Authors: Reza Pourramezan, Sadegh Vaez-Zadeh, and Hamid Reza Nourzadeh Published in 2007 IEEE Power Engineering Society General Meeting (PES) DOI: 10.1109/PES.2007.385692

1. 1
Abstract—In this paper, power system multi input-multi output
identification methods that are useful for simultaneous coordi-
nated design of Power System Stabilizer and Thyristor Con-
trolled Series Capacitors controller are presented. The Output
Error and the Auto Regressive Exogenous input structures are
used separately to identify the multi input-multi output transfer
function of a power system. Different time domain responses and
mode comparisons are presented to evaluate the identified mod-
els. In order to add more damping to low-frequency oscillations, a
coordinated design of controllers is carried out by optimizing
suitable objective functions using genetic algorithm. The per-
formances of the actual system and the identified models under
the controllers are simulated extensively. A comparison of the
results confirms the effectiveness of the proposed power system
identification methods.
Index Terms—genetic algorithms, identification, power system
dynamic stability, PSS, TCSC.
I. INTRODUCTION
OWADAYS, in addition to Power System Stabilizers
(PSSs), which are the power system primary oscillation
damping controls, the Flexible AC Transmission Systems
(FACTS) Device Stabilizers are applied to power systems to
enhance the stability performance and improve the opera-
tional constraints. Particularly, Thyristor Controlled Series
Capacitors (TCSC) Power Oscillation Damping (POD) con-
trollers, have been widely addressed in the literature and have
been used in practice to enhance the system stability. It has
been shown that simultaneous use of PSS and FACTS POD
controllers can significantly improve power system stability
and performance; although the system can be adversely af-
fected by interactions among the controllers while they are not
designed coordinately [1]-[3].
During the last two decades, researchers have studied the
application of different control theories in power system
multi-controller designs. Advanced suitable control tech-
niques, such as H∞, µ-synthesis and Linear Matrix Inequalities
(LMIs), which use linearized models around a number of op-
This work was supported in part by the Center of Excellence on Applied
Electromagnetic Systems, University of Tehran.
R. Pourramazan is with the School of Electrical Engineering, University of
Tehran, Tehran, 14395-515 IRAN (e-mail: rpour@ece.ut.ac.ir).
S. Vaez-Zadeh is with the School of Electrical Engineering, University of
Tehran, Tehran, 14395-515 IRAN (e-mail: vaezs@ut.ac.ir).
H. Nourzadeh is with the School of Electrical Engineering, K. N. Toosi Uni-
versity of Technology, Tehran, 14317-14191 IRAN (e-mail: hrnour-
zadeh@ieee.org).
erating conditions and have the potential to achieve multi-
objective control aims, have been developed [4], [5]. To apply
most of these methods, deriving accurate linear models
around several operating points of a system is necessary.
Generally, a system linear model around an operating point
is derived from nonlinear equations, with some simplifications
and constraints. In case of large scale power systems, such
methods may be confronted with computational burden and
modeling errors. Linear identification methods that develop
low-order transfer functions using time domain data obtained
from actual power systems or transient stability analysis pack-
ages, could be employed to overcome such limitations [6],[7].
Various identification methods, such as Prony signal
analysis, Steiglitz-McBride method and Eigensystem realiza-
tion algorithm, have been used to develop Single Input-Single
Output (SISO) power system transfer functions [8]-[10]. A
comparative study has been shown that these methods identify
the zeros of a power system transfer function less accurate
than the poles [11]. A complementary Genetic Algorithm
(GA) has been presented to improve the accuracy of system
zeros identified by Prony method [12]. However, the design
of PSSs was performed by using SISO identified transfer
functions. This may cause system instability due to the inter-
actions among the controllers.
In this paper the Output Error (OE) method [13] and the
Least Square (LS) method for Auto Regressive Exogenous
(ARX) input model structure [6] are used separately to achieve
Multi Input-Multi Output (MIMO) linear transfer functions of
a power system in different operating conditions.
In order to achieve a MIMO transfer function, the speci-
fied system inputs are perturbed simultaneously by applying
different Pseudo Random Binary Sequence (PRBS). After-
wards, the specified system outputs are measured and re-
corded. Using the recorded data, the MIMO system transfer
functions are determined by OE and ARX methods separately.
