North American Power Symposium (NAPS), Laramie, Wyoming, October 1997, pp. 49{54.

Fundamental Frequency Model of Static Synchronous Compensator

Edvina Uzunovic Claudio A. Ca~nizares John Reeve
University of Waterloo
Department of Electrical & Computer Engineering
Waterloo, ON, Canada N2L 3G1
Abstract|A balance, 60 Hz model of the transformer; it can generate or absorb reactive power to
Static Synchronous Compensator (STATCOM), a regulate the voltage prole of the bus at which it is con-
FACTS controller based on voltage-sourced con- nected [5].
verters with Gate Turn-O (GTO) thyristors, is It should be noted that the STATCOM may be known
proposed in this paper. Electromagnetic Tran- by other terminology, and that several application varia-
sient Program (EMTP) simulations are carried tions are possible. For example, if the voltage-sourced in-
out in a sample system with variable load, to verter is employed in series with the transmission line via
compare the operation of the detailed controller a series transformer, the device is referred to as a Static
representation and its suggested reduced model. Synchronous Series Compensator (SSSC). This can also
The proposed quasi-steady-state model is suitable generate or absorb reactive power from the series con-
for transient stability studies as well as other sys- nected line, and in that way change the series impedance
tem analysis techniques, such as voltage collapse of the transmission line as well as the power owing
studies, that required accurate representation of through it [6]. Also, two series and shunt connected
fundamental frequency operation and control of voltage-sourced inverters, coupled by a common dc capac-
power system controllers. itor, become the Unied Power Flow Controller (UPFC)
Keywords: FACTS, STATCOM, EMTP, funda- [7]. The UPFC oers the unique opportunity to directly
mental frequency models. exchange active power with the ac system, in addition
to independently control shunt and series reactive power
I. Introduction compensation.
Before these controllers are installed in a power sys-
Today's power systems are highly complex, sometimes tem, it is important to investigate and clearly identify
made of thousands of buses and hundreds of generators. the potential application and benets arising from the
New power generation is primarily determined based on installation. In order to do so, it is necessary to equip
environmental and economic reasons, and are somewhat power system engineers with all tools necessary to ac-
inexpensive and relatively easy to build and operate, es- complish this task, i.e. adequate models and software
pecially nowadays with the availability of \cheap" natu- tools to accurately represent these controllers in dierent
ral gas and high performance gas turbines. On the other types of studies. Several authors have demonstrated the
hand, new transmission systems are expensive and take importance of realistic modeling of FACTS controllers for
considerable amount of time to build. Hence, in order steady-state and transient studies [8, 9, 10]. In the cur-
to meet increasing power demands, utilities must rely rent literature, the STATCOM is modeled in steady-state
on power export/import arrangements through existing as part of the UPFC [11, 12]; the STATCOM is decou-
transmission systems. While the power ow in some of pled from the SSSC and represented usually by a voltage
these transmission lines is well below their thermal lim- or current source. These voltage or current sources are
its, certain lines are overloaded, which has the eect of modeled without limits and, therefore, the STATCOM is
deteriorating voltage proles and decreasing system sta- represented as capable of generating or absorbing unlim-
bility. This requires the review of traditional transmission ited amounts of reactive power. The current paper pro-
methods and practices, and the creation of new concepts poses a fundamental frequency model of this controller
to allow for the use of existing transmission systems with- so that operating and control limits are represented in a
out reduction in system security. more realistic manner. A rather detailed model for the
Flexible AC Transmission Systems (FACTS) is a new STATCOM, suitable for Electromagnetic Transient Pro-
approach to a more ecient use of existing power sys- gram (EMTP) types of studies, is used as a test-bed for
tem resources based on the utilization of high-current, the development of the proposed fundamental frequency
high-voltage power electronic controllers [1, 2, 3, 4]. The model.
authors in [2, 3] propose the use of a Static Synchronous In Section II. the basic operating principles of the
Compensator (STATCOM) as a FACTS controller. It STATCOM are described, and a detailed EMTP model
is basically a voltage-sourced inverter using GTOs and of this controller is discussed. The results of using this
dc capacitor to generate a three phase synchronous volt- device in a test system that simulates a variable load are
age at fundamental frequency. The STATCOM is shunt- also presented in this section. Section III. discusses the
connected to the transmission system via a step-down development of a 60-Hz model for the STATCOM, and
1
presents the results of using this model in the same test AC System
system, comparing the results obtained for both detailed
and 60-Hz models. Finally, Section IV. summarizes the I
main ideas presented in this paper as well as discussing
future research directions. STATCOM
Transformer

II. STATCOM Detailed Model

A. Basic Operation DC/AC
Inverter
The basic electronic block of the STATCOM is the
voltage-sourced inverter that converts an input dc volt-
age into a three phase output voltage at fundamental fre-
quency. The steady-state characteristics of the STAT- DC Voltage

