Abstract— Power system oscillation is one of the major problems in power system operation. If not damped, these oscillations can grow and decrease transmission capacity of the lines which may cause interruption in energy supply. Several methods for damping of these oscillations are reported in literature. Traditionally, these oscillations have been damped by power system stabilizers. Recently, FACTS devices such as static synchronous compensator (STATCOM) equipped with a power oscillation damper (POD) have been also efficiently used for damping oscillation. It should be noted that, the main objective of STATCOM is to regulate voltage at its terminal by changing the amount of reactive power exchanges with the power system and POD is a secondary function provided by this device. This paper proposes the application of the residue factor method to obtain the best location of STATCOM for damping oscillations. The residue factor used is related the critical oscillatory modes. Also presented in this paper is a comparison of power system stabilizer (PSS) and STATCOM for the enhancement of oscillations damping. IEEE 14-Bus test system was used to demonstrate the effectiveness of the proposed method for placement and the comparison of PSS and STATCOM on damping oscillations. From the simulation results it is seen that STATCOM has better ability in damping oscillation when compared to PSS.
Index Terms—Power System Oscillation, Static Synchronous
Compensator, Power System Stabilizer, FACTS
I. INTRODUCTION
Power system stability problem is usually associated with
insufficient damping of oscillations. Power system oscillations
are usually in the range between 0.1 and 2 Hz depending on
number of the generators in a system, and can be classified as
local and inter-area oscillations. In local mode oscillations,
with a frequency between 1.0 and 2.0 Hz, one generator
oscillate against the rest of the system while inter-area
oscillations, with a frequency 1.0 Hz and less, are related to
the phenomenon where synchronous generators in one area
oscillate with the ones in another area.
The traditional approach to damp out inter-area and local
oscillations is to install PSS that provides supplementary
control action through the generator excitation system. PSSs
are widely used to damp out local and inter-area modes of
oscillations [1, 2]. Power utilities worldwide have been using
PSS as an effective excitation controller in order to enhance
the system stability [4]. However, there have been problems
experienced with PSS over the years of operation. Some of
these problems were owing to the limited capability of PSS as
it is capable of damping only local modes of
electromechanical oscillations. Furthermore, PSS can result in
great variations in the voltage profile under severe
disturbances. They may even lead to leading power factor
operation, and losing stability [5].
In addition to providing reactive power, and voltage
control, flexible AC transmission system (FACTS) controllers
equipped with supplementary controllers effectively damp out
power system oscillations. In this work, Power Oscillation
Damper (POD) was applied to STATCOM as a supplementary
controller. FACTS controllers sometimes are found to provide
much better damping for inter-area mode of oscillations than
the PSSs [3]. Shunt FACTS controllers, such as Static Var
Compensator and STATCOM, are capable of damping power
swing mode effectively [6].
This paper deals with two aspects. One aspect is to
determine the best location of STATCOM in order to damp
out oscillations. The other aspect is to make a comparison
between STATCOM and PSS for their effectiveness in
enhancing damping oscillation. The first aspect is studied with
the help of residue method presented in [7], where the method
is applied to STATCOM. The second aspect is evaluated
using simulation program called Power System Analysis
Toolbox (PSAT).
This paper is structured as follows: section II presents
STATCOM unit; section III presents residue method; section
IV presents POD controller design approach; section V
presents power system stabilizer model; section VI presents
simulations and results, and section VII concludes the paper.
II. STATCOM UNIT
STATCOM is a shunt-connected reactive power
compensation device. It is a device used to provide voltage
support to the system by injecting or absorbing reactive power
to/from the system. Fig. 1 shows the main three components
of a STATCOM: voltage source converter (VSC) with a
capacitor in the DC side, coupling transformer, and the control
system. The relation between the AC system voltage and the
voltage at the STATCOM AC side terminals provide the
Determination of the Best Location and Performance
Analysis of STATCOM for Damping Oscillation
Gokhan Cakir
Electrical and Computer
Engineering Department
Tennessee Technological
University Cookeville, TN
38505
Kenan Hatipoglu
Electrical and Computer
Engineering Department
Tennessee Technological
University Cookeville, TN
38505
Ghadir Radman
Electrical and Computer
Engineering Department
Tennessee Technological
University Cookeville, TN
38505
978-1-4799-0053-4/13/$31.00 ©2013 IEEE
control of reactive power flow. If the voltage at the
STATCOM terminals is higher than the system voltage,
reactive power will be injected from STATCOM to the system
and STATCOM will work as a capacitor. When the voltage at
the STATCOM is less than the AC voltage, STATCOM will
work as an inductor, and reactive power flow will be reversed.
[9]
Phase Locked Loop
PI VSC
AC SystemBus
1V
tjX
d cIcR
C
dcV
Q
refQ
Fig. 1. STATCOM Model
STATCOM tries to keep the bus terminal voltage close to a
set reference value by controlling the AC side voltage of the
VSC through a PI-control. Under normal operating condition,
both voltage phasors will be equal and there will be no active
power exchange between the STATCOM and the system [9].
