ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012  Optimal Feed-back Switching Control for ...
ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012                                          ...
ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012In view of the above optimal control analy...
ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012                                          ...
ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012                    ACKNOWLEDGEMENT       ...
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Optimal Feed-back Switching Control for the UPFC Based Damping Controllers

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The Unified Power Flow Controller (UPFC) is a multifunctional
flexible AC Transmission (FACTS) device, whose
primary duty is power flow control. The secondary functions
of the UPFC can be voltage control, transient stability
improvement, oscillations damping. It combines features of
both Static Synchronous Compensator (STATCOM) and
Static Synchronous Series Compensator (SSSC).

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

  1. 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.comAbstract—-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 havedamping controllers for damping low frequency oscillations shown the control inputs and to provide robustin a power system. Detailed investigations have been carriedout considering switching between two optimal damping performance when compared to the other damping controllerscontrollers; one with respect to modulating index of shunt by applying a phase compensation control technique withinverter and another with respect to modulating index of respect to state space variable speed. In [3] authors haveseries inverter . The proposed UPFC switching model presented iterative particle swarm optimization (IPSO) based UPFC controller to achieve improved robust performance andpresented here is tested on the modified SMIB linearisedPhillips-Heffron model of a power system installed with UPFC to provide superior damping in comparison with theusing MATLAB/SIMULINK® platform. The investigations conventional particle swarm optimization (CPSO) for thereveal that the proposed optimal feed-back switching control control inputs and . In [4] author has presented multibetween UPFC damping controllers and provides machine system, where some of the states having largermoderately better performance with respect to settling time settling time with conventional LQR are well regulated withfor both individual controllers as well as coordinated damping multistage LQR.controller. In the current paper, for the modified SMIB linearisedIndex Terms—- OFSC, COC, UPFC, LQR, SMIB, Phillips- Phillips-Heffron model, after doing a preliminary controlHeffron 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 casesfunctional 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 SMIBof the UPFC can be voltage control, transient stability linearised Phillips-Heffron model is described. It is followedimprovement, oscillations damping. It combines features of by some preliminary analysis, first with individual controllersboth Static Synchronous Compensator (STATCOM) and later with coordinated controller in Section III. Section IVStatic 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 controlcommunity. Wang [1] has presented a modified linearised II. DYNAMIC MODEL OF POWER SYSTEM WITH UPFCPhillips-Heffron model of a power system installed with UPFCand addressed basic issues pertaining to design of UPFC H.F. Wang has presented the following state space modelbased power oscillation damping controller along with for the modified SMIB linearised Phillips-Heffron powerselection 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 themost 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 arestate variables. However, in recent times, researchers are modulating index and phase angle of shunt inverterworking on the selection of UPFC control parameter for the and modulating index and phase angle of seriesdesign of UPFC damping controller by applying different inverter . A and B represent the state and controlcontrol techniques like Phase Compensation, Fuzzy Logic, input matrices given byoptimal control techniques like Linear Quadratic Regulator© 2012 ACEEE 49DOI: 01.IJCSI.03.02.79
  2. 2. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012 Figure 1: COC for Rotor Angle DeviationAll the relevant k-constants and variables along with theirvalues used in the experiment are described in the appendixsection at the end of paper. III. PRILIMINARY OPTIMAL CONTROLANALYSIS In this section, a preliminary analysis is done bycontrolling 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 insightinto the system behavior and to arrive at a suitable switchingstrategy. Analysis is done in two stages. In the first stage the Figure 2: COC for Speed Deviationconventional optimal control(COC) analysis is done byselecting or as the control inputs individually resultingin two separate Single Input Single Output (SISO) systems,Where the first column of the B matrix for theinput , and for the inputThe Control law is given byWhere, and are the controller gains forthe inputs and respectively. Both and weredesigned by conventional LQR method and state variables Figure 3: COC for q-axis Component Deviationwere analysed. Refer Fig. 1 to 4. In the second stage COCanalysis is done by selecting both and as the coordinatedinputs resulting in a Multi Input Multi Output (MIMO) systemwithNow controller gain K is 2x4 matrixes for this MIMO modelobtained by LQR algorithm for MIMO system. Analysis re-sults for all the state variables are presented below in Fig. 1to 4. Figure 4: COC for field voltage Deviation© 2012 ACEEE 50DOI: 01.IJCSI.03.02.79
  3. 3. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012In view of the above optimal control analysis, investigation Where Q and R are the positive-definite Hermitian or realof 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, Rd) The coordinated inputs and provides better performance and Q, which will balance the relative importance of the inputfor 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 allbetween 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 UPFCstate 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-Heffronsystem 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 ofsubsystems guided by a switching law that governs thechange among the subsystems. Use of appropriate switchingin control has proved to give better performance when B. Switching Algorithmcompared to the performance of a system without switching The switching control algorithm based on [7, 8] can becontrol. 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 systemsThe switching strategy shown in (2) takes values 1 and2 based on switching rule decided by the supervisor leading RESULTS AND CONCLUSIONSto closed loop and . Thecontroller gain vectors can be obtained from, linear quadratic The experimental set-up to test the proposed algorithmregulator theory. For the sake of completeness LQR theory is consists of linearised Phillips-Heffron model of SMIB installednow briefly described [4]. The LQR controller generates the with UPFC described by A and B (modeling and) matricesparameters of the gain by minimizing the error criteria in (4). below. The primary controller and alternate controller areConsider a linear system characterized by (1) where (A, B) is obtained by solving Riccati equation using R=1 and. Thestabilizable. Then the cost index that determines the matrix K matrix C is a vector with zeros along with 1 in any one positionof 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 51DOI: 01.IJCSI.03.02.79
  4. 4. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 02, March 2012 Figure 8: OFSC for q-axis component DeviationThe dynamic response curves for the four state spacevariables 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 OFSCSwitch and for the proposed optimal feed-backswitching control (OFSC) damping controllers. Inorder toshow the effectiveness of our proposed method settling timeis also tabulated for the COC and proposed OFSC. From Fig. 1 to 4 of COC and Fig. 6 to 9 of OFSC and Tableone conclude that the proposed optimal feed-back switchingcontrol provides robust performance in the steady stateperiod and moderately better performance in the settling timein all the four state space variables simultaneously comparedto system response with optimally controlled individualinputs without switching as well as optimally controlledcoordinated 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 52DOI: 01.IJCSI.03.02.79
  5. 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 BasedRPS-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 Output1. H. F. Wang, “A Unified Model for the Analysis of FACTS Devices Feed-back UPFC Controllers for Damping of Electromechanicalin Damping Power System Oscillations - part lll: Unified Power Oscillations Using PSO,” ELSEVIER Article of Energy ConversionFlow 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, “Hybrid2. 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 onOscilltions 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 Control3. 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, LouisianaElectrical Power and Energy System Engineering, pp. 151-156, State University, Dec- 2005.2009.© 2012 ACEEE 53DOI: 01.IJCSI.03.02.79

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