Journal of productivity and development 1(3) 2015:57-68
www.pdjour.com
57
Abstract
The main objective of this paper is a comparative investigate in enhancement of damping power system oscillation via
coordinated design of the power system stabilizer (PSS) and Static Var Compensator(SVC)and STATic synchronous
COMpensator(STATCOM). The design problem of FACTS-based stabilizers is formulated as a GA based optimization
problem. In this paper eigenvalue analysis method is used on small signal stability of single machine infinite bus (SMIB)
system installed with SVC and STATCOM. The generator is equipped with a PSS. The proposed stabilizers are tested on a
weakly connected power system with different disturbances and loading conditions. This aim is to enhance both rotor angle
and power system stability. The eigenvalue analysis and non-linear simulation results are presented to show the effects of
these FACTS-based stabilizers and reveal that STATCOM exhibits the best effectiveness on damping power system
oscillation.
Keywords: Damping Oscillations, PSS, SVC, STATCOM, Coordination Design, Optimization, Power System Stability
Introduction:
Electromechanical oscillations have been observed in many power systems [1],[2],[3]. The oscillations may be
local to a single generator or generator plant(local oscillations), or they may involve a number of generators
widely separated geographically (inter-area oscillations). Electromechanical oscillations are generally studied
by modal analysis of a linearized system model [2],[4].The synchronizing power is defined as the component of
real power in phase with the rotor angle deviation, while the damping power is defined as the component of the
real power in phase with the rotor speed deviation. However, lack of damping power causes oscillatory
instability, while lack of synchronizing power causes a periodic instability. Such lack of synchronizing power
and damping power occurs particularly in power systems with long transmission line.To enhance system
damping, the generators are equipped with power system stabilizers (PSSs) that provide supplementary
feedback stabilizing signals in the excitation systems. PSSs extend the power system stability limit by
enhancing the system damping of low frequency oscillations associated with the electromechanical modes [5–
8].
Despite the potential of modern control techniques with different structures, power system utilities still prefer
the conventional lead-lag power system stabilizer (CPSS) structure [9–11]. Kundur et al. [11] have presented a
comprehensive analysis of the effects of the different CPSS parameters on the overall dynamic performance of
the power system. It is shown that the appropriate selection of CPSS parameters results in satisfactory
performance during system upsets. The advent of high-power electronic equipment to improve utilization of
transmission capacity, as Envisaged in the concept of flexible alternating current transmission systems
(FACTS) controllers, provides a system planner with additional leverage to improve the stability of a system.
FACTS controllers like static var compensator (SVC),thyristor controlled series compensator (TCSC), static
synchronous compensator (STATCOM), static synchronous series compensator (SSSC), and unified power
flow controller (UPFC) can provide variable shunt and/or series compensation [12]. Recently, to improve
overall system performance, many researches were made on the coordination between FACTS controllers and
PSS on damping power system oscillation [13–17]. Barati et al. [18] presented a coordinated PSS, SVC and
TCSC control for a synchronous generator. Nonlinear optimization algorithm was presented to coordinate
parameters adjustment for a TCSC, a SVC and a PSS in a power system[19]. In [20], a gain adjustment
approach for a TCSC, a SVC and a PSS was introduced and the effect of gain tuning on oscillation modes and
on overall power system performance are investigated. The availability of high power gate-turn-off thyristors
Damping Power System Oscillationswith Single and Coordinated
Design of the Power System Stabilizer and FACTS Controllers
J.Barati1, S.S. Mortazavi
2, o.rahat
3
1Electrical Engineering Department, Ramhormoz Branch, Islamic Azad University, Ramhormoz, Iran 2Electrical Engineering Department, ShahidChamran University, Ahvaz, Iran
2 Electrical Engineering Department, Ramhormoz Branch, Islamic Azad University, Ramhormoz, Iran
Journal of productivity and development 1(3) 2015:57-68
www.pdjour.com
58
has led to the development of a STATCOM which is one of the FACTS devices connected in shunt and to
improve transmission stability and to dampen power oscillations.
The Phillips–Heffron model of the single machine infinite bus(SMIB) power system with FACTS devices is
obtained by linearizing non-linear equations around a nominal operating point of the power system [21].
The design problem is transformed into an optimization problem and GA optimization techniques are employed
to search for the optimal PSS and FACTS controller‟s parameters.
