1.IJASCSE, VOL 1, ISSUE 4, 2012Dec. 31Performance analysis of a model predictive unified power flow controller (MPUPFC) as a solution of power system stabilityMd. Shoaib Shahriar1, Md. Saiful Islam2, B. M. Ruhul Amin31 School of Engineering and Computer Science (SECS), Independent University Bangladesh (IUB), Bashundhara R/A, Baridhara, Dhaka, Bangladesh.2Department of Electrical and Electronic Engineering, Islamic University of Technology (IUT), BoardBazar, Gazipur-1704, Bangladesh.3Department of Electrical and Electronic Engineering, Bangladeh University of Business and Technology (BUBT),Mirpur-1216, Bangladesh.Abstract This paper addresses model predictive attractive and effective features. It is capable ofcontroller (MPC) as a powerful solution for providing simultaneous control of voltage magnitudeimproving the stability of an FACTS device like and active and reactive power flows, in adaptiveunified power flow controller (UPFC) connectedfashion. It has the ability to control the power flow insingle machine infinite bus (SMIB) power system.transmission line, improve the transient stability,UPFC is mainly used in the transmission systems mitigate system oscillation and provide voltagewhich can control the power flow by controlling support [1, 4].the voltage magnitude, phase angle andA number of researches had been done to find out theimpedance. And as a controller, MPC, not only control schemes for performing the oscillation-provides the optimal control inputs, but also damping task of UPFC. Among the controllers whichpredicts the system model outputs which enable it are used to control the FACTS devices, modelto reach the desired goal. So, model predictivepredictive controller (MPC) has got a wide range ofunified power flow controller (MPUPFC), aattractive and versatile features. Now a day, thiscombination of UPFC and MPC along withcontroller is widely used in the field of industry as itproper system model parameters can provide asatisfactory performance in damping out the has the ability to implement constraints in controlsystem oscillations making the system stable. process system. A good overview of industrial linearSimulation is done in Matlab. Response is shown MPC techniques can be found in [5-7].for 4 different states. Effects are shown for 4 In this paper, model predictive Controller (MPC) hascontrol signals of UPFC operating individuallybeen chosen to control UPFC. Attractive features ofand combining 2 at a time.these two tools jointly provide a very satisfactorysolution to the system stability. System model of Keywords Power system stability, system model,SMIB system along with UPFC is controlled hereUPFC, FACTS, MPC. with MPC for four different control signals of UPFC.Impact of the system for different combinations ofI. INTRODUCTION control signals is also investigated.Power system oscillations are an inevitablephenomenon of the system. Faults and weakprotective relaying operation can cause the oscillation II.SYSTEM DYNAMIC MODELto collapse the system [1]. In order to damp thesepower system oscillations, different devices andThe power system [8] that is studied in this papercontrol methods are used [2]. FACTS technology is consists of a synchronous generator connected tothe newest way of improving power system operationtransmission lines and an infinite bus via twotransformers. The UPFC consists of an excitationcontrollability and power transfer limits which hastransformer (ET), a boosting transformer (BT), twobeen added in the stream with the progress in thethree-phase GTO based voltage source convertersfield of power electronics devices. FACTS devices (VSCs); which are connected to each other with acan cause a substantial increase in power transfercommon dc link capacitor [1].limits during steady state operation [3]. Among the Fig. 1 shows a SMIB system equipped with anFACTS devices, UPFC is the one having veryUPFC. The four input control signals to the UPFCwww.ijascse.in Page 56

2. IJASCSE, VOL 1, ISSUE 4, 2012Dec. 31are mE, mB, E, and B. Where, mE is the excitation By applying Parks transformation and neglecting theamplitude modulation ratio, resistance and transients of the ET and BTmB is the boosting amplitude modulation ratio,transformers, the UPFC can be modeled by theE is the excitation phase angle, and following equations (5-7):B is the boosting phase angle. mE cos E vdc vEtd iEd 2 [ ] + vEtq iEq mE s in E vdc 2 (5) mB cos B vdc vBtd iBd 2 [ ] + vBtq iBq mB s in B vdc 2Fig 1: SMIB power system equipped with UPFC (6) 3mE3mIn stability and control studies of power system vdc (cos E iEd sin E iEq ) B (cos BiBd sin BiBq ) 4Cdc 4Cdcoscillations, the linearized model can be used. In thispaper dynamic model of the system for