This article was downloaded by: [Eastern Michigan University]On: 11 October 2014, At: 08:20Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Electric Power Components and SystemsPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/uemp20

Static Synchronous CompensatorDamping Controller Design Using FastOutput Sampling Feedback TechniqueVinay Pant a , Biswarup Das a & Annapurna Bhargava ba Department of Electrical Engineering , Indian Institute ofTechnology Roorkee , Roorkee, Indiab Department of Electrical Engineering , Rajasthan TechnicalUniversity , Kota, IndiaPublished online: 18 Nov 2009.

To cite this article: Vinay Pant , Biswarup Das & Annapurna Bhargava (2009) Static SynchronousCompensator Damping Controller Design Using Fast Output Sampling Feedback Technique, ElectricPower Components and Systems, 37:12, 1348-1364, DOI: 10.1080/15325000903055289

To link to this article: http://dx.doi.org/10.1080/15325000903055289

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.

This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Electric Power Components and Systems, 37:1348–1364, 2009

Copyright © Taylor & Francis Group, LLC

ISSN: 1532-5008 print/1532-5016 online

DOI: 10.1080/15325000903055289

Static Synchronous Compensator Damping

Controller Design Using Fast Output Sampling

Feedback Technique

VINAY PANT,1 BISWARUP DAS,1 and

ANNAPURNA BHARGAVA2

1Department of Electrical Engineering, Indian Institute of Technology

Roorkee, Roorkee, India2Department of Electrical Engineering, Rajasthan Technical University,

Kota, India

Abstract In this article, the design of a damping controller for a static synchronouscompensator using a fast output sampling feedback technique is presented. The pro-

posed technique needs only the information of locally available signals, and moreover,by this technique, a very simple controller in the form of a simple gain matrix

is obtained, which is effective over a range of operating conditions. Because ofthese two reasons, the control system designed by the proposed technique is very

easy to implement. The effectiveness of the proposed technique has been validatedthrough detailed non-linear simulation studies on the 10-machine 39-bus New England

system.

Keywords static synchronous compensator, damping control, fast output samplingfeedback technique

1. Introduction

Owing to various reasons, such as the ever-increasing demand of electric power, dereg-

ulation, restriction on construction of new transmission corridors, today’s modern power

system is forced to carry a large amount of power, thereby operating in a much stressed

condition. Under this stressed condition, power transfer between two areas over a tie line

is often restricted by low-frequency inter-area oscillations in the power system [1, 2],

which, in turn, threaten the power system security. Traditionally, power system stabilizers

(PSSs) have been applied [3] to damp out the low-frequency oscillations. However, a

PSS is generally most effective in damping local modes [4], but in certain cases, it is not

sufficient to provide the necessary damping for inter-area oscillations. Therefore, for en-

hancing power system security, the development of the most effective method of damping

the inter-area mode of low-frequency oscillation is still a major area of research today.

Now, in the last decade and and a half, power electronic device based equipment,

commonly known as flexible AC transmission system (FACTS) controllers [5], have been

implemented in various parts of the world to achieve better utilization of the existing

Received 2 January 2009; accepted 15 April 2009.Address correspondence to Dr. Vinay Pant, Department of Electrical Engineering, Indian

Institute of Technology Roorkee, Roorkee, 247 667, India. E-mail: vpantfee@gmail.com

1348

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

STATCOM Damping Controller Design Using FOSFT 1349

power grid. These controllers make the transmission system more flexible in terms

of controlling active/reactive power transfer and the voltage profile of power systems.

Because of their fast power control capability, these FACTS controllers can be used

effectively to damp out the inter-area oscillations. They also provide added flexibility

that enables a line to carry an amount of power close to its thermal rating and, therefore,

are becoming an integral component of modern power transmission systems.

Among the various FACTS controllers, the static synchronous compensator (STAT-

COM) is one of the most prominent devices. It is basically shunt-connected equipment

whose main objective is to control the bus voltage. However, by using the voltage

controller only, the STATCOM may not be able to effectively damp out the inter-

area oscillations and, in some cases, may even aggravate the problem [6, 7]. Therefore,

the design of an auxiliary damping controller is often needed, which would provide a

superimposed damping signal to its voltage loop [6].

Because of the above requirement, researchers around the world have paid attention

to the problem of damping controller design for STATCOMs in the recent past. The

different control schemes, which have been suggested to improve power system damping

using a STATCOM, can be broadly classified as:

� conventional techniques,

� linear system theory based techniques,

� non-linear control techniques, and

� artificial intelligence (AI) and optimization-based techniques.