COM are similar to those of a rotating synchronous com- Source + -

pensator but with no inertia, so that its response is ba- Fig. 1. STATCOM functional model.
sically instantaneous and it does not signicantly alter
the existing system impedance; the latter is an advan-
tage over Static var Compensators (SVCs). a small amount of real power from the ac system to re-
In its simplest form, the STATCOM is made up of a plenish its internal losses and, thus, keep the capacitor
coupling transformer, a voltage-sourced inverter and a dc voltage constant.
capacitor. In this arrangement, the steady-state power
exchange between the device and the ac system is mainly B. EMTP Modeling
reactive. A functional model of the STATCOM is shown
in Figure 1. A three phase voltage-sourced inverter is typically
The reactive power exchange of the STATCOM with made of six controlled switches (GTO valves) to shape
the ac system is controlled by regulating the amplitude the output waveform. There are also six uncontrolled
of the STATCOM output voltage. If the amplitude of the switches (diodes) to provide a path for inductive output
STATCOM output voltage is increased above the ampli- current whenever the controlled switches are switched o.
tude of the ac system voltage, the current ows through The twelve switches form two bridges connected in anti-
the transformer reactance from the STATCOM to the ac parallel. Each GTO valve and diode within a switch car-
system, and the device generates reactive power (capac- ries alternatively a 90 segment of the output current in
itive). If the amplitude of the STATCOM output volt- each cycle; thus, the current ratings of the GTO valve
age is decreased to a level below that of the ac system, and diode are the same. When the output current is ca-
then the current ows from the ac system to the STAT- pacitive, the GTO valve has to be turned o at the peak
COM, resulting in the device absorbing reactive power of the current, whereas in inductive operation the valve
(inductive). If the amplitudes of the STATCOM output commutates naturally when the current drops to zero.
voltage and the ac system voltage are equal, the reac- The inverter bridge within the STATCOM is typically
tive current is zero and the STATCOM does not gener- made of several 6-pulse inverters to reduce the harmonics
ate/absorb reactive power. Since the STATCOM is gen- present in the output current. The 6-pulse inverter out-
erating/absorbing only reactive power, the output voltage put voltages are combined by means of an array of several
and the ac system voltage are in phase, when neglecting coupling transformers to form a multi-pulse \sinusoidal"
circuit losses. The current drawn from the STATCOM voltage. In practice, for transmission line applications,
is 90 shifted with respect to the ac system voltage, and a 24 or higher pulse arrangement is required to achieve
it can be leading (generates reactive power) or lagging adequate waveform quality without the need of passive l-
(absorbs reactive power). ters. In 1995, a 100 Mvar STATCOM with eight invert-
A capacitor is used to maintain dc voltage to the in- ers, to produce a 48-pulse output voltage waveform, was
verter. The inverter itself keeps the capacitor charged commissioned for the Tennessee Valley Authority (TVA)
to the required levels. Thus, by controlling the inverter [13].
output voltage lead or lag with respect to the ac sys- In this paper, a 12-pulse STATCOM is modeled in the
tem voltage, the capacitor voltage can be decreased or EMTP to obtain the basic waveforms and to illustrate
increased, respectively, to control the reactive power out- the operation of this device. This detailed model is then
put of the device. When the inverter voltage leads the used to validate the proposed 60 Hz model. Due to the
bus voltage, the capacitor supplies active power to the \low" number of inverter pulses used, lters are added
system, reducing its voltage; on the other hand, when to improve the output voltages and currents. The control
the inverter voltage lags the bus voltage, the capacitor is part of the STATCOM is modeled using TACS (Transient
charged by consuming active power from the system. In Analysis of Control Systems), which basically uses a PI
steady-state, the output voltage of the inverter slightly controller to directly change the phase-shift, within lim-
lags the ac system voltage, so that the inverter absorbs its, between the inverter output ac voltage and the bus
2
 a
b
c +

v a,Y

- 6-Pulse
Inverter

+
v a,∆
6-Pulse
- Inverter
Vdc
(lags above
inverter by
30 degrees)

Fig. 2. Twelve-pulse STATCOM arrangement.

voltage and, hence, control the charging and discharging 5 AC System Voltage
of the capacitor as previously indicated. x 10

Figure 2 shows a typical 12-pulse inverter arrangement

1

utilizing two transformers with their primaries connected 0

V
in series. −1
The rst inverter is connected to the system through 0.155 0.16 0.165 0.17 0.175
a Y-Y arrangement, whereas a Y-
connection is used 5
x 10 Statcom Output Voltage

for the second inverter. Each inverter operates as a 6- 2

pulse inverter, with the Y-
inverter being delayed by
30 with respect to the Y-Y inverter. The instantaneous
0

