![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
1
Research Scholar, E& C Dept, S J College of Engineering, Mysore, India.
Email: yathisha_171@yahoo.co.in
2
Associate Professor, E & C Dept, S J College of Engineering, Mysore, India.
Email: pk.sudarshan@gmail.com
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
series inverter . The proposed UPFC switching model
presented iterative particle swarm optimization (IPSO) based
UPFC controller to achieve improved robust performance and
presented here is tested on the modified SMIB linearised
Phillips-Heffron model of a power system installed with UPFC to provide superior damping in comparison with the
using MATLAB/SIMULINK® 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
© 2012 ACEEE 49
DOI: 01.IJCSI.03.02.79](https://image.slidesharecdn.com/79-120910025252-phpapp02/85/Optimal-Feed-back-Switching-Control-for-the-UPFC-Based-Damping-Controllers-1-320.jpg)
![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,
Switched systems are composed of a group 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
controller gain vectors can be obtained from, linear quadratic The experimental set-up to test the proposed algorithm
regulator theory. For the sake of completeness LQR theory is consists of linearised Phillips-Heffron model of SMIB installed
now briefly described [4]. The LQR controller generates the with UPFC described by A and B (modeling and) matrices
parameters of the gain by minimizing the error criteria in (4). below. The primary controller and alternate controller are
Consider a linear system characterized by (1) where (A, B) is obtained by solving Riccati equation using R=1 and. The
stabilizable. Then the cost index that determines the matrix K matrix C is a vector with zeros along with 1 in any one position
of the LQR vector is depending on the state variables on which the peak overshoot
and settling time is based. The proposed optimal feed-back
(4) switching rule S between two controls vector of and is also
given below.
© 2012 ACEEE 51
DOI: 01.IJCSI.03.02.79](https://image.slidesharecdn.com/79-120910025252-phpapp02/85/Optimal-Feed-back-Switching-Control-for-the-UPFC-Based-Damping-Controllers-3-320.jpg)
Optimal Feed-back Switching Control for the UPFC Based Damping Controllers
- 1. 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 1 Research Scholar, E& C Dept, S J College of Engineering, Mysore, India. Email: yathisha_171@yahoo.co.in 2 Associate Professor, E & C Dept, S J College of Engineering, Mysore, India. Email: pk.sudarshan@gmail.com 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 series inverter . The proposed UPFC switching model presented iterative particle swarm optimization (IPSO) based UPFC controller to achieve improved robust performance and presented here is tested on the modified SMIB linearised Phillips-Heffron model of a power system installed with UPFC to provide superior damping in comparison with the using MATLAB/SIMULINK® 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 © 2012 ACEEE 49 DOI: 01.IJCSI.03.02.79
- 2. 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 CONTROLANALYSIS 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 © 2012 ACEEE 50 DOI: 01.IJCSI.03.02.79
- 3. 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, Switched systems are composed of a group 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 controller gain vectors can be obtained from, linear quadratic The experimental set-up to test the proposed algorithm regulator theory. For the sake of completeness LQR theory is consists of linearised Phillips-Heffron model of SMIB installed now briefly described [4]. The LQR controller generates the with UPFC described by A and B (modeling and) matrices parameters of the gain by minimizing the error criteria in (4). below. The primary controller and alternate controller are Consider a linear system characterized by (1) where (A, B) is obtained by solving Riccati equation using R=1 and. The stabilizable. Then the cost index that determines the matrix K matrix C is a vector with zeros along with 1 in any one position of the LQR vector is depending on the state variables on which the peak overshoot and settling time is based. The proposed optimal feed-back (4) switching rule S between two controls vector of and is also given below. © 2012 ACEEE 51 DOI: 01.IJCSI.03.02.79
- 4. 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 © 2012 ACEEE 52 DOI: 01.IJCSI.03.02.79
- 5. 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 6. H. Shayeghi, H. A. Shayanfar and A. Safari, “Design of Output 1. H. F. Wang, “A Unified Model for the Analysis of FACTS Devices Feed-back UPFC Controllers for Damping of Electromechanical in Damping Power System Oscillations - part lll: Unified Power Oscillations Using PSO,” ELSEVIER Article of Energy Conversion Flow Controller” IEEE Transactions on Power Delivery, Vol. 15, and Management, JES - 2009. no 3, pp. 978-983, 2000. 7. Yathisha L, S. Patil Kulkarni and R. S. Ananda Murthy, “Hybrid 2. N. Tambey and M. L. Kothari, “Unified Power Flow Controller Modelling and Switching Algorithm for Power System with FACTS (UPFC) Based Damping Controllers for Damping Low Frequency Based Controllers,” Proceedings of International Conference on Oscilltions in a power system,” IE (I) Journal - EL, Vol. 84, pp. 35- System Dynamics and Control, pp. 367-372, 2010. 41, 2003. 8. Lalitha S Devarakonda, “Performance Based Switching Control 3. Amin Safari and Shayeghi, “Optimal Design of UPFC Based for Single Input Linear Time Invariant System,” M.S Thesis, Damping Controller using Iteration PSO,” International Journal of Department of Electrical and Electronics Engineering, Louisiana Electrical Power and Energy System Engineering, pp. 151-156, State University, Dec- 2005. 2009. © 2012 ACEEE 53 DOI: 01.IJCSI.03.02.79