To design a robust control, power system is identified at two
different operating conditions. The identified models are
evaluated by modal analysis. The results obtained from the
models are also compared with the time domain responses of
the actual system.
The identified power system models are used in the opti-
mal design of coordinated PSS and TCSC POD controller by
GA. Eventually, the performance of the actual system under
the designed controllers is evaluated while different contin-
gencies occur.
Power System MIMO Identification for Coordi-
nated Design of PSS and TCSC Controller
Reza Pourramazan, Sadegh Vaez-Zadeh, Senior Member, IEEE, and Hamidreza Nourzadeh, Student
Member, IEEE
N
1-4244-1298-6/07/$25.00 ©2007 IEEE.

2. 2
The paper is organized as follows. The two-area test
power system, PSS and TCSC POD controller are briefly de-
scribed in section II. The identification process together with
the OE and ARX model structures are presented in section III.
Section IV describes The GA-based coordinated design of
controllers. The results of power system identifications, the
coordinated tuning of controllers using identified models and
the time domain evaluation of tuned controllers are presented
in section V. The conclusion is given in section VI.
II. POWER SYSTEM AND CONTROLLERS
A. Power System
Fig. 1 presents the single line diagram of the two-area
power system which is particularly designed for inter-area
oscillations studies [14]. It consists of two generators in each
area. All generators are equipped with similar simple exciters.
The two areas are connected via a 220-km weak tie line. With
400MW power flow from area 1 to area 2, a poorly damped
inter-area mode of frequency 0.61 Hz and two local modes of
1.18 and 1.14 Hz are the system most critical modes. The
most contingency for this system is the loss of a line between
the two areas. This contingency leads to system low-
frequency oscillations. Hence, the controllers should be tuned
to work properly in both system pre-fault (Fig. 1) and post-
fault configuration (while a line is opened).
Area 1 Area 2
1G
4G
3G
2G
A
B
9L 10L
1 5 6 9 11 10
2 4
8 7 3
Fig. 1. Two-area test power system single line diagram.
B. PSS and TCSC POD Controller
In this paper, a PSS is installed on generator 3 which the
participation factor analysis shows it is the most critical gen-
erator. As the principal function of TCSC is to compensate for
the inductive impedance of weak lines, a TCSC is installed on
tie A. Therefore, the installing location of the TCSC POD
controller must be on tie A. Local signals, such as line current
magnitude, line active power and bus voltages, can be used as
TCSC POD controller input [15]. In this paper, the line cur-
rent magnitude is used as the controller input. Fig. 2 presents
linear structures that are used for controllers [12], [15].
The structures consist of a gain, a washout filter, a two-
stage dynamic compensator and a first-order lag block. The
gain Kw determines the amount of damping added to the sys-
tem by a controller. The washout filter prevents the controller
response to dc changes of input signal. The dynamic compen-
sator consists of two (or more) lead-lag blocks to provide nec-
essary phase-lead characteristics. Finally, the control signals,
V*
PSS and Xm, pass through the lag blocks, which represent the
PSS and TCSC regulators natural responses.
TCSC TCSC
TCSC
W W
W
sK T
1 sT+
TCSC
TCSC
1
2
1 sT
1 sT
+
+
TCSC
TCSC
3
4
1 sT
1 sT
+
+ TCSCe
1
1 sT+
mXlineI TCSCX
refX
maxX
minX
PSS PSS
PSS
W W
W
sK T
1 sT+
PSS
PSS
1
2
1 sT
1 sT
+
+
PSS
PSS
3
4
1 sT
1 sT
+
+
genω PSSV ∗
PSSV
PSSe
1
1 sT+
maxPSSV
minPSSV
(a)
(b)
Fig. 2. Power system controller block diagrams: (a) PSS (b) TCSC controller.
The output of the PSS regulator is VPSS which modifies the
exciter reference voltage. The output of TCSC regulator,
XTCSC, is a capacitive reactance with a reference value Xref
ordered by the power flow control. If a perturbation occurs,
the POD controller will modulate Xm to change TCSC capaci-
tive reactance XTCSC to damp the oscillations.
III. MIMO LOW-ORDER IDENTIFICATION
Fig. 3 illustrates the Two Input- Two Output (TITO) power
system plant equipped with PSS and TCSC POD controller.
