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Advances in Natural and Applied Sciences, 8(8) July 2014, Pages: 196-200
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Advances in Natural and Applied Sciences
ISSN:1995-0772 EISSN: 1998-1090
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Power System Stabilizer Design based on the Full State Feedback Method
Reza Saki, Somayeh Yarahmadi, Faranak Nikabadi, Vahid Chegeni
Department of Electrical Engineering, Doroud Branch, Islamic Azad University, Doroud, Iran
ARTICLE INFO
Article history:
Received 25 January 2014
Received in revised form 12
March 2014
Accepted 14 April 2014
Available online 5 May 2014
ABSTRACT
Full state feedback is a suitable method to place the closed-loop poles of a plant in predetermined locations in the s-plane. This method can be used to replace the power
system Eigen-values and enhancing system stability. This paper presents the state
feedback method to design power system stabilizer (PSS). The simulations results are
carried out based on the typical power system. Nonlinear simulations are used to denote
the effectiveness of the proposed method.
Keywords:
Full State Feedback
Power System Stabilizer
Stability Eigen-Values
© 2014 AENSI Publisher All rights reserved.
To Cite This Article: Reza Saki, Somayeh Yarahmadi, Faranak Nikabadi, Vahid Chegeni, Power system stabilizer design based on the full state
feedback method. Adv. in Nat. Appl. Sci., 8(8): 196-200, 2014
INTRODUCTION
Theory is a method employed in feedback control system theory to place the closed-loop poles of a plant in
pre-determined locations in the s-plane. This method has been used in electric power system for different
purposes (El-Sherbiny et al., 1996; Bettayeb and Randhawa, 1999; Lin and Wu, 2011; Li et al., 2012; Mahmud
et al., 2014; Schuler et al., 2014). Paper (Mahmud et al., 2014) presents an approach to design a nonlinear
observer-based excitation controller for multi-machine power systems to enhance the transient stability. The
controller is designed based on the partial feedback linearization of a nonlinear power system model, which
transforms the model into a reduced-order linear one with an autonomous dynamical part. Then a linear state
feedback stabilizing controller is designed for the reduced-order linear power system model using optimal
control theory which enhances the stability of the entire system. The states of the feedback stabilizing controller
are obtained from the nonlinear observer and the performance of this observer-based controller is independent of
the operating points of power systems. The performance of the proposed observer-based controller is compared
to that of an exact feedback linearizing observer-based controller and a partial feedback linearizing controller
without observer under different operating conditions. Paper (Lin and Wu, 2011) investigates global complete
synchronization of two identical power systems and global robust synchronization of two power systems with
parameter mismatch and external disturbance, both under the master–slave linear state-error feedback control.
Some criteria for achieving the synchronization via a single-variable linear coupling are derived and formulated
in simple algebraic inequalities. These algebraic criteria are further optimized so as to improve their
performances. The effectiveness of the new algebraic criteria is illustrated by the numerical examples. Paper
(Bettayeb and Randhawa, 1999) presents the incorporation of time-weighted linear quadratic regulator
(TWLQR) state and output feedback control for power system dynamic stability problems. The effectiveness of
the TWLQR control is shown for a single machine infinite bus (SMIB) system. The simulation results show that
the TWLQR control is superior to linear quadratic regulator (LQR) control for both state and output feedback
cases. Paper (Schuler et al., 2014) considers the problem of constructing decentralized state feedback controllers
for linear continuous-time systems. Different from existing approaches, where the topology of the controller is
fixed a priori , the topology of the controller is part of the optimization problem. Structure optimization is done
in terms of a minimization of the required feedback links and subject to a predefined bound on the tolerable loss
of the achieved H∞H∞-performance of the decentralized controller compared to an H∞H∞-optimal centralized
controller. We develop a computationally efficient formulation of the decentralized control problem by convex
relaxations which makes it attractive for practical applications. The proposed design algorithm is applied to
design sparse wide area control of a 3-area, 6-machine power system.
Corresponding Author: Reza Saki, Islamic Azad University, Department of Electrical Engineering, Doroud, Iran.
E-mail: [email protected]
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Reza Saki et al, 2014
Advances in Natural and Applied Sciences, 8(8) July 2014, Pages: 196-200
This paper presents the state feedback method to design power system stabilizer (PSS). The simulations
results are carried out based on the typical power system. Nonlinear simulations are used to denote the
effectiveness of the proposed method.
State feedback:
The state of a dynamical system is a collection of variables that permits prediction of the future
development of a system. We now explore the idea of designing the dynamics a system through feedback of the
state. We will assume that the system to be controlled is described by a linear state model and has a single input.
The feedback control will be developed step by step using one single idea: the positioning of closed loop
eigenvalues in desired locations. Figure 1 shows a diagram of a typical control system using state feedback. The
full system consists of the process dynamics, which we take to be linear, the controller elements, K and kr , the
reference input, r, and processes disturbances, d. The goal of the feedback controller is to regulate the output of
the system, y, such that it tracks the reference input in the presence of disturbances and also uncertainty in the
process dynamics. An important element of the control design is the performance specification. The simplest
performance specification is that of stability: in the absence of any disturbances, we would like the equilibrium
point of the system to be asymptotically stable. More sophisticated performance specifications typically involve
giving desired properties of the step or frequency response of the system, such as specifying the desired rise
time, overshoot and settling time of the step response. Finally, we are often concerned with the disturbance
rejection properties of the system: to what extent can we tolerate disturbance inputs d and still hold the output y
near the desired value (Aström and Murray, 2010).
