MMC-STATCOM Control System Research Based on Equivalent Parameter Model and Carrier Pulse

Phase-Shifting Modulation

Hui Chen1, Yukun Sun1,Weiwei An2 and Yonghong Huang1 1Jiangsu University, Jiangsu Province, China

2State Grid SuQian Power Supply Company, Jiangsu Province, China Abstract—To study the components and parameters relationship between MMC-STATCOM and traditional STATCOM, the mathematical model of MMC-STATCOM is established. Then, the equivalent expressions for MMC-STATCOM module capacitance and inductance bridge arm are derived, compared with traditional STATCOM. On account of the corresponding complementary in the pulses of upper and lower bridge arm module, a carrier phase shift pulse modulation method is proposed, which simplifies the pulse generation. Also, the control strategy is designed, especially the module voltage balance control, considering the difference value of actual module voltage between the reference voltage and the direction of arm current. In the end, some simulations are done in Matlab/Simulink. The model and control method are both validated.

Keywords-MMC-STATCOM; mathematical model; CPPS

I. INTRODUCTION

Modular Multilevel Converter Static Synchronous Compensator (MMC-STATCOM) has attracted wide attention as a kind of reactive power compensation device in electric power system. It has the advantages of highly modular, easy to expand, convenient redundant design, the independent active power and reactive power control, high output voltage quality [1-4].

MMC topology [5] has gradually been introduced into the high-voltage Direct Current transmission (High Voltage Direct Current, HVDC) and the Unified trend Controller (Unified Power Flow Controller, UPFC) [6]. Scholars mainly concern the mathematical modeling of MMC structure, analysis of circulation, sub module voltage control strategy, dc voltage control, the transient simulation, harmonic analysis and suppression [8-13].

The MMC-STATCOM mathematical model is studied in this paper and the parameter corresponding relations with the traditional STATCOM is derived. It simplifies the MMC- STATCOM parameter analysis. In addition, a modified modulation method called Carrier Pulse Phase-Shifting (CPPS) is proposed. The MMC - STATCOM control system are designed based on MMC - STATCOCM mathematical model and CPPS modulation method. Finally, a five level MMC - STATCOM model is built in MATLAB/SIMULINK to verify the performance of the design.

II. MMC STATCOM MATHEMATICAL MODELING

1s

2s

1D

2D

1aSM

2aSM

anSM

1anSM

2anSM

2a nSM 2b nSM

2bnSM

1bnSM

bnSM

2bSM

1bSM 1cSM

2cSM

cnSM

1cnSM

2cnSM

2c nSM

dcV0L

0L

0L

0L

0L

0L

sL

sL

sL

FIGURE I. MMC STATCOM TOPOLOGY

In Figure I, the MMC-STATCOM topology is shown. The SM (Sub Modular, SM) in upper and lower arm switch are complementary in order to ensure MMC-STATCOM DC link voltage constant. The number of input SM at any time for each phase is N.

Assuming that the SM capacitor voltage is constant and

the value is cV . The DC side voltage is dcV , which will satisfy

(1) and (2) at any time.

Pj Njn n N (1)

c dcNV V

(2)

where, 1, 2,3( , , )j a b c ,the number of sub modular for the

upper bridge arm is Pjn , the number of sub modular for the

lower bridge arm is Njn . Therefore, each bridge arm is

equivalent to a voltage source, the equivalent circuit of MMC-STATCOM is shown in Figure II.

International Conference on Energy, Power and Electrical Engineering (EPEE 2016)

© 2016. The authors - Published by Atlantis Press 255

0L 0L 0L

0L 0L 0L

pav pbv pcv

nav nbv ncv

sai

pai pbi pci

nai nbinci

2dcV

di

sbisci

a

'a

sR

sR sL

sR sL

sL

2dcV

OMav Mbv

Mcv

FIGURE II. EQUIVALENT CIRCUIT OF MMC-STATCOM

where, i pa i pb i pc are upper bridge arm currents; ina inb inc are

lower bridge arm currents; v pa v pb v pc are equivalent voltage

sources of upper bridge arm; vna vnb vnc are equivalent voltage

sources of lower bridge arm; 0L is the inductance value of

bridge arm; Ls is the connection inductance of AC side; Rs is

the equivalent connection resistance of AC side; id is the DC

bus current; isa isb isc are AC currents which are put into

MMC-STATCOM; O is the DC neutral point.