A conventional root locus method based technique was suggested in [8] for designing

a STATCOM damping controller. The developed control strategy has been validated

on the two-area four-machine system using only a simplified second-order generator

model. Several linear control techniques, such as combined state and output feedback [9],

two-state multi-modal linear matrix inequality (LMI) approach based output feedback

technique [10], robust control techniques [11, 12], H2-norm-based approach [13], have

also been reported in the literature. While a single-machine infinite-bus (SMIB) system

for the validation of the developed control strategies was used in [9, 11], a two-area

four-machine system has been adopted in [10, 12, 13] for testing the performance of the

proposed control schemes.

Different non-linear control strategies, such as direct feedback linearization [14],

variable structure control [15], cascaded controller architecture based multi-variable non-

linear control strategy [16], have also been developed in the literature. In [14, 16],

the controller performance was tested on an SMIB system, while in [15], a two-area

two-generator system was used for validating the controller. Moreover, in [16], a PSS

was also used along with the STATCOM. In [17, 18], studies were carried out to

evaluate the additional damping provided by a STATCOM based on the rate of dissipation

of the transient energy in the post-fault period. While in [17], a remote signal was used

for controlling the STATCOM current, in [18], the author hinted that the developed

method was aimed only for the determination of additional damping provided by a

STATCOM.

Apart from the different mathematical control techniques, various AI- and optimi-

zation-based techniques, such as the adaptive critic [19, 20], fuzzy logic [21, 22], the

artificial neural network (ANN) [23], as well as the genetic algorithm (GA) [24, 25]

and simulated annealing [26], have also been proposed in the literature for designing

the damping controller for a STATCOM. In [19, 20], a 3-machine 12-bus system was

used for validating the performance of the developed strategies. In [19], using remote

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

1350 V. Pant et al.

machine speed signals as inputs, a multi-input, single-output (MISO) damping controller

was designed, while in [20], a multi-input multi-output (MIMO) wide-area controller

employing global measurements was developed. In [21], a Takagi-Sugeno (TS) fuzzy

controller scheme was developed and tested on the two-area four-machine system having

PSSs on all the generators. In [22], multiple fuzzy controllers were used for a STATCOM

damping control design which has been validated on the two-area four-machine system.

A neuro sliding-mode STATCOM damping controller was designed and tested on the

two-area four-machine system having PSSs on all the generators in [23]. A comparative

study of the performances of the Lavenberg-Marquardt (LM) algorithm and the GA for

the optimal coordinated design of a PSS and STATCOM damping controller was reported

in [24]. A 16-machine 68-bus system having PSSs on all the machines and a STATCOM

was used for the study. In [25], a real-coded genetic algorithm (RCGA) was used for

the optimized design of a STATCOM damping controller, and the developed method was

tested on an SMIB system. Another coordinated optimal design of a PSS and STATCOM

damping controller was reported in [26], in which a modified simplex simulated annealing

technique was used; the developed controller was validated on the 10-machine 39-bus

system having multiple PSSs.

Careful review of the different control strategies proposed in the literature reveals that

many techniques have been validated on relatively smaller test systems (SMIB or two-

area four-machine system). The techniques validated on larger systems have either used

(a) PSSs on all the machines, (b) multiple FACTS devices, or (c) multiple remote input

signals. Moreover, in many instances, the effectiveness of the proposed control schemes

have not been adequately evaluated over a range of operating conditions. Therefore,

there is still a need for developing a STATCOM control strategy that is simple, easy to

implement, utilizes only locally available input signals, has proven stability properties,

and is effective over a range of operating conditions. Also, the developed technique should

not require any other stabilizing device, such as a PSS or other FACTS device, for stability

improvement. For this purpose, in this article, the use of fast output sampling feedback

technique (FOSFT) is proposed for designing a damping controller for a STATCOM. As

already shown in [27, 28], the controller designed by the FOSFT has a simple structure,

i.e., the controller is essentially a simple gain matrix that can be made effective over

a range of operating conditions. In the literature, this technique has been applied for

designing PSSs for the SMIB system [28] and the multi-machine system [29]. While the

standard FOSFT was followed in [28], a de-centralized design of a PSS was carried out

in [29], in which a very simple modification of the standard FOSFT was proposed so that

any particular PSS would require the necessary information only from the corresponding

machine. However, to the best of knowledge of the authors, the application of this

technique has yet not been reported for designing a damping controller for a STATCOM

in the literature.