In this paper the eigenvalue analysis and the nonlinear simulation results are used for small signal stability of
single machine infinite bus (SMIB) system installed with PSS and FACTS controllers. This analysis shows that
coordinated design of PSS and STATCOM-based controllers has significant performance to promote the
damping power system oscillations compared with SVC-Based controllers.
I. SYSTEM MODEL
I.1. Generator model
The power system is represented by a single machine infinite-bus(SMIB) with FACTS devices is shown in
Fig.1. The generator is equipped with a PSS. The generator has a local load of admittance Y L = g + jb . The
transmission line has impedances of Z=R + jX. The SVC and STATCOM are used at the middle point in
transmission line for power oscillations damping. The system is modeled for low frequency oscillations studies
and the linearized power System model is used for this purpose. The generator is represented by the 3rd
order
model consisting of the electromechanical swing equation and the generator internal voltage equation. The
dynamics of rotor angle δ and velocity ω is described by the so called swing equations:
(1)
' ' '
1
1 /
/
b
m e
q fd d d d q do
P P D M
E E x x i E T
II.2
Exciter and PSS
Fig. 2 shows the IEEE Type-ST1 excitation system is considered in this work. It can be described as:
(2) /fd A ref pss fd AE K V V u E T
V
G
Vb
VSC
YL
Vm
Z/2 Z/2
IDC
SVC
i
iL
il1
iSVC
il2
STATCOMCDC
Xt
o DCV CV
is
C
ψ
Figure 1. SMIB with PSS and FACTS Devices
Journal of productivity and development 1(3) 2015:57-68
www.pdjour.com
59
The inputs to the excitation system are the terminal voltage V and reference voltage Vref . K A and T A ,
respectively are represented the gain and time constants of the excitation system.
In equations (1) and (2): Pe and V are related by the following equations:
e d d q qP V i V i
(3)
1/2
2 2
'
:
d q q
d q
q q d d
V x i
V V V
V E x i
(4)
Where xq is the q-axis reactance of the generator. Moreover, Fig. 2 shows the transfer function of the PSS. It
consists of an amplification block, a wash out block and two lead-lag blocks [9]. The objective of the washout
block is to act as a high pass filter that eliminates DC offset. The lead-lag blocks provide the appropriate phase-
lead characteristic to compensate for the phase lag between the exciter input and the generator electrical torque.
The output of the PSS is limited to guarantee that the PSS does not counteract the voltage regulator action of the
AVR.
31
2 4
11
1 1 1
ST STSTK
ST ST ST
1
A
A
K
ST
Min
Max
Max
Min
fdE'
refV
V
PSSU
Lead Lag PSS
Figure 2. IEEE Type-ST1 excitation system with
PSS
II.3 SVC -Based Stabilizer
The complete SVC controller structure with a lead-lag compensator is shown in Fig. 3. The susceptance of the
SVC, B, could be expressed as:
(5 )
/REFSVC S SVC SVC SVC SB K B U B T
31
2 4
11
1 1 1
ST STSTK
ST ST ST
Min
Max
Max
Min
SVCB
SVCU
refSVCU
+-
Lead LagControler
1
S
S
K
ST
Figure 3. SVC with lead-lag controller
Referring to Fig.1, the d and q components of the machine current i and terminal voltage V can be written as:
(7 )d q
d q
i i ji
V V jV
Journal of productivity and development 1(3) 2015:57-68
www.pdjour.com
60
(8 )
By linearizing eqns. 1 and 2 it is possible to obtain:
(9 )
' ' '
/
/
/
b
e
q fd d d d q do
fd fd A A
P D M
E x x i E T
E E K V T
Where
(10
)
'1 2
'3 4
'5 6
e q PB SVC
do q fd qB SVC
q vB SVC
P K K E K B
K sT E E K K B
V K K E K B
Where K1-K6 , KPB, KqB and KvB are linearization constants. substituting eqn. 10 into eqn. 9 one can obtain the
linearized model of the power system installed with the SVC as[18]:
(11 )
1 2
34
' ' '' '
5 6
0 00 377 0 0
00
10 0
10
PB
pss
qB
q
do do doq do Sfd
A A A vBAfd
A A A A A
KK KD
UMM M M
KKKE
T T T T BE
K K K K K KK
T T T T T
VC
In short;
(12 )P x A x B u
Here, the state vector X is [∆δ , ∆ω , ∆E'q, ∆Efd ]
T, and the control vector U is [UPSS , ,∆B]
T. K1-K6,Kp,Kq and Kv
are linearization constant.