STATCOM output voltage for phase a can be computed V

−2

in this case as 0.155 0.16 0.165

Statcom Input Current
0.17 0.175

v
v = a1 v + a2 p
a;
a a;Y
3 100

0
A

where a1 and a2 are the voltage ratios of the correspond-

ing inverter transformers. The current owing into each −100

inverter is the same, scaled by the transformer ratio, as 0.155 0.16 0.165 0.17 0.175

the current being drawn from the system by the STAT-

Statcom DC Current
2000
COM; for the Y-
inverter, the current is also delayed by
30 with respect to the current of the Y-Y inverter. The 0
A

STATCOM output voltage and input currents, as well as

the corresponding dc current and voltage, are depicted in −2000
0.155 0.16 0.165 0.17 0.175
Figure 3 for the device operating in capacitive mode. Statcom DC Voltage
The 5-bus test system depicted in Figure 4 is used 6000

here to illustrate the STACOM operation in a variable 4000

load environment. This system is based on a test sys-

V

2000
tem introduced in [15] to test SVCs. Initially, a shunt
capacitor bank is connected at Bus 2 to bring the ini- 0
0.155 0.16 0.165 0.17 0.175
tial voltage close to 1 p.u.; these capacitors are then re-
placed by a STATCOM connected to Bus 2 through a Fig. 3. STATCOM waveforms for capacitive operation.
100 MVA, 138/6 kV transformer. The transformer resis-
tance and magnetizing reactance are assumed to be very
small and are, therefore, neglected; the leakage reactance
is assumed to be 14.5 %. The inverter transformers are
rated at one half of the total MVA transformer output,
i.e., 50 MVA. The load is modeled using TACS control-
lable current sources to simulate a variable RL load, and
is assumed to increase to full load in two steps to bring
the voltage down and, thus, activate the STATCOM.
The voltage of the ac system is subjected to dynamic
variations due to load changes at 0.4 s and 0.8 s. The
proper function of the STATCOM is to minimize the mag-
nitude and duration of these disturbances by regulating
the voltage at Bus 2. For the system with xed capacitive
3
 x 10
5 Voltage at Bus 2 − Phase A
1.5

0.5

V
−0.5

−1

−1.5
0 0.2 0.4 0.6 0.8 1
Voltage at Bus 2 − Phase A

0.8

0.6

pu
0.4

0.2

0
0 0.2 0.4 0.6 0.8 1
x 10
7 Load Power Demand − Phase A
3

Fig. 4. Test system. 2.5

W/phase
support, Figure 5 shows the active power load demand as 1.5

well as the instantaneous load phase voltage and its mag- 1

nitude; observe the low p.u. voltage levels as the load is 0.5

increased. 0
0 0.2 0.4 0.6 0.8 1

Hence, to keep the voltage in the system at acceptable

levels, a 100 Mvar STATCOM is then connected at Bus Fig. 5. Test system results without STATCOM.
2, replacing the capacitor bank, to bring the voltage to
the desired 1 p.u. The results with the STATCOM added
to the system are depicted in Figure 6 which indicates x 10
7 Load Power Demand − Phase A

adequate load voltage regulation.

4
W/phase

III. Fundamental Frequency Model 0

0 0.2 0.4 0.6 0.8 1
In order to develop a 60 Hz, balanced model of the Voltage at Bus 2 − Phase A

STATCOM, a power balance technique, somewhat similar 1.5

to the one proposed in [14] for d-q axis control strategies, 1

is used here. Thus, the instantaneous power owing into

pu

0.5
the inverter from the ac bus, when neglecting transformer
losses, may be represented by
0
0 0.2 0.4 0.6 0.8 1
x 10
5 Statcom Output Voltage − Phase A
V V
p=3 ac inv
sin  2
X 0
V

where V is the rms voltage of the sinusoidal STATCOM

ac

bus voltage; X is the coupling transformer equivalent −2

impedance;  is the phase shift between the bus phase 0 0.2 0.4 0.6
Statcom DC Voltage
0.8 1

voltage v and the corresponding output voltage of the

ac

inverter v , i.e., 10000

p
inv
V

v = 2 V sin(!t + ) (1) 5000

ac
p ac

) v = 2 V sin(!t +  , )
inv inv
0
0 0.2 0.4 0.6 0.8 1
Alpha
i.e., when  > 0 (p > 0), the inverter output voltage
lags the bus voltage (the capacitor charges), whereas for 6
4
 < 0 (p < 0), the inverter ac voltage leads the bus
deg.

voltage (the capacitor discharges). V is the rms value

inv
0
−2
of the inverter output voltage on the primary side of the −4
0 0.2 0.4 0.6 0.8 1
coupling transformer, i.e.,
Fig. 6. Test system results with detailed STATCOM model.
V =kV
inv dc (2)
4
 x 10
7 Load Power Demand − Phase A In this case, steady-state operation requires a small, pos-
4 itive value  =  , i.e., a small amount of power owing
o
W/phase from the system to supply for the inverter losses, as pre-
2
viously discussed. Thus,  can be determined from the
o

0
following equation:
3 k V sin  = V o
0 0.2 0.4 0.6 0.8 1
Voltage at Bus 2 − Phase A dc
1.5
X ac o
R
1
This equation may also be used to determine the value of
pu

0.5 R from the value of  obtained in the detailed simula-

o

0 tions shown in Figure 6.

0 0.2 0.4 0.6 0.8 1
With the help of a voltage tracking system described in
[15], the inverter is represented in the EMTP as a TACS
x 10
5 Statcom Output Voltage − Phase A

controlled voltage source based on equations (1) and (5);

2

0 all basic  control equations are identical to the ones used

V

in the detailed model. In order to obtain adequate results,

−2
much care must be taken when choosing the values of
k and X , as well as properly initializing the dc voltage
0 0.2 0.4 0.6 0.8 1
Statcom DC Voltage
10000
V . The inverter losses represented by R must also be
dc

modeled in this case in order to be able to obtain similar

5000
results with both the detailed model and the fundamental
V

frequency model. In the results of the simulation for the

0
0 0.2 0.4 0.6 0.8 1 60 Hz model in Figure 7, all results for the same load
Alpha
variation in the test system are similar except in the start-
6 up period due to the \forced" initialization of V , which
dc
4 is not necessary when the detailed model is used. These
deg.

2
0 results fully validate the proposed 60 Hz model.
−2
0 0.2 0.4 0.6 0.8 1
IV. Conclusions
Fig. 7. Test system results with 60 Hz STATCOM model.
This paper presents an operative description and de-
tailed EMTP implementation of a STATCOM. The re-
where V is the average dc voltage on the capacitor, and k
dc sults of using the detailed controllers model for load volt-
is a constant corresponding to the fundamental frequency age control in a test system are used as a benchmark
representation of the inverter output voltage and the total to evaluate the behavior of a proposed 60 Hz, balanced
transformer voltage ratios, e.g., k = 0:9 a, a = V1 =V2, for model with the help of the EMTP. The simulation results
a 12-pulse inverter. demonstrate the validity of the proposed fundamental fre-
If inverter losses are neglected as well, the power bal- quency model, which can be used for transient as well as
ance between the ac and dc sides is given by steady-state power system analyses.
The development of 60 Hz models of FACTS device
3 V XV
ac inv
sin  = V I dc dc (3) is important to allow for a more accurate representa-
tion of these devices in a variety of power system stud-
= C V ddVt dc
dc
ies, so that reliable results can be obtained for integrated
ac/dc/FACTS systems in planning as well as system oper-
Hence, from (2) and (3), it follows that the V voltage dc
ation. Similar models for the SSSC and UPFC, as well as
becomes a nonlinear, dierential function of , i.e., an improved version of the proposed STATCOM model,
so that GTO current limits can be directly represented
dV = 3 k V sin  dc
(4) are being developed.
dt CX ac

Observe that for  > 0 , dV =dt > 0, i.e., the capacitordc References
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dc
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5
 [4] P. G. Therond, P. Cholley, D. Daniel, E. Joncquel, L. La- John Reeve received the B.Sc., M.Sc., Ph.D. and D.Sc. degrees
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Edvina Uzunovic was born in Sarajevo, Bosnia-Herzegovina.
She was graduated from the University of Sarajevo in Electrical
Engineering in 1990. After professional positions in Sarajevo, she
joined the Department of Electrical & Computer Engineering at
the University of Waterloo as a graduate student in 1993, where
she completed her M.A.Sc. degree with a research thesis in voltage
stability of ac/dc transmission systems in 1995, and is currently a
Ph.D. student.
Claudio A. Ca~nizares was born in Mexico, D.F. in 1960. In
April 1984, he received the Electrical Engineer diploma from the
Escuela Politecnica Nacional (EPN), Quito-Ecuador, where he held
dierent positions from 1983 to 1993. His MS (1988) and PhD
(1991) degrees in Electrical Engineering are from the University of
Wisconsin{Madison, where he attended as an EPN, Organization
of American States (OAS) and Fulbright Scholar. Dr. Ca~nizares is
currently an Assistant Professor at the University of Waterloo, De-
partment of Electrical & Computer Engineering, and his research
activities are mostly concentrated in computational, modeling, and
stability issues in ac/dc/FACTS systems. He is a Professional En-
gineer in the province of Ontario, Canada, and an active member
of IEEE, CIGRE and Sigma Xi.