Since the AC output side of MMC-STATCOM is connected to the reactor, it could guarantee that the output voltage current is more approximate to the sine wave to a certain extent. Therefore, we make the following assumptions:

Due to the existence of the connection reactor, the output of the AC voltage and current of the MMC-STATCOM is a sine wave;

Each bridge arm of the SM module capacitor voltage are equal at any time;

In MMC-STATCOM modeling, only the fundamental component of the voltage is considered and the harmonic component is neglected.

It should be explained that when the device has internal active power loss, the DC bus voltage is no longer a fixed value. According to Figure II, formula (3) can be got on the base of KVL.

02

02

div pjdc v v LpjMjdtdiv njdc v v LnjMjdt

(3)

Formula (4) can be got on the base of formula (3):

1 1(v ) 0

2 2

disjv v Lnj pjMj

dt (4)

On the AC side of MMC-STATCOM formula (5) can be got

Mj

disjv v L R isj s s sj

dt (5)

Formula (6) can be got according to formula (4) and (5)

( ) ( )01 1 '2 2

disjv L L R i v v vsj s s sj nj pj

dtMj

(6)

where the equivalent inductance can be expressed as

0 0

1

2s sL L L .The formula (6) indicates that the upper and

lower bridge arm inductances can be equivalent to the AC output side and the equivalent inductors are connected in parallel. The formula (6) can be written as three-phase mathematical equation.

s0

'

'

'

disa

dt vv iMasa sadisb v v R issb Mb sbdt v ivsc scMcdisc

dt

L

(7)

The number of SM in the MMC-STATCOM is 6N, namely there are 6N capacitor voltage variables, while the number of capacitor voltage variably reduces to 6 according to hypothesis (3). In addition, the sub module voltage fluctuates based on the rated voltage, so the voltage can be divided into two parts. One part is the DC rated voltage and the other part is AC the fluctuation components. Therefore, the 6 voltage variables can be written as

v v vcpa c cpa

v v vccpb cpb

v v vcpc c cpc

(8)

where, cpabcv is the three-phase upper bridge arm sub module

capacitor voltage; cpabcv is the three phase lower bridge arm

sub module capacitor voltage. MMC-STATCOM internal energy can be expressed as

1 1 12 2 2( )2 2 21 1 12 2 22 2 2

W t CNv CNv CNvM cpa cna cpb

CNv CNv CNvcnb cpc cnc

(9)

where, C is the capacitance value of the SM (sub module), the formula (9) can be gotten according to (7) and (8)

3 2( )C

W t vM dcN

(10)

256

The formula (10) indicates that the energy in the capacitor is proportional to the square of the DC voltage, so that the dispersed sub module capacitor can be equivalent to the DC

side and the expression is 0

6CC

N . The power in

MMC-STATCOM can be regarded as DC power after getting rid of the equivalent bridge arm inductance. Formula (11) can be gotten considering the balance of instantaneous power in MMC-STATCOM

6 ' ' 'dvC dcv v i v i v isa scMa Mcdc Mb sbN dt

(11)

Formula (12) can be gotten according to (7) and three-phase current balance condition

s0

1

0

disa

dti vsa sadisb A i vsb sb

dt vdcdvdc

dt

L

(12)

where, the expression of A matrix is

s0 s0

s0 s0

0 cos( t )2

20 cos( t )

2 3

1 13 cos( t ) 3 cos( t )

6 2 012 12

s

s

R m

L L

R mA

L L

Nm Nm

C C

The formula (13) can be gotten after Park transformation on the base of formula (12)

0 s0

0 s0 0

3 1* cos( )

2 2

3 1 1* sin( ) 0

2 20

3 3* cos( ) * sin( ) 0

2 12 2 12

sMd

s

Md sMq s

Mqs s

dcdc

RdI mL Ldt I V

dI Rm I

dt L L Lv

dv Nm Nmdt C C

(13)

