MMC-STATCOM Control System Research Based on Equivalent ...
Transcript of MMC-STATCOM Control System Research Based on Equivalent ...
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)
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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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