For coordinated design of controllers, the identified model
should be a MIMO transfer function Gjk(s), which includes
four SISO transfer functions from jth inputs to kth output.
According to the Fig. 3, the inputs are PSS regulator reference
voltage V*
PSS and TCSC regulator modulating reactance Xm,
and the outputs are generator rotor speed ωgen and line current
magnitude Iline.
lineI
genωPSSV ∗
mX
( )jkG s
PSS
TCSC
Controller
Fig. 3. Power system two input-two output block diagram.
To achieve a suitable model, the identification input data,
which is a probing signal applied to the system optional in-
puts, should excite all modes of interest. The PRBS is one of
the most common signals used for identification that can be
produced by using a shift-register with feedback. Two differ-
ent PRBS probing signals are used for simultaneous excitation
of the power system inputs (V*
PSS and Xm illustrated in Fig. 3).
The amplitude and duration of PRBSs are selected such that
the system remains in linear operational region. During the
simulations, the power system outputs (ωgen and Iline) are
measured by an appropriate sampling time.
Using input/output identification data sets, different model
structures can be used to describe the system dynamic behav-
ior. The OE and ARX structures are used as power system

3. 3
model structures. Two subsequent sections represent a brief
description of these models and the methods to optimize their
parameters [6], [7], [13].
A. Multivariable OE Structure
The Output Error method estimates the parameters of a
linear model described by:
1
( )
ˆ ( ) ( ) ( ) (1)
( )
jn
jk
k j
jkj
B z
y t u t v t
F z=
= +∑
where t is the sampled data number, uj and ˆky are the model
optional inputs and outputs respectively and v(t) is the noise.
Bjk(z) and Fjk(z) are the OE nominator and denominator poly-
nomials respectively, that are given by:
11
0 1
1
1
( )
( ) 1 (2)
− +−
−−
= + + +
= + + +
L
L
bjk
f jk
n
jk jk jk jkn
n
jk jk jkn
B z b b z b z
F z f z f z
Because of nonlinear parameterization, the multivariable
OE and its parameters have to be estimated with nonlinear
optimization techniques [7]. Assuming that the model orders
nbjk and nfjk are given, the output error method estimates the
parameters by using Prediction Error Method (PEM) iterative
search algorithm to minimize the loss function given by:
2
1
1
( ) ( ) (3)
s
N
OE OE
s t n
V t t
N n
ε
= +
=
− ∑
where N is the number of data samples, ns is the number of
parameters to be optimized. The prediction error criterion,
εOE(t), is defined by:
( )
1
( )
( ) ( ) ( ) 4
( )
jn
jk
OE j
jkj
B z
t y t u t
F z
ε
=
= − ∑
where y is the actual system output. The full description of
this method can be found in [13].
B. Multi-variable ARX Structure
If it is assumed that all denominators polynomials in (1)
are identical (Fjk = Ak), the ARX model structure will be de-
fined as:
1
ˆ( ) ( ) ( ) ( ) ( ) (5)
=
= +∑
jn
k k jk j
j
A z y t B z u t v t
where Bjk(z) is similar to that of in (1) and Ak(z) is defined by:
1
1( ) 1 (6)
−−
= + + +L j
j
n
k k knA z a z a z
A multi-variable ARX can be identified by linear regres-
sion techniques. Therefore, the ARX model parameters can be
estimated by a linear least square technique. The least squares
estimation problem is solved by using QR factorization to
optimize the ARX model parameters. The least squares loss
function is defined as:
2
1
( ) (7)
= +
= ∑s
N
LS ARX
t n
V tε
where the equation error criterion εARX(t), is described by:
1
( ) ( ) ( ) ( ) ( ) (8)
=
= − ∑
jn
ARX k k jk j
j
t A z y t B z u tε
the ARX structure and algorithm details are described in [7].
Obtaining the model orders and parameters, the identified
models can be evaluated by comparing their outputs with the
actual system outputs. To evaluate identified models, a fitness
criterion can be performed as:
( )2
2
ˆ1
100 (9)
− −
= ×
−
k k
k k
y y
Fitness
y y
where y is the mean of y and ˆy is the identified model output
resulting from the same PRBS applied to the actual system.
Moreover, mode comparisons and different time domain re-
sponses using alternative probing signals can be performed
for further evaluation.