II.4 STATCOM-Based Stabilizers
As shown in Fig.1, The STATCOM consists of a three phase gate turn-off (GTO) – based voltage source
converter (VSC) and a DC capacitor . The STATCOM model used in this study is founded well enough for the
low frequency oscillation stability problem. The STATCOM is installed through a step- down transformer with
a leakage reactance of Xt . The voltage difference across the reactance produces active and reactive power
exchange between the STATCOM and the transmission network. The STATCOM resembles in many respects a
synchronous compensator, but without the inertia. The STATCOM is one of the important FACTS devices and
can be used for damping electromechanical oscillations in a power system to provide stability improvement.
This study examines the application of STATCOM for damping electromechanical oscillations in a power
system.
The VSC generates a controllable AC voltage source V CVo DC behind the leakage reactance. The voltage
difference between the STATCOM-bus AC voltage Vm(t) and Vo(t) produces active and reactive power
exchange between the STATCOM and the power system, which can be controlled by adjusting the magnitude
CVDC and the phase . In Fig. 1, we have [22]:
(13 )
(cos sin ) , , ( cos sin )DC DCs sd sq sd sq
DC DC
dV I CV CV CV j I I jI I Io DC DC dt C C
Journal of productivity and development 1(3) 2015:57-68
www.pdjour.com
61
where C = mk , k is the ratio between the AC and DC voltage depending on the converter structure, m is the
modulation ratio defined by pulse width modulation (PWM) ; V DC is the DC voltage;and ψ is the phase defined
by PWM. Furthermore, DCC is the DC capacitor value and DCI is the capacitor current while sdI and sqI are
the d and q components of the FACTS current sI respectively. Fig. 4 illustrates the block diagram of
STATCOM AC/DC voltage PI controller with a damping stabilizer. The proportional and integral gains are
KACP, KACI and KDCP, KDCP for AC and DC voltages respectively. The STATCOM damping stabilizers are lead-
lag structure where KC and Kψ are the stabilizer gains, Tw is the washout time constant, and T1C, T2C, T3C, T4C,
T1ψ, T2ψ, T3ψ, and T4ψ are the stabilizer time constants.
Min
Max
Max
Min
refV
DCIDCP
KK
S
1
1 CST
C
CU
ConverterDynamics
PI AC Voltage Regolature
Max
refV
DCIDCP
KK
S
1
1 CST
ConverterDynamics
PI DC Voltage Regolature
VAC
VDC
1 3
2 4
1 1
1 1 1
w C C
w C C
ST ST STK
ST ST ST
Figure 4. STATCOM AC/DC Voltage Regulator
with supplementary damping control in the AC
control loop
III.4 Linearizing Model STATCOM
In electromechanical mode damping stabilizers analysis, the linearized incremental model around a nominal
operating point is usually employed [23]. Linearizing the expressions of id and iq and substituting into the linear
form of (1)-(4),(7)-(9) and (13) yield the following linearized expressions.
i s is the current flow from STATCOM , and the d-q axis measure is:
(14)
'7 8 11
'9 10 12
sin cos
cos sin
d q b q DC
d q b q DC
C i C i V C E CV
C i C i V C E CV
(15)
Solving (14) and (15) simultaneously, id and iq expressions can be obtained.
(16)
'7 8 11
'9 10 12
cos cos cos sin
sin sin sin cos
d q b q DC DC
d q b q DC DC DC
C i C i V C E C V V C CV
C i C i V C E C V V C CV
(17)
Solving (16) and (17) simultaneously, Δid and Δiq can be expressed as:
(18)
'19 21 23 25 27
'20 22 24 26 28
d q DC
q q DC
i C C E C V C C C
i C C E C V C C C
(19)
The constants C7-C28 are expressions of: '
0 0 0 0 0, , , , , , , ,L d q q d qZ Y x x i i E C
The constants C1-C24 are expressions of:
(20)
'
d q q
q q d d
v x i
v E x i
(21)
Journal of productivity and development 1(3) 2015:57-68
www.pdjour.com
62
Using Equations (∆Id) and (∆Iq), the following expressions can be easily obtained
(22
)
'1 2e q pDC DC pC pP K K E K V K C K
(23
)
' '3 4( )do q fd qDC DC qC qK sT E E K K V K C K
(24
)
'5 6 q vDC DC vC vv K K E K V K C K
(25
)
'7 8DC q DC DC CV K K E K V K C K
Where K1-K8, KDCP , KPC, Kpψ, KqDC, KqC, Kqψ, KvDC, KvC , Kvψ , KDC, K∆C, and K∆ψ are linearization constants.