small signal.. (7)stability improvement is used. Nominal parameters Where, vEt , iE , vBt , and iB are the excitation voltage,used for system modeling are given in Appendix-I. excitation current, boosting voltage, and boostingcurrent, respectively; Cdc and vdc are the DC linkThe nonlinear model of the SMIB system of Fig 1 capacitance and voltage.can be expressed by the following differentialequations (1-4) [8]:By combining and linearizing the equations (1-7) base ( 1) (1) state space equations of system will be obtainedwhich are present in equations (8). In this process1 [ Pm Pe D( 1)] (2)there are 28 constants denoted by k are being used.2H= AX + BU . (8) 1where the state vector X and control vector U areEq [ E fd Eq ( xd xd )id ] (3)X = [ EqEfd Vdc]T TdoU = [Upss mE E mB B]T 1E fd K A ((Vref v U pss ) E fd ) (4)WhereTAwhere Pm and Pe are the input and output power, 0b 000 respectively. P vd id vqiq , vt e v 2d v2q , K1D K20 K pd M M vd xqiq xq iiq ilq , vq Eq xdid ,M MK qd K K31A 4 0 id iEd iBd , iq iEq iBq , T d 0 T d 0T d 0T d 0 M and D the inertia constant and damping K A K5 0 K A K6 1K K A vd coefficient, respectively; base the synchronous speed; TA TATA TA and the rotor angle and speed, respectively; Eq , K70 K8 0 K9 Efd, and v the generator internal, field and terminalvoltages, respectively; Tdo the open circuit field timeconstant; xd and xd the d-axis reactance, d-axistransient reactance respectively; KA and TA theexciter gain and time constant, respectively; Vref thereference voltage; and uPSS the PSS control signal.andwww.ijascse.in Page 57 3. IJASCSE, VOL 1, ISSUE 4, 2012Dec. 31 0 0 000 prediction horizon is infinite, one could apply the K peK pdeK pbK pdb control strategy found at current time k for all times. 0 However, due to the disturbances, model-plantMM M M mismatch and finite prediction horizon, the true K qe K qdeK qbK qdb B 0 system behavior is different from the predicted T d 0T d 0 T d 0T d 0 behavior. In order to incorporate the feedback information about the true system state, the computed KA K A K ve K A K vdeK A K vbK K A vdb optimal control is implemented only until the next TA TA TA TA TA measurement instant ( k , k 1 ), at which point the 0 K ceK cdeK cb K cdb entire computation is repeated [10].III. DAMPING CONTROL MPC approach can be expressed considering theThe unique feature of MPC which has made itfollowing finite horizon cost function [10]H 1J ( xt ,[u0 (t ),..., uH 1 (t )]) h( xt iT (u), ui (t )) g ( xt H T (u))different from other controllers is the ability to rhpredict the future response of the plant. At eachcontrol interval an MPC algorithm attempts toi 1optimize future plant behavior by computing asequence of future manipulated variable adjustments where t is the current time; H is the length of the[9]. Figure 2 shows the basic working principle of optimization horizon; T is the sample period. If i >MPC.Prediction horizon (TP) is the time range which, 0, then xt iT (u ) denotes the controlled trajectory at time t iT from xt under piecewise controlsfuture system outputs are predicted in it. Controlhorizon (Tc) is the time steps number that inputcontrol sequence calculations for the prediction u [u0 (t ),..., ui 1 (t )] U H ; h is the running cost;horizon are done [9]. In this plant model, value ofand g is the terminal cost. We assume that h is non-prediction horizon is taken 20 and control horizon is negative function and g satisfies g ( x) x xeq2. for all x, where xeq is some desired equilibrium and Set-point >0 is some positive constant. That is, g is an past futuretrajectory upward function whose lowest point is at the system equilibrium. This condition on g(.) ensures Predicted Output that the control design attempts to reach the system equilibrium.Manipulated u(k) Fig 3 shows a complete block representation ofInputs UPFC connected SMIB system controlled with MPC.k k+1k+Hck+HpInput horizon A,BLinearized System Model Output horizon x Ax Buy-Fig 2: The receding horizon principle of model+ xQuadratic Programmingu y Power System (SMIB)(QP) Problempredictive control yref Plant Cost Function andAt a current instant k, the MPC solves an Constraints Equationoptimization problem over a finite prediction horizonMPC[k , k H P ] with respect to a predeterminedobjective function such that the predicted stateFig 3: Block diagram representation of UPFC variable x or output y can optimally stay close to aconnected SMIB system controlled with MPCreference trajectory. The control is computed over a The UPFC connected SMIB power system plant iscontrol horizon [k , k H C ] , which is smaller than connected here with the MPC block. The output ofthe prediction horizon ( H C H P ). If there were nothe plant (y) enters into