Following the above discussion, this article attempts to design a FOSFT-based damp-

ing controller for a STATCOM. Moreover, for maximizing the effect of the damping

controller, a procedure for choosing the proper STATCOM location and the suitable

local stabilizing signal has also been proposed. The article is organized as follows. In

Section 2, a brief description of the FOSFT is given. The linearized model of power

system with a STATCOM is presented in Section 3. A description of the procedure

adopted for selection of the proper STATCOM location and appropriate local stabilizing

signal is given in Section 4. Finally, the performance evaluation of the designed controller

through non-linear simulation on the 10-machine 39-bus system is presented, and the

relevant conclusions are derived in Sections 5 and 6, respectively.

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

STATCOM Damping Controller Design Using FOSFT 1351

2. FOSFT

In this technique, the output is sampled several times during one input sampling period,

and the control law is constructed from these output samples. It has been shown by

Werner and Furuta [27] that it is possible to arbitrarily assign the system poles of a

discrete-time linear time invariant (LTI) system using the FOSFT, and it also ensures

the stability of the ensuing closed-loop system. Consider a plant described by Eqs. (1)

and (2):

Px D Ax C Bu; (1)

y D Cx; (2)

such that .A; B/ is controllable and .C; A/ is observable. The plant is assumed to be

sampled with a sampling time � and zero-order hold. Assume that a state feedback gain

F exists, such that the closed-loop system

x.k� C �/ D .ˆ� C � � F/x.k�/ (3)

is stable and has no poles at the origin [27]. The objective of FOSFT is to realize the

effect of the state feedback gain F by output feedback, as described below. Let � D �=N ,

where N is the number of sampling subintervals of sampling time � . Now define

u.t/ D ŒL0 L1 � � � LN�1�

2

6

6

6

6

4

y.k� � �/

y.k� � � C �/

:::

y.k� � �/

3

7

7

7

7

5

D Lyk (4)

for k� � t � .k C 1/� , where matrix L represents output feedback gains. 1=� is the rate

at which the loop is closed, but the output sampling is N times faster at rate 1=� [27].

Discretizing the continuous system at the rate 1=�, the discrete-time system having the

input uk D u.k�/, state xk D x.k�/, and output yk at time t D k� are obtained as

follows:

xkC1 D ˆ� xk C � �uk ; (5)

ykC1 D C 0xk C D0uk ; (6)

where

C 0 D

2

6

6

6

6

4

C

Cˆ

:::

CˆN�1

3

7

7

7

7

5

; D0 D

2

6

6

6

6

6

6

6

6

4

0

C�

:::

C

N�2X

j D0

ˆj�

3

7

7

7

7

7

7

7

7

5

:

Now, assume that the state feedback gain F has been designed such that .ˆ� C �� F/ has

no eigenvalues at the origin. Then we have

u.t/ D Fx.k�/ (7)

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

1352 V. Pant et al.

during the intervals k� � t � .k C 1/� . From Eqs. (5)–(7), the fictitious measurement

matrix [28] can be obtained as follows:

Cm.F; N / D .C 0 C D0F/.ˆ� C � � F/�1 : (8)

Equation (8) satisfies the fictitious measurement equation

yk D Cmxk: (9)

From Eqs. (4), (7), and (9), it can be shown that for the feedback gain matrix L to

realize the effect of state feedback gain F, the following condition should be satisfied:

LCm D F: (10)

Now, as mentioned in [28], if � is the observability index of .ˆ; �/, then it is

possible to show that for N � �, generically Cm has full column rank, and as a result,

it is possible that any state feedback gain can be realized by the fast output sampling

gain L. Also, if the initial state is unknown, there may be an error �uk D uk � Fxk in

constructing the control signal under state feedback. Under this condition, the closed-loop

dynamics, as shown in Eq. (11), is obtained [28]:

"

xkC1

�ukC1

#

D"

ˆ� C � �F � �

0 LD0 � F� �

# "

xk

�uk

#

: (11)

With the notations above and following the same arguments as discussed in [28], the

following inequalities are solved for computing the gain matrix L:

kLk < �1; (12)

kLD0 � F� �k < �2; (13)

kLCm � Fk < �3: (14)

Equations (12)–(14) can be rewritten in the form of LMI, as given in Eqs. (15)–(17):

"

��21I L

LT �I

#

< 0; (15)

"

��22I .LD0 � F� � /

.LD0 � F� � /T �I

#

< 0; (16)

"

��23I .LCm � F/

.LCm � F/T �I

#

< 0: (17)

By solving the above LMIs, the gain matrix L for the controller would be obtained,

which would stabilize the plant at the given operating point.