The STATCOM equations in d-q reference frame are
summarized as follows [8]:
where and are the d-axis, and q-axis STATCOM
current components, , are the resistance and leakage
reactance of the coupling transformer, is the capacitor
voltage, represent the leakage resistance of the electronic
component, and is the angular frequency [9].
The reactive output power of the compensator is varied to
control the voltage at connection point in order to keep the
voltage within the permissible limits. STATCOM can provide
reactive power almost instantly via controlling the VSC firing
angle and hence improving system transient stability [9].
III. RESIDUE METHOD
Mathematical model of the overall dynamic system is
expressed using a set of non-linear differential equations as
follows:
(4)
The overall linearized system model including STATCOM
is represented by the following equation:
(5)
(6)
where b and c are the column–vector input matrix and the
row-vector output matrix, respectively. is the measured data
which is active power flow deviation, and is the input data
such as VSC firing angle. Assuming Λ, , and ψ are the
diagonal matrix of eigenvalues and matrices of right and left
eigenvectors, respectively; then we have:
(7)
(8)
(9)
The modal controllability and modal observability matrices
are expressed as follows:
(10)
(11)
A mode is uncontrollable if the corresponding row of the
matrix is zero. A mode is unobservable if the corresponding
column of the matrix is zero. If a mode is either
uncontrollable or unobservable, feedback between the input
and output will have no effect on the mode [10]. The open
loop transfer function of the system is as follows:
(12)
can be expanded using partial fractions in terms of c
and b vectors, and the right and left eigenvectors are as
follows [10]:
(13)
where N is the total number of eigenvalues.
Each term of the summation in the numerator is a scalar
called residue. can be expressed as follows:
(14)
Where and denote the right and left eigenvectors
respectively associated with the ith
eigenvalue [7]. This can be
considered in terms of mode controllability and observability.
The modal controllability is as follows:
(15)
The modal observability is as follows:
(16)
According to (15) and (16), (17) can be expressed as follows:
(17)
The residue of a particular mode i gives the
measurement of that mode’s sensitivity to a feedback between
the output y and the input u for a SISO system. The residue is
the product of the mode’s observability and controllability [7].
A. Eigenvalue Analysis
Stability issue can be analyzed by studying the eigenvalues.
An operating point is stable if all of the eigenvalues are on the
left-hand side of the imaginary axis of the complex plane;
otherwise it is unstable [11]. Let be the ith
eigenvalue of the state matrix A. The real parts of the
eigenvalues give the damping, and the imaginary parts give
the frequency of oscillation. If a real eigenvalue is negative,
the associated mode decays over time. The larger the
magnitude of the mode, the quicker it decays. On the other
hand, if one of the real eigenvalues is positive, the
corresponding mode is unstable [12]. Given the state matrix A
is real, the complex eigenvalues always occur in conjugate
pairs. Conjugate complex pair eigenvalues
correspond to an oscillatory mode. A pair with a positive
represents an unstable oscillatory mode because these
eigenvalues yield an unstable time response of the system. In
contrast, a pair with a negative represents a stable
oscillatory mode. The damping ratio is calculated by:
(18)
Generally, the oscillatory modes having damping ratio less
than 3% are said to be critically or poorly damped oscillatory
modes, and eigenvalues corresponding to these damping ratios
are called dominant modes because their contribution
dominates the time response of the system. However, in power
systems, states are considered to be well damped if the
damping ratio for all eigenvalues is greater than 5% [11].
IV. FACTS POD CONTROLLER DESIGN
Fig. 2 represents a power system including STATCOM
unit and POD controller. POD is used as a feedback
controller. Active power flow deviation which is local signal
has been used as the feedback signal for STATCOM
supplementary controller (POD). When applying the feedback
control, eigenvalues of the system are changed. The change of
the eigenvalues must be directed towards the left half complex
plane for damping improvement [10]. The movement can be
achieved with a transfer function consisting of an
amplification block, a wash-out block, and stage of lead-
lag blocks [10].
Fig. 2. Power system with POD control
Transfer function of the POD controller [10] is
(19)
where K is a positive constant gain, and is the transfer
function of the wash-out, and lead-lag blocks. The washout
time constant, is usually equal to 5-10 s. [10]. The lead-lag
parameters are determined in [10] as follows:
(20)
,
where is the corresponding critical mode number,
denotes phase angle of the residue , is the frequency of
the critical mode to be damped in rad/sec, is the number of
compensation stages (usually =2) [10]. The controller gain
is computed in [10] as follows:
(21)
V. POWER SYSTEM STABILIZER MODEL
PSSs are typically used for damping power system
oscillation. Many different models have been proposed in the
literature for PSS. All models accept the rotor speed, the
active power, and the bus voltage magnitude as input signals.
PSS is connected to the Automatic Voltage Regulator (AVR)
[13]. In this study, PSS type II [13] is used.