the summing junction where it has been compared with the reference value (yref).disturbances, no model-plant mismatch and theSubtracted result (y) goes into the MPC block. Thewww.ijascse.in Page 58 4. IJASCSE, VOL 1, ISSUE 4, 2012Dec. 31information about the plant (system matrix A,B) are vxtE vEtvBtvb xBValready given to the MPC block. So, the linearizediBxBsystem model of the plant gives the future output (u)itVSC EVSC B iE BTwith the help of Quadratic Programming (QP)function of MPC and proper constraints of the MPCxEblock. Predicted output of the controller, u enters into ETthe plant and creates the next result y. Thus the loop vdcwill continue until it reaches the desired referencetrajectory of the plant.mE EmB BFigure 4 show the circuital representation of UPFCconnected SMIB system controlled with MPC which MPC Controlleris actually the modification of Fig 1.Four control signals of UPFC (mE, mB, E, and B) are Change in speed orpower outputentering into the UPFC connected SMIB plant Fig 4: Circuital representation of UPFC connectedthrough MPC. Thus MPC is connected with theSMIB system controlled with MPC (modification ofsystem model through UPFC. Fig 1)IV.SIMULATION RESULTS A disturbance of pulse type signal is given in the Response of MPC on proposed model is observed for 4 systems Pe. Disturbance duration (period) is 0.1 sec,different states , , Eq and Efd. Individual effects disturbance amplitude (size) is 1 unit and disturbance of 4 different control signals mE, E, mB and B on system occurring time is 1 sec. states are observed first in figure (5-8) Value of prediction horizon is taken as 10, control horizon is 2 and control interval is chosen as 0.5 in Matlab MPC toolbox.Fig 5: Responses for control signal mE for states (i) , (ii) , (iii) Eq,and (iv) EfdFig 6: Responses for control signal mB for states (i) , (ii) , (iii) Eq,and (iv) Efdwww.ijascse.in Page 59 5. IJASCSE, VOL 1, ISSUE 4, 2012Dec. 31Fig 7: Responses for control signal E for states (i) , (ii) , (iii) Eq,and (iv) EfdFig 8: Responses for control signal B for states (i) , (ii) , (iii) Eq,and (iv) EfdIt has been seen that mE (Fig. 5) and E (Fig. 7) give the worse applications involve plants having multiple inputs and outputs.response. They can bring stability only in state . Control Here, combination of different control signals of UPFC is nowsignal B also doesnt have a good response characteristicsapplied as input to the plant to observe the responses on(Fig. 8). It can stable several states but takes a long time for different states.that. Among the four signals, mB gives the best output makingThen, the responses are observed for different combinations ofall the 4 states stable at a reasonable time of below 6 secondscontrol signals two at a time. Four different combinations of(Fig. 6).two control signals are observed in this paper in fig (9-12).An exceptional and effective feature of MPC is the ability toprovide support to the MIMO plants. Most MPC toolboxwww.ijascse.in Page 60 6. IJASCSE, VOL 1, ISSUE 4, 2012Dec. 31 Fig 9: Responses for control signal mB and mE together for states (i) , (ii) , (iii) Eq,and (iv) EfdFig 10: Responses for control signal B and E together for states (i) , (ii) , (iii) Eq,and (iv) Efd Fig 11: Responses for control signal mB and B together for states (i) , (ii) , (iii) Eq,and (iv) Efd Fig 12: Responses for control signal mB and E together for states (i) , (ii) , (iii) Eq,and (iv) Efdwww.ijascse.in Page 61 7. IJASCSE, VOL 1, ISSUE 4, 2012Dec. 31Observing the combined effect of two different time to settle (Fig. 10). But the other 4 states arecontrol signals, it has been found that the responsessettled down within 3 seconds. Combination of mB-Bare significantly improved for every case than (Fig. 11), mE-mB (Fig. 9) and mB-E (Fig. 12) showapplying them individually. Among the 5the best responses here making all the 5 states stablecombinations, combination of E and B takes a longwithin a short time of 3 seconds.CONCLUSION proposed model is the use of MPC with four controlIn this paper by linearizing and combining the signals of UPFC at a time.equations of single machine infinite bus powersystem and unified power flow controller, a complete Appendix:state space model of SMIB power system includingUPFC was presented. Effect for model predictiveThe parameters used in system model:controller for stability analysis is observed then for Generator: M = 8 MJ/MVA, Td0 = 5.044 s, D =different states of the system model. Different0 , Xq = 0.6 pu, Xd = 1.0 pu, Xd = 0.3 pucombinations and individual impacts of four differentTransformers: XT = 0.1 pu, XE = 0.1 pu, XB = 0.1 pucontrol signals of UPFC are analyzed. It has beenTransmission line : XL = 0.1 pufound that the