Optimal Feed-back Switching Control for the UPFC Based Damping Controllers

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ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012
Optimal Feed-back Switching Control for the UPFC
Based Damping Controllers
Yathisha L1 and S Patil Kulkarni2
1Research Scholar, E& C Dept, S J College of Engineering, Mysore, India.
Email: [email protected]
2Associate Professor, E & C Dept, S J College of Engineering, Mysore, India.
Email: [email protected]
Abstract---This paper presents an optimal feed-back switching
(LQR), H-infinity, particle swarm optimization etc [2-6].
concept for the Unified Power Flow Controller (UPFC) based
Some of the examples are described here. In [2] authors have
damping controllers for damping low frequency oscillations
shown the control inputs
and
to provide robust
in a power system. Detailed investigations have been carried
out considering switching between two optimal damping

performance when compared to the other damping controllers
controllers; one with respect to modulating index of shunt
by applying a phase compensation control technique with
inverter
and another with respect to modulating index of
respect to state space variable speed. In [3] authors have
presented iterative particle swarm optimization (IPSO) based
series inverter
. The proposed UPFC switching model
UPFC controller to achieve improved robust performance and
presented here is tested on the modified SMIB linearised
to provide superior damping in comparison with the
Phillips-Heffron model of a power system installed with UPFC
using MATLAB/SIMULINK(R) platform. The investigations

conventional particle swarm optimization (CPSO) for the
reveal that the proposed optimal feed-back switching control
control inputs
and
. In [4] author has presented multi
between UPFC damping controllers and provides
machine system, where some of the states having larger
moderately better performance with respect to settling time
settling time with conventional LQR are well regulated with
for both individual controllers as well as coordinated damping
multistage LQR.
controller.
In the current paper, for the modified SMIB linearised
Index Terms--- OFSC, COC, UPFC, LQR, SMIB, Phillips-
Phillips-Heffron model, after doing a preliminary control
Heffron Model.
analysis with individual inputs and coordinated inputs, a
switching strategy between individual controllers is
I. INTRODUCTION
suggested for UPFC devices such that the steady state
response and settling time will be moderately better for all
The Unified Power Flow Controller (UPFC) is a multi-
the four state space variables simultaneously for either cases
functional flexible AC Transmission (FACTS) device, whose
of individual inputs as well as coordinated inputs.
primary duty is power flow control. The secondary functions
Paper is organized as follows, in Section II, modified SMIB
of the UPFC can be voltage control, transient stability
linearised Phillips-Heffron model is described. It is followed
improvement, oscillations damping. It combines features of
by some preliminary analysis, first with individual controllers
both Static Synchronous Compensator (STATCOM) and
later with coordinated controller in Section III. Section IV
Static Synchronous Series Compensator (SSSC).
describes the switching model for Philips-Heffron plant with
Design of control strategies using FACTS devices such
UPFC controllers along with the proposed switching rule.
as UPFC for optimal power flow with improved performance
Results and analysis follow in the concluding section.
is a major research concern of power system control
community. Wang [1] has presented a modified linearised
II. DYNAMIC MODEL OF POWER SYSTEM WITH UPFC
Phillips-Heffron model of a power system installed with UPFC
and addressed basic issues pertaining to design of UPFC
H.F. Wang has presented the following state space model
based power oscillation damping controller along with
for the modified SMIB linearised Phillips-Heffron power
selection of input parameters of UPFC to be modulated in
system [1, 5].
order to achieve desired damping. Wang has not presented a

(1)
systematic approach for designing the damping controllers.
Where, the state variables are the rotor angle deviation
,
Further, no effort seems to have been made to identify the
most suitable UPFC control inputs, in order to arrive at a
speed deviation
, q-axis component deviation
,
robust damping controller for optimal performance of all the
field voltage deviation
and input variables are
state variables. However, in recent times, researchers are
modulating index and phase angle of shunt inverter
working on the selection of UPFC control parameter for the
and modulating index and phase angle of series
design of UPFC damping controller by applying different
inverter
. A and B represent the state and control
control techniques like Phase Compensation, Fuzzy Logic,
input matrices given by
optimal control techniques like Linear Quadratic Regulator
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ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012
Figure 1: COC for Rotor Angle Deviation
All the relevant k-constants and variables along with their
values used in the experiment are described in the appendix
section at the end of paper.
III. PRILIMINARY OPTIMAL CONTROL ANALYSIS
In this section, a preliminary analysis is done by
controlling modulating index of shunt and series inverters
and
(the two chosen inputs for the current research)
using LQR based controllers, in order to gain some insight
into the system behavior and to arrive at a suitable switching
strategy. Analysis is done in two stages. In the first stage the
Figure 2: COC for Speed Deviation
conventional optimal control(COC) analysis is done by
selecting
or as the control inputs individually resulting
in two separate Single Input Single Output (SISO) systems,

Where
the first column of the B matrix for the
input
, and
for the input
The Control law is given by

Where,
and
are the controller gains for
the inputs
and
respectively. Both
and
were
designed by conventional LQR method and state variables
Figure 3: COC for q-axis Component Deviation
were analysed. Refer Fig. 1 to 4. In the second stage COC
analysis is done by selecting both and as the coordinated
inputs resulting in a Multi Input Multi Output (MIMO) system
with