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

STATCOM Damping Controller Design Using FOSFT 1353

3. Mathematical Model of Multi-machine System Installedwith STATCOM

Consider an m-machine, n-bus power system in which a STATCOM is assumed to be

installed at bus number s, as shown in Figure 1. Without any loss of generality, it is also

assumed that the m generators are connected at bus numbers 1; 2; : : : ; m. The detailed

equations, in p.u., for the machines, STATCOM, and network are as follows.

Machine differential equations [30]:

dıi

dtD !i � !s; (18)

d!i

dtD !s

2Hi

ŒTmi � E 0

qi Iqi � .x0

qi � x0

di /Idi Iqi � E 0

di Idi � Di .!i � !s/�; (19)

dE 0

qi

dtD 1

T 0

doi

ŒEfdi � E 0

qi � .xdi � x0

di /Idi �; (20)

dE 0

di

dtD 1

T 0

qoi

Œ�E 0

di C .xqi � x0

qi /Iqi �; (21)

dEfdi

dtD 1

TEi

Œ�.SEi.Efdi / C KEi /Efdi C VRi �; (22)

dRf i

dtD 1

TF i

�

KF i

TFi

Efdi � Rf i

�

; (23)

dVRi

dtD 1

TAi

�

�VRi C KAi Rf i � KAi KF i

TFi

Efdi C KAi .Vref i � Vi /

�

; (24)

for i D 1; : : : ; m:

Figure 1. STATCOM connection to the system at bus s.

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

1354 V. Pant et al.

Stator algebraic equations [30]:

E 0

di � Vi sin.ıi � �i / � Rsi Idi C x0

qi Iqi D 0; (25)

E 0

qi � Vi cos.ıi � �i / � Rsi Iqi � x0

di Idi D 0; (26)

for i D 1; : : : ; m:

Network equations at generator buses [30]:

Idi Vi sin.ıi � �i / C Iqi Vi cos.ıi � �i / C PLi �m

X

kD1

Vi VkYik cos.�i � �k � ˛ik/ D 0;

(27)

Idi Vi cos.ıi � �i / � Iqi Vi sin.ıi � �i/ C QLi �m

X

kD1

Vi VkYik sin.�i � �k � ˛ik/ D 0;

(28)

for i D 1; : : : ; m:

Network equations at load buses (except the STATCOM bus) [30]:

PLi �n

X

kD1

Vi VkYik cos.�i � �k � ˛ik/ D 0; (29)

QLi �n

X

kD1

Vi VkYik sin.�i � �k � ˛ik/ D 0; (30)

for i D m C 1; : : : ; n and i ¤ s:

STATCOM equations [31]:

dIdst

dtD �!sRst

Xst

Idst C !sIqst � !s sin.˛ C �s/

Xst

Vdc C !s

Xst

Vs cos �s; (31)

dIqst

dtD �!sIdst � !sRst

Xst

Iqst C !s cos.˛ C �s/

Xst

Vdc C !s

Xst

Vs sin �s; (32)

dVdc

dtD �

p3!sXdc sin.˛ C �s/Idst �

p3!sXdc cos.˛ C �s/Iqst : (33)

In the above equations, angle ˛ denotes the angle difference between the voltage of the

bus .Vs/, at which the STATCOM is connected, and the voltage of the STATCOM .Vst /.

Network equations at the STATCOM bus:

PSTATCOM C PLs �n

X

kD1

VsVkYsk cos.�s � �k � ˛sk/ D 0; (34)

QSTATCOM C QLs �n

X

kD1

VsVkYsk sin.�s � �k � ˛sk/ D 0: (35)

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

STATCOM Damping Controller Design Using FOSFT 1355

From Figure 1, the expressions for STATCOM real power (PSTATCOM) and STATCOM

reactive power (QSTATCOM) can be written as

PSTATCOM C jQSTATCOM D VsVst e�j˛ � V 2

s

Rst � jXst

: (36)

Now, noting that in p.u. Vst D Vdc and subsequently separating the real and imaginary

parts of Eq. (36), the following two expressions of PSTATCOM and QSTATCOM are obtained:

