reference generator*

, ,uo vo wov

*, ,us vs wsv

uvw

dq

55

components and DC components of circulating currents that generated by the upper and

lower arm balancing controller and the leg balancing controller are added in the

circulating current controller and the circulating currents are regulated by a Proportional-

Integral-Resonant (PIR) controller. Finally, the references of the DC bus voltage, the

output EMFs, and the leg internal voltages are processed in the arm output voltage

reference generator to make arm output voltage references.

Practically, because of measurement error (usually the sensor measurement offset, scale

error), EMI noise, limited precision of digital processing, and employment of output

limiting blocks that usually necessary in practical controllers, nullification of common

mode component of the leg internal voltages may not be always guaranteed. To deal with

this problem, the entire arm capacitor energy controller including a leg capacitor energy

balancing controller, an upper and lower arm capacitor energy balancing controller, and a

circulating current controller can be fully constructed in the stationary dq reference frame

instead of the stationary abc frame as briefly shown in Fig 3-27.

56

Figure 3-27 Brief conceptual block diagram of the proposed cascade structured arm

capacitor energy balancing controller in the stationary dq reference frame.

(a) Leg capacitor energy balancing controller in the stationary dq frame.

(b) Upper and lower arm capacitor energy balancing controller in the stationary dq frame.

(c) Circulating current controller in the stationary dq frame.

3.5 Ride Through Strategy of the AC Grid Single Line to Ground

(SLG) Short Circuit Fault

Single Line to Ground (SLG) fault is one of the most frequent faults in an AC

transmission system. In case of a SLG fault, the HVDC transmission line is required to

transmit electricity continuously. It calls for fault ride through capability of the converter.

While a SLG fault occurs, not only the positive sequence voltage but also the negative

sequence voltage and zero sequence voltage would appear in the AC grid. Since the AC

side of the converter is connected to the AC grid through a wye-delta connected

dq,com

uvw,u fltE

,v fltE

,w fltE

,d fltE

,q fltE

,com fltE

PI

PI

PI

AC grid or DC bus

controller

*totalP

*,do cirDCi

*,qo cirDCi

*dcV

dq,com

uvw,u fltE

,v fltE

,w fltE

,d fltE

,q fltE

,com fltE

PI

PI

PI

*comP

*dP

*qP

Circulating

Current

Reference

Making

*,do cirACi

*,qo cirACi

*, ,us vs wsv

+

+

*,dqo cirDCi

+-

,dqo ciri

2 2CI CR

CP

o

K K sK

s s

*,dqo cirACi

*,dqo ciri *

dqovdq

uvw

* * *, ,uo vo wov v v

(a)

(b)

(c)

+-

+-

+-

* 2x ratedE E

0

0

+-

0

+-

0

+-

0

57

transformer, the zero sequence voltage would be excluded from the converter. If an AC

SLG bus bar fault occurs, magnitude of the negative sequence voltage of the grid can be

as high as 50% of that of the positive sequence voltage, and the MMC has to operate in

an AC side severe unbalanced condition.

In such situation, the positive sequence AC grid current and the negative sequence AC

grid current should be controlled independently, and it calls for two independent AC grid

current vector controllers, namely a positive sequence AC grid current controller and a

negative sequence AC grid current controller.

Figure 3-28 Schematic of the AC grid current vector controller for SLG fault ride through.

Fig. 3-28 shows control block diagram of the AC grid current vector controller for SLG

58

fault ride through [9]. The positive sequence grid current controller is implemented in an

anticlockwise rotating synchronous dq frame, and the transformed grid current is filtered

out by a double line frequency notch filter to cut off the negative sequence grid current

which appears as twice line frequency component in the anticlockwise rotating

synchronous dq frame. Reference of the q-axis current depends on operation mode of the

converter. As an example, Fig. 3-28 shows schematic control block diagram of the

controller for the MMC in rectifier mode.

The negative sequence grid current controller is implemented in a clockwise rotating

synchronous dq frame, and the transformed grid current is filtered by a twice line

frequency notch filter to cut off the positive sequence grid current which appears as twice

line frequency component in the clockwise rotating synchronous dq frame. It is a

common fashion to set the reference of the negative sequence grid current as null to

generate only balanced current into the AC grid [9].

The positive sequence grid current controller only generates reference of the positive

sequence output EMF, and the negative grid current controller only generates reference of

the negative sequence output EMF.

As discussed in section 3.3.2 and section 3.3.3, control of the DC bus current and the

circulating current are not affected by AC grid side by the proposed method, no matter the

AC grid is balanced or not. It is shown in section 3.4.2 that the output EMF does not

contribute to power that associated with leg capacitor energy balancing. However, since

the upper and lower arm capacitor energy control strategy proposed in section 3.4.3 is

conducted under an assumption of balanced AC grid, the unbalanced AC grid during SLG

fault would result in disturbance power that associated with upper and lower arm

capacitor energy balancing control.

In unbalanced AC grid condition, without loss of generality the positive and negative

59

sequence components of the output EMF of the MMC are defined as (3.74) and (3.75).

*

*

*

sin( )

sin( 2 / 3) .

sin( 2 / 3)

us ms o v

vs ms o v

ws ms o v

v V t

v V t

v V t

(3.74)

*

*

*

sin( )

sin( 2 / 3).

sin( 2 / 3)

us ms o v

vs ms o v

ws ms o v

v V t

v V t

v V t

(3.75)

If the positive and negative circulating currents represented as (3.76) and (3.77) are

injected inside the converter, then the upper and lower arm balancing control associated

power contributed by positive sequence output EMF and positive sequence circulating

current, positive sequence output EMF and negative sequence circulating current,

negative sequence output EMF and positive sequence circulating current, and negative

sequence output EMF and negative sequence circulating current are calculated as (3.78),

(3.79), (3.80), and (3.81) respectively.

*,

*,*,

sin( )

sin( 2 / 3) .

sin( 2 / 3)

uo cirAC cirAC o i

vs cirAC cirAC o i

ws cirAC cirAC o i

i I t

i I t

i I t

(3.76)

*,

*,*,

sin( )

sin( 2 / 3) .

sin( 2 / 3)

uo cirAC cirAC o i

vs cirAC cirAC o i

ws cirAC cirAC o i

i I t

i I t

i I t

(3.77)

* *,

* *,

* *,

2 cos( )

2 cos( ) .

2 cos( )

u us uo cirAC ms cirAC v iDC

v vs vo cirAC ms cirAC v iDC

w ws wo cirAC ms cirAC v iDC

P v i V I

P v i V I

P v i V I

(3.78)

60

* *,

* *,

* *,

2 cos( )

2 cos( 2 / 3) .

2 cos( 2 / 3)




P v i V I

P v i V I

P v i V I

(3.79)

* *,

* *,

* *,

2 cos( )

2 cos( 2 / 3) .

2 cos( 2 / 3)




P v i V I

P v i V I

P v i V I

(3.80)

* *,

* *,

* *,

2 cos( )

2 cos( ) .

2 cos( )




P v i V I

P v i V I

P v i V I

(3.81)

According to (3.78)-(3.81), if the positive sequence circulating current is in phase with

the positive sequence output EMF, namely v i , then cirACI , cirACI

, and i

provides

three DOFs for upper and lower arm capacitor energy balancing. Transforming (3.78)-

(3.81) to the stationary dqo reference frame, (3.82)-(3.84) can be deduced. If the

transformation in (3.73) is employed, then the negative sequence components can be

deduced as DC components in synchronous rotating reference frame of the positive

sequence components as shown in (3.82)-(3.84).

, , , , , , , ,

1{ ( )}3

1( )

3

cos( ) cos( )

( ).

comcom u v w

u u v v w w

ms cirAC v i ms cirAC v i

e e e e e e e ems d cirAC d ms q cirAC q ms d cirAC d ms q cirAC q

dE dP E E E

dt dt

P P P P P P

V I V I

V I V I V I V I

(3.82)

61

, , , , , , , ,

2 1 1( )3 3 3

2 1 1( ) ( ) ( )

3 3 3

cos( ) cos( )

(

dd u v w

u u v v w w

ms cirAC i v ms cirAC v i

e e e e e ems d cirAC d ms q cirAC q ms d cirAC d ms q cirAC

dE dP E E E

dt dt

P P P P P P

V I V I

V I V I V I V I

).eq

(3.83)

, , , , , , , ,

3 3( )

3 3

3 3( ) ( )

3 3

sin( ) sin( )

( ).

qq v w

v v w w

ms cirAC i v ms cirAC v i

e e e e e e e ems q cirAC d ms d cirAC q ms q cirAC d ms d cirAC q

dE dP E E

dt dt

P P P P

V I V I

V I V I V I V I

(3.84)

Comparing (3.82)-(3.84) to (3.70), it can be concluded that the negative sequence

output EMF results in disturbance terms to comP , dP , and qP, and the following

relations would not be valid any more if the circulating current reference calculation

method that derived under assumption of balanced AC grid is employed in the

unbalanced grid condition.

*

*

*

.

com com

d d

q q

P P

P P

P P

(3.85)

For simplifying equations, the synchronous rotating q-axis is oriented to the space

vector of the positive sequence output EMF, and the negative sequence output EMF and

the negative sequence circulating current are transformed by (3.86) to the stationary

frame to make the space vectors of them rotate synchronously with the vector of the

positive sequence output EMF.

62

2 1 1

3 3 3.

3 30

3 3

uds

vqs

w

ff

ff

f

(3.86)

Then the power terms in (3.82)-(3.84) can be fully represented by the variables

transformed to the synchronous rotating reference frame as (3.87).

,, , ,

, , ,

,, ,

0 .

0

ee e ecirAC qms q ms d ms qcom

e e ed ms q ms q cirAC d

ee eq cirAC qms d ms q

IV V VP

P V V I

P IV V

(3.87)

In accordance with (3.87), to guarantee (3.85) in spite of disturbance power term

caused by the negative sequence output EMF, references of line frequency circulating

currents should be calculated by (3.88) instead of (3.70) and (3.72). In (3.88) D is

calculated by (3.89). It is noticed that if the negative sequence output EMF is null,

namely , 0ems dV and , 0e

ms qV , then the 3-by-3 matrix in (3.88) is a block diagonal

matrix and it naturally coincides with the equations derived in balanced AC grid

condition in (3.70). It means that proposed SLG fault ride through control strategy is a

generally valid method regardless of the AC grid condition and provides seamless

transition between balanced and unbalanced conditions.

2*, , , , ,,

* 2 2, , , , , , ,

* 2 2, , , , , , ,

( )

1( ) ( )

( ) ( )

e e e e eems q ms q ms d ms q ms qcirAC d

e e e e e e ecirAC d ms q ms q ms d ms q ms q ms d

e e e e e e ecirAC q ms q ms d ms q ms q ms d ms q

V V V V VI

I V V V V V VD

I V V V V V V

*

*

*

.

com

d

q

P

P

P

(3.88)

2 2 2, , , ,( ) ( ) ( ) .e e e e

ms q ms q ms d ms qD V V V V (3.89)

In summary, the control strategy of the converter total capacitor energy and the control

strategy of leg capacitor energy balancing that proposed in section 3.4.1 and section 3.4.2

63

are valid in unbalanced AC grid condition such as a SLG fault. However, for the upper

and lower arm capacitor energy balancing, reference of line frequency circulating current

should be generated by (3.88) in which the disturbance power caused by the negative

sequence output EMF are considered.

64

4. Direct Modulation Based Control Strategy of the

MMC

One of the interesting characteristics of the direct modulated MMC is the natural

regulation of the arm capacitor energy without any closed loop control. While an MMC

operates by direct modulation, the energy stored in the capacitors of different arms is

naturally regulated and balanced. However, its mechanism and dynamics were not

investigated clearly until a first approach on this issue had been published in 2013 [23].