IV. COORDINATED DESIGN OF CONTROLLERS
GA optimization methods are based on natural selection,
which is a process of biological evolution. GA can be applied
to solve the optimization problems that are not well suited for
classical optimization methods, particularly the problems in
which the objective function is discontinuous, highly non-
linear or non-differentiable.
GA repeatedly modifies a population of individuals, which
are possible solutions of an optimization problem. The algo-
rithm starts with an initial random population. GA selects the
best individuals of a population to be parents of next genera-
tion's children. During successful generations, the population
approaches an optimal solution. GA implemented in MATL-
AB find a solution to minimize a given objective function.
The full description of GA can be found in [16].
For coordinated design of controllers, the transfer function
from the kth input to the jth output, Gjk(s) illustrated in Fig. 3,
can be expressed in term of system eigenvalues and the corre-
sponding residues as:
( )
( )1
s = (10)
n
ijk
jk
i i
R
G
s λ= −
∑
where Rijk is the residue associated with ith eigenvalue λi, and
n is the number of system’s eigenvalues.
The system phase lag at poorly damped mode frequency

4. 4
(ωi), which must be compensated by lead-lag compensators, is
given by [17]:
( )180 arg (11)lag ijkRφ = −
As mentioned before, controllers should perform appropri-
ate phase lead characteristics in both pre-fault and post-fault
configurations of the system. Once the system pre-fault and
post-fault phase lags are obtained from identified models, an
objective function for every controller is minimized using GA.
Considering that the inter-area mode frequency is different in
pre-fault and post-fault configurations, the objective function
ofφ is defined as the Integral of Squared Errors (ISE) of the
system phase lag and the compensator phase lead at the same
frequency (inter-area mode frequency):
( ) ( )
2 2
, , , , (12)= − + −lag pre C pre lag post C postofφ φ φ φ φ
where φlag,pre and φlag,post are the system phase lag in pre-fault
and post-fault respectively. φC,pre and φC,post are the phase lead
produced by compensators in pre-fault and post-fault respec-
tively.
Once the compensator parameters T1, T2, T3 and T4 are ob-
tained separately for each controller, the coordinated design
of controllers is reduced to tuning the washout time constants
Tw and the gains Kw. The washout time constants are selected
Tw = 10 sec. and the lag block time constants are selected Te =
10 ms. for both PSS and TCSC POD controller [17], [18]. For
gain tuning (Kw,PSS and Kw,TCSC), the identified models perform
under both controllers, and a mixed objective function can be
optimized by GA to reach the desirable performance.
Let λi = αi ± jβi be the ith closed-loop system eigenvalue.
Its damping ratio ξi can be found as:
2 2
(13)i
i
i i
αξ
α β
=
+
It is clear that by increasing the controllers gain the inter-
area mode will be shifted to the left hand side of complex
plane. However, further increase of the PSS gain and the
TCSC controller gain, the local mode and a higher frequency
mode called controller mode approach the imaginary axis
respectively, and ultimately become instable. The objective
function is provided to maximize the damping ratio of inter-
area mode. If all closed-loop eigenvalues for both pre-fault
and post-fault configurations, are in a convex region in the left
hand side of complex plane with damping ratio greater than a
specific value, the objective function ofξ to be minimized by
GA, is defined as:
( )2 2
, ,- (14)I pre I postofξ ξ ξ= +
where ξI,pre and ξI,post are inter-area mode damping ratio in
pre-fault and post-fault configurations respectively.
If one of the closed-loop poles are instable or their damp-
ing ratio is lower than the specific value, the objective func-
tion will then be set to a high value (Infinity). Thus, the GA
minimizes the objective function and the controllers gain will
be obtained simultaneously to maximize the ISE of inter-area
mode damping ratio in both configurations.
V. RESULTS
A. Identification Results
To identify the MIMO models in pre-fault and post-fault
configurations, the methods described in section III are ap-
plied and controllers design are carried out followed by exten-
sive simulations. All time domain simulations and modal
analyses in this paper were performed by using Power System
Analysis Toolbox (PSAT), which is incorporated in MATLAB
[19]. MATLAB Genetic algorithm and Direct Search Tool-
box was used for objective function optimizations [20].
The magnitudes of simultaneously applied PRBSs are 0.5
and 1 percent of exciter and TCSC reference values respec-
tively. Therefore, during the simulations the system remains
in the linear region. To ensure that all system low-frequency
modes are excited, the PRBSs are produced such that to ex-
cite an approximate frequency range of 0.005 ≤ f ≤ 3.33 Hz.