PSTATCOM D VsVdcRst cos ˛ C VsVdcXst sin ˛ � RstV2

s

R2st C X2

st

; (37)

QSTATCOM DVsVdcXst cos ˛ � VsVdcRst sin ˛ � XstV

2s

R2st C X2

st

: (38)

As the primary job of a STATCOM is to control the bus voltage, it is always equipped

with a bus voltage regulator. The schematic diagram of the STATCOM bus voltage

regulator is shown in Figure 2. From this diagram, the following dynamic equation can

be written for the regulator:

d˛

dtD � ˛

Ts

C Ks

Ts

.Vref C Vaux � Vs/: (39)

Linearizing Eqs. (18)–(35) and (37)–(39) together and eliminating the non-state

variables, one gets�

d

dt�X

�

D ŒA�Œ�X� C ŒB�Œ�U�; (40)

where

Œ�X� D Œ�ı �! �E0

q �Efd �E0

d �Rf �VR �iDst �iQst �vdc �˛�T

is the state variable vector, and

Œ�U� D Œ�Tm �Vref �Vaux�T

is the vector of the input quantities.

Figure 2. STATCOM bus voltage regulator and auxiliary damping controller.

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

1356 V. Pant et al.

Equation (40) is the state-space representation of a power system with a STATCOM.

It is to be noted that the various symbols used in Eqs. (18)–(40) are quite standard and,

therefore, are not explained in this article. Moreover, in this work, it is assumed that

the vectors Tm and Vref are constant and, therefore, �U D �Vaux. In order to apply the

FOSFT for designing the damping controller, one needs to select the proper STATCOM

location along with the suitable local stabilizing signal. In the next section, the procedure

adopted in this work for the above two purposes is described.

4. Selection of Proper STATCOM Location andStabilizing Signal

In this work, only the local signals at the STATCOM bus have been considered as possible

choices for the stabilizing signal. In the literature, mostly line power flows have been

used as the stabilizing signals for the design of a STATCOM damping controller [22,

24, 26]. Accordingly, in this article, line real power flow (PLine) and line reactive power

flow (QLine) on the lines incident to the STATCOM bus have been considered as possible

choices of stabilizing signals.

For selecting the most appropriate stabilizing signal out of the possible choices, the

right half-plane (RHP) zeros and Hankel singular value (HSV) approach [32] is used.

The steps of the selection process are explained as follows:

Step 1: Screening of possible STATCOM location bus(es).

Generally in a power system, no STATCOM is placed either at any of

the generator buses or at the secondary bus of the generator transformer.

Therefore, in an m-machine, n-bus system, only .n � 2m/ buses remain to

be considered as possible candidate buses for STATCOM placement. In this

work, all studies have been carried out on the 10-machine 39-bus system

[31], as shown in Figure 3. From this figure, it is observed that the possible

candidate buses are {11, 13, 14, 15, 17, 18, 19, 21, 24, 26, 27, 28, 31, 32,

33, 34, 35, 36, 37, and 38}.

Step 2: Calculation of RHP zeros and HSVs.

According to [32], for any stabilizing signal, if the resulting closed-loop

single-input single-output (SISO) system has an RHP zero, then this signal

must be discarded. On the other hand, if multiple signals having no RHP

zeros in their corresponding SISO closed-loop system exist, then the signal

having largest HSV is the most preferred [32]. Guided by this principle, the

STATCOM has been placed at all candidate buses (as obtained in step 1) one

by one. Once a STATCOM has been placed at any specific bus, the various

signals available from the adjoining lines (incident to the STATCOM bus)

are checked for the existence of an RHP zero in the associated closed-loop

SISO system. Only the signals with no RHP zeros are retained for further

processing. If, for any STATCOM location, all possible stabilizing signals

(PLine and QLine) are found to have RHP zeros, then this particular location is

eliminated from the list of probable choices. The results for the calculations

of RHP zeros for the test system obtained with the above procedure are

given in Table 1.

From Table 1, it is observed that in this system, out of 20 possible candidate buses,

only the signals at four buses, namely, buses 14, 15, 32, and 35, meet the above selection

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

STATCOM Damping Controller Design Using FOSFT 1357

Figure 3. Single-line diagram of 10-machine 39-bus power system.

criterion. At these four probable STATCOM locations, a total of five stabilizing signals

with no RHP zeros are available for further consideration.