In this approach [23], a stiff DC voltage source was presumed at the DC bus of the

MMC and mechanism and dynamics of arm capacitor energy natural regulation were

analyzed independently for each phase.

However, different from the conventional two-level converter or three-level converter

based VSC-HVDC system, there is no capacitor in the DC bus. Moreover, a smoothing

reactor is usually installed in series in the DC bus and the DC bus reveals more current

sourced characteristic instead of voltage source characteristic. For a point-to-point HVDC

transmission system, natural balancing phenomenon of capacitor energy of different arms

has been observed and reported by simulation in [4,5,11,12]. It means that the direct

modulated MMC might have natural arm capacitor energy balancing capability even with

generalized DC bus.

In this thesis, as a further approach, mechanism and dynamics of arm capacitor energy

natural balancing of the direct modulated MMC are investigated and analyzed for the case

of the generalized DC bus.

65

4.1 Modeling of the Direct Modulated MMC with Stiff Voltage

Sourced DC Bus

4.1.1 Arm Output Voltage and Insertion Ratio

For a direct modulated MMC, references of upper and lower arm output voltage are

represented as (4.1) and (4.2). Different from indirect modulation, the direct modulation

acquires the insertions ratio by a fixed rated DC bus voltage instead of the measured

voltages of the cell capacitors in each arm, as shown in (4.3) and (4.4).

* * .

2

dcxu xs

Vv v (4.1)

* * .

2

dcxl xs

Vv v (4.2)

*

* 2 .

dcxs

xudc

Vv

nV

(4.3)

*

* 2 .

dcxs

xldc

Vv

nV

(4.4)

If each arm consists of N cells, then the number of inserted cells of the lower arm is

given by (4.5), and the number of inserted cells of upper arm is by (4.6). Then according

to (4.5) and (4.6), (4.7) can be easily concluded, which means that the sum of number

of inserted cells of the upper arm and the lower arm is always N at any instant.

*

round .2

xsxl

dc

vNN

V

(4.5)

*

round .2

xsxu

dc

vNN

V

(4.6)

66

.xu xlN N N (4.7)

To simplify analysis, some assumptions are necessary.

(a) The individual capacitor voltages within each arm of the converter are balanced

well by the sorting and selection mechanism.

(b) Both the number of cells in each arm, namely N and the sampling frequency are

high enough to represent the inserted arm voltage as continuous variables.

Then according to (4.3) and (4.4), the arm output voltages of both the upper arm and

the lower arm of phase x can be calculated by (4.8) and (4.9).

*

*, ,

1.

2

xsxu xu c xu c xu

dc

vv n v v

V

(4.8)

*

*, ,

1.

2

xsxl xl c xl c xl

dc

vv n v v

V

(4.9)

Then according to (3.6) and (3.7), the output EMF and the leg internal voltage of

phase x of an direct modulated MMC can be calculated as (4.10) and (4.11).

, , , ,* .

2 4

c xu c xl c xl c xu

xs xsdc

v v v vv v

V

(4.10)

*

, ,, ,

2.

2

c xu c xl xsdc c xu c xl

dcxo

v v vV v v

Vv

(4.11)

67

4.1.2 Analysis of Grid Current and Leg Current

Figure 4-1 Conceptual structure of the controller of the direct modulated MMC.

Fig. 4-1 shows a conceptual structure of the controller of the direct modulated MMC.

For a direct modulated MMC, the grid currents are regulated by a vector controller,

however, the leg current or the circulating current is not regulated by a specified closed

loop controller. Moreover, arm capacitor energy regulation is realized by inherent

regulation property of the direct modulated MMC instead of a closed loop energy

controller.

It should be noticed that there exist both a DC component and a small twice line

frequency ripple component that caused by the nature of single phase converter in the

sum of voltages of capacitors in each arm. Then the sums of voltages of capacitors of the

upper arm and the lower arm of phase x can be represented as (4.12) and (4.13).

, , , .c xu c xu c xuv v v (4.12)

, , , .c xl c xl c xlv v v (4.13)

It has been proven mathematically that the twice line frequency ripples in the upper

arm capacitor voltage and in the lower arm capacitor voltage are with the same magnitude

and phase, as analyzed by [17]. Eq. (4.14) represents these twice line frequency ripple

components of each arm capacitor voltages.

CCPcom

Qcom

ixs vgs

*

*

2

2

xsdown

dc

xsup

dc

vNn round

V

vNn round

V

Sorting

Algorithm

ndown

nup

Module

Interface

Vdc Idc

*xsv

68

, ,2

, ,2

sin 2.

sin 2

c xu c

c xl c

v V t

v V t

(4.14)

Then by substituting (4.12), (4.13), and (4.14) into (4.10) and (4.11), the

synthesized output EMF and the leg internal voltage can be represented as (4.15) and

(4.16).

, , , , , ,* * .

2 2 4

c xu c xl c xu c xl c xl c xu

xs xs xsdc dc

v v v v v vv v v

V V

(4.15)

, ,

,2 , , *sin 22 .2 2 2

c xu c xldc

c c xu c xlxo xs

dc

v vV V t v v

v vV

(4.16)

In the steady state, if the upper arm capacitor energy and the lower arm capacitor

energy are regulated to its rated value, namely as (4.17), the (4.15) and (4.16) are

described as (4.18) and (4.19).

,

,

.c xu dc

c xl dc

v V

v V

(4.17)

, ,* * .

2

c xu c xl

xs xs xsdc

v vv v v

V

(4.18)

,2 sin 2

.2

cxo

V tv

(4.19)

For the AC grid current control, the second and the third terms in the right hand side of

(4.15) appears as disturbance terms, and the gain of the first term in the right hand side of

(4.15) is not unity if the upper and lower arm capacitor voltage (or energy) are not

converged to rated value as shown in Fig. 4-2(a). As shown in Fig. 4-2(a), there are a DC

69

disturbance voltage, a line frequency disturbance voltage, and a triple line frequency

disturbance voltage in the AC side of the MMC. Since the bandwidth of the current

controller can be up to as high as hundreds of Hz, it is reasonable to assume that the AC

grid current tracks its reference as (4.20) in spite of the disturbance terms.

* .xs xsi i (4.20)

Figure 4-2 Per-phase extracted models of AC grid current and leg current of a direct

modulated MMC with stiff voltage sourced DC bus.

(a) Extracted model of AC grid current. (b) Extracted model of leg current.

ixs+-vxg + -

s ssL R2

o osL R

MMC

+

- dcV

+-

+

- dcV

AC Grid

2 o osL R

(a)

(b)

ixo

, , *

2

c xu c xl

xsdc

v vv

V

+ -

, , *

2

c xu c xl

xsdc

v vv

V

, ,

4

c xl c xuv v

+ -, ,

2

c xu c xldc

v vV

+

-

,2 sin 2

2

cV t

+

-

, , *

2

c xu c xlxs

dc

v vv

V

MMC DC Bus

70

For the leg current, since there is no corresponding controller in the direct modulated

MMC, it is determined by the disturbance terms in (4.16). The leg current then can be

calculated as (4.21).

, ,

,2 , , *sin 21 2 .2 2 2

c xu c xldc

c c xu c xlxo xs

o o dc

v vV V t v v

i vsL R V

(4.21)


Regulation of the MMC with Stiff Voltage Sourced DC Bus

As stated above, one of the main characteristics of the direct modulated MMC is that

arm capacitor energy is regulated to its rated value inherently without any closed loop

control. It means that the sum of upper and lower arm capacitor energy converges to rated

leg capacitor energy and the difference of upper and lower arm capacitor energy

converges to null inherently.

If the loss is neglected, then time derivatives of upper and lower arm capacitor energy

are the power calculated by multiplication of the arm output voltages and the currents

flow through arms as (4.22).

,

, , .xu xl

xu xl xu xl

dEv i

dt (4.22)

In accordance with the characteristics of capacitors, (4.22) can be represented as

(4.23).

71

2, , ,

, ,

1 1

2, , ,

, ,

1 1

( )

2.

( )

2

i iN Nc xu c xu c xuixu cell cell

cell c xu c xu

i i

i iN Nc xl c xl c xlixl cell cell

cell c xl c xl

i i

dv dv d vdE C CC v v

dt dt N dt N dt

dv dv d vdE C CC v v

dt dt N dt N dt

(4.23)

Then by substituting (4.23) and (4.8) into (4.9), the following dynamic equations of

the arm capacitor voltages are obtained.

, *

, *

.

c xucellxu xu

c xlcellxl xl

dvCn i

N dt

dvCn i

N dt

(4.24)

Dynamics of sum of upper and lower arm capacitor voltages are deduced as (4.25),

and dynamics of difference of upper and lower arm capacitor voltages are deduced as

(4.26).

*, * * .

c xcell xs xsxu xu xl xl xo

dc

dvC v in i n i i

N dt V

(4.25)

*, * * 21

.2

c xcell xs xoxu xu xl xl xs

dc

dvC v in i n i i

N dt V

(4.26)

4.2.1 Dynamics of Sum of Upper and Lower Arm Capacitor Voltages

The second term in the right hand side of (4.25) is determined by the converter

operation and would not contribute to regulation of sum of upper and lower arm capacitor

voltages. If there is a DC component included in the first term in the right hand side of

(4.25), then it would increase or decrease ,c xv .

As shown in (4.21), there are a DC component, a line frequency component, and a

twice line frequency component in the leg current. It should be mentioned that the DC

72

component and the line frequency component would disappear as long as the arm

capacitor voltage converges to rated value. However, the twice line frequency component

would exist as long as the MMC outputs apparent power into the AC grid. The deviation

between instantaneous DC component of sum of upper and lower arm capacitor voltages

and its corresponding rated value is denoted as (4.27).

, ,ˆ 2 .c x c x dcv v V (4.27)

Then according to (4.21), dynamics of the DC component included in the leg current

are calculated as (4.28).

,,

ˆ.

4

c xxo DC

o o

vi

R sL

(4.28)

Then substituting (4.27) and (4.28) into (4.25), dynamics of deviation ,ˆc xv are

derived as (4.29). Then poles, decay time constant, and oscillating period of (4.29) are


2

,2ˆ 0.

4

oc x

o cell o

Rd t d Nv

dt L C Ldt

(4.29)

2

1,2 2

2

2

1

2

2.

4

o o

o o o

o

o

osc

o

o o

R RNp j

L CL L

L

R

T

RN

CL L

(4.30)

In (4.30), since the real parts of the poles are located in the left half plane, the

73

deviation ,ˆc xv would decay to zero naturally, which means that for a direct modulated

MMC, the sum of upper and lower arm capacitor voltages converges to its rated value

2Vdc in an underdamped second order transient process inherently.

4.2.2 Dynamics of Difference of Upper and Lower Arm Capacitor Voltages

The first term in the right hand side of (4.26) is determined by the converter operation

and it would not contribute to regulation of difference of upper and lower arm capacitor

voltages. If there is a DC component included in the second term in the right hand side of

(4.26), in other words, there is a line frequency component included in the leg current,

then it would increase or decrease ,c xv . According to (4.21), the line frequency

component included in the leg current is calculated as (4.31).

, , *,

1.

2

c xu c xlxo AC xs

o o dc

v vi v

sL R V

(4.31)

The deviation between instantaneous DC component of difference of upper and lower

arm capacitor voltages and its corresponding rated value, namely zero, is denoted as

(4.32). The reference of output EMF is defined as (4.33). Since the dynamics of arm

capacitor voltages are much slower than those of a line frequency variable, substituting

(4.33) and (4.31) into (4.26), dynamics of deviation ,ˆc xv can be concluded as (4.34).

, , ,ˆ .c x c xu c xlv v v (4.32)

* sin( ).xs msv V t (4.33)

2

,2 2 22 2

1ˆ 0.