The above linearizing procedure yields the following linearized power system model
(26)
1 2
34
' '
5 6
7 8 9
0 377 0 0 0 0 0
0
10
'
10
00
pDC
qDC
qq do dodo do
fdA A A vDC
fdDC
A A A A
DC
KK KD
M M M M
KKKE
T TT TE
K K K K K KVT T T T
K K KV
0
0
0
0
pC P
PSSqC q
do do
A vC A vA
A A A
C
K K
M Mu
K KC
T T
K K K KK
T T T
K K
Using vector representation, the above equation can be written as:
(27) P x A x B u
Here, the state vector X is [∆δ , ∆ω , ∆E'q, ∆Efd , ∆VDC ]
T, and the control vector U is [UPSS , ∆C, ∆ψ]
T. K1-
K9,Kp,Kq, Kv and K∆ are linearization constant.
II. PROBLEM FORMULATION
II.1. Stabilizer Structure
The commonly used lead-lag structure is chosen in this study. The transfer function of the stabilizer is:
(28) 31
2 4
11
1 1 1
w
w
sT sTsTu K y
sT sT sT
where u and y are the stabilizer output and input signals respectively, K is the stabilizer gain, Tw is the washout
time constant, and T1, T2, T3, and T4 are the stabilizer time constants. From the viewpoint of the washout
function, the value of TW is not critical and may be in the range of 1–20 s [19]. In the lead–lag structured
controllers, the washout time constants Tw is usually prespecified [14,20].In the present study a washout time
constant Tw = 10 s is used. The controller gain K and time constants T1, T2 , T3 and T4 are to be determined.
Furthermore, In the design of a robust damping controller, selection of the appropriate input signal is a main
issue. Input signal must give correct control actions when a disturbance occurs in the power system. Both local
and remote signals can be used as control. However, local control signals, although easy to get, may not contain
the desired oscillation modes. For local input signals, line active power, line reactive power, line current
magnitude and bus voltage magnitudes are all candidates to be considered in the selection of input signals for
the FACTS power oscillation damping controller [25].
Similarly, generator rotor angle and speed deviation can be used as remote signals. However, rotor speed seems
to be a better alternative as input signal for FACTS-based controller [26]. In this study, the input signal of the
proposed damping stabilizers is the speed deviation, Δω.
Journal of productivity and development 1(3) 2015:57-68
www.pdjour.com
63
II.2. Objective Function
A widely used conventional lead–lag structure for both PSS and FACTS-based stabilizers, shown in Figs. 2, 3,4
and 5, is considered. In this structure, the washout time constant Tw is usually prespecified. It is worth
mentioning that the damping controller is designed to minimize the electromechanical mode oscillation while
the internal PI controllers are designed to minimize the variations in ac and dc voltages of the STATCOM.
Therefore, the following weighted-sum multi objective function is proposed in order to coordinate among the
damping stabilizers and the internal ac and dc PI controllers. Therefore, to increase the system damping to
electromechanical modes, an objective function J defined below is proposed.
(29) 0
( )simt t
J t dt
In the above equations tsim is the simulation time. It is aimed to minimize this objective function in order to
improve the system response in terms of the settling time and overshoots.
II.3. Optimization problem
In this study, it is aimed to minimize the proposed objective function J. The problem constraints are the PSS
and FACTS controller parameter bounds. Therefore, the design problem can be formulated as the following
optimization problem.
Minimize J
Subject to : min max min max min max min max
1 1 1 2 2 2 3 3 3 4 4 4
min max min max min max
min max min max min max min max
, , ,
, ,
, , ,
PSS PSS PSS ACP ACP ACP ACI ACI ACI
DCI DCI DCI DCP DCP DCP C C C
T T T T T T T T T T T T
K K K K K K K K K
K K K K K K K K K K K K
The proposed approach employs genetic algorithm [14] to solve this optimization problem and search for
optimal set of the controller parameters. Based on the linearized power system model, Genetic Algorithm (GA)
has been applied to the above optimization problem to search for optimal settings of the proposed stabilizer. In
this study, PSS and FACTS-based damping controllers as discussed in the following combination cases:
Case 1: without compensation (base case)
Case 2: Single and coordinated compensation Design Approach (PSS and SVC)
Case 4: STATCOM internal AC and DC PI voltage controllers with PSS and C-based damping stabilizer.
