STATCOM Modeling for Voltage and Angle

Stability Studies

Claudio A. Cañizares ∗
University of Waterloo, Dept. Electrical & Computer Eng., Waterloo, ON,
N2L-3G1, Canada

Massimo Pozzi, Sandro Corsi

CESI, Via R. Rubattino 54 , 20134 Milan, Italy

Edvina Uzunovic
New York Power Authority, 123 Main Street, 6th floor, White Plains, NY, 10601,
USA

Abstract

This paper proposes and validates models to accurately represent STATic Syn-
chronous Shunt COMpensators (STATCOM) in voltage and angle stability studies
of powers systems. The proposed STATCOM stability models are justified based
on the basic operational characteristics of this Flexible AC Transmission System
(FACTS) controller for both phase and PWM control strategies. These models are
first validated by means of EMTP simulations on a test system, and then are imple-
mented into two different programs used to study voltage and angle stability issues
in the system. All details of the model implementation, the controls used, and the
data for the test system are provided in the paper.

Key words: STATCOM, FACTS, modeling, voltage stability, angle stability, small
signal stability, transient stability

This work was supported by the Italian Ministry of Industry under the grant
“Ricerca di Sistema” DM 17/04/2001, and by the National Science and Engineering
Research Council (NSERC) of Canada.
∗ Corresponding author.
Email addresses: C.Canizares@ece.uwaterloo.ca (Claudio A. Cañizares),
Pozzi.Massimo@cesi.it (Massimo Pozzi), Edvina.Uzunovic@nypa.gov (Edvina
Uzunovic).

Article to be published in Electrical Power & Energy Systems 25 (2003) 1–20

1 Introduction

The development and use of FACTS controllers in power transmission systems

has led to many applications of these controllers to improve the stability of
power networks [1,2]. Thus, many studies have been carried out and reported
in the literature on the use of these controllers in a variety of voltage and
angle stability applications, proposing diverse control schemes and location
techniques for voltage and angle oscillation control [2].

Several distinct models have been proposed to represent FACTS in static and
dynamic analyses [3]. The current paper concentrates on describing in detail
adequate STATCOM models for these types of studies, based on an energy
balance criterion previously used in the modeling and simulation of this Volt-
age Sourced Converter (VSC)-based controller [4–7]. It is demonstrated here
that the proposed models allow to accurately and reliably represent a STAT-
COM, operating under either phase or PWM control schemes, for voltage and
angle stability studies using power flow, steady state and transient stability
programs, as the models allow for an appropriate representation of the typical
control limits for this controller [5,8,9].

Details of the implementation and use of the STATCOM models proposed here
are discussed in regards to two programs used for steady state and transient
stability analyses of power systems. These programs are UWPFLOW [10], a
program designed for voltage stability analysis of power systems, and EASY5
[11], a program designed for modeling general linear and nonlinear control
systems, and used at ENEL and CESI for model validation studies as well
as steady state and transient stability analyses of sample power systems. The
results of using these programs for the study of the stability of a test system are
presented and thoroughly analyzed here, together with all the data required
to reproduce these results in any simulation program.

Section 2 describes the proposed STATCOM models, based on the fundamen-

tal operation of this controller under both phase and PWM control strate-
gies; improvements of these models with respect to models previously used
to represent this controller in power flow and transient stability studies are
also discussed in this section. In Section 3, the results of implementing the
proposed STATCOM models into two programs used for voltage and angle
stability analyses of a sample system are discussed in detail. Finally, Section
4 summarizes the implementation issues associated with the proposed model
and discusses its limitations.

2
 V δ

I θ Filters

a:1

Vi α

Zero Switching
Crossing PLL Logic

Magnitude
C
α m
(PWM)
Vref Controller
V
dc
PWM
Magnitude

Vdc
ref

Fig. 1. Block diagram of a STATCOM with PWM voltage control.

2 STATCOM Models

The basic structure of a STATCOM with PWM-based voltage controls is

depicted in Fig. 1 [5,8]. Eliminating the dc voltage control loop on this figure
would yield the basic block diagram of a controller with a typical phase angle
control strategy.

The STATCOM models proposed here is based on the power balance equation

P = Pdc + Ploss (1)

which basically represents the balance between the controller’s ac power P

and dc power Pdc under balanced operation at fundamental frequency (these
are the basic assumptions on which steady state and transient stability studies
of power systems are based). For the models to be accurate, it is important
to represent the losses of the controllers (Ploss ), as discussed below; previously
proposed models in [3] do not consider this issue.