2

ms oc x

cell dc o o o o

V Rd Nv

dt C V R L R L

(4.34)

As shown in (4.34), since the real part of the pole is located in the left half plane, the

74

deviation ,ˆc xv would decay to zero naturally. It means that for a direct modulated MMC,

the difference of upper and lower arm capacitor voltages converges to null in a first order

transient process inherently.

In summary, the deviation between sum of upper and lower arm capacitor voltages and

its rated value generates a DC leg internal voltage to draw a DC leg current from the

infinite DC bus to increase or decrease sum of upper and lower arm capacitors to its rated

value. The deviation between difference of upper and lower arm capacitor voltages and

zero generates an AC leg internal voltage to draw a line frequency component of the leg

current from the infinite DC bus to decay the deviation to null inherently.

4.3 Modeling of the Direct Modulated MMC with Generalized DC

Bus

Figure 4-3 Configuration of an MMC station in HVDC application.

However, in HVDC application there is no stiff voltage source in the DC bus. Different

vuu

vul

iuu

iul

ius

UiDC

V W

iuo

ivu iwu

ivl iwl

+

-

+

-

+

-

+

-

+

-

+

-

ivo

iwo

ivs

iws

vvu vwu

vvl vwl

AC Grid

sLs+RssLo+Ro

sLo+Ro

dcv

75

from the case analyzed in section 4.1 and section 4.2, in HVDC application a direct

modulated MMC operates like a two-level VSC-HVDC converter. The energy stored in

the whole capacitors of the MMC is regulated by power in the AC grid side or in the DC

bus side as it is usually done in two-level converter based VSC-HVDC transmission

system. As it is revealed in this section, a DC circulating current and a line frequency

circulating current would flow inside the converter while an arm capacitor energy

unbalance happens to naturally balance energy stored in the capacitors of six arms. As a

first approach, the circulating current is analyzed for the direct modulated MMC in case

of arm capacitor energy unbalance. For a direct modulated MMC, three independent

equations associated with three phases can be derived by (4.8) and (4.9) to describe

instantaneous DC bus voltage as (4.35), (4.36), and (4.37).

*, ,

, ,,

( ) 2( ) .2

c uu c ul usdc c uu c ul o o uo

dc rated

v v v dv v v L R i

V dt

(4.35)

*, ,

, ,,

( ) 2( ) .2

c vu c vl vsdc c vu c vl o o vo

dc rated

v v v dv v v L R i

V dt

(4.36)

*, ,

, ,,

( ) 2( ) .2

c wu c wl wsdc c wu c wl o o wo

dc rated

v v v dv v v L R i

V dt

(4.37)

Then by adding (4.35)-(4.37), the instantaneous DC bus voltage can be expressed by a

unified equation as (4.38).

*, ,

, ,

, , , , ,

( ) 2( )2

.3

c xu c xl xsc xu c xl o o dc

dcx u v w x u v wdc

v v v dv v L R i

V dtv

(4.38)

According to the definition of circulating current by (3.38), dynamic equation of

circulating current is derived by substituting (4.38) into (4.35)-(4.37), as (4.39).

76

, ,

, , , , ,

*

, ,*,, ,

, ,,

,

2

2 3

( )

( )3

2( )

c xu c xl

c xu c xl x u v w

DC

xsc xu c xl

dc ratedx u v wxsc xu c xl

dc rated

AC

o o xo cir

v v

v v

vv v

Vvv v

V

dL R i

dt

.

(4.39)

As shown by (4.39), unbalance of leg capacitor voltages would introduce a DC

component in the circulating current, and unbalance of upper and lower arm capacitor

voltages would introduce a line frequency component in the circulating current. Since the

DC component and the line frequency component of the circulating current are

introduced by independent events, dynamics of the DC component and the line frequency

component of the circulating current can be described by two independent equations

extracted from (4.39), as (4.40) and (4.41).

, ,

, , , , ,,

22( ) .

2 3

c xu c xl

c xu c xl x u v wo o xo cirDC

v v

v v dL R i

dt

(4.40)

77

*

, ,*,, ,

, ,,

,

( )

( )3

2( ) .

xsc xu c xl

dc ratedx u v wxsc xu c xl

dc rated

o o xo cirAC

vv v

Vvv v

V

dL R i

dt

(4.41)


Balancing of the MMC with Generalized DC Bus

As analyzed in section 4.2, a DC leg current affects sum of upper and lower arm

capacitor voltages, and a line frequency leg current affects difference of upper and lower

arm capacitor voltages. In this section, mechanism and dynamics of arm capacitor energy

balancing of the MMC with generalized DC bus are analyzed.

4.4.1 Dynamics of Balancing of Leg Capacitor Voltages

As stated in section 4.2, dynamics of sum of upper and lower arm capacitor voltages

can be represented as (4.42), (4.43), and (4.44).

,

, .3

c ucell dcuo uo cir

dvC ii i

N dt

(4.42)

,

, .3

c vcell dcvo vo cir

dvC ii i

N dt

(4.43)

,

, .3

c wcell dcwo wo cir

dvC ii i

N dt

(4.44)

In the point of view of arm capacitor energy (or voltage) control, only the DC

component excluding the ripple component of the arm capacitor voltages should be

considered. For leg capacitor voltage control, only the differential components of three

78

phase leg capacitor voltages should be taken into consideration in balancing issue since

the common component is controlled by the MMC total capacitor energy controller. Then

according to (4.42)-(4.44), dynamics of differential component of three leg capacitor

voltage are derived as (4.45).

, , ,,

,,

, , ,, , ,

,,

, , ,,

3

.3

3

c u c v c wc u

u diffuo cirDC

c u c v c wcell cellc v v diff vo cirDC

wo cirDCw diff

c u c v c wc w

v v vv

vi

v v vC Cd dv v i

N dt N dti

vv v vv

(4.45)

Dynamics of the DC component of circulating currents are derived from (4.40) as

(4.46). Then by substituting (4.46) into (4.45), dynamics of differential components of

three-phase leg capacitor voltages are derived as (4.47).

,,

, ,

, ,

1.

4

u diffuo cirDC

o o vo cirDC v diff

wo cirDC w diff

vid

L R i vdt

i v

(4.46)

,2

,2

,

0

( ) 0 .4

0

u diff

ov diff

o o

w diff

v

Rd t d Nv

L dt CLdtv

(4.47)

Poles, decay time constant, and oscillating period of the dynamics described by (4.47)

are deduced as (4.48). The differential components of three leg capacitor voltages decay

to zero in a manner described in (4.47). It means that for a direct modulated MMC, three

leg capacitor voltages converge to a balanced state inherently.

79

2

1,2 2

2

2

1

2

2.

4

o o

o o o

o

o

osc

o

o o

R RNp j

L CL L

L

R

T

RN

CL L

(4.48)

4.4.2 Dynamics of Differences of Upper and Lower Arm Capacitor Voltages

As stated in section 4.2, dynamics of differences of upper and lower arm capacitor

voltages can be described as (4.49), (4.50), and (4.51).

**, ,22

.c u us uo circell us uo

dc dc

dv v iC v i

N dt V V

(4.49)

**, ,22

.c v vs vo circell vs vo

dc dc

dv v iC v i

N dt V V

(4.50)

**, ,22

.c w ws wo circell ws wo

dc dc

dv v iC v i

N dt V V

(4.51)

As shown in (4.41), differences of upper and lower arm capacitor voltages introduce

an AC circulating current. At first, the line frequency AC circulating current contributed

by common components of three phase upper and lower arm capacitor voltage differences

are analyzed. Without loss of generality, phasors of references of converter output EMF

are represented as (4.52).

2 2

3 3, , .j j

ms ms msV V e V e

* * *us vs wsV V V (4.52)

Then the phasor of the positive sequence leg internal voltage generated by common

80

component of three phase upper and lower arm capacitor voltage differences can be


2

2 2, , ,23 3

, , ,

2, 3

,

1( )

3

3

, .

j jc com c com c com

ms ms msdc rated dc rated dc rated

jc comms

dc rated

v v vV V e V e

V V V

vV where e

V

+uo,AC uo,AC vo,AC wo,ACV V αV α V

α α

α

(4.53)

Similarly, the phasor of the negative sequence leg internal voltage generated by

common components of three phase upper and lower arm capacitor voltage differences is


2

2 2, , ,2 3 3

, , ,

2

3

1( )

3

1

3

0, .

j jc com c com c comms ms ms

dc rated dc rated dc rated

j

v v vV V e V e

V V V

where e

- * * *uo,AC uo,AC vo,AC wo,ACV V α V αV

α α

α

(4.54)

An interesting property has been obtained in (4.53) and (4.54). In section 3.4, it has

been proven that a positive sequence circulating current can eliminate only common

components of three phase upper and lower arm capacitor voltage differences. On the

other hand, the common components of three phase upper and lower arm capacitor

voltage differences generate only a positive sequence circulating current while an MMC

is direct modulated. Then by substituting (4.53) into (4.49)-(4.51), dynamics of the

common components of differences of three phase upper and lower arm capacitor

voltages are deduced as (4.55) and its pole is calculated as (4.56). Since the pole locates

in the left half plane, the common components of differences of three phase upper and

81

lower arm capacitor voltages decay to zero inherently.

2

,,2 2 2 2 2

,

1.

2 ( ) ( )

c com ms oc com

cell dc rated o o o o

dv V RNv

dt C V R L R L

(4.55)

2

2 2 2 2 2,

1.

2 ( ) ( )

ms o

cell dc rated o o o o

V RNp

C V R L R L

(4.56)

Besides the common components of differences of upper and lower arm capacitor

voltages, the differential components should be taken into consideration. The phasors of

the positive sequence and the negative sequence leg internal voltages introduced by the

differential components of differences of upper and lower arm capacitor voltages are

calculated as (4.57) and (4.58).

2

2, ,

, 3

, ,

2, ,

2 3

,

2

3

1( )

3

1 3( )

2 2

3

1 3( )

2 2

3

0, .

c d c qjc d

ms msdc rated dc rated

c d c qj

msdc rated

j

v vvV V e

V V

v v

V eV

where e

+uo,AC uo,AC vo,AC wo,ACV V αV α V

α

α

α

(4.57)

82

2

2, ,

, 2 3

, ,

2, ,

3

,

, ,

,

1( )

3

1 3( )

2 2

3

1 3( )

2 2

3

( ),

2

c d c qjc d

ms msdc rated dc rated

c d c qj

msdc rated

jc d c qms

dc rated

v vvV V e

V V

v v

V eV

v jvVwhere e

V

- * * *uo,AC uo,AC vo,AC wo,ACV V α V αV

α

α

α

2

3 .

(4.58)

An interesting property has been obtained in (4.57) and (4.58). In section 3.4, it has

been proven that a negative sequence circulating current can eliminate only differential

components of three phase upper and lower arm capacitor voltage differences. On the

other hand, the differential components of differences of three phase upper and lower arm

capacitor voltage generate only a negative sequence circulating while an MMC is direct

modulated. Then by substituting (4.58) into (4.49)-(4.51), dynamics of the differential

components of differences of three phase upper and lower arm capacitor voltages are

deduced as (4.59). By transforming (4.59) to the stationary dq reference frame, the

dynamic equations of differential components of differences of three phase upper and

lower arm capacitor voltage are represented by (4.60).

83

2, ,,

2 2 2,

2 , ,,

2 2 2,

2 , ,,

2,

4 ( )

3 3( ) ( )

2 2 2 2

4 ( )

3 3( ) ( )

2 2 2 2

4

o c d o c qc u ms

cell dc rated o o

o oo c d o c q

c v ms

cell dc rated o o

o oo c d o c q

c w ms

cell dc rated

R v L vdv VN

dt C V R L

R LL v R vdv VN

dt C V R L

R LL v R vdv VN

dt C V R

2 2

.