Case 5: STATCOM internal AC and DC PI voltage controllers with PSS and ψ-based damping stabilizer.
III. SIMULATION RESULTS
Simulations on the SMIB system (shown in Fig. 1) are performed to evaluate the effectiveness of the PSS and
FACTS controllers to damping power system oscillations and its design by the methods proposed using GA in
the paper are demonstrated by example power systems. The relevant parameters of the power system are given
in Appendix. To validate the effectiveness of the proposed controllers, two different operating conditions
(Normal & Heavy) as given in Table 1 are considered. Parameters for the proposed stabilizers are given in
Table 2.
TABLE I: LOADING CONDITIONS
Loading Pe (pu) Qe (pu)
Normal 1.0 0.015
Heavy 1.1 0.4
Journal of productivity and development 1(3) 2015:57-68
www.pdjour.com
64
III.1. Eigenvalues Analysis
The system eigenvalues and their damping ratios with and without PSS, SVC and STATCOM (single and
coordinated design) for nominal and heavy loading conditions are given in Tables 3-5, respectively.
The eigenvalue analysis reveals the effectiveness of GA Based single and coordinated of PSS and FACTS –
Based controllers to damping power system oscillations and power system stability Enhancement.
TABLE II: OPTIMAL PARAMETER SETTING OF THE PROPOSED STABILIZERS
Controlle
r optimal
paramete
r
Single design Coordinated design
PSS SVC PSS SVC
C-based
Stabiliz
er
ψ-based
Stabilize
r
T1 0.561 0.280
1
0.189
4 0.795
0.492 0.0092
T2 0.100
0
0.300
0
0.100
0
0.300
0
0.5000 0.5000
T3 0.267
1
0.012
4
0.137
2
0.518
6
0.720 0.138
T4 0.100
0
0.300
0
0.100
0
0.300
0
0.5000 0.5000
K 16.02
1 310 61.45 87.18
41.50 53.65
KPAC -- -- -- -- 513.5 340.3
KIAC -- -- -- -- 30.32 798.0
KPDC -- -- -- -- 287 171.06
KIDC -- -- -- -- 915.56 831.6
TABLE I: SYSTEM EIGENVALUES IN NOMINAL LOADING CONDITION, SINGLE AND COORDINATED
DESIGN
Single Design Coordinated Design
No
Control
PSS SVC STATCO
M only
PSS&SVC C-based
Stabilizer
ψ-based
Stabilizer
-
0.3±j4.96
-
1.93±j3.55
-
0.72±j5.98
-1.082±
j2.658
-2.04±j1.74 -1.15± j1.29 -3.068±
j0.863
TABLE II: SYSTEM EIGENVALUES IN NOMINAL LOADING CONDITION, SINGLE AND COORDINATED
DESIGN
Single Design Coordinated Design
No
Control
PSS SVC STATCO
M only
PSS&SV
C
C-based
Stabilizer
ψ-based
Stabilizer
-
0.49±j3.69
-
1.02±j2.4
-
0.53±j5.54
-0.717±
j1.854
-
3.212±j3.95
-1.611±
j2.50
-2.72± j2.30
Journal of productivity and development 1(3) 2015:57-68
www.pdjour.com
65
TABLE III: DAMPING OF SYSTEM ELECTROMECHANICAL MODE IN BOTH OF LOADING
CONDITIONS, SINGLE AND COORDINATED DESIGN
Single Design Coordinated Design
Loading No
Control
PSS
only
SVC
only
STATCOM
only
PSS&SVC C-based
Stabilizer
ψ-based
Stabilizer
Normal -
0.0600
0.4776 0.1195 0.3783 0.7616 0.6628 0.9628
Heavy -
0.1310
0.3911 0.0968 0 .3608 0.6309 0.5393 0.7643
III.2. Non Linear TimeDomain Simulation
To assess the effectiveness of the proposed PSS and FACTS devices to improve the stability of SMIB
powersystem shown in Fig. 1 is considered for nonlinear simulation studies. 6-cycle 3-φ fault on the infinite bus
was created, at both loading conditions given in Table 1, to study the performance of the proposed controller.