Now controller gain K is 2x4 matrixes for this MIMO model
obtained by LQR algorithm for MIMO system. Analysis re-
sults for all the state variables are presented below in Fig. 1
to 4.
Figure 4: COC for field voltage Deviation
(c) 2012 ACEEE
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ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012
In view of the above optimal control analysis, investigation
Where Q and R are the positive-definite Hermitian or real
of Fig. 1 to 4 reveals that:
symmetric matrix. From the above equations,
a) Any of the above COC can not provide better performance

(5)
for all the four state space variables with respect to peak
And hence the control law is,
overshoot and settling time.
(6)
b)
Provides better performance for q-axis component
In which P must satisfy the reduced Riccati equation:
deviation.
c)
Provides better performance for rotor angle and speed
(7)
deviations.
The LQR function allows you to choose two parameters, R
d) The coordinated inputs and provides better performance
and Q, which will balance the relative importance of the input
for the field voltage deviation.
and state in the cost function that you are trying to optimize.
This optimal control analysis suggests that suitable switching
Essentially, the LQR method allows for the control of all
between controllers and (corresponding to inputs and)
outputs.
may improve the steady state performance of all the four
Here the two controller gains
and
model the UPFC
state space variables.
gains with respect to
and
. The controller gain is the
primary controller and is the secondary controller. Thus the
IV. PROPOSED OPTIMAL FEED-BACK SWITCHING CONTROL
two closed-loop parameters will now be
In this section, mathematical modeling of Phillips-Heffron
system with UPFC devices as a switched linear systems and
and
. In order for
to correspond to
,
the proposed switching algorithm will be explained.
define
and for
to correspond to
,
A. Switched Linear System
define
Now note that,
Switch ed systems ar e composed of a gr oup of
subsystems guided by a switching law that governs the
change among the subsystems. Use of appropriate switching
in control has proved to give better performance when
B. Switching Algorithm
compared to the performance of a system without switching
The switching control algorithm based on [7, 8] can be
control. A switched-linear system model (refer Fig. 5) for the
explained in the following steps:-
current problem is as follows:
1. Define
as the primary controller for
and
for

(2)
where
asymptotically stable and

(3)

not necessarily stable.
2. Determine
by solving the algebraic Lyapunov Equation

3. Using,
define the switching matrix
4. Now, the switching rule is, use secondary controller
with
Figure 5: General implementation of switched linear systems
The switching strategy
shown in (2) takes values 1 and
2 based on switching rule decided by the supervisor leading
RESULTS AND CONCLUSIONS
to closed loop
and
. The
The experimental set-up to test the proposed algorithm
controller gain vectors can be obtained from, linear quadratic
consists of linearised Phillips-Heffron model of SMIB installed
regulator theory. For the sake of completeness LQR theory is
with UPFC described by A and B (modeling and) matrices
now briefly described [4]. The LQR controller generates the
below. The primary controller and alternate controller are
parameters of the gain by minimizing the error criteria in (4).
obtained by solving Riccati equation using R=1 and. The
Consider a linear system characterized by (1) where (A, B) is
matrix C is a vector with zeros along with 1 in any one position
stabilizable. Then the cost index that determines the matrix K
depending on the state variables on which the peak overshoot
of the LQR vector is
and settling time is based. The proposed optimal feed-back
(4)
switching rule S between two controls vector of and is also
given below.
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ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012
Figure 8: OFSC for q-axis component Deviation
The dynamic response curves for the four state space
variables rotor angle deviation
, speed deviation
,
q-axis component deviation
, field voltage deviation
Figure 9: OFSC for field voltage Deviation
are plotted as shown in the Fig. 6 to 9 with the legend
TABLE I: COMPARISON OF SETTLING TIME FOR COC AND OFSC
Switch
and
for the proposed optimal feed-back
switching control (OFSC) damping controllers. Inorder to
show the effectiveness of our proposed method settling time
is also tabulated for the COC and proposed OFSC.
From Fig. 1 to 4 of COC and Fig. 6 to 9 of OFSC and Table
one conclude that the proposed optimal feed-back switching
control provides robust performance in the steady state
period and moderately better performance in the settling time
in all the four state space variables simultaneously compared
to system response with optimally controlled individual
inputs without switching as well as optimally controlled
coordinated input (MIMO model).
APPENDIX
Synchronous Machine:
Excitation System:

Constants for the nominal operating conditions:
Figure 6: OFSC for the Rotor Angle Deviation
Figure 7: OFSC for Speed Deviation
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ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012
ACKNOWLEDGEMENT
4. R. K. Pandey, "Analysis and Design of Multi - stage LQR UPFC,"
IEEE Proceedings, 2010.
Project is Sponsered under the AICTE Grant: 8273/BOR/
5. M. Sobha, R. Sreerama Kumar and Saly George, "ANFIS Based
RPS-72/2007-08.
UPFC Supplemetary Controller for Damping Low Frequency
Oscillations in Power Systems," Regular Paper, JES - 2010.
REFERENCES
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