( )o oL

(4.59)

,2 2 2 2

,

,,2 2 2 2

2

2 2 2,

( ) ( )

( ) ( )

1, .

4 ( )

o oc d

c do o o o

o o c qc q

o o o o

ms

cell dc rated o o

R Ldv K KvR L R Ldt

L KR vdv KR L R Ldt

VNwhere K

C V R L

(4.60)

As shown by (4.60), there is a coupling between d-axis component and q-axis

component of differences of upper and lower arm capacitor voltage. Poles, time constant,

and oscillation period of dynamics (4.60) are calculated as (4.61).

1,22 2 2 2

1

2 2

1

2 2

( ) ( )

.

( )

1

2( )

o o

o o o o

o

o o

oosc

o o

R Lp K jK

R L R L

RK

R L

LT K

R L

(4.61)

In summary, for a direct modulated MMC, the arm capacitor voltages of six arms are

balanced inherently without any closed loop control. For three phase leg capacitor

84

voltages, to balance three phase leg capacitor voltages a DC component of the circulating

current is introduced naturally in case of unbalanced leg capacitor voltages. For upper and

lower arm capacitor voltage balancing, a line frequency AC component of circulating

current is introduced naturally to balance three phase upper and lower arm capacitor

voltages.

However, dynamics of the inherent balancing process are not controllable and are fully

determined by converter parameters as shown by (4.48), (4.56), and (4.61). For three

phase leg capacitor voltage balancing, the decay ratio of voltage unbalance is proportional

to the resistance of the arm inductor and inversely proportional to the inductance of the

arm inductor. Since the resistance of a transmission level high power converter is very

small, the decay process would present quite slow dynamics. For an indirect modulated

MMC with the proposed control strategy in Chapter 3, the characteristics of the voltage

unbalance decay process are fully controllable and can be designed by setting gains of the

controller. For three phase upper and lower arm capacitor voltage balancing, the decay

ratio of voltage unbalance is inversely proportional to the reactance of the arm inductor

and proportional to the impedance angle of the arm inductor. Since the impedance angle

of the arm inductor is almost zero, the decay process of upper and lower arm capacitor

voltage unbalance would present very slow dynamics. For an indirect modulated MMC

with the proposed control strategy in Chapter 3, the equivalent reactance and impedance

angle of the arm inductor are fully controllable in active manner and the characteristics of

the voltage unbalance decay process are fully controllable.

85

5. Control of an MMC Based Point-to-Point HVDC

Transmission System

For each converter in VSC-HVDC application, there should be several controllers such

as an active power controller implemented in the form of a fixed AC grid active power

controller, a fixed DC bus voltage controller, or a frequency controller and a reactive

power controller implemented in the form of a fixed reactive power controller or a fixed

PCC voltage controller. In a VSC-HVDC system, the active power controllers which are

employed for the two stations play important roles in stability and control of active power

flow between two stations. Since this thesis focuses on the active power control of the

VSC-HVDC system, only the active power type controllers are investigated.

5.1 Direct Modulation Based Control Strategy of the Point-to-

Point HVDC Transmission System

In [11], it is revealed that the terminal behavior of a direct modulated MMC is like a

two-level converter and the DC bus voltage is coupled with the energy stored in the

capacitors of the MMC. The control strategy of the conventional two-level converter

based VSC-HVDC system should be reviewed. A typical control strategy of a two-level

converter based VSC-HVDC system is the Voltage-Power (VP) control method.

86

Figure 5-1 Conceptual structure of a two-level converter based VSC-HVDC transmission

system.

Fig. 5-1 shows the conceptual structure of a two-level converter based VSC-HVDC

transmission system. It is assumed that the Station I operates in rectifier mode and the

Station II operates in inverter mode. The rectifier employs a constant DC bus voltage

controller, which control the DC bus voltage, in other words the energy stored in the

capacitors, by regulating the active power from the Grid I. Fig. 5-2 shows the constant

DC bus voltage controller. The DC bus voltage of the rectifier is controlled as a constant

value regardless of the power flow in the HVDC transmission line. The inverter employs

a constant power controller, which control the power flows into the Grid II by regulating

the active current. Fig. 5-3 shows the constant power controller. The inverter delivers a

constant power (its commanded value) regardless of the DC bus voltage.

Grid I Grid II

Station I - Rectifier Station II - Inverter

Vdc_I Vdc_II

87

Figure 5-2 Constant DC bus voltage controller for the rectifier.

(a) Controller block diagram. (b) DC bus characteristics.

Figure 5-3 Constant power controller for the inverter.

(a) Controller block diagram. (b) DC bus characteristics.

In the VSC-HVDC system employing a VP controller, the power flow in the HVDC

transmission line is controlled by the inverter. And the DC bus voltage of the inverter is

controlled indirectly by controlling the DC bus voltage of the rectifier.

In the steady state, the difference of the DC bus voltages of the rectifier and the

inverter is only the voltage drop across the resistance of the transmission line. In the

transient state, the DC transmission line looks like a capacitor-inductor-capacitor coupled

circuit since there is considerable inductance in the transmission line. The coupling of the

capacitors and the inductor would induce fluctuation and inrush voltage in the

+

-PI

*_dc IV

_dc IV

*,q Grid Ii

*_dc IV

_dc IV

DCP

(a) (b)

+

-PI

*DCP

DCP

*,q Grid IIi

DCP

(a) (b)

_dc IIV

88

transmission line voltage during the power flow variation.

5.2 Indirect Modulation Based Control Strategy of Point-to-Point

HVDC Transmission System

For an indirect modulated MMC, the DC bus voltage and the energy stored in the

capacitors can be fully decoupled by the proposed control strategy in Chapter 3, and the

DC bus of the MMC looks like a high speed controlled voltage source behind an inductor


Figure 5-4 Conceptual structure of VSC-HVDC transmission system based on an indirect

modulated MMC.

5.2.1 Proposed Voltage-Voltage (VV) Control Strategy of VSC-HVDC Transmission

System Based on Indirect Modulated MMC

If the VSC-HVDC transmission is connected to two strong grids, both stations can

operate in rectifier mode and the system can employ the Voltage-Voltage (VV) control

strategy.

+

-

*

_dc IV

+-

+-

+-

+ -

+ -

+ -

+

-

*

_dc IIV+ -

+ -

+ -

+-

+-

+-

Grid I Grid IIStation I Station II

idc

89

Figure 5-5 Structure of the proposed VV controller.

(a) Constant capacitor energy controller. (b) Power flow controller.

As both two stations operate in rectifier mode, two constant converter total capacitor

energy controllers are employed as shown in Fig. 5-5(a). The DC bus voltage of the

Station II is set as the rated transmission line voltage in an open loop manner. The

transmission power is controlled by regulating the transmission line current, and the

transmission line current is regulated actively and directly by the DC bus voltage of the

Station I as shown in Fig. 5-5(b). Since the transmission line current is controlled directly

by two high speed controlled voltage sources, fluctuation and inrush voltage in the

transmission line voltage during fast power flow variation can be fully damped by the

proposed VV control strategy.

5.2.2 Proposed Voltage-Power (VP) Control Strategy of VSC-HVDC Transmission

System Based on Indirect Modulated MMC

If the VSC-HVDC transmission is to feed a weak grid or a passive grid, the VV control

strategy is not valid since the rectifier mode is only practical for strong grid case. For the

station connected with a weak grid or a passive grid, constant power control is necessary

for the AC grid side to control the grid frequency or to feed the passive grid. Then Station

*_total IE

_total IE

PI*,q Grid Ii

*_total IIE

_total IIE

PI

(a)

*DCP

DCP

PI *dci

*,q Grid IIi

*dci

dci

PI

*_dc IV

(b)

*_dc IIV,dc ratedV

,dc ratedV

90

I which is connected with a strong grid should operate in rectifier mode to build up the

HVDC transmission line voltage, and the Station II should operate in inverter mode to

feed the weak grid or the passive grid.

Figure 5-6 Structure of the proposed VP controller.

(a) Constant capacitor energy controller. (b) Power flow controller.

As shown in Fig. 5-6, the converter total capacitor energy of the rectifier is regulated

by drawing active current from the strong AC grid, namely the Grid I, and the capacitor

energy of the inverter is regulated by drawing DC current from the transmission line. The

output voltage of the DC bus of the rectifier is set as its rated value in an open loop

manner, and the transmission line current is regulated actively and directly by the DC bus

voltage of the inverter. The power flow is controlled by regulating the active current of

the weak grid. Since the transmission line current is controlled by two high speed

controlled voltage sources directly in an active manner, fluctuation and inrush voltage in

the transmission line voltage during fast power flow variation can be fully damped by the

proposed VP control strategy.

*_total IE

_total IE

PI*,q Grid Ii

*_total IIE

_total IIE

PI *dci

(a)

*DCP

DCP

PI *,q Grid IIi

(b)

*dci

dci

PI *_dc IIV

*_dc IV,dc ratedV

,dc ratedV

91

6. Simulations and Experimental Verification

To verify the validity of the conducted work in this thesis, computer simulations and

experiments are performed by full scale simulation models and a down scale

experimental setup.

6.1 Simulation of an MMC under Indirect Modulation Based

Control Strategy

To verify the validity of the proposed arm capacitor energy control strategy, PSIM

simulations of a 217 level, ±200kV MMC described in Appendix A in detail are

performed. Since the proposed arm capacitor energy balancing strategy is achieved by the

injection of the circulating current that flows only inside the MMC, the control strategy

shall be valid for both no load condition and loaded condition. In the simulation, a 400

Ohm resistor load is connected with the DC bus of the MMC through a circuit breaker

and the MMC operates in rectifier mode.

6.1.1 Simulation of a 217 Level, ±200kV MMC in No Load Condition

Performance of the proposed arm capacitor energy control strategy is investigated in no

load condition. The DC bus of the MMC is isolated from the resistor load and the MMC

operates in rectifier mode. At t=0.5s, the converter total capacitor energy controller is

activated. At t=1.0s, the leg capacitor energy balancing controller is activated. At t=1.5s,

the common error eliminating module of the upper and lower arm capacitor energy

balancing controller is activated. At t=2.0s, the differential error eliminating module of

the upper and lower arm capacitor energy balancing controller is activated.

92

Figure 6-1 Simulation waveforms of leg capacitor energy and differences of

upper and lower arm capacitor energy in no load condition.

As shown in Fig. 6-1, the average value of the three phase leg capacitor energy is

regulated to its rated reference value, namely 4.7MJ after the total capacitor energy

controller is activated at t=0.5s. The three phase leg capacitor energy are balanced after

the leg capacitor energy balancing controller is activated at t=1.0s. The common error of

three phase upper and lower arm capacitor energy is eliminated after the common error

eliminating module of the upper and lower arm capacitor energy balancing controller is

activated at t=1.5s. The differential error of three phase upper and lower arm capacitor

energy is eliminated after the differential error eliminating module of the upper and lower

arm capacitor energy balancing controller is activated at t=2s

As shown in Fig. 6-2, after the converter total capacitor energy controller is activated,

the MMC starts to draw an active current from the AC grid to boost up the converter total

capacitor energy to its reference value.

As shown in Fig. 6-3, after the leg capacitor energy balancing controller is activated, a

2.5M

3M

3.5M

4M

4.5M

5M

5.5MDA0 DA1 DA2 (DA0+DA1+DA2)/3

1 1.5 2 2.5 3 3.5 4Time (s)

0K

-500K

-1000K

500K

1000KDA3 DA4 DA5 (DA3+DA4+DA5)/3

,,, ,[MJ] [M [MJ J]J ][M ] wv flu tflt ave fltflt EE EE

, ,, [MJ] [M[M J]J] [MJ]u v fltflt t comw fl EEEE

5.5

5.0

4.5

4.0

3.5

3.0

2.5

1.0

0.5

0

-0.5

-1.0

Time (s)0 0.5 1.0 1.5 2.0 2.5 3.0

93

DC component of the circulating current is injected inside the MMC to exchange energy

between three different legs to balance leg capacitor energy. It is shown that the

circulating current tracks its DC reference well by the proposed control strategy.