The system data is given in the appendix. Figures 5-7 show the rotor angle response with above mentioned
disturbance at nominal and heavy loading conditions respectively. The response with coordinated design is
much faster, with less overshoot and settling time compared to CPSS and single design. It can be observed from
Figs. that, the coordinated design approach provides the best damping characteristic and enhance greatly the
first swing stability at two loading conditions. Response when CPSS and designed individually and in
coordinated manner at nominal and heavy loading conditions are compared and show in Figs.(5-7),respectively.
It is clear that the control effort is greatly reduced with the coordinated design approach.
(a) (b)
Figure 5. Machine rotor angle response for a six cycles fault with nominal(a) & heavy(b) loading conditions.
0 1 2 3 4 5 6-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Time(s)
Ro
tor
An
gle
(ra
d)
0 1 2 3 4 5 6-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Time(s)
Ro
tor
An
gle
(ra
d)
Journal of productivity and development 1(3) 2015:57-68
www.pdjour.com
66
Figure 6. Machine rotor angle responsefor a six cycles fault with nominal loading condition
Figure 7. Machine rotor angle for a six cycles fault with heavy loading condition
IV. Conclusion
In this study, the power system stability enhancement via PSS and FACTS device are presented and discussed
The stabilizer design problem has been formulated as a multi objective optimization problem, which was solved
by genetic algorithms (GA). The proposed stabilizers have been applied and tested on power system under
severe disturbance and different loading condition. It is also evident that the coordinated design of PSS and
FACTS-based stabilizer provides great damping characteristics and enhance significantly the system stability
compared to individual design. It is clear from the eigenvalues analysis that the system stability is greatly
enhanced with the proposed stabilizers. The eigenvalues results presented show that the system stability is
greatly enhanced with the coordinated design of the proposed stabilizers. The simulations results presented
show that both FACTS devices improve the system stability, furthermore the STATCOM-based stabilizer
provide a better effectiveness than SVC-based stabilizer on damping power system oscillation. Moreover it can
be seen that the coordinated PSS and ψ -based stabilizer provide better damping characteristics and enhances
the first swing stability greatly compared to the coordinated PSS and C-based stabilizer case.
0 1 2 3 4 5 60.8
1
1.2
1.4
1.6
1.8
2
Time(s)
Ro
tor
An
gle
(ra
d)
Conventional PSS[1]
Proposed PSS
Proposed SVC
Coordinated PSS & SVC
Coordinated PSS & C - Based Stabilizer
Coordinated PSS & - Based Stabilizer
0 1 2 3 4 5 61.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
Time(s)
Ro
tor
An
gle
(ra
d)
Conventional PSS[1]
Proposed PSS
Proposed SVC
Coordinated PSS & SVC
Coordinated PSS & C - Based Stabilizer
Coordinated PSS & - Based Stabilizer
Journal of productivity and development 1(3) 2015:57-68
www.pdjour.com
67
Acknowledgements
Funding support of this research was provided by the Islamic Azad University, Ramhormoz Branch,
khozestan, Iran. Moreover, this paper was derived from a plan named “Damping Low Frequency
Oscillationswith Single and Coordinated Design of the Power System Stabilizer and FACTS Controllers“.
Appendix
Power system data in per unit value:
M=9.26 ; Tdo=7.76 ; D=0; x=0.973 ;xd=0.19; xq=0.55 ; R=0.234 ; X=0.997 ; g=0.249 ; b=0.262 ; Kc=1.0 ;
Tc=0.05 ; |Efd|≤ 7.3 pu ; Vdc=1 , KA=20 , TA=0.01.
References
[1] Y.-Y. Hsu, S.-W. Shyue, and C.-C. Su, “Low Frequency Oscillation in Longitudinal Power Systems: Experience with
Dynamic Stability of Taiwan‟s Power System,” IEEE Trans. Power Systems, Vol. 2, No. 1, pp. 92–100,Feb.1987.
[2] D. N. Koterev, C.W. Taylor, and W. A. Mittelstadt, “Model Validation for the August 10, 1996 WSCC System
Outage,” IEEE Trans. Power Systems, Vol. 14, No.3,pp.967–979,Aug.1999.
[3] G. Rogers, Power System Oscillations, Kluwer, Norwell,MA,2000.