The system is perturbed by two different PRBSs groups of 30
sec. duration. One of the two data sets is used for model esti-
mation and the second is used for model validation. The sam-
pling interval is 50ms.
Using estimation data, two input-one output models of sys-
tem (ωV,X and IV,X ), are identified by means of either OE or
ARX methods. To evaluate, the validation PRBS is applied to
identified models and the resulting outputs are compared with
the actual validation data sets. Fig. 4 depicts the error between
rotor speed of identified models and that of the actual system
in pre-fault configuration.
0 5 10 15 20 25 30
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
x 10
-6
Time [sec.]
RotorSpeedDeviations[p.u.]
Modeling Error, Pre-Fault
OE
ARX
Fig. 4. Modeling error of rotor speed model, Pre-fault configuration.
Fig. 5 illustrates the error between the line current of the
identified models and the actual system in pre-fault configura-
tion. Fig. 6 and Fig. 7 depict the rotor speed and the line cur-
rent modeling errors of the post-fault identified system, re-
spectively. It is clear from Fig. 4 to Fig. 7 that when a PRBS is
applied, the outputs of the identified models follow the out-

5. 5
puts of the actual system with negligible differences. Al-
though, in some cases the OE modeling error is lower than
that of the ARX (Fig. 5 and Fig. 7), and in some other cases
the ARX models are more accurate (Fig. 4 and Fig. 6). Table I
lists these differences by means of the fitness of the identified
models.
0 5 10 15 20 25 30
-1
-0.5
0
0.5
1
1.5
2
x 10
-3
Time [sec.]
LineCurrentMagnitude[p.u.]
Modeling Error, Pre-Fault
OE
ARX
Fig. 5. Modeling error of line current model, Pre-fault configuration.
0 5 10 15 20 25 30
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
x 10
-6
Time [sec.]
RotorSpeedDeviations[p.u.]
Modeling Error, Post-Fault
OE
ARX
Fig. 6. Modeling error of rotor speed model, Post-fault configuration.
0 5 10 15 20 25 30
-1
-0.5
0
0.5
1
1.5
2
x 10
-3
Time [sec.]
LineCurrentMagnitude[p.u.]
Modeling Error, Post-Fault
OE
ARX
Fig. 7. Modeling error of line current model, Post-fault configuration.
All 12-ordered identified models present the inter-area
mode and the local mode of area 2 of the 40-ordered actual
system. The comparison between the actual and the identified
modes is presented in Table II. It can be observed that using
both methods, the inter-area mode is identified more accurate
than the local mode.
TABLE I
FITNESS OF TWO INPUT-ONE OUTPUT IDENTIFIED MODELS.
TABLE II
MODE COMPARISON OF ACTUAL AND IDENTIFIED MODELS.
For further evaluation of the identified models, step re-
sponse comparisons are performed. A 1% step is applied to
the exciter reference voltage at t = 0.2 sec. and after 30ms a
5% step is applied to the TCSC reference reactance. Fig. 8
depicts the rotor speed step response of the actual system and
the identified models in pre-fault configuration. Fig. 9 pre-
sents the line current magnitude step response in pre-fault
configuration. Fig. 10 and Fig. 11 depict the same step re-
sponses of the system post-fault configuration.
0 5 10 15 20 25 30
-3
-2
-1
0
1
2
3
4
5
6
7
x 10
-5
Time [sec.]
RotorSpeedDeviations[p.u.]
Rotor Speed Step Response, Pre-fault
Actual
OE
ARX
Fig. 8. Rotor speed step response, pre-fault configuration.
It can be concluded from Fig. 8 to Fig. 11 that OE- identi-
fied models are more effective than ARX-identified models in
following the actual system step response, although the vali-
dation data with PRBS excited signals and mode comparisons
did not distinguish the difference. As the mode comparison
shows, the two methods approximately determine poles with
the same accuracy. Hence, the difference between the identi-

6. 6
fied models may arise from the identified zeros. So, one can
suggest that OE method identifies zeros more accurately than
ARX method.
0 5 10 15 20 25 30
2.12
2.125
2.13
2.135
2.14
Time [sec.]