After the signals with no RHP zeros are obtained, the next step is to calculate

the HSVs corresponding to these signals. The HSVs are calculated for all five possible

signals, and the results are shown in Figure 4. From this figure, it can be observed that out

of these five signals, the signal PLine from bus 35 to 36 has the highest HSV. As a result,

this signal has been chosen as the final stabilizing signal for the STATCOM damping con-

troller with the STATCOM assumed to be located at bus 35. The STATCOM parameters

Table 1

Signals with no RHP zeros in 10-machine system

Signals with no RHP zeros

STATCOM candidate bus Signal type From bus To bus

14 PLine 14 34

15 PLine 15 16

32 PLine 32 31

32 PLine 32 33

35 PLine 35 36

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

1358 V. Pant et al.

Figure 4. HSVs for the selected signals in 10-machine system.

are given in the appendix. It is to be noted that in Figure 4, only HSVs greater than

0.0001 have been shown.

After having selected the location and the stabilizing signal for the STATCOM,

the damping controller shown in Figure 2 has been designed by using the FOSFT,

and the gains obtained are shown in Figure 5. It is to be noted that as there is only one

STATCOM present in the study system (thereby having only one damping controller),

the issue of decentralized design is not applicable in this work, and as a result, in this

article, the standard FOSFT design procedure has been followed without incorporating the

modification suggested in [29]. In this work, following the discussion of [28], the number

of gains (N ) has been set equal to 74 (the number of system states in the 10-machine

system).

Essentially, as shown in Figure 2, based on the stabilizing signal presented at its

input, the damping controller produces an output signal Vaux, which, in turn, modulates

the reference voltage of the voltage controller of the STATCOM. The detailed non-linear

simulation results for demonstrating the effectiveness of the designed damping controller

are presented in the next section.

5. Performance Evaluation

To test the effectiveness of the designed FOSFT controller for damping enhancement,

several detailed non-linear fault simulation studies have been carried out using the fourth-

order Runge-Kutta method on a MATLAB platform [33] for various self-clearing, as well

as permanent, faults at different locations and loading conditions in the test system. For

all fault simulation studies carried out in this work, the duration and the fault resistance

have been assumed to be five cycles and 0.0 ohm, respectively. Moreover, the fault has

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

STATCOM Damping Controller Design Using FOSFT 1359

Figure 5. FOSFT gains for 10-machine system.

been assumed to have taken place at t D 1:0 sec. As it is not possible to include all the

results due to space limitations, only a few representative results are shown below. In

the following figures, the rotor angles of the machines have been measured with respect

to the center of inertia (COI) reference [30].

The performance of the controller for a self-clearing fault at bus 34 at a base case

loading condition (the loading condition given in [31]) is shown in Figure 6. In this

figure, only the variation of the machine internal angle of generator 10 is shown for

two cases: (a) with the STATCOM voltage controller only and (b) with both STATCOM

voltage and damping controllers. From this figure, it is observed that with the FOSFT-

based controller, the STATCOM is able to damp out the oscillations of the generators

appreciably. It is to be noted here that none of the ten generators is equipped with a

PSS. For a more rigorous evaluation of the performance of the designed damping con-

trollers, fault simulation studies (with self-clearing faults) at different locations at higher

loading conditions (120% loading) have been carried out. Some of the representative

results are shown in Figures 7 and 8. From these simulation results, it is observed that

the designed controller is able to damp the system oscillations quite effectively. The

performance of the controller has also been evaluated for permanent faults (the fault

has been cleared by removing the faulted line) at different locations for a 120% loading

condition. The results corresponding to two representative cases are shown in Figures 9

and 10. These figures (Figures 6–10) establish the effectiveness of the proposed controller

for improving the system damping with a STATCOM and also bring out the fact that it

is possible to achieve a significant amount of damping with a single STATCOM only,

without the help of any other damping controller (FACTS devices or any PSS) in the

system.

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

1360 V. Pant et al.

Figure 6. Rotor angle of Generator 10 at base load for self-clearing fault at bus 34.

Figure 7. Rotor angle of Generator 5 at 120% loading for self-clearing fault at bus 26.

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

STATCOM Damping Controller Design Using FOSFT 1361

Figure 8. Rotor angle of Generator 8 at 120% loading for self-clearing fault at bus 12.

Figure 9. Rotor angle of Generator 2 at 120% loading for fault at bus 12 followed by removal of

line 12–13.

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

1362 V. Pant et al.

Figure 10. Rotor angle of Generator 7 at 120% loading for fault at bus 34 followed by removal

of line 33–34.