The equivalent model of MMC-STATCOM is shown in Figure III.

s0

1

ssL R

0

1

s ssL R

0sL

0sL

sdV

sqV

'MqV

'MdV

MdI

MqI

FIGURE III. EQUIVALENT MODEL OF MMC-STATCOM

The model only has three state variables through the mathematical derivation. The parameters corresponding relationship between MMC-STATCOM and the traditional STATCOM can be expressed as

0 s0

0

1

26

sL L L

CC

N

(14)

where,0s

L is the connection inductance of traditional

STATCOM, 0

C is the DC side capacitor value of traditional

STATCOM.

III. CARRIER PULSE PHASE-SHIFTING MODULATION

METHOD

CPS-SPWM mode combines the carrier phase shift (CPS-SPWM) and pulse phase shift (PPS-SPWM) which can guarantee at any time the number of the input sub-module in each phase is constant. There are two bridge arms in each phase of MMC-STATCOM and the number of SM in each arm is N. A-phase is discussed in this paper due to three-phase symmetry. The SMs in each bridge arm are numbered from top to bottom and i represents the ith SM in upper arm as well as j represents the jth SM in lower arm. The phase of triangular carriers, corresponding with N SMs in upper bridge arm, is followed by a difference of

π. The frequency of sine

modulation wave is 50Hz. As a result, the modulation mode in upper arm is traditional CPS-SPWM, but the pulses of each SM in lower arm are achieved through the complementary relationship with SM in upper arm. If N is even and i and j have the relationship of (15), the pulses of i and j are complementary.

2 j i N （ ） 1 , 1i N j N （ ） (15)

If N is odd and i and j have the relationship of (16), the pulses of i and j are complementary.

2 1j i N （ ） 1 , 1i N j N （ ） (16)

Figure IV is the AC side output voltage waveform of MMC-STATCOM under CPPS modulation.

257

FIGURE IV. THE AC SIDE OUTPUT VOLTAGE WAVEFORM OF

MMC-STATCOM UNDER CPPS MODULATION. 

IV. MMC-STATCOM CONTROL SYSTEM

The control system is designed based on MMC-STATCOM mathematical model and CPPS modulation scheme. It includes DC link voltage control, reactive power control, current decoupling control and sub-module voltage control.

A. Outer Loop Voltage and Power Control refQ

sdv 3

2

Mqi

PI refMqi

dcV

refdcV

refMdiPI

FIGURE V. OUTER LOOP VOLTAGE AND POWER CONTROL

ref

dcV is the reference value of DC bus voltage, dcV is the

detection value of DC bus voltage, ref

Q is the reactive power

reference value of MMC-STATCOM, ref

Mdi is the active current

reference value and ref

Mqi is the reactive current reference value

of MMC-STATCOM .

B. Inner Current Decoupling Control

The formula (17) can been got from formula (13)

0

0

dIsdV L R Id s s sddtdIsq

V L R Iq s s sqdt

0

0

'

's

s

V L Id sd

V L Iq sq

(17)

So the AC component of formula (13) can be rewritten as

' '

' 'Md sd d q

Mq sq q d

V V V V

V V V V

(18)

where, 'dV and '

qV are the coupling compensation component,

dV and qV are the output of first derivative which can be

expressed as the formula (19)

1 1

2 2

( ) K ( )

( ) K ( )

ref ref

d P sd sd I sd sdref ref

q P sq sq I sq sq

V K i i i i dt

V K i i i i dt

(19)

where, ref

sdi and ref

sqi are the active and reactive current reference

value of PCC. 1PK and 2PK are proportional coefficient, 1K I

and 2K I are the integral coefficient.