LineCurrentMagnitude[p.u.]
Line Current Step Response, Pre-fault
Actual
OE
ARX
Fig. 9. Line current step response, pre-fault configuration.
0 5 10 15 20 25 30
-5
0
5
10
x 10
-5
Time [sec.]
RotorSpeedDeviations[p.u.]
Rotor Speed Step Response, Post-fault
Actual
OE
ARX
Fig. 10. Rotor speed step response, post-fault configuration.
0 5 10 15 20 25 30
4.2
4.21
4.22
4.23
4.24
4.25
4.26
4.27
4.28
4.29
4.3
Time [sec.]
LineCurrentMagnitude[p.u.]
Line Current Step Response, Post-fault
Actual
OE
ARX
Fig. 11. Line current step response, post-fault configuration.
B. Coordinated Design of Controllers
Table III lists the system pre-fault and post-fault phase lag
together with the corresponding frequencies that are obtained
from OE and ARX identified models. It is seen that the resi-
dues obtained from OE and ARX models are close but not the
same. Using the mentioned objective function ofφ and the GA-
based phase compensation design within a wide bound of
search, the compensator parameters listed in Table IV, are
obtained for OE and ARX models. Due to the similarity of
residues listed in Table III, the parameters of OE and ARX
designed controllers are also similar. The gains of controllers
are then simultaneously tuned using damping ratio objective
function ofξ optimized by GA. The obtained gains of PSS and
TCSC controllers for both OE and ARX models are also listed
in Table IV.
TABLE III
RESIDUES OF IDENTIFIED MODELS USED FOR CONTROLLER TUNING.
TABLE IV
CONTROLLER PARAMETERS OBTAINED USING GA APPLIED TO THE IDENTIFIED
MODELS.
Table V shows the critical modes of the actual and the OE
models under the OE-based designed controllers. It is clear
that the inter-area and local modes of the actual closed-loop
system are shifted to the left and their damping ratios have
increased compared to those of the open-loop system. The
controller mode associated with TCSC controller has been
kept away sufficiently from the imaginary axis. The same
results for ARX-based designed control are listed in Table VI.
TABLE V
MODE COMPARISON OF CLOSED-LOOP ACTUAL AND OE MODELS DESIGNED
BY USING OE MODELS.
It can be deduced from Table V and Table VI that the
identified models have generally an acceptable similarity with
the actual one. Nevertheless, the inter-area and local modes of
the closed-loop identified and actual models are not com-
pletely the same. It is clear that they present the damping ratio
of the inter-area mode, slightly greater than that of the actual
model. They also show the damping ratio of the local mode
lower than that of the actual one. However, damping ratio of

7. 7
the controller mode is identified exactly. It can be concluded
that, applying any design method, the controllers will improve
the overall system performance.
TABLE VI
MODE COMPARISON OF CLOSED-LOOP ACTUAL AND ARX MODELS DESIGNED
BY USING ARX MODELS.
Ultimately, time domain simulations are performed to
show the performance of the designed controllers. Two con-
tingencies are considered:
• Contingency 1: Loss of line B that is parallel with line A
where the TCSC is located, at t = 0.2 sec. (post-fault
configuration).
• Contingency 2: A 1% step change in generator 3 exciter
reference voltage at t = 0.2 sec. (pre-fault configura-
tion).
Both contingencies lead to system low-frequency oscilla-
tions which are poorly damped without complementary con-
trollers. Fig. 12 depicts the active power flow of line A for the
actual system without and with PSS and TCSC POD control-
ler, while contingency 1 occurs. It can be seen that with both
OE and ARX-based designed controls, the oscillations are
damped in a few seconds.
0 1 2 3 4 5 6 7 8 9 10
3.4
3.6
3.8
4
4.2
4.4
Time [sec.]
LineActivePowerDeviations[p.u.]
Time Domain Response
No Controller
OE Model Designed Controller
ARX Model Designed Controller
Fig. 12. Line active power deviations of actual model, Contingency 1.
Fig. 13 depicts the active power flow of line A for open-
loop and closed-loop actual systems in pre-fault configuration,
while contingency 2 occurs. Once again, it is seen that both
OE and ARX-based controls improve the system performance
significantly; although, the OE designed control damps the
oscillations slightly faster.