[4] P. Kundur, M. Klein, G. J. Rogers, and M. S. Zywno, "Application of Power System Stabilizers for Enhancement of
Overall System Stability," IEEE Trans. PWRS,Vol.4,No.2,1989,pp.614-626.
[5] Y. N. Yu, Electric Power System Dynamics, Academic Press, 1983.
[6] Anderson PM, Fouad AA. Power system control and stability. Ames, Iowa: Iowa State Univ Press; 1977.
[7] deMello FP, Concordia C. Concepts of synchronous machine stability as affected by excitation control. IEEE Trans
PAS 1969;88:316–29.
[8] Abdel-Magid YL. A generalized perturbation model for multi-machine interconnected systems. Mediterranean
Electromechanical Conference MELECON‟83, Athens, Greece, 24–26 May, 1983.
[9] Larsen E, Swann D. Applying power system stabilizers. IEEE Trans PAS 1981;100(6):3017–46.
[10] Tse GT, Tso SK. Refinement of conventional PSS design in multimachine system by modal analysis. IEEE Trans
PWRS 1993;8(2):598–605.
[11] Kundur P, Klein M, Rogers GJ, Zywno MS. Application of power system stabilizers for enhancement of overall
system stability. IEEE Trans PWRS 1989;4(2):614–26.
[12] N. Hingorani and L. Gyugyi, Understanding FACTS. New York: IEEE Press, 2000.
[13] J.M. Ramirez, I. Castillo, PSS and FDS simultaneous tuning, Electr. Power Syst. Res. 68 (2004) 33–40.
[14] Q.J. Liu, Y.Z. Sun, T.L. Shen, Y.H. Song, Adaptive nonlinear coordinated excitation and STATCOM controller based
on Hamiltonian structure for multimachine-power-system stability enhancement, IEE Proc. Gen. Trans. Distrib. 150
(2003) 285–294.
[15] X. Lei, X. Li, D. Povh, A nonlinear control for coordinating TCSC and generator excitation to enhance thetransient
stability of long transmission, Electr. Power Syst. Res. 59 (2001) 103–109.
[16] L.J. Cai, I. Erlich, Simultaneous coordinated tuning of PSS and FACTS damping controller in a large power system,
IEEE Trans. Power Syst. 20 (2005) 294–300.
[17] Eslami, Mandiyeh; Shareef, Hussain; Mohamed, Azah,´Application of PSS and FACTS Devices for Intensification of
Power System Stability,´ International Review of Electrical Engineering(IREE), vol 5(issue 2): 552 570, MAR-APR,
2010.
[18] JamshidBarati, S. S. Mortazavi, A. Saidian ,´ Analysis and Assessment of FACTS-Based Stabilizers for Damping
Power System Oscillations Using Genetic Algorithms,´ International Review of Electrical Engineering(IREE), Vol. 5,
N. 6,pp. 2819-2827, NOV-DEC, 2010.
[19] X. Lei, E.N. Lerch, and D. Povh, “Optimization and Coordination of Damping Controls for Improving System
Dynamic,” IEEE Trans. on Power Systems, Vo1. 16, No. 3, pp. 473-480, Aug. 2001.
[20] N. Mithulananthan, C.A. Canizares, and J. Reeve, “Tuning, performance and interactions of PSS and FACTS
controllers,” Power Engineering Society Summer Meeting, 2002 IEEE, Vol. 2, pp. 981 – 987, 21 – 25 July, 2002.
[21] H . F. Wang Phillips-Heffron model of power systems installed with STATCOM and applications(IEE Proc-Gener.
Transm. Distrib., Vol. 146, No. 5, September 1999,pp.521-527).
[22] „Modelling of power electronics equipment (FACTS) in load flow and stability programs‟. CIGRE.
[23] P. Kundur, Power System Stability and Control, McGraw-Hill, New York, 1994.
[24] N.G. Hingorani, L. Gyugyi, Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems,
IEEE Press, New York, 2000.
Journal of productivity and development 1(3) 2015:57-68
www.pdjour.com
68
[25] A.D. Del Rosso, C.A. Canizares, V.M. Dona, A study of TCSC controller design for power system stability
improvement, IEEE Trans. Power Syst. 18 (4) (2003) 1487–1496.
[26] Y. Chang, Z. Xu, A novel SVC supplementary controller based on wide area signals, Electr. Power Syst. Res. 77
(2007) 1569–1574.
[27]