Therefore, the decoupled current control system shown in Figure VI can be got from (18) and (19)

Mai

MciMbi

Mqi

Mdi

refMdi

refMqi

sdV

sqV

PI

PI

'sL

'sL

'MdV

'MqV

'

1

s ssL R

'

1

s ssL R

'sL

'sL

sdV

sqV

'MqV

'MdV sdI

sqI

/dq abcC

FIGURE VI. CURRENT DECOUPLING CONTROL

C. Sub-Module Voltage Control

In order to clarify the physical meaning of sub-modules voltage control, where the voltage control sub-module is divided into two parts, one is voltage control of the sub-module in the same phase, called the voltage equalization control; the other part is sub-modules voltage control between the three-phase, called average voltage control.

1) Average voltage control: The average voltage is composed with outer loop voltage control and inner loop current control and the control system is shown in Figure VII.

),,( cbaj zji

pji

nji

1

2

refcV

cjV

refzji

BjV

FIGURE VII. AVERAGE VOLTAGE CONTROL

where, cjV is the average voltage of the series capacitor

module in one phase ref

zji is the inner current reference value.

When ref

cV > cjV , ref

zji increases and the DC capacitor is charged;

when ref

zji < cjV , ref

zji decreases and the DC capacitor is

discharged.

2) Voltage equalization control: When the sub-module capacitor voltage instantaneous value is less than the rated value and the arm current is positive, the sub-module should put in charge to make the capacitor voltage increase; while the arm current is negative, the sub-module should be bypass.

When the sub-module capacitor voltage instantaneous value is greater than the rated value and the arm current is positive, the sub-module should be bypass to prevent the capacitor voltage is increased further; while the arm current is negative, the sub-module should be put in charge. In CPPS modulation, lower arm pulse signal can be got according to formula (15) (16) The voltage equalization control process shown in Figure VIII and the control strategy shown in Figure IX.

258

refc cjpiV V

refcV

cjpiV

* 0cjpi pjV i

cjpiV

pji

Y

N

*cjpi pjV i *cjpi pjV i

FIGURE VIII. THE FLOWCHART OF VOLTAGE EQUALIZATION

CONTROL

bK

bK

bK

refcV

1cjpV

cjpNV

2cjpV 2AjpV

( ) 0refc cjpi pjV V i

( ) 0refc cjpi pjV V i

, ,j a b c 1, 2,...,i N

AjpNV

1AjpV

FIGURE IX. THE UPPER ARM BRIDGE MODULE VOLTAGE

EQUALIZATION CONTROL

ref

cV is the reference voltage of sub-module, cjpiV , cjniV

(j=a,b,c; i=1,2,...,n)are upper and lower arms submodules

capacitor voltage detection value; Kb is the proportional

control coefficient which is positive; AjpiV , AjniV are the output

of upper and lower arm sub-module voltage balance control

V. THE ANALYSIS OF SIMULATION

A 3.3kV MMC-STATCOM simulation model is built in Matlab / Simulink simulation platform; the number of series sub-module in one arm is 4; the voltage rating of sub-module is 1500V; carrier frequency fc = 2kHz; the value of sub-module capacitance C = 3mF; the value of arm inductance is 0 6L mH ; the value of connecting reactance is 6sL mH .

Figure X to Figure XV are the simulation results of the MMC-STATCOM which accesses systems with constant load. MMC-STATCOM access system at 0.05s.It can be seen from Figure XI and Figure XII that the system does not generate voltage and current impact. Figure X shows that MMC-STATCOM can work normally after a cycle, voltage and current of PCC are in the same phase nearly. Figure XIIIshows that the DC bus voltage of MMC-STATCOM work in stability, Figure XIV shows the sub-module voltage fluctuations within the allowable range.

FIGURE X. COMPENSATION EFFECT OF PCC

FIGURE XI. OUTPUT VOLTAGE OF MMC-STATCOM

FIGURE XII. OUTPUT CURRENT OF MMC-STATCOM

FIGURE XIII. DC LINK VOLTAGE OF MMC-STATCOM

FIGURE XIV. MODULE VOLTAGE OF UPPER AND LOWER ARM

BRIDGE

FIGURE XV. MMC-STATCOM OUTPUT CURRENT HARMONICS

FIGURE XVI. PCC VOLTAGE AND CURRENT WITH LOAD

FLUCTUATIONS

259

FIGURE XVII. MMC-STATCOM REACTIVE CURRENT

Figure I6 and Figure I7 show that the system is stable after two cycles when the load fluctuates suddenly and the reactive power of load is compensated totally. PCC voltage and current are in the same phase nearly, MMC-STATCOM changed the issue of inductive reactive power into the state of the absorption of reactive power and the control system can track the load changes quickly