0 1 2 3 4 5 6 7 8 9 10
1.978
1.98
1.982
1.984
1.986
1.988
1.99
1.992
1.994
1.996
1.998
Time [sec.]
LineActivePowerDeviations[p.u.]
Time Domain Response
No Controller
OE Model Designed Controller
ARX Model Designed Controller
Fig. 13. Line active power deviations of actual model, Contingency 2.
VI. CONCLUSIONS
In this paper, the OE and the ARX identification methods
are separately used to develop power system MIMO low-
order transfer functions, suitable for coordinated design of
PSS and TCSC POD controller. The above mentioned con-
trollers are simultaneously tuned by applying appropriate GA-
based optimizations to identified transfer functions.
The two input-two output transfer functions of a two-area
power system have been identified and then evaluated in dif-
ferent ways including the comparison of time domain re-
sponses of the identified models with those of the actual sys-
tem, the comparison of the inter-area and local modes of the
identified models with those of the actual system and com-
parisons between the step responses of the identified and the
actual system. The results of all evaluations show that the
identified models are accurate and suitable for dynamic stud-
ies.
The GA-based coordinated controllers tuning method is
applied to the obtained models. First, the parameters of com-
pensators block are tuned such that to compensate for the
phase-lag characteristics of the system. The simultaneous gain
tuning of the controllers is then provided.
Eventually, the actual power system is equipped with the
tuned controllers. In each operating condition, a contingency
is simulated. The performances of model-based controllers
show the potential benefits of PSS and TCSC POD controller
to enhance power system stability, and also confirm the valid-
ity of the identification methods.
The authors are currently working on providing a decen-
tralized control design that satisfies both system H∞ norm
minimization and regional pole placement. The preliminary
results show that the identified models are also suitable for
use in such designs. It is suggested that the proposed identifi-
cation methods are applied to large-scale power plants for
further evaluation.

8. 8
VII. REFERENCES
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VIII. BIOGRAPHIES
Reza Pourramazan was born in Sari, Iran, on September
30, 1979. He received the B.S. degree from Shahid
Beheshti University, Tehran, Iran, in 2003, and the M.S.
degree from School of Electrical Engineering, University
of Tehran, Tehran, Iran, in 2006, all in Electrical
Engineering.
His main research fields are Power System analysis,
modeling and control. He is currently working on coordinated use of PSS and
FACTS device stabilizers.
Sadegh Vaez-Zadeh (S'95–A'03–SM’05) received the
B.Sc. degree from Iran University of Science and
Technology, Tehran, Iran in 1985 and the M.Sc. and
Ph.D. degrees from Queen’s University, Kingston, ON,
Canada, in 1993 and 1997 respectively, all in Electrical
Engineering.
He has been with several research and educational
institutions in different positions before joining the
University of Tehran as an assistant professor in 1997
where he became an associate professor in 2001 and a full professor in 2005. He
served the university as the Head of Power Division from 1998 to 2000 and
currently is the Director of Advanced Motion Systems Research Laboratory
which he founded in 1998 and the Director of Electrical Engineering Laboratory
since 1998.
His research interests include advanced rotary and linear electric machines and
drives, magnetic levitation, electric vehicles and power system analysis and
control. He has published over 130 research papers. Dr. Vaez-Zadeh is an Editor
of IEEE Transactions on Energy Conversion, a Co-Editor of Journal of Asian
Electric Vehicles and a founding member of the editorial board of Iranian Jour-
nal of Electrical and Computer Engineering. He has been very active in IEEE
sponsored conferences as a member of technical and steering committees as well
as session chair.
Prof. Vaez-Zadeh is a member of IEEE PES Motor Sub-Committee and Power
System Stability Control Sub-Committee. He has received a number of awards
domestically including a best paper award form Iran Ministry of Science, Re-
search and Technology in 2001 and a best research award form the University of
Tehran in 2004.
Hamid Reza Nourzadeh (SM’2006) was born in Te-
hran, Iran, on September 18, 1978. He received the B.S.
degree from Shahid Beheshti University, Tehran, Iran, in
2003, and the M.S. degree from School of Electrical
Engineering, K. N. Toosi University of technology,
Tehran, Iran, in 2006, all in Electrical Engineering.
His main fields of interest are system identification and
robust control. He is currently with Process laboratory,
K. N. Toosi University of technology, working on Adaptive Universal Control
System.