6. Conclusion

In this article, the performance of a FOSFT-based STATCOM damping controller in a

multi-machine power system is presented. For this purpose, initially, a linearized model

of a multi-machine power system with a STATCOM has been developed. Further, the

suitable location of the STATCOM and the appropriate local stabilizing signal have been

selected based on the analysis of the RHP zeros and HSV of the resulting linear power

system model. The effectiveness of the designed controller has been rigorously tested

using detailed non-linear simulation studies under different loading conditions and fault

locations. It has been observed that a single STATCOM with a FOSFT-based damping

controller is capable of substantially enhancing the system damping for all the operating

conditions considered in the absence of any PSS or any other FACTS devices in the

system.

References

1. Klein, M., Rogers, G. J., and Kundur, P., “A fundamental study of inter-area oscillation in

power system,” IEEE Trans. Power Syst., Vol. 6, No. 3, pp. 914–921, August 1991.

2. Kundur, P., Power System Stability and Control, New York: McGraw Hill, Inc., 1993.

3. Larsen, E. V., and Swann, D. A., “Applying power system stabilizers, Part I, II, and III,” IEEE

Trans. Power Apparatus Syst., Vol. 100, No. 6, pp. 3017–3046, 1981.

4. Mithulananthan, N., Canizares, C. A., Reeve, J., and Rogers, G. J., “Comparison of PSS, SVC

and STATCOM controllers for damping power system oscillations,” IEEE Trans. Power Syst.,

Vol. 18, No. 2, pp. 786–792, May 2003.

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

STATCOM Damping Controller Design Using FOSFT 1363

5. Gyugyi, L., and Hingorani, N. G., Understanding FACTS, New York: IEEE Press, 1999.

6. Noroozian, M., Ghnadhari, M., Andersson, G., Gronquist, J., and Hiskens, I., “A robust control

strategy for shunt and series reactive compensators to damp electromechanical oscillations,”

IEEE Trans. Power Delivery, Vol. 16, No. 4, pp. 812–817, 2001.

7. Haque, M. H., “Use of energy function to evaluate the additional damping provided by a

STATCOM,” Elect. Power Syst. Res., Vol. 72, No. 2, pp. 195–202, December 2004.

8. Padiyar, K. R., and Prakash, V. S., “Tuning and performance evaluation of damping controller

for a STATCOM,” Int. J. Elect. Power Energy Syst., Vol. 25, No. 2, pp. 155–166, February

2003.

9. Lee, Y.-S., and Sun, S.-Y., “STATCOM controller design for power system stabilization with

sub-optimal control and strip pole assignment,” Int. J. Elect. Power Energy Syst., Vol. 24,

No. 9, pp. 771–779, November 2002.

10. Xue, C. F., Zhang, X. P., and Godfrey, K. R., “Design of STATCOM damping control with

multiple operating points: A multimodel LMI approach,” IEE Proc. Generat. Transm. Distrib.,

Vol. 153, No. 4, pp. 375–382, July 2006.

11. Rahim, A. H. M. A., Al-Baiyat, S. A., and Al-Maghrabi, H. M., “Robust damping controller

design for a static compensator,” IEE Proc. Generat. Transm. Distrib., Vol. 149, No. 4, pp. 491–

496, July 2002.

12. Farsangi, M. M., Song, Y. H., Fang, W. L., and Wang, X. F., “Robust FACTS control design

using the H1 loop-shaping method,” IEE Proc. Generat. Transm. Distrib., Vol. 149, No. 3,

pp. 352–358, May 2002.

13. Nassif, A. B., Castro, M. S., Da Costa, V. F., and Da Silva, L. C. P., “H2 norm-oriented

STATCOM tuning for damping power system oscillations,” Elect. Power Compon. Syst.,

Vol. 33, No. 12, pp. 1363–1383, December 2005.

14. Cong, L., and Wang, Y., “Co-ordinated control of generator excitation and STATCOM for rotor

angle stability and voltage regulation enhancement of power systems,” IEE Proc. Generat.

Transm. Distrib., Vol. 149, No. 6, pp. 659–666, November 2002.

15. Puleston, P. F., González, S. A., and Valenciaga, F., “A STATCOM based variable structure

control for power system oscillations damping,” Int. J. Elect. Power Energy Syst., Vol. 29,

No. 3, pp. 241–250, March 2007.