VI. CONCLUSION

The MMC-STATCOM equivalent model is established in this paper. The arm inductance is equivalent to the AC output side and the sub-module capacitance is equivalent to the DC side. So, the relationship between the MMC-STATCOM capacitance and inductance parameters and traditional STATCOM parameters could be got. It simplifies the analysis of MMC-STATCOM dynamic characteristics. In addition, the CPPS modulation strategy is proposed, which simplifies the pulse modulation strategy and reduces the requirements for hardware storage. MMC-STATCOM control system is designed on the basis of MMC-STATCOM equivalent model and CPPS modulation strategy. And, the simulation in MATLAB/SIMULINK demonstrates the excellent characteristics of the control system.

REFERENCES [1] K. Ilves, A. Antonopoulos, S. Norrga, and H. -P. Nee, “A new

modulation method for the modular multilevel converter allowing fundamental switching frequency,” IEEE Transactions on Power Electronics, vol. 27, no. 8, pp. 3482-3494, Aug. 2012.

[2] Zhao Haiwei, Qin haihong, Ma Ceyu, Zhu Ziyue “STATCOM integrated control strategy research based on the MMC topology”, Power System and Automation, 2016,38 (1): 55-61.

[3] S.Rohner,S.Bernet,M.Hiller and R.Sommer,Modulation, Losses, and Semiconductor Requirements of Modular Multilevel Converters, IEEE transactions on Industrial Electronics, Vol.57, No.8, 2010.

[4] Friedrich K. Modern HVDC PLUS application of VSC in Modular Multilevel Converter topology[C]/Industrial Electronics (ISIE),2010 IEEE International Symposium on. IEEE,2010:3807-3810.

[5] Marquardt R, Lesnicar A. New concept for high voltage—modular multilevel converter[C]//Power Electronics Specialists Conference (PESC). Aachen, Germany,2004:1-5.

[6] Cao Chungang Zhao Chengyong, Chen Xiaofang “MMC - STATCOM System Mathematical Model and Control Strategy” Power System and Automation, 2012, 24(4): 13-18.

[7] Fei Juntao, Luo Shanshan “Review of MMC-UPFC Cross Decoupling Control Strategy” Jiangsu Electrical Engineering, 2016,35(1):45-48.

[8] Xu Jianzhong,Zhao Chengyong,“Research on the Thévenin’s Equivalent based Integral Modelling Method of the Modular Multilevel Converter (MMC)”, 2015,35(8):1919-1929.

[9] Jiang Lin, Zhou Shijia, Li Zishou, Xiang Wand, Hu Jizhou, Cheng Jie, Wen Jinyu “Equivalent Electromagnetic Model and Averaged Value Model of MMC for Operating Condition Simulation” SOUTHERN POWER SYSTEM TECHNOLOGY, 2016,10(2):11-17.

[10] Du Xiaozhou,Mei Jun,Deng Kai,Miao Huiyu,Zhang Zhe,Wang Zhihe,“Voltage Balance Control Method of MMC” Power System Technology, 2016,40(1):26-31.

[11] Xu Jianzhong, Zhao Chengyong, Liu Wenjing “Accelerated Model of Ultra-large Scale MMC in Electromagnetic Transient Simulations” Proceedings of the CSEE, 2013,33(10):114-120.

[12] Guan Minyuan, Xu Zheng“Modular multilevel converter fast electromagnetic transient simulation method”, Electric Power Automation Equipment, 2012, 32 (6):36-40.

[13] Zhao Xin Zhao Chengyong, Li Guangkai, “Multilevel Inverter Capacitor Voltage Balance Control Based on Carrier Phase Shifting Technology of Modularization”, Proceedings of the CSEE, 2011,31(21): 48-55.

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