As shown in Fig. 6-4, after the common error eliminating module of the upper and

lower arm capacitor energy balancing controller is activated, a positive sequence line

frequency circulating current is injected into the MMC to eliminate the common error. As

shown in Fig. 6-5, after the differential error eliminating module is activated, a negative

sequence line frequency circulating current is injected inside the MMC to eliminate the

differential error. It is shown that the circulating current tracks its AC reference well by

the proposed control strategy.

Figure 6-2 Simulation waveforms of leg capacitor energy and grid current while the

converter total capacitor energy controller is activated in no load condition.

2.5M

3M

3.5M

4M

4.5M

5M


1.2 1.4 1.6 1.8Time (s)

0

-200

-400

-600

200

400

600iuu-iul ivu-ivl iwu-iwl DA7


5.5

5.0

4.5

4.0

3.5

3.0

2.5[A] [A] [ ]] A[Aus ws svs qi ii i

600

400

200

0

-200

-400

0.2 0.4 0.6 0.8Time (s)

-600

94

Figure 6-3 Simulation waveforms of leg capacitor energy and circulating currents while

the leg capacitor energy balancing controller is activated in no load condition.


and circulating currents while the common error eliminating module of the upper and

lower arm capacitor energy balancing controller is activated at no load condition.

4M

4.5M

5M


1.8 1.9 2 2.1 2.2Time (s)

0

-100

-200

100

200(Iuu+Iul)/2 (Ivu+Ivl)/2 (Iwu+Iwl)/2 DA6


, ,,,*[A [A] [ ]][A] Awouo cir v uci oo c rir ciri ii i

5.5

5.0

4.5

4.0

200

100

0

-100

-2000.8 0.9 1.0 1.1 1.2

Time (s)

0K

-500K

-1000K

500K


2.3 2.4 2.5 2.6 2.7Time (s)

0

-100

-200

100

200(Iuu+Iul)/2 (Ivu+Ivl)/2 (Iwu+Iwl)/2 DA6, ,,,

*[A [A] [ ]][A] Awouo cir v uci oo c rir ciri ii i


1.0

0.5

0

-0.5

-1.0

1.8 1.9 2.0 2.1 2.2

Time (s)

200

100

0

-100

-200

95


and circulating currents while the differential error eliminating module of the upper and

lower arm capacitor energy balancing controller is activated at no load condition.

Figure 6-6 Simulation waveforms of leg capacitor energy and references of the leg

internal voltages while the leg capacitor energy balancing controller is activated in no

load condition.

0K

-500K

-1000K

500K


2.8 2.9 3 3.1 3.2Time (s)

0

-100

-200

100

200(Iuu+Iul)/2 (Ivu+Ivl)/2 (Iwu+Iwl)/2 DA6, ,,,

*[A [A] [ ]][A] Awouo cir v uci oo c rir ciri ii i


1.0

0.5

0

-0.5

-1.0

1.8 1.9 2.0 2.1 2.2Time (s)

200

100

0

-100

-200

4M

4.5M

5M


1.8 1.9 2 2.1 2.2Time (s)

0K

-4K

-8K

4K



1.8 1.9 2.0 2.1 2.2Time (s)

* *,

* * [kV[kV][kV kV]] [] wo xo covoo muv v vv

5.5

5.0

4.5

4.0

8.0

4.0

0

-4.0

-8.0

96


and references of the leg internal voltages while the common error eliminating module is

activated at no load condition.


and references of the leg internal voltage while the differential error eliminating module

is activated at no load condition.

0K

-500K

-1000K

500K


2.3 2.4 2.5 2.6 2.7Time (s)

0K

-4K

-8K

4K



* *,


1.0

0.5

0

-0.5

-1.0

8.0

4.0

0

-4.0

-8.01.8 1.9 2.0 2.1 2.2

Time (s)

0K

-500K

-1000K

500K


2.8 2.9 3 3.1 3.2Time (s)

0K

-4K

-8K

4K



* *,


1.0

0.5

0

-0.5

-1.0

8.0

4.0

0

-4.0

-8.01.8 1.9 2.0 2.1 2.2

Time (s)

97

As shown in Fig. 6-6, Fig. 6-7, and Fig. 6-8, the common mode component of the

reference of the leg internal voltages is inherently nullified by the proposed arm capacitor

energy control strategy. It guarantees stability and good performance of circulating

current control and fully decouples the AC grid current control, the DC bus current

control, and the circulating current control.

6.1.2 Simulation of a 217 Level, ±200kV MMC in Loaded Condition

Performance of the proposed arm capacitor energy control strategy is investigated in

loaded condition. At t=0.5s, a 400 Ohm load resistor is connected to the DC bus. At

t=1.5s the reference of the DC bus voltage *dcV is changed from 400kV to 390kV, and at

t=2.5s the reference of the DC bus voltage *dcV is again changed from 390kV to 410kV.

Figure 6-9 Simulation waveforms of leg capacitor energy and DC bus current in loaded

condition.

4M

4.2M

4.4M

4.6M

4.8M

5MDA0 DA1 DA2

2 3 4 5 6Time (s)

0K

-0.5K

-1K

-1.5K

0.5K

1K

1.5KIdc


5.0

4.8

4.6

4.4

1.5

1.0

0.5

0

-0.5

4.2

4.0

-1.0

-1.5

Time (s)0 1.0 2.0 3.0 4.0

[kA]dci

98


energy and DC bus current in loaded condition.

As shown in Fig. 6-9 and Fig. 6-10, three phase leg capacitor energy are controlled to

the reference value 4.7MJ by the proposed control method in loaded condition, and the

differences of upper and lower arm capacitor energy are controlled as null by the

proposed control method in loaded condition.

0K

-500K

-1000K

500K

1000KDA3 DA4 DA5

2 3 4 5 6Time (s)

0K

-0.5K

-1K

-1.5K

0.5K

1K

1.5KIdc


[kA]dci

Time (s)0 1.0 2.0 3.0 4.0

1.0

0.5

0

-0.5

-1.0

1.5

1.0

0.5

0

-0.5

-1.0

-1.5

99

Figure 6-11 Simulation waveforms of grid current and DC bus current in loaded condition.

Figure 6-12 Simulation waveforms of DC bus voltage, converter total capacitor energy,

and grid current in loaded condition.

As shown in Fig. 6-11, the DC bus current and the AC grid current are decoupled and

the DC bus current is a pure DC component ignoring the high frequency switching ripples.

0K

-1K

-2K

1K

2Kiuu-iul ivu-ivl iwu-iwl DA7

2.4 2.45 2.5 2.55 2.6Time (s)

0K

-0.5K

-1K

-1.5K

0.5K

1K

1.5KIdc

[A] [A] [ ]] A[Aus ws svs qi ii i2.0

1.0

0

-1.0

-2.0

Time (s)0.4 0.45 0.5 0.55 0.6

1.5

1.0

0.5

0

-0.5

-1.0

-1.5

[kA]dci

200K

250K

300K

350K

400K

450K

500KV1634 (DA0+DA1+DA2)/10/3/2

3 3.5 4 4.5 5Time (s)

0K

-1K

-2K

1K

2Kiuu-iul ivu-ivl iwu-iwl DA7

[kV]dcv500

450

400

350

300

250

200

30

27

24

21

18

15

12

[MJ]totalE

2.0

1.0

0

-1.0

-2.0

[A] [A] [ ]] A[Aus ws svs qi ii i

Time (s)1.0 1.5 2.0 2.5 3.0

100

Since the MMC operates in rectifier mode, it starts to draw active current from the AC

grid as soon as it is loaded.

As shown in Fig. 6-9, Fig. 6-10, and Fig. 6-12, different from the two-level converter

or the direct modulated MMC, the DC bus side, the AC grid side and the energy of the

distributed capacitors stored in the MMC can be totally decoupled. The DC bus voltage

can be updated at every sampling point without variation of the converter total capacitor

energy.

Fig. 6-13 shows the transient process of the DC bus current while the load resistor is

connected to the DC bus of the MMC. The transient process presents a first order R-L

transient process and coincides with the theoretical prediction by the extracted DC bus

current model in Fig. 3-15(b), in which the DC bus of the MMC is modeled as a

controlled DC voltage source behind an inductor.

Figure 6-13 Simulation waveforms of DC bus current and theoretically predicted DC bus

current by the extracted DC bus current model.

2.4995 2.5 2.5005 2.501Time (s)

0

-500

-1000

-1500

500Idc ,[kA A]] [kdc theodci i

Time (s)0.499 0.4995 0.5 0.5005 0.501

0.5

0

-0.5

-1.0

-1.5

101

6.2 Experimental Verification of an MMC under Indirect

Modulation Based Control Strategy

To verify the validity of the proposed arm capacitor energy control strategy,

experiments of a down scale 7 level, 300V experimental setup described in Appendix B in

detail are performed. Since the proposed arm capacitor energy balancing strategy is done

by injection of the circulating current flows only inside the MMC, it is valid for both no

load condition and loaded condition. In the experiment, an R-L load is connected to the

DC bus of the MMC through a circuit breaker, and the MMC operates in rectifier mode.

The constructed experimental setup of a 7-level 300V MMC is shown in Fig. 6-14.

Figure 6-14 Constructed 7-level 300V experimental setup.

102

6.2.1 Experimental Verification of a 7-Level, 300V MMC in No Load Condition

Performance of the proposed control strategy in no load condition is investigated. In

the no load condition, the DC bus of the MMC is not connected to anywhere.

Figure 6-15 Experimental waveforms of leg capacitor energy in no load condition.

Figure 6-16 Experimental waveforms of AC grid current and converter total capacitor

energy in no load condition.

, ,, , [[30J/ div][30J/ div] 30J/ div][30J/ div] w ave fltv flt ltu t ffl EE E E

[1s/div]

Converter total capacitor energy

controller was activated.Leg capacitor energy balancing

controller was activated.

[10A/ di[10A v] [90J/[ div10A/ d /] ]iv div]wu v otals ts si i i E

[20ms/div]

[1s/div]

Converter total capacitor energy


Zoom in

103

Figure 6-17 Experimental waveforms of differences of leg capacitor energy and

circulating current in no load condition.

As shown in Fig. 6-15, three phase leg capacitor energy becomes unbalanced as soon

as the grid current vector controller is activated. The average value of three phase leg

capacitor energy is regulated to its reference value 81J after the converter total capacitor

energy controller is activated, and three phase leg capacitor energy are balanced after the

leg capacitor energy balancing controller is activated. As shown in Fig. 6-16 and Fig. 6-

17, converter total capacitor energy is regulated to its reference value by drawing active

current from the AC grid, and three phase leg capacitor energy are balanced by injecting

DC circulating current inside the converter .

, ,, ,[5J/ di[ [1A/ div]v5J ]/ di [1A/ div] ]v do qcird fl o ctt l irq f i iE E

[1s/div]

Leg capacitor energy balancing


104


energy in no load condition.

As shown in Fig. 6-18, the differential component of differences of upper and lower

arm capacitor energy is eliminated after the differential error eliminating module of the

upper and lower arm capacitor energy balancing controller is activated. And, the common

component of differences of upper and lower arm capacitor voltage is eliminated after the

common error eliminating module of the upper and lower arm capacitor energy balancing

controller is activated.

[1s/div]

, ,, , ,, [10J/ div][10J/ div [10J/ div[10J/ div]] ]u fu f lt v fltv f w flt w fltl tt l E E EE EE

Arm capacitor energy differential

error controller was activated.