16. Sahoo, N. C., Panigrahi, B. K., Dash, P. K., and Panda, G., “Multivariable nonlinear control of

STATCOM for synchronous generator stabilization,” Int. J. Elect. Power Energy Syst., Vol. 26,

No. 1, pp. 37–48, January 2004.

17. Haque, M. H., “Damping improvement by FACTS devices: A comparison between STATCOM

and SSSC,” Elect. Power Syst. Res., Vol. 76, No. 9–10, pp. 865–872, June 2006.

18. Haque, M. H., “Use of energy function to evaluate the additional damping provided by a

STATCOM,” Elect. Power Syst. Res., Vol. 72, No. 2, pp. 195–202, December 2004.

19. Mohagheghi, S., Venayagamoorthy, G. K., and Harley, R. G., “Optimal neuro-fuzzy external

controller for a STATCOM in the 12-bus benchmark power system,” IEEE Trans. Power

Delivery, Vol. 22, No. 4, pp. 2548–2558, October 2007.

20. Mohagheghi, S., Venayagamoorthy, G. K., and Harley, R. G., “Optimal wide area controller

and state predictor for a power system,” IEEE Trans. Power Syst., Vol. 22, No. 2, pp. 693–705,

May 2007.

21. Morris, S., Dash, P. K., and Basu, K. P., “A fuzzy variable structure controller for STATCOM,”

Elect. Power Syst. Res., Vol. 65, No. 1, pp. 23–34, April 2003.

22. Mak, L. O., Ni, Y. X., and Shen, C. M., “STATCOM with fuzzy controllers for interconnected

power systems,” Elect. Power Syst. Res., Vol. 55, No. 2, pp. 87–95, August 2000.

23. Morris, S., Dash, P. K., and Basu, K. P., “A neuro-sliding mode controller for STATCOM,”

Elect. Power Compon. Syst., Vol. 32, No. 2, pp. 131–147, February 2004.

24. Ramírez, J. M., and Castillo, I., “PSS and FDS simultaneous tuning,” Elect. Power Syst. Res.,

Vol. 68, No. 1, pp. 33–40, January 2004.

25. Abido, M. A., “Analysis and assessment of STATCOM-based damping stabilizers for power

system stability enhancement,” Elect. Power Syst. Res., Vol. 73, No. 2, pp. 177–185, February

2005.

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014

1364 V. Pant et al.

26. Fang, D. Z., Yuan, S. Q., Wang, Y. J., and Chung, T. S., “Coordinated parameter design of

STATCOM stabiliser and PSS using MSSA algorithm,” IET Proc. Generat. Transm. Distrib.,

Vol. 1, No. 4, pp. 670–678, July 2007.

27. Werner, H., and Furuta, K., “Simultaneous stabilization based on output measurement,” Ky-

bernetika, Vol. 31, No. 4, pp. 395–411, 1995.

28. Gupta, R., Bandyopadhyay, B., and Kulkarni, A. M., “Design of power system stabilizer for

single machine system using robust fast output sampling feedback technique,” Elect. Power

Syst. Res., Vol. 65, No. 3, pp. 247–257, June 2003.

29. Gupta, R., Bandyopadhyay, B., and Kulkarni, A. M., “Robust decentralized fast-output sam-

pling technique based power system stabilizer for a multi-machine power system,” Int. J. Syst.

Sci., Vol. 36, No. 5, pp. 297–314, April 2005.

30. Sauer, P. W., and Pai, M. A., Power System Dynamics and Stability, Singapore: Pearson

Education, 2005.

31. Sharma, N. K., A Novel Placement Strategy for FACTS Devices in Multi-machine Power

Systems, Ph.D Thesis, Indian Institute of Technology Kanpur, India, July 2000.

32. Farsangi, M. M., Song, Y. H., and Lee, K. Y., “Choice of FACTS device control inputs for

damping interarea oscillations,” IEEE Trans. Power Syst., Vol. 19, No. 2, pp. 1135–1143, May

2004.

33. The Math Works Inc. MATLAB/SIMULINK Software, Version 7.0.1, Release 14, Natick, MA.

Appendix

� STATCOM voltage controller parameters: Ks D �2, Ts D 0:05 sec

� STATCOM rating: ˙500 MVAR

� STATCOM parameters [31]: Rst D 0:01 p.u., Xst D 0:1 p.u., Xdc D 0:065 p.u.

Dow

nloa

ded

by [

Eas

tern

Mic

higa

n U

nive

rsity

] at

08:

20 1

1 O

ctob

er 2

014