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

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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

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

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

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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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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.

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