Fig. 1: A feedback control system with state feedback (Aström and Murray, 2010).
State feedback theory or pole placement, is a method employed in feedback control system theory to place
the closed-loop poles of a plant in pre-determined locations in the s-plane. Placing poles is desirable because the
location of the poles corresponds directly to the Eigen-values of the system, which control the characteristics of
the response of the system. The system must be considered controllable in order to implement this method. The
state space model of system can be represented as (1) and then, the poles of the system are the roots of the
characteristic equation given by (2).
 x  A x  Bu

 y  C x  Du
sI  A  0
Full state feedback is utilized by commanding the input vector u as (3).
u  K x
(1)
(2)
(3)
Eventually, the state space equations can be derived as follows;
 x  A  BK x
 y  C  DK x

(4)
The roots of the state feedback system are given by the characteristic equation as follows:
det sI  A  BK
(5)
Comparing the terms of this equation with those of the desired characteristic equation yields the values of
the feedback matrix K which force the closed-loop eigenvalues to the pole locations specified by the desired
characteristic equation.
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Reza Saki et al, 2014
Advances in Natural and Applied Sciences, 8(8) July 2014, Pages: 196-200
Test System:
A single machine power system which is installed with a infinite bus is chosen as case study. Figure 2
shows the test system with two areas and interconnection lines. The system is taken from (El-Sherbiny et al.,
1996).
Simulation Results:
The proposed state feedback in section 2 is designed. The output signal Δω is assumed as input of feedback
and ΔVref is considered as output of state feedback. The feedback gain is obtained as 4.21. In order to show the
ability of this method to damp out the oscillations, two operating conditions are considered as follows:
Nominal operating condition: No changing the parameters
Heavy operating condition: 20 % increasing load
Figures 3 to 7 show the generator speed following 6 cycles three phase short circuit at bus 1. The results
show the PSS can enhance the system stability and damp out the oscillations. In addition, along with increasing
load, the oscillation become larger and the most oscillations are seen under heavy loading condition. Figure 4
shows the rotor angle and it is clear that fault is occurred at second 1 and after 6-cycles is removed. The rotor
angle oscillations show that system become stable after 15 seconds. Voltage of bus 1 and its angle are depicted
in Figures 5 and 6. The oscillations of these parameters are also damp out after few seconds. Figure 7 shows the
generator speed under heavy loading condition and the oscillations are significantly increased in comparison
with the nominal condition.
Bus 1
Transformator
Infinite Bus
Bus 2
Bus 3
G
Load
Fig. 2: single line diagram of power system.
1.0008
1.0006
Speed G (p.u.)
1.0004
1.0002
1
0.9998
0.9996
0.9994
0
5
10
Time (s)
15
20
Fig. 3: Gnerator speed at nominal operating condition.
1.24
1.235
Rotor angle (Rad)
1.23
1.225
1.22
1.215
1.21
1.205
1.2
1.195
0
5
Fig. 4: Rotor angle at nominal operating condition.
10
Time (s)
15
20
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Reza Saki et al, 2014
Advances in Natural and Applied Sciences, 8(8) July 2014, Pages: 196-200
0.505
Angle of voltage at bus 1 (Rad)
0.5
0.495
0.49
0.485
0.48
0.475
0.47
0
5
10
Time (s)
15
20
Fig. 5: Angle of voltage at bus 1 at nominal operating condition.
1.015
Voltage of bus 1 (Rad)
1.01
1.005
1
0.995
0.99
0.985
0
5
10
Time (s)
15
20
10
Time (s)
15
20
Fig. 6: Voltage of bus 1 at nominal operating condition.
1.0008
1.0006
Speed G (p.u.)
1.0004
1.0002
1
0.9998
0.9996
0.9994
0
5
Fig. 7: Generator speed at heavy operating condition.
Conclusions:
This paper presented a new state feedback to design power system stabilizer at a two-area interconnected
power system. The proposed system was installed with a infinite bus. Two operating conditions were considered
to study the performance of the system under uncertainty. Simulation results demonstrated that the proposed
PSS is very effective to damp out the oscillations.
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REFERENCES
Aström, K.J. and R. M. Murray, 2010. Feedback systems: an introduction for scientists and engineers:
Princeton university press.
Bettayeb, M. and A.Q. Randhawa, 1999. “Time-weighted optimal state and output feedback control of
power systems,” Electric Power Systems Research, 52(1): 77-86, 10/1/.
El-Sherbiny, M.K., A.M. Sharaf, G. El-Saady, 1996. “A novel fuzzy state feedback controller for power
system stabilization,” Electric Power Systems Research, 39(1): 61-65, 10//,.
Li, W., X. Liu, and S. Zhang, 2012. “Further results on adaptive state-feedback stabilization for stochastic
high-order nonlinear systems,” Automatica, 48(8): 1667-1675, 8//.
Lin, Q. and X. Wu, 2011. “The sufficient criteria for global synchronization of chaotic power systems under
linear state-error feedback control,” Nonlinear Analysis: Real World Applications, 12(3): 1500-1509, 6//.
Mahmud,M.A., M.J. Hossain and H.R. Pota, 2014. “Transient stability enhancement of multimachine
power systems using nonlinear observer-based excitation controller,” International Journal of Electrical Power
& Energy Systems, 58(0): 57-63, 6//.
Schuler, S., U. Münz, and F. Allgöwer, 2014. “Decentralized state feedback control for interconnected
systems with application to power systems,” Journal of Process Control, 24(2): 379-388, 2//.