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

gcakir42@students.tntech.edu

Kenan Hatipoglu

Electrical and Computer

Engineering Department

Tennessee Technological

University Cookeville, TN

38505

khatipogl42@students.tntech.edu

Ghadir Radman

Electrical and Computer

Engineering Department

Tennessee Technological

University Cookeville, TN

38505

gradman@tntech.edu

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