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298 NOVEL FUZZY OPTIMAL CONTROLLER BASED ON STATCOM BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS
Zahra Rahimkhani
could also be brought to the power system which could
cause severe damages to the shaft of the generator unit
(Xie et al 2012 and Zhu et al 2014).
SSR is a condition of an electrical power system
where electrical networks exchange energy with the
mechanical system of the generator at frequencies less
than the nominal frequency of the transmission line. At
this situation, the turbine-generator oscillates at a fre-
quency corresponding to the torsional mode frequency.
The torsional oscillations may raise and result in the
failure of the turbine shaft (Orman et al 2012).
Numerous papers have been published about damp-
ing the SSR phenomenon, (Fouad et al 1978, Iravani
et al 1994), frequency scanning method (Framer et al
1985, Rana et al 2009), time domain simulation (Zhu
et al 1995) and using exible AC transmission systems
(FACTSs) controllers such as the static synchronous
series compensator (SSSC) Padiyar et al (2006) (Bon-
giorno et al (2008), the uni ed power ow controller
(UPFC) (Bo et al (2002), the thyristor controlled series
capacitor (TCSC) (Pilotto et al (2003)) and high voltage
direct current (HVDC) transmission systems (Jiang et al
(2005) have been applied to prevent the SSR in power
systems.
Rotor oscillations of generator at a torsion mode fre-
quency, (fm) induce armature voltage components at
frequencies (fern) given by:
When the sub synchronous component term is close
to electrical resonant frequency, the sub synchronous
torques produced by sub synchronous voltage compo-
nents can be sustained. This interplay between electrical
and mechanical systems is termed as torsional oscilla-
tions ( Xie et al (2012).
As a new type of reactive power compensation FACTS
device, STATCOM has a fast and smooth control per-
formance. By applying appropriate control strategies,
STATCOM could be used to damp power frequency oscil-
lation, enhancing power transfer and voltage stability.
In this paper, the damping of torsional oscillations
using STATCOM has been studied and novel supplemen-
tary sub synchronous damping controller based on fuzzy
optimal technique is proposed. Optimal control method
which is used along fuzzy damping controller will be
designed based on linear quadratic regulator (LQR) that
minimizes the cost function in order to achieve the
optimal tradeoff between the use of control effort, the
magnitude and the speed of response. Also it guaran-
tees a stable control system. The Fuzzy logic is used to
design of control system in outer loops of controller and
designed supplementary controller for damping oscilla-
tion in STATCOM. Simulation results which is obtained
by MATLAB, veri es the effectiveness of the STATCOM
and its control strategy for damping SSR oscillations.
DYNAMIC MODELLING OF STATCOM
The system considered is an IEEE benchmark used to
study subsynchronous resonance. The modeling aspects
of the electromechanical system are given in detail in
reference. This system is shown in Fig.1.
One convenient method for studying balanced three-
phase system (especially in synchronous machine
problems) is to convert the three phase voltages and
currents into synchronous rotating frame by abc/dq
transformation. The bene ts of such arrangement are:
the control problem is greatly simpli ed because the
system variables become DC values under balanced
condition; multiple control variables are decoupled so
that the use of classic control method is possible, and
even more physical meaning for each control variable can
be acquired. Equations (2) to (4) give the mathematical
expression of the STATCOM shown in Fig 1.
Fig. 2 illustrates the detailed control block diagram
of STATCOM according to dynamic equations (Xin et al
2009 and Yidan et al 2011).
OPTIMAL CONTROLLER BASED ON LQR
The theory of optimal control is concerned with operat-
ing a dynamic system at minimum cost. The case where
the system dynamics are described by a set of linear dif-
ferential equations and the cost is described by a quad-
ratic function is called the LQ problem. One of the main
results in the theory is that the solution is provided by
the linear-quadratic regulator (LQR), a feedback control-
ler whose equations are given below.
This method determines the feedback gain matrix
that minimizes the cost function in order to achieve the
optimal tradeoff between the use of control effort, the
magnitude and the speed of response. In addition, this
method guarantees a stable control system.
Given a linear system:
Where x (t) are the system’s states, u(t) is the system
input and y(t) is the output. The objective is to design a
(1)
(2)
(3)
(4)
(5)