PWM controls are becoming a more practical option for transmission system
applications of VSC-based controllers, due to some recent developments on
power electronic switches that do not present the high switching losses of
GTOs [12], which have typically restricted the use of this type of control
technique to relatively low voltage applications. In PWM controls, switching
losses associated with the relatively fast switching of the electronic devices and
their snubbers play an important role in the simulation, as these have a direct
effect on the charging and discharging of the capacitor, and hence should be

3
 V δ

I θ Filters

P+jQ a:1
Magnitude

Vref R+jX

k Vdc α
α
Controller
k (PWM)
PWM Vdc C RC
Vdc
ref
Magnitude

Fig. 2. Transient stability model of a STATCOM with PWM voltage control.

considered in the modeling. The models discussed in this paper assume the
use of PWM control techniques, as these allow for developing more general
models that can readily be adapted to represent other control techniques (e.g.
phase angle control).

2.1 Transient Stability Model

Assuming balanced, fundamental frequency voltages, the controller can be ac-

curately represented in transient stability studies using the basic model shown
in Fig. 2 [5,7]. The p.u. differential-algebraic equations (DAE) corresponding
to this model can be readily written as follows:

 
 ẋc 
 
 
 α̇  = fc (xc , α, m, V, Vdc , Vref , Vdcref ) (2)
 
 
ṁ
V I GC R I2
V̇dc = cos(δ − θ) − Vdc −
C Vdc C C Vdc

4
  
 P − V I cos(δ − θ) 
 
 
 
 
 
 Q − V I sin(δ − θ) 
 
 
 
 
 
 
0= 2
 P − V G + k Vdc V G cos(δ − α) 

 
 
 +k Vdc V B sin(δ − α) 
 
 
 
 
 
 
Q + V2 B −k V V B cos(δ − α) 
 dc 
 
+k Vdc V G sin(δ − α)

where most of the variables are explained on Fig. 2. The admittance G + jB =

(R + jX)−1 is used to represent the transformer impedance and any ac series
filters (e.g. smoothing reactors), whereas GC is used to model the “switching
inertia” of the converter due to the electronic switches and their associated
snubber circuits, which
 have a direct effect on the capacitor voltage dynamics.
The constant k = 3/8 m is directly proportional to the modulation index
m.

The variables xc and functions fc (·) in (2) stand for the internal control system
variables and equations, respectively, and hence vary depending on whether a
PWM or phase control technique is used in the controller. For example, in the
simple PWM voltage controller shown in Fig. 3 [13], the variables and differ-
ential equations associated with the various control blocks directly define xc
and fc (·). Observe that in this PWM controller, the ac bus voltage magnitude
is controlled through the modulation index m, as this has a direct effect on
the VSC voltage magnitude, whereas the phase angle α, which basically deter-
mines the active power P flowing into the controller and hence the charging
and discharging on the capacitor, is used to directly control the dc voltage
magnitude. Note also that the controllers have a bias, which corresponds to
the steady state value of the modulation index mo for the voltage magnitude
controller, and to the phase angle δ of the output voltage of the STATCOM
for the dc voltage controller (this value changes as the system variables change
during the simulation). Although the latter complicates the simulation, it is
needed to guarantee a direct control of the charging and discharging of the
capacitor, which basically depends on the power flow between the VSC and
the ac bus, i.e. it depends on (δ − α). (This can be simplified by setting the
bias of the dc voltage control to the constant value αo = δo , where δo stands
for the bus voltage phase-shift when the STATCOM is not connected [14].)
Typically, the modulation index control would be “faster” than the phase an-
gle control, as there is a significant charging and discharging “inertia” of the

5
 I max

+ K ( 1 + S T1 ) +
Vref m
KD+ S T 2
- +

KM I min mo
ac
1 + S TM
ac

V
Vdc
max

+ KI +
Vdcref KP + α
S
- +

KM Vdc δ
dc min
1 + S TM
dc

Vdc

Fig. 3. Basic STATCOM PWM voltage control.

capacitor due to its relative large value, whereas the modulation index has an
immediate effect on the output voltage of the controller.

The second equation in (2) is the direct result of applying the power balance
equation (1), and allows to represent fairly accurately the dynamics of the dc
voltage in the controller model, as demonstrated in Section 3 for a realistic test
system. The adequate modeling of the Vdc dynamics is important, given the
fact that the time constants associated with the dc voltage on the capacitor
are in the order of the time constants of interest in stability studies. These dc
voltage dynamics are basically defined by the GC parameter in the proposed
model, as its value directly affects the capacitor’s charging and discharging
time constant. The losses and dc voltage dynamics are considered in the models
proposed in [5,7], whereas in the STATCOM model proposed in [3], these are
not fully considered, since GC is not represented in the model, thus introducing
errors in the controller representation as demonstrated here.

The control limits of the controller are directly defined in terms of both the
current limits in the electronic switches, which is the main limiting factor in
VSC-based controllers, and the dc voltage, which is a secondary operational
limit in this controller. This direct implementation of limits allows to closely
duplicate the steady state V-I characteristics of the controller shown in Fig. 4,
as well as allowing for an adequate representation of the basic control limits on
an actual STATCOM [2]. In time domain simulations, the integrator blocks,

6
such as those shown in Fig. 3, are “stopped” whenever the converter current
I or dc voltage Vdc reach a limit. An alternative way of handling these limits
for both PWM and phase control techniques to allow temporary controller
overload is discussed in Section 3. (Another way to simulate these limits is
to determine the values of the modulation index m and phase angle α cor-
responding to the current and dc voltage limits, respectively, by solving the
steady state equations of the converter, as discussed in [14].)

2.2 Steady State Model

The steady state or “power flow” model can be readily obtained from (2) by
replacing the corresponding differential equations with the steady state equa-
tions of the dc voltage and the voltage control characteristics of the STATCOM
(see Fig. 4 [2]). Thus, the steady state equations for the PWM controller are

 
 V − Vref ± XSL I 
 
 
 
 
 
V − V 
 dc dcref 
 
 
 
 
 
 2 2 
 P − GC Vdc − R I 
 
 
 
 
 
 
 P − V I cos(δ − θ) 
 
 
0=


 (3)
 
 
 Q − V I sin(δ − θ) 
 
 
 
 
 
 
P −V 2 G + k V V G cos(δ − α) 
 dc 
 
 
 +k Vdc V B sin(δ − α) 
 
 
 
 
 
 
 Q + V 2 B − k Vdc V B cos(δ − α) 
 
 
+k Vdc V G sin(δ − α)

where on the first equation, the positive sign is used when the device is op-
erating on the capacitive mode (Q < 0) and negative for the inductive mode
(Q > 0), since I ≥ 0.

7
 V

X SL

Vref
(mo ,α o )

Vdc
min

I (Q<0) I Imax I (Q>0)

min
Capacitive Inductive

Fig. 4. Typical steady state V-I characteristics of a STATCOM.

Observe that the controller droop XSL is directly represented on the V-I char-
acteristic curve, with the controller limits being basically defined by its ac
current limits Imax and Imin . Usually, Imax > Imin as the electronic switches
self commutate on the inductive region. Furthermore, Vdcmax and Vdcmin are
typically not an issue on steady state models, given their corresponding rela-
tively high and low values with respect to the typical range of application of
these models.

A phase control technique can be readily modeled by simply replacing the

dc voltage control equation in (3) with an equation for k, i.e. for a 12-pulse
VSC, replace 0 = Vdc − Vdcref with 0 = k − 0.9. In this case, the dc voltage
changes as α changes, thus charging and discharging the capacitor to control
the converter voltage magnitude.

These equations can be directly used to compute the control steady state
values and biases as well as its limits. For example, the modulation index bias
and steady state is determined by setting I = 0, yielding


8 Vref
mo =
3 Vdcref

 
ko

Modulation index and phase-shift control limits corresponding to the con-

troller ac current and dc voltage limits can be readily determined by solving
equations (3) [14].

The limits on the current I, as well as any other limits on the steady state
model variables, such as the modulation ratio represented by k or the voltage

8
 I > I max I < I max & Q > 0 I > I min
I = I max Q>0 Q<0 I = I min
I < I min & Q < 0
o o
Vref >Vref o 0 < Vref < Vref
o
Vref <Vref Vref =Vref o
Vref >Vref

Fig. 5. Handling of limits in the STATCOM steady state model.

phase angle α, can be directly introduced in this model. It is important to

properly represent the control mode switching when these limits are reached,
as this is needed to properly model FACTS controllers in voltage stability stud-
ies [15]. The switching logic depicted in Fig. 5 is proposed here to represent
the steady state control mode switching for the STATCOM, which is mainly
associate with the controller ac current, as previously discussed. When either
maximum or minimum current limits are reached, depending on whether the
controller is operating in the inductive or capacitive region, respectively, volt-
age control is lost; the controller is allowed to recover from its limits when the
voltage is again within the control voltage range as defined by the controller
voltage droop.

The model presented here allows for a more adequate representation in steady
state analysis of the STATCOM than the typical power flow models based
on reactive power source representations of the controller (e.g. [7]). In these
types of models, limits are usually represented through limits in reactive power,
i.e. the STATCOM is basically modeled as a synchronous condenser using a
standard PV bus model. This would somewhat represent the controller current
limits if its terminal voltage is known; however, this is not always the case, as
this voltage depends on control droops, the system conditions, the STATCOM
controlled bus, and other controller limits. Hence, the PV bus model presents
the following limitations:

• The controller droop cannot be readily modeled.

• Certain controller limits, such as limits on the dc voltage, phase angle and/or
modulation ratio cannot be properly represented,
• If the STATCOM controls the voltage at a “remote” bus, the limits in the
reactive power will not adequately model the controller current limits.

The proper representation of control droops and controller limits is of partic-

ular importance in voltage stability studies [16], as controller limits may lead
a power system to voltage collapse problems. These limitations are clearly
illustrated through simulations on a realistic test system in the next section.

9
3 Implementation and Results

The STATCOM model described here was implemented into two software
packages that may be used for the stability analysis of power systems, namely,
UWPFLOW [10] and EASY5 [11]. The results obtained with these programs
were compared with results extracted from [5], where the Electromagnetic
Transient Program (EMTP) is used to validate the proposed model. The de-
tails of the STATCOM model implementation in these programs and the re-
sults obtained from the stability analysis of a realistic test system are discussed
in this section.

3.1 Test System

The test system depicted in Fig. 6 is used here to validate the implementation
of the STATCOM model into the programs UWPFLOW and EASY5 based
on detailed EMTP simulation results.

The EMTP is used in [5] to simulate a detailed switching model of the STAT-
COM operating under phase control, and to compare the results obtained
from this model against those obtained for the controller model described in
Section 2. The results of this comparison are depicted on Fig. 7. A load re-
jection fault is simulated by connecting a large load at Bus 6 at 4.5s, and
then opening breaker 3-5 at 4.65 s. Observe how close the results are for the
“external” variables, i.e. voltage magnitudes and angles, for the detailed and
the reduced models. The “internal” STATCOM variables Vdc and ∆α do not
match exactly, although the general trends are similar, as the switching cannot
be represented in the stability model. Observe that a value of GC = 0, which
basically corresponds to a typical STATCOM stability model [3], yields fairly
different results from those obtained for the detailed switching studies.

All the data and controls required for typical stability studies of the given test
system were extracted from the detailed 3-phase EMTP data of the system,
and are depicted in Figs. 8 and 9, and Tables 1, 2 and 3. It is important
to highlight the fact that the value of GC was carefully chosen to match the
system losses and dc voltage dynamics obtained from the EMTP detailed
switching studies.

3.2 Voltage Stability Results

The program UWPFLOW, as described in [10], is a tool that can be used

to determine the steady state operating conditions of power systems as cer-

10
 Bus 3

1
0
Bus 4 Bus 5 Bus 6

245.5 MW

Generator
0
1
0
1
15 mi

952 MW
13.8 kV 267 Mvar

Bus 1 Bus 2 Bus 8 Bus 9 Bus 10

90 mi 125 mi 15 mi
Transf.
321 MW
Infinite bus Z Thevenin 43 MVar
Filter

230 kV

STATCOM

Fig. 6. Test system.

Detailed Model
Reduced Model
G =0 Model
Gen. Angle [deg.]

C
50

−50
4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6
VBus 4 [p.u.]

0.5

0
4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6
1.5
VBus 10 [p.u.]

1
0.5
0
4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6
15
Vdc [kV]

10
5
0
4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6
10
α [deg.]

−10
4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6
t [s]

Fig. 7. EMTP results for the test system with different models for a phase-controlled
STATCOM.

11
 V4

1
1 + S 0.001

-
+ 750 +
1 Vf
(0.11+S 0.01)(0.17+S 0.95)
- +

1
S 0.04
1+S

Fig. 8. EMTP generator AVR model for the test system.

V8
∆α max= .7145 rad (10o)

-
+ 3.9652 (1.5+S 0.0115) -
1 α
(1+S 0.001)(11+S 0.03)
+

∆α min=-.1745 rad δ
(-10o) 8

Fig. 9. EMTP phase control for the STATCOM in the test system.
Table 1
Generator data in p.u. with respect to a 200 MVA and 13.8 kV base.
Variable Value [p.u./s] Variable Value [p.u./s]
Poles 2 H 2.7113
Ra 0.001096 D 0
Xl 0.15 Td o 6.19488
Xd 1.7 Tqo 0
Xq 1.64 Tdo 0.028716
Xd 0.238324 Tqo 0.07496
Xd 0.18469 Xq 0.185151

tain system parameters change. It can be used to partially study the steady
state stability of these systems, especially the issue of voltage stability with
respect to a variety of system changes (e.g. load changes). UWPFLOW is
basically a continuation power flow program with fairly detailed steady state
models of generators and HVDC links, including some of their control systems
and corresponding limits. It also contains SVC and TCSC controller models
to represent these popular Thyristor Control Reactor (TCR)-based FACTS
controllers in power flow and voltage stability studies [15].

12
Table 2
Transmission system data in p.u. with respect to a 240 MVA base.
Element R X B/2

1-2 0.0003 0.0684 0

2-3 0.0159 0.2275 0.0754
3-8 0.022 0.316 0.1047
4-3 0 0.08 0
5-6 0.0026 0.0379 0.0126
6-7 0 0.12 0
8-9 0.0026 0.0379 0.0126
9-10 0 0.12 0
Filter 0.0087 -4.3 0

Table 3
STATCOM data in p.u. with respect to a 150 MVA and 12 kV base.
Variable Value

R 0
X 0.145
GC 2.16
C 0.0432
k (Phase) 0.9
Vdcref (PWM) 1
Imax 1
Imin 1

The model corresponding to equations (3) was programmed into UWPFLOW,

which was used to obtain the PV curves and maximum loading conditions for
this system as shown in Fig. 10. As expected, the loading margin and voltage
profiles of the system are significantly improved by the introduction of the
STATCOM, especially for the phase control mode, as the dc voltage is free to
change while the current is within its limits, whereas in PWM control mode,
the dc voltage is kept constant at a value that could be considered low for
the test system. In all cases, current limits are reached before the maximum
loading point.

For comparison purposes, the STATCOM was also modeled as a PV bus.

Note that modeling the STATCOM as a PV bus with fixed reactive power
limits (Qmax = −Qmin = 1 p.u. for Imax = Imin = 1 p.u.) does not properly

13
 240

220

200

180

160 No STATCOM
kV BUS 8

With PWM STATCOM

With phase STATCOM
PV STATCOM model
140

120

100

80

60
0 20 40 60 80 100 120 140 160 180 200
L.F. [MVA]

Fig. 10. PV curves obtained with UWPFLOW for the test system with and without
STATCOM.

+
Vdc =1.2 0.25
max
-

Vdc
I max=-1
+ M 1 + S 0.5 - α
0.2 I
N S 0.5
- +

Q/V
+ δ8o
Vdc =0.8 0.25
min
-

Vdc
-Imin=-1
+ M
0.2 A
X
-

Q/V
Vref= 1 +
0.25
-

V8

Fig. 11. STATCOM phase controller in EASY5.

represent the controller for these types of studies, as previously discussed.

14
 Vdc =1.2
-
0.25
max
+
Vdc
Imax
+ M 1 + S 0.01 + m
=-1 0.2 I
N S 0.01
- +

Q/V
- mo
Vdc =0.8 0.25
min
+
Vdc
-Imin=-1
+ M
0.2 A
X
-

Q/V
Vref= 1
+
0.25
-

V8

Vdc = 1 + 1 + S 0.5 - α
0.25
ref S 0.5
- +

Vdc
δ8o

Fig. 12. STATCOM PWM controller in EASY5.

3.3 Transient Stability Results

EASY5 is a program by BOEING used for the simulation of linear and non-
linear control systems [11]. This program allows to graphically represent any
linear and nonlinear control system through the definition of its equations and
associated graphical icons. Linear matrix analysis tools and nonlinear integra-
tion tools allow for the analysis of the steady state as well as the transient
stability of any control system defined by the user. Libraries can be read-
ily developed, so that new systems and elements can be easily defined and
integrated into other simulations. The different element models and the con-
nections between these elements in a given system must be defined together
with the numerical analysis techniques required for its analysis. Thus, as with
SIMULINK-MATLAB, the program can be used to graphically model power
systems. This program has been successfully used at ENEL and CESI to model
and test a variety of power system controllers [17].

The model corresponding to equations (2) for a phase and PWM controllers
were implemented in EASY5. The STATCOM phase and PWM controllers are
depicted in Figs. 11 and 12, respectively. The generator AVR and STATCOM
phase controllers implemented in this program for the test system are not
exactly the same as the ones used in the EMTP, particularly for the STAT-

15
COM phase and PWM controls, which are significantly different from the ones
discussed in Section 2 in the way the limits are implemented. The reason for
these modeling differences, particularly in the implementation of the STAT-
COM limits, is to improve the dynamic voltage control characteristics of the
system controllers, as transient overload of the STATCOM is allowed to im-
prove its dynamic response; this does not affect the steady state behavior of
the controller.

The results of using this program and the corresponding voltage controls to
model the test system fault depicted in Fig. 6 are illustrated in Figs. 13 and
14. As in the EMTP example, a load rejection problem is simulated by sud-
denly applying a large load on Bus 6 at 4.5s, and then disconnecting it at 4.65s
by opening the breaker 3-5. Observe that the results are somewhat similar to
those obtained with the EMTP; however, one cannot expect an exact match,
as the STATCOM controls are basically different and the generator loading
conditions are not exactly the same (there is an approximate 2◦ difference
between the EMTP and ESAY5 simulations in the internal generator angle
at the initial steady state conditions). It is interesting to notice that under
PWM control, the STACOM internal variables, i.e. Vdc and α, show less varia-
tions than under phase control; however, the controlled load voltage basically
presents the same transient response in both cases.

4 Conclusions

The STATCOM transient stability and power flow models proposed in this
paper are basically improved versions of models previously proposed in the
literature. Thus, the current paper concentrates in discussing and justifying
the improvements to these models so that proper voltage and angle stability
studies can be performed on networks that contain this kind of FACTS con-
troller. The implementation of the STATCOM model into a couple of stability
analysis tools, and the results presented and discussed for a simple test system
show how these models can be readily and reliably used for stability studies
of power systems.

The models discussed here are all based on the assumption that voltages and
currents are sinusoidal, balanced, and operate near fundamental frequency,
which are the typical assumptions in transient stability and power flow studies.
Hence, these models have several limitations, especially when studying large
system changes occurring close to FACTS controllers:

(1) These models cannot be reliably used to represent unbalanced system

conditions, as they are all based on balanced voltage and current condi-
tions.

16
 Generator Phase Angle
0.425
0.4
0.375

radians
0.35
0.325
0.3
0.275
4 4.5 5 5.5 6
s
Generator Terminal Voltage
1.02

0.98
p.u.

0.96

0.94

0.92
4 4.5 5 5.5 6
s
Generator Active Power
1
0.95
0.9
0.85
p.u.

0.8
0.75
0.7
4 4.5 5 5.5 6
s

Load Voltage
1.11
1.08
1.05
1.02
p.u.

0.99
0.96
0.93
0.9
4 4.5 5 5.5 6
s
Statcom DC Voltage
9.3
9
8.7
kV

8.4
8.1
7.8
7.5
4 4.5 5 5.5 6
s
Alpha
0.02

0.01
radians

-0.01

-0.02
4 4.5 5 5.5 6
s

Fig. 13. Fault simulation results obtained with EASY5 for the STATCOM operating
under phase control.

17
 Generator Phase Angle
0.425
0.4
0.375

radians
0.35
0.325
0.3
0.275
4 4.5 5 5.5 6
s
Generator Terminal Voltage
1.02

0.98
p.u.

0.96

0.94

0.92
4 4.5 5 5.5 6
s
Generator Active Power
1
0.95
0.9
0.85
p.u.

0.8
0.75
0.7
4 4.5 5 5.5 6
s

Load Voltage
1.11
1.08
1.05
1.02
p.u.

0.99
0.96
0.93
0.9
4 4.5 5 5.5 6
s
Statcom DC Voltage
8.6
8.4
8.2
kV

8
7.8
7.6
7.4
4 4.5 5 5.5 6
s
Alpha
0.02

0.01
radians

-0.01

-0.02
4 4.5 5 5.5 6
s

Fig. 14. Fault simulation results obtained with EASY5 for the STATCOM operating
under PWM control.

18
(2) Large disturbances that yield voltage and/or currents with high har-
monic content, which is usually the case when large faults occur near
power electronics-based controllers, cannot be accurately studied with
these models, as they are all based on the assumptions of having sinu-
soidal signals.
(3) The above also applies for cases where voltage and current signals undergo
large frequency deviations.
(4) Internal faults as well as some of the internal variables of the controller
cannot be reliably represented with these models.

For all of these cases, detailed EMTP types of studies are required to obtain
reliable results. It is important to highlight the fact that these limitations
also apply to most models typically used to represent a variety of devices and
controllers in transient stability and power flow studies.

References

[1] N. G. Hingorani, Flexible AC Transmission Systems, IEEE Spectrum (1993)

40–45.

[2] FACTS Applications, Technical report 96TP116-0, IEEE PES (1996).

[3] Modeling of Power Electronics Equipment (FACTS) in Load Flow and Stability
Programs: A Representation Guide for Power System Planning and Analysis,
Technical brochure no. 145, TF 38-01-08, CIGRE (Aug. 1999).

[4] C. Schauder, H. Mehta, Vector Analysis and Control of Advanced Static Var
Compensators, IEE Proceedings–C 140 (4) (1993) 299–306.

[5] E. Uzunovic, C. A. Cañizares, J. Reeve, Fundamental Frequency Model of

Static Synchronous Compensator, in: Proc. North American Power Symposium
(NAPS), 1997, pp. 49–54, Laramie, Wyoming.

[6] E. Uzunovic, C. A. Cañizares, J. Reeve, Fundamental Frequency Model of

Unified Power Flow Controller, in: Proc. North American Power Symposium
(NAPS), 1998, pp. 294–299, Cleveland, Ohio.

[7] D. N. Koseterev, Modeling Synchronous Voltage Source Converters in

Transmission System Planning Studies, IEEE Trans. Power Delivery 12 (2)
(1997) 947–952.

[8] C. Schauder, M. Gernhardt, E. Stacey, T. Lemak, L. Gyugyi, T. W. Cease,

A. Edris, Development of a ±100 MVAr Static Condenser for Voltage Control
of Transmission Systems, IEEE Trans. Power Delivery 10 (3) (1995) 1486–1493.

[9] P. Rao, M. L. Crow, STATCOM Control for Power Applications, in: Proc. North
American Power Symposium (NAPS), 1997, pp. 172–178, Laramie, Wyoming.

19
[10] C. A. Cañizares, UWPFLOW: Continuation and Direct Methods to Locate
Fold Bifurcations in AC/DC/FACTS Power Systems, University of Waterloo,
available at www.power.uwaterloo.ca (Sep. 2000).

[11] EASY5 User’s Guide, Program’s manual, BOEIGN (Jul. 1989).

[12] P. K. Steimer, H. E. Gruning, J. Werninger, E. Carrol, S. Klaka, S. Linder,

IGCT-A New Engineering Technology for High Power, Low Cost Inverters,
IEEE Industry Applications Magazine (1999) 12–18.

[13] E. Uzunovic, C. A. Cañizares, J. Reeve, EMTP Studies of UPFC Power

Oscillation Damping, in: Proc. North American Power Symposium (NAPS),
1999, pp. 405–410, San Luis Obispo, California.

[14] C. A. Cañizares, Modeling and Implementation of TCR and VSI Based FACTS
Controllers, Internal report, ENEL and Politecnico di Milano, Milan, Italy (Oct.
1999).

[15] C. A. Cañizares, Z. T. Faur, Analysis of SVC and TCSC Controllers in Voltage

Collapse, IEEE Trans. Power Systems 14 (1) (199) 158–165.

[16] Voltage Stability Assessment: Concepts, Practices and Tools, Power System
Dynamic Performace Committee special publication, IEEE/PES, Available at
www.power.uwaterloo.ca (Aug. 2002).

[17] M. Pozzi, Implementation of Dynamic Models and Controls for HVDC and
FACTS Systems: The Macro Components of the Power System Library in the
Simulation Tools Easy5x from Boeing, Report no. 99/594, ENEL Ricerca, Area
Trasmissione e Dispacciamento (Dec. 1999).

20