The PSS Type II is depicted in Fig. 3, and is described by
the following equations [13]:
(22)
(23)
(24)
(25)
The PSS output signal is the state variable , which
modifies the reference voltage of the AVR. The output signal
is subjected to an anti-windup limiter and its dynamic is
given by a small time constant = 0.001 [13].
Fig. 3. Power System Stabilizer Type II
VI. SIMULATION AND RESULTS
The performance of STATCOM and PSS have been
verified on IEEE 14 Bus test system [13] shown in Fig. 4, and
the results are presented in this section.
Fig. 4. IEEE 14 bus test system
Each generator of the test system is equipped with the
AVR Type II which is the simplest AVR model that can be
used for rough stability evaluations [13]. The generator is
described by six order non-linear mathmetical model while
exciter by third order. The sixth order model of generator is
obtained assuming the presence of a field circuit and an
additional circuit along the d-axis and two additional circuits
along q-axis. The generator state variables are
while exciter has the following state
variables [13]. The state variables are also defined
in [14]. Eigenvalue analysis was obtained in PSAT, and the
results are calculated for three different cases: no controller,
with PSS, and with STATCOM. Table I gives the eigenvalues
and damping ratios for the critical mode.
The placement of PSS is determined based on the dominant
eigenvalues and their damping ratios. As mentioned earlier,
the damping ratio must not be less than 5%. Moreover, all the
real eigenvalues must be on the left hand side of the real axis
of a complex plane. According to Table I, modes associated to
machine-1 (e1q_Syn_1, vf_Exc_1) appear to have a small
damping ratio of 0.0072; therefore, best location for PSS is at
machine-1.
TABLE I
EIGENVALUE ANALYSIS OF THE CASE STUDY NETWORK
Critical Mode
States
Dominant
Eigenvalue
Damping
Ratio
No Controller e1q_Syn_1,
vf_Exc_1 -0.05858±8.1392i 0.0072
With PSS e1q_Syn_1,
vf_Exc_1 -2.3862±14.1743i 0.1660
With
STATCOM
e1q_Syn_1,
vf_Exc_1 -1.5439±8.2249i 0.1845
where e1q_Syn_1 is q-axis voltage of generator-1, and
vf_Exc_1 is field voltage of generator-1.
Table II shows the residue values for different cases where
in each case a STATCOM is connected to the bus shown in
first column of the Table II . The largest residue indicates the
most effective location of STATCOM device [10]. According
to Table II, the best place for STATCOM is Bus number 2
since it has the highest residue value.
TABLE II RESIDUE VALUES DUE TO CORRESPONDING STATCOM LOCATION
Bus No Residues
1 0.0003024
2 0.2031
3 0.1150
4 0.0723
5 0.1221
6 0.0097
7 0.011
8 0.003
9 0.012
10 0.0069
11 0.0042
12 0.0022
13 0.0043
14 0.0035
The damping ratio of the base case is 0.0072 (0.72%) which
is relatively low. The eigenvalue pair of -0.05858±8.1392i
corresponding to critical mode for this system is the poorly
damped oscillatory mode. Table I demonstrates that adding
STATCOM controller to the power system increases the
damping ratio to 0.1845 (18.45%) while adding a PSS to the
system increase the damping ratio to 0.1660 (16.60%) for
critical mode. It is obvious that STATCOM has been proven
to be of better ability in damping oscillation when compared
to PSS.
A. Performance Evaluation of the System
In order to test the best location, simulation of the system
was performed using PSAT. A three phase fault was applied at
Bus 5 in order to observe the impacts of STATCOM and PSS
devices on damping oscillation. It is observed from Fig. 5 that
the oscillation are damped out in about 4s with STATCOM
placement, which is quite less when compared with the PSS
placement. Fig. 6 shows the frequency at generator-4 for three
diferent case. Similarly, Fig. 6 proves that STATCOM has
better ability than PSS.
Fig. 5. Voltage response at Bus 1 with three phase fault
Fig. 6. Frequency at Generator 4 with three phase fault
VII. CONCLUSION
This paper studied STATCOM placement using residue
method, and compared the performance of STATCOM and
PSS using small signal analysis.
The best placement of STATCOM is obtained by using
residue method. The IEEE 14 Bus test system was used for the
study. Eigenvalues of the test system were computed in order
to find poorly damped oscillatory mode. A supplementary
controller called POD was designed for STATCOM.
The results show that STATCOM is more effective in
damping oscillation when compared with power system
stabilizer (PSS). All of the simulations were performed using
Power System Analysis Toolbox (PSAT) in MATLAB
environment.
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0 2 4 6 8 10 12 14 16 18 20
1.055
1.06
1.065
1.07
1.075
1.08
Time (s)
Vo
ltag
e (
pu
)
No Controller
With PSS
With STATCOM
0 1 2 3 4 5 6 7 8 9 10
0.9985
0.999
0.9995
1
1.0005
1.001
1.0015
Time (s)
Fre
qu
en
cy (
pu
)
No Controller
With PSS
With STATCOM
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