Arm capacitor energy common


105


energy differential error controller is activated in no load condition.


energy common error controller is activated in no load condition.

In Fig. 6-19, a negative sequence line frequency circulating current is injected inside

the MMC as soon as the arm capacitor energy differential error controller is activated to

eliminate the differential error. In Fig. 6-20, a positive sequence line frequency circulating

current is injected inside the MMC as soon as the arm capacitor energy common error

controller is activated to eliminate the common error. By the proposed control strategy,

the circulating current tracks its reference well.

,*

,, ,[1A/ div[ [1A/ div] [1A/ div1A/ div] ]] wo cuo uo ciricir r rvo ci i ii i

[1s/div]

[20ms/div]

Zoom in

Arm capacitor energy differential error controller was activated.

Zoom in

[20ms/div]

[1s/div]

Arm capacitor energy common error controller was activated.

,*

,, ,[1A/ div[ [1A/ div] [1A/ div1A/ div] ]] wo cuo uo ciricir r rvo ci i ii i

106

Figure 6-21 Experimental waveforms of references of leg internal voltage while the arm

capacitor energy differential error controller is activated in no load condition.

Figure 6-22 Experimental waveforms of references of leg internal voltage while

the arm capacitor energy common error controller is activated in no load condition.

As shown in Fig. 6-21 and Fig. 6-22, nullification of the common mode component of

the leg internal voltages is guaranteed by the proposed control strategy.

*,

** * [2.5V/ [2.5V/ div[2.[2 5Vdiv / di. v5V/ di ]]]v] wo xo c mvu oo ov v v v

Zoom in

[1s/div]

[20ms/div]

Arm capacitor energy differential


*,

** * [2.5V/ [2.5V/ div[2.[2 5Vdiv / di. v5V/ di ]]]v] wo xo c mvu oo ov v v v

Zoom in

[1s/div]

[20ms/div]

Arm capacitor energy common error controller was activated.

107

6.2.2 Experimental Verification of a 7-Level, 300V MMC in Loaded Condition

Figure 6-23 Experimental waveforms of leg capacitor energy in loaded condition.


energy in loaded condition.

The circuit breaker between the DC bus of the MMC and the R-L load is switched on

and the MMC is loaded. As shown in Fig. 6-23 and Fig. 6-24, three phase leg capacitor

energy are controlled to the reference value 81J by the proposed control method in loaded

condition, and the differences of upper and lower arm capacitor energy are controlled as

, ,, [30J/ div [2.5[30J/ di [30J/ div A/ div]]v] ] w flu flt v l dctf tEE E i

Zoom in

[1s/div]

[100ms/div]

DC bus was connected to an R-L load.

, ,, [10J/ div [2.5[10J/ di [10J/ div A/ div]]v] ] w flu flt v l dctf tEE E i

Zoom in

[100ms/div]

[1s/div]


108

null.

Figure 6-25 Experimental waveforms of grid current in loaded condition.

In Fig. 6-25, the MMC starts to draw active current from the AC grid as soon as the DC

bus is loaded since the MMC operates in rectifier mode.


converter total capacitor energy, and active current of grid side.

It is observed in Fig. 6-26 that a switching frequency ripple is included in the

instantaneous DC bus voltage. As soon as the DC bus is connected to the R-L load, the

[5A/ div [5A/ div[5A/ d [5i A ]] ]]v / divws qsus vs i ii i

Zoom in


[1s/div]

[20ms/div]

[2.5A/ div [10A/ div][90J/ div]][150V/ div] tot l qsadc dc E iv i

Zoom in

[1s/div]

[100ms/div]


109

DC bus current increases in an R-L load without oscillation, which would be existed in

the case of a two level converter or a direct modulated MMC. The converter total

capacitor energy is regulated as reference value 243J.


converter total capacitor energy, and active current of grid side while the DC bus voltage

command is changed from 300V to 330V.




Zoom in[1s/div]

[50ms/div] was changed from 300V to 330V.*dcv


, [2.5A[15 / di0V/ div v [10A/[2.5A/ div]] [90J/ div] ] div]tdc the qsd ldc o oc taE iiv i

Zoom in[1s/div]


110




As shown in Fig. 6-27 to Fig. 6-29, different from the two level converter or the direct

modulated MMC, an indirect modulated MMC controlled by the proposed control

strategy can change DC bus voltage in fast dynamics (at sampling frequency) without

changing the converter total capacitor energy and no oscillation occurs in the DC bus

voltage during the transient. In Fig. 6-28, the transient of the DC bus current while the

DC bus voltage command is changed from 330V to 270V coincides with the theoretical

waveform calculated by the extracted DC bus model in Fig. 3-15(b) and the validity of

the proposed MMC modeling for the generalized DC bus is verified.

6.3 Simulation of an MMC during an AC Grid SLG Fault

The proposed AC grid SLG fault ride through strategy is verified by simulation of an

MMC in Appendix A during an AC grid SLG fault. The MMC operates in the rectifier

mode and delivers 200MW power before the fault occurs. At t=1.0, a line to ground short

circuit fault occurs in the U phase of the AC grid bus bar, namely the U phase of the

Zoom in[1s/div]



111

primary side of the grid transformer. After 0.2s, the short circuit fault is cleared and the

AC grid is recovered.

Figure 6-30 Simulation waveforms of AC bus bar voltages and AC side voltages of the

MMC during the SLG fault.

As shown in Fig. 6-30, a negative sequence voltage appears in the AC side of the

MMC, namely the secondary side of the grid transformer. Since the MMC is connected to

the AC grid by a wye-delta type transformer, the zero sequence voltage appears in the AC

grid during the SLF fault is isolated by the transformer.

0K

-100K

-200K

100K

200KEa_pri Eb_pri Ec_pri

1.9 2 2.1 2.2 2.3Time (s)

0K

-100K

-200K

100K

200KV1643 V1644 V1645

0.9 1.0 1.1 1.2 1.3Time (s)

100

0

-100

-200

200

100

0

-100

-200

200

[kV][kV kV] [ ]U V W

[kV][kV kV] [ ]U V W

AC Busbar Voltages

AC Side Voltages of MMC

112

Figure 6-31 Simulation waveforms of AC grid currents, DC transmission line current, and

the DC bus voltage during the SLG fault.

In Fig. 6-31, since a negative sequence grid current controller is employed in the

proposed fault ride through strategy, the negative sequence component of the AC grid

current is prevented in spite of the severely unbalanced AC grid during the SLG fault. As

the magnitude of the positive sequence component of the AC grid voltage decreases

during the SLG fault, the magnitude of the grid current increases to support the 200MW

power flow. It is clearly presented in the Fig. 6-31 that since the AC grid side and the DC

bus side of the MMC are fully decoupled by the proposed control strategy, the DC bus of

the MMC is not affected by the SLG fault occurs in the AC grid side. The inrush voltage

and twice line frequency oscillation in the transmission line voltage during the SLG fault

are prevented which commonly occurs in the two-level converter based HVDC system

and the direct modulated MMC based HVDC system.

0K

-1K

-2K

1K

2Kius ivs iws

0

-200

-400

-600

-800

idc

2 2.1 2.2 2.3Time (s)

300K

350K

400K

450K

500Kvdc

[k [kA]] A[kA ]us s wsv ii i2

1

0

-1

-2

0

-0.2

-0.4

-0.6

-0.8

500

450

400

350

300

[kA]dci

[kV]dcv

0.9 1.0 1.1 1.2 1.3

Time (s)

113

Figure 6-32 Simulation waveforms of leg capacitor energy and differences of upper and

lower arm capacitor energy during the SLG fault.

In Fig. 6-32, the three phase leg capacitor energy are regulated as its rated value during

the SLG fault, and the upper and lower arm capacitor energy are kept balanced during the

SLG fault by the proposed fault ride through strategy.

6.4 Simulation of an MMC under Direct Modulation Based

Control Strategy

Mechanism and dynamics of arm capacitor energy natural balancing of the MMC with

generalized characteristic DC bus analyzed in Chapter 4 are verified by simulations of a

201-level MMC described in Appendix C. At the beginning of the simulation, initial

capacitor voltages in each arm are set as different values, and the balancing dynamics are

observed in no load condition to verify the analysis in Chapter 4.

0

1e+006

2e+006

3e+006

4e+006

5e+006

6e+006DA0 DA1 DA2

1.5 2 2.5 3Time (s)

0M

-1M

-2M

-3M

1M

2M

3MDA3 DA4 DA5

,,, [MJ] MJ[ J] [ ]Mv flt w fltu fltE EE


5

4

3

2

1

0

6

2

1

0

-1

-2

-3

3

Time (s)0.5 1.0 1.5 2.0

114

Figure 6-33 Simulation waveforms of differential components of leg capacitor voltage of

a direct modulated MMC.


voltages of a direct modulated MMC.

Fig. 6-33 shows the differential components of three phase leg capacitor voltages. The

oscillation period is 0.079s and it coincides well with 0.081s, which is calculated

0 0.2 0.4 0.6 0.8 1Time (s)

0K

-50K

-100K

50K

100K2/3*(legU_Vsum-legV_Vsum*0.5-legW_Vsum*0.5) sqrt(3)/3*(legV_Vsum-legW_Vsum)

0.1 0.2

100

50

0

-50

-1000 0.6 5

Time (s)0.4 0.80.2

, ,[kV [kV] ]cc qd VV

Simulation waveform

Predicted decay envelope

0 2 4 6 8Time (s)

0K

-50K

-100K

-150K

50K

100K

150K(legU_vdiff+legv_vdiff+legw_vdiff)/3 sqrt(3)/3*(legv_vdiff-legw_vdiff) 2/3*(legu_vdiff-0.5*legv_vdiff-0.5*legw_vdiff)

150

100

50

0

-50

-100

0 6Time (s)

4 82

,,, [kV] [kV] [kV]c d c qc com VV V

-150

Simulation waveform

Predicted decay envelope

115

theoretically by (4.48). The theoretical predictions of decay envelopes by (4.48) are

shown by dashed lines in Fig. 6-33, and it coincides well with the simulation results.

Fig. 6-34 shows the differences of upper and lower arm capacitor voltages in stationary

dqo frame. At first, it is shown clearly that natural decay process of the common

component of the differences of upper and lower arm capacitor voltages is a first-order

process without oscillation, and the natural decay process of the differential component of

the differences is a second-order underdamped process with oscillations. The theoretical

predictions of the decay envelopes of both common and differential components of the

differences by (4.56) and (4.61) are shown by dashed lines in Fig. 6-34, and they

coincides with the simulation results well. The oscillation period is 2.25s and it coincides

well with 2.36s, which is calculated theoretically by (4.61).

116

Figure 6-35 Simulation waveforms of circulating currents of a direct modulated MMC.

Fig. 6-35 shows circulating currents of the direct modulated MMC. In Fig. 6-35(a),

during t=0~0.3s, since three phase leg capacitor voltages are not balanced and the upper

and lower arm capacitor voltages are neither balanced, both a DC component and an AC

component flows in the circulating current. In Fig. 6-35(b), during t=2~2.3s, since the

three phase leg capacitor voltages are balanced, there is only AC components (including a

positive sequence component and a negative sequence component) flows in the

0.05 0.1 0.15 0.2 0.25Time (s)

0K

-0.5K

-1K

-1.5K

0.5K

1K

1.5K(ivu+ivl)/2 (iwu+iwl)/2 (Iuu+Iul)/2

7.5 7.55 7.6 7.65 7.7 7.75 7.8Time (s)

0

-200

-400

200

400(ivu+ivl)/2 (iwu+iwl)/2 (Iuu+Iul)/2

2 2.05 2.1 2.15 2.2 2.25 2.3Time (s)

0

-200

-400

200

400(ivu+ivl)/2 (iwu+iwl)/2 (Iuu+Iul)/2

1.5

1.0

0.5

0

-0.5

-1.0

-1.5

0.4

0.2

0

-0.2

-0.4

0.4

0.2

0

-0.2

-0.4

,,, [kA] kA[ A] [k ]vo ci wo circ r ruo i ii i



0 0.05 0.1 0.15 0.2 0.25 0.3

Time (s)

2 2.05 2.1 2.15 2.2 2.25 2.3

Time (s)

7.5 7.55 7.6 7.65 7.7 7.75 7.8

Time (s)

(a)

(b)

(c)

117

circulating current. In Fig. 6-35(c), during t=7.5~7.8s, since the common component of

the differences of upper and lower arm capacitor voltages is almost extinct, only a

negative sequence component flows in the circulating current.


under Direct Modulation Based Control Strategy

Simulations of a point-to-point HVDC transmission system under direct modulation

based control strategy are performed. Parameters of the simulated transmission system

are shown in Appendix D, and both MMC stations operate under direct modulation based

control strategy. In the simulation, the Station I operates in rectifier mode to support the

HVDC transmission line voltage, and the Station II operates in inverter mode. The

transmission system is controlled as the conventional two-level converter based VSC-

HVDC system. The DC bus voltage of the Station II is controlled by controlling the DC

bus voltage of the Station I. The Station II starts to deliver 400MW electricity at t=0.5,

and to deliver -400MW electricity at t=2.0s. It is requested to deliver 400MW electricity

again at t=4.0s and to deliver -400MW electricity at t=6.0s. The slope of the power

reference is limited by 800MW/s.

118


voltages of the direct modulated MMC based HVDC transmission system.

Fig. 6-36 shows that the power flow between two stations tracks its reference well.

However, since the terminal behavior of a direct modulated MMC is like a two-level

converter and the DC bus voltage is coupled with the energy stored in the capacitors of

the converter, oscillation occurs in the DC bus voltages of the converters during the

power flower variation.

0K

-0.5K

-1K

-1.5K

0.5K

1K

1.5KIdc

1 2 3 4 5 6 7 8 9 10Time (s)

380K

390K

400K

410K

420KVdc Vdc2

420

410

400

390

380

1.0

0.5

0

-0.5

-1.0

-1.5

1.5[kA]dci

_ _[kV] [kV]dcd IIc I vv

1 3 5 7 8Time (s)

0 2 4 6 9

119

Figure 6-37 Simulation waveforms of three phase leg capacitor energy and differences of

upper and lower arm capacitor energy of the Station I of the direct modulated MMC

based HVDC transmission system.

Three phase leg capacitor energy and differences of upper and lower arm capacitor

energy of the Station I are shown in Fig. 6-37. The leg capacitor energy is regulated as

reference value well and the upper and lower arm capacitor energy are balanced for three

phases. Since a considerable twice line frequency component is induced in the circulating

current, fluctuations appear in both sums and differences of upper and lower arm

capacitor energy of three phases.


under Indirect Modulation Based Control Strategy

Simulations of a point-to-point HVDC transmission system under indirect modulation

based control strategy are performed. Parameters of the simulated transmission system

are shown in Appendix E. The transmission line starts to deliver 400MW electricity at

3M

3.2M

3.4M

3.6M

3.8M

4MDA0 DA1 DA2

1 2 3 4 5 6 7 8 9 10Time (s)

0K

-500K

-1000K

500K

1000KDA3 DA4 DA5

1 3 5 7 8Time (s)

0 2 4 6 9


1.0

0.5

0

-0.5

-1.0


4.0

3.8

3.6

3.4

3.2

3.0

120

t=0.5 from the Station I to the Station II, and to deliver -400MW electricity at t=2.0s from

Station I to the Station II. It is requested to deliver 400MW electricity again at t=4.0s and

to deliver -400MW electricity at t=6.0s. The slope of the power reference is limited by

800MW/s.

6.6.1 Simulation of a HVDC System Employing VV Control

The transmission line connects two active AC grids and it employs VV control strategy.

Both MMC operate in rectifier mode and the reference of the DC bus voltage of the

Station II is set as a constant value, namely its rated value 400kV. The power flow

between two stations is controlled by regulating the transmission line current, and the

transmission line current is controlled actively by the Station I.



control.

In Fig. 6-38, the transmission line tracks its reference well. It can be seen in the figure

0K

-0.5K

-1K

-1.5K

0.5K

1K

1.5KIdc

2 3 4 5 6 7 8 9 10 11Time (s)

380K

390K

400K

410K

420KVdc_StationI Vdc_StationII_ _[kV] [kV]dcd IIc I vv

[kA]dci

420

410

400

390

380

1.0

0.5

0

-0.5

-1.0

-1.5

1.5

1 3 5 7 8Time (s)

0 2 4 6 9

121

that different from the two-level converter based VSC-HVDC system or the direct

modulated MMC based VSC-HVDC system, no oscillation or inrush voltage occurs

during the power flow variation, and only the DC bus voltage of the Station I varies

slightly to compensate the voltage drop across the transmission line.


upper and lower arm capacitor energy of the Station I of the indirect modulated MMC

based HVDC transmission system by VV control.

In Fig. 6-39, the leg capacitor energy and the differences of the upper and lower arm

capacitor energy of the Station I are presented. The leg capacitor energy tracks the rated

reference value well and the upper and lower arm capacitor energy are balanced during

the power flow variation.

4M

4.2M

4.4M

4.6M

4.8M

5MDA0_I1 DA1_I1 DA2_I1

2 3 4 5 6 7 8 9 10 11Time (s)

0K

-500K

-1000K

500K

1000KDA3_I1 DA4_I1 DA5_I1

1 3 5 7 8Time (s)

0 2 4 6 9


1.0

0.5

0

-0.5

-1.0


5.0

4.8

4.6

4.4

4.2

4.0

122



control in sudden power flow variation.

As shown in Fig. 6-40, transmission line voltage fluctuation is fully suppressed by the

proposed method even while the power flow varies suddenly between -400MW and

400MW in 0.01s.

6.6.2 Simulation of a HVDC System Employing VP Control

The transmission line connected two active AC grids and it employs VP control

strategy. The Station I operates in rectifier mode and the Station II operates in inverter

mode. The reference of the DC bus voltage of the Station I is set as a constant value,

namely its rated value 400kV. The power flow between two stations is controlled by

regulating the active power flows into Grid II, and the energy stored in the capacitors of

the Station II is regulated by controlling the transmission line current. The transmission

line current is actively controlled by the Station II which operates in inverter mode.

0K

-0.5K

-1K

-1.5K

0.5K

1K

1.5KIdc

3.5 4 4.5 5 5.5 6 6.5

Time (s)

380K

390K

400K

410K

420KVdc_StationI Vdc_StationII

420

410

400

390

380

1.0

0.5

0

-0.5

-1.0

-1.5

1.5

_ _[kV] [kV]dcd IIc I vv

[kA]dci

0 1.0 2.0

Time (s)0.5 1.5 2.5 3.0

123


voltages of the indirect modulated MMC based HVDC transmission system by VP

control.


upper and lower arm capacitor energy of the Station II of the indirect modulated MMC

based HVDC transmission system by VP control.

0K

-0.5K

-1K

-1.5K

0.5K

1K

1.5KIdc

2 3 4 5 6 7 8 9 10 11Time (s)

380K

390K

400K

410K


[kA]dci

420

410

400

390

380

1.0

0.5

0

-0.5

-1.0

-1.5

1.5

1 3 5 7 8Time (s)

0 2 4 6 9

4M

4.2M

4.4M

4.6M

4.8M


2 4 6 8 10Time (s)

0K

-500K

-1000K

500K


1 3 5 7 8Time (s)

0 2 4 6 9


1.0

0.5

0

-0.5

-1.0


5.0

4.8

4.6

4.4

4.2

4.0

124

In Fig. 6-41, as soon as the Station II starts to deliver active power to the Grid II, it

draws current from the Station I through the transmission line to balance the power flows

into the capacitors of the Station II. The DC bus voltage of the Station I is maintained

constant as 400kV and the DC bus voltage of the Station II varies slightly to compensate

the voltage drop across the transmission line.

In Fig. 6-42, the leg capacitor energy and the differences of the upper and lower arm

capacitor energy of the Station II are presented. The leg capacitor energy tracks its

reference value and the upper and lower arm capacitor energy are balanced during the

power flow variation.

6.6.3 Simulation of a HVDC System Employing VP Control to Feed a Passive Grid

The transmission line is connected to feed a passive grid, namely the Grid II and it

employs VP control strategy. The Station I is connected with a strong grid, the Grid I, and

it operates in rectifier mode. The Station II operates in inverter mode to feed a passive

grid and to support its voltage. The reference of the DC bus voltage of the Station I is set

as a constant value, namely its rated value 400kV. The power flow between two stations

is determined by the active power fed into Grid II, and the energy stored in the capacitors

of the Station II is regulated by controlling the transmission line current. The transmission

line current is actively controlled by the Station II which operates in inverter mode. At

t=1.0s, the passive grid is loaded by a 400MW resistor load.

125


voltages of the indirect modulated MMC based HVDC transmission system feeding

passive grid.


upper and lower arm capacitor energy of the Station II of the indirect modulated MMC

based HVDC transmission system feeding a passive grid.

0K

-0.5K

-1K

-1.5K

0.5K

1K

1.5KIdc

2.5 3 3.5 4Time (s)

380K

390K

400K

410K


[kA]dci

420

410

400

390

1.0

0.5

0

-0.5

-1.0

-1.5

1.5

0.5 1.5Time (s)

0 1.0 2.0380

4M

4.2M

4.4M

4.6M

4.8M


2 2.5 3 3.5 4Time (s)

0K

-500K

-1000K

500K


0.5 1.5Time (s)

0 1.0 2.0


1.0

0.5

0

-0.5

-1.0


5.0

4.8

4.6

4.4

4.2

4.0

126

In Fig. 6-43, as soon as the passive grid is loaded, the Station II starts to draw power

from the Station I through the transmission line to support the passive grid. In Fig. 6-44,

the leg capacitor energy and the differences of the upper and lower arm capacitor energy

of the Station II are presented. The leg capacitor energy tracks its reference value and the

upper and lower arm capacitor energy are balanced during the power flow variation

6.7 Experimental Verification of a Point-to-Point HVDC

Transmission System under Indirect Modulation Based Control

Strategy

A point-to-point HVDC transmission system under indirect modulation based control

strategy is investigated by a 300V down-scale experimental setup as shown in Fig. 6-45.

The parameters of the setup are shown in Appendix F. The reference value of the DC bus

voltage of the Station II is set as a constant value, namely its rated value 300V. The

Station II is emulated by a bidirectional DC power supply. The transmission line current

is controlled actively by the Station I, namely the 7-level MMC. The transmission line is

emulated by a series connected resistor and an inductor.

127

Figure 6-45 Constructed 300V down scale experimental setup of a point-to-point HVDC

transmission system.

6.7.1 Experiment of a HVDC System Employing Proposed VV Control

Performance of the proposed VV control strategy is investigated by experiments and

the Station I, namely the 7-level MMC operates in rectifier mode. Before the starting

procedure, the transmission line breaker and the bypass switch of the starting resistor are

open. The DC bus voltage of the Station II is controlled as 300V. The capacitor voltages

of the cells of the Station I are boosted up to reference value, namely 50V by drawing

energy from the Grid I and are balanced well. The DC bus voltage of the Station I is

synthesized as 300V in an open loop manner.

Cells in one armMMC Control board

Arm inductor

DC supply

Starting resistor

Emulated transmission line

128

In the starting procedure, at first the transmission line breaker is closed and a low

current flows through the transmission line, which is induced by the synthesization error

of the DC bus voltage of the Station I. Then the transmission line current controller for

Station I is activated and the transmission line current is regulated to zero. At last, the

starting resistor is bypassed by the bypass switch and the two stations are connected.

Experimental waveforms of the DC bus voltages of the Station I and the Station II,

transmission line current, and the active current of Grid I during starting procedure are

shown in Fig 6-46.

Figure 6-46 Experimental waveforms of the DC bus voltages of the Station I and Station

II, transmission line current, and the active current of Grid I during starting procedure.

[1s/div]

Station I was connected to the DC

transmission line.

DC transmission line current


Starting resistor was bypassed.

__ [150V/ div[ [5A/ d[90J150V/ d / div viv] ]] i ]tdc suppl ddc MM ty coC alE iv v

129

Figure 6-47 Experimental waveforms of the DC bus current and the leg capacitor energy

of the Station I during power flow variation in VV control.

Figure 6-48 Experimental waveforms of the DC bus current and the differences of upper

and lower arm capacitor energy during power flow variation in VV control.

In the proposed VV control strategy, the power flow is controlled by regulating DC

transmission line current actively and directly by Station I. As shown in Fig. 6-47 and Fig.

6-48, the leg capacitor energy are controlled as its reference value 81J, and the upper and

lower arm capacitor energy are balanced for three phases by the proposed control strategy

, ,, [30J/ di[ [ [530J/ di 30J/ di A/ div]v ]] v v]u df vl w ft lfl t ct iEE E

[1s/div]

, ,, [10J/ di[ [ [510J/ di 10J/ di A/ div]v ]] v v]u df vl w ft lfl t ct iEE E

[1s/div]

130

during power flow variation.


total capacitor energy of the Station I, and the DC bus current in VV control.


current during power flow variation in VV control.

In Fig. 6-49 and Fig. 6-50, the Station I starts to inject active current into Grid I as soon

as the transmission line delivers power from Station II to Station I to regulate the

converter total capacitor energy. It can be seen clearly that by the proposed method, the


[1s/div]

(a)

[10A/ div] [10[10A/ div] A/ div [5A/ div] ]us dcwsvs ii ii

[1s/div]

Zoom in

[100ms/div]

131

DC bus voltage of the Station I varies slightly to compensate the voltage drop across the

transmission line and neither oscillation nor inrush voltage occurs in the DC bus voltage

during the power flow variation.

6.7.2 Experiment of a HVDC System Employing Proposed VP Control

Performance of the proposed VP control strategy is investigated by experiments and

the Station I, namely the 7-level MMC operates in inverter mode. In the proposed VP

control strategy, the power flow is controlled by regulating Grid I side active current.

Figure 6-51 Experimental waveforms of the active current of Grid I and the leg capacitor

energy of the Station I during power flow variation in VP control.

, ,, [30J/ div[ [1030J/ div ] A[30J/ di / div]v]] w f qsu fl lt v tflt EE iE

[1s/div]

132

Figure 6-52 Experimental waveforms of the active current of Grid I and the differences of

upper and lower arm capacitor energy during power flow variation in VP control.

As shown in Fig. 6-51 and Fig. 6-52, the leg capacitor energy are controlled as its

reference value 81J, and the upper and lower arm capacitor energy are balanced for three

phases by the proposed control strategy during power flow variation.


total capacitor energy of the Station I, and the DC bus current in VP control.

, ,, [10J/ div[ [1010J/ div ] A[10J/ di / div]v]] w f qsu fl lt v tflt EE iE

[1s/div]


[1s/div]

133


current during power flow variation VP control.

In Fig. 6-53 and Fig. 6-54, the Station I starts to draw DC current from the DC

transmission line as soon as it starts to import active current into Grid I to regulate the

converter total capacitor energy. It can be seen clearly that by the proposed method, the

DC bus voltage of the Station I varies slightly to compensate the voltage drop across the

transmission line and neither oscillation nor inrush voltage occurs in the DC bus voltage

during the power flow variation.

[10A/ div] [10[10A/ div] A/ div [5A/ div] ]us dcwsvs ii ii

[1s/div]

Zoom in

[100ms/div]

134

7. Conclusions

7.1 Conclusions

For the indirect modulation based control of the MMC, a stiff DC bus voltage source is

presumed in the previous work. While the DC bus of the MMC is connected with a stiff

voltage source, each phase of the MMC can be analyzed and controlled independently.

However, for an HVDC application, there is no stiff voltage source in the DC bus of the

MMC. Moreover, since the DC bus of the MMC is connected with a smoothing reactor in

series, the DC bus reveals current sourced characteristics. The conventional modeling is

not valid for real HVDC application and the conventional control strategy based on it

leads to poor dynamics of arm capacitor energy control of the MMC and can even make

the system unstable.

A modified modeling of the MMC with the generalized characteristic DC bus is

proposed in this thesis. In the proposed modeling, the MMC circuit is divided into an

extracted AC grid current model, an extracted DC bus current model, and an extracted

circulating current model. It is mathematically proven that the circulating current which

flows only inside the converter can be employed to balance energy stored in the

capacitors of six different arms. A DC component of the circulating current can be

injected to balance leg capacitor energy. A positive sequence line frequency component of

the circulating current can be injected to eliminate common component of differences of

three phase upper and lower arm capacitor energy, while a negative sequence line

frequency component of the circulating current can be injected to eliminate the

differential component of differences of three phase upper and lower arm capacitor

energy.

135

For the direct modulated MMC, the mechanism of the natural regulation behavior of

arm capacitor energy while an MMC is connected to a stiff DC bus voltage source is

revealed in previous work. In this thesis, the mechanism and the dynamics of natural

balancing of energy stored in the capacitors of six arms are analyzed for the MMC with

generalized characteristic DC bus. Unbalance of leg capacitor energy inherently induces a

DC component of the circulating current to balance the leg capacitor energy. And, the

unbalance of upper and lower arm capacitor energy inherently induces a positive

sequence and a negative sequence circulating current to balance the upper and lower arm

capacitor energy.

For a two-level converter based VSC-HVDC system or a direct modulated MMC based

VSC-HVDC system, the instantaneous DC bus voltage is coupled with the energy stored

in the capacitors. The DC transmission line is a Capacitor-Inductor-Capacitor coupling

circuit and a fluctuation of the transmission line voltage occurs while the power flow is

varying.

If an indirect modulated MMC is controlled by the proposed control strategy, the

instantaneous DC bus voltage is fully decoupled from the energy stored in the capacitors,

and the DC bus of the MMC operates like a controlled voltage source (at sampling

frequency) behind an inductor. Hence, the DC transmission line is a Controlled Voltage

Source-Inductor-Controlled Voltage Source circuit. By the proposed indirect modulation

based control strategy, the fluctuation of the transmission line voltage during power flow

variation can be fully suppressed. The control of the point-to-point transmission system

presents excellent performance by the proposed method compared to the two-level

converter based VSC-HVDC system or a direct modulated MMC based VSC-HVDC

system.

136

7.2 Contributions

Contributions of this thesis are concluded as follows.

i. Modeling of the MMC with generalized characteristic DC bus has been

proposed, in which the MMC is divided into an extracted AC grid current

model, an extracted DC bus current model, and an extracted circulating

current model.

ii. Based on the proposed modeling, an indirect modulation based control

strategy of arm capacitor energy has been proposed. In the proposed method,

arm capacitor energy is only balanced by injection of the circulating current

which only flows inside the converter.

iii. Based on the proposed MMC control strategy, an AC grid SLG fault ride

through strategy is developed.

iv. Based on the proposed MMC control strategy, a novel control concept of the

MMC-based VSC-HVDC transmission system has been proposed. Since the

instantaneous DC bus voltage is decoupled from the energy stored in the cell

capacitors and can be updated at sampling frequency, the transmission line

voltage fluctuation caused by the capacitor-inductor-capacitor equivalent

circuit in previous work is fully suppressed.

v. Mechanism and dynamics of natural balancing behavior of arm capacitor

energy are analyzed mathematically for the direct modulated MMC with

generalized characteristic DC bus.

7.3 Future Work

Several research topics for future work are suggested as follows.

137

i. Investigation of mechanism and dynamics of natural balancing behavior of

arm capacitor energy in unbalanced AC grid condition for the direct

modulated MMC with generalized DC bus.

ii. Control and dispatching strategy of an MMC multi-terminal HVDC grid

based on the proposed indirect modulation based control method.

iii. Control strategy of the MMC for weak AC grid connection.

138

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140

APPENDIX A

Figure. A-1 Structure of the MMC station investigated in Section 6.1 and Section 6.3

Table A-1 Parameters of the MMC station investigated in Section 6.1 and Section 6.3

Quantity Values

Number of cells per arm 216

Rated DC bus voltage 400 kV

Rated cell capacitor voltage 2.2 kV

Cell capacitor 4.5 mF

Transformer primary side voltage 180.5 kV

Transformer secondary side voltage 180.5 kV

Arm inductor inductance 15.0 mH

Arm inductor resistance 367.0 mΩ

Sampling frequency 10.0 kHz

DC load resistance 400 Ω

MMC

AC Grid Transformer

DC

Bu

s

Res

isto

r L

oad

141

APPENDIX B

Figure B-1. Structure of the MMC converter investigated in Section 6-2.

Table B-1. Parameters of the MMC converter investigated in Section 6-2.

Quantity Values


Rated DC bus voltage 300V

Rated cell capacitor voltage 50V

Cell capacitor 5.4mF

Grid voltage 110V



DC bus R-L load inductance 3.0 mH

DC bus R-L load resistance 60 Ω


Cell1

Cell2

Cell3

Cell6

Cell1

Cell2

Cell3

Cell6

Cell1

Cell2

Cell3

Cell6

Cell1

Cell2

Cell3

Cell6

Cell1

Cell2

Cell3

Cell6

Cell1

Cell2

Cell3

Cell6

Rload

Lload

Breaker

142

APPENDIX C

Figure. C-1 Structure of the MMC station investigated in Section 6.4

Table C-1 Parameters of the MMC station investigated in Section 6.4

Quantity Values




Cell capacitor 45 mF



Arm inductor inductance 150 mH

Arm inductor resistance 3.67 Ω



MMC

AC Grid Transformer

DC

Bu

s

Res

isto

r L

oad

143

APPENDIX D

Figure. D-1 Structure of the point-to-point HVDC transmission system investigated in

Section 6.5

Table D-1 Parameters of the transmission system investigated in Section 6.5

Quantity Values




Cell capacitor 45 mF



Arm inductor inductance 150 mH

Arm inductor resistance 3.67 Ω



Transmission line resistance 1.0 Ω

Transmission line inductance 1.0 mH

MMC

Grid I Transformer

MMC

Grid IITransformer

Transmission LineStation I Station II

144

APPENDIX E

Figure. E-1 Structure of the point-to-point HVDC transmission system investigated in

Section 6.6

Table E-1 Parameters of the transmission system investigated in Section 6.6

Quantity Values




Cell capacitor 4.5 mF








MMC

Grid I Transformer

MMC

Grid IITransformer

Transmission LineStation I Station II

145

APPENDIX F

Figure. F-1 Structure of the point-to-point HVDC transmission system investigated in

Section 6.7

Table F-1. Parameters of the transmission system investigated in Section 6-7.

Quantity Values


Rated DC bus voltage 300V

Rated cell capacitor voltage 50V

Cell capacitor 5.4mF

Grid voltage 110V





Cell1

Cell2

Cell3

Cell6

Cell1

Cell2

Cell3

Cell6

Cell1

Cell2

Cell3

Cell6

Cell1

Cell2

Cell3

Cell6

Cell1

Cell2

Cell3

Cell6

Cell1

Cell2

Cell3

Cell6

BreakerStarting resistor

Bypass switch

DC

Power Supply

+

-

vdc_MMC

+

-

vdc_supply

idc

Conversion Station I Conversion Station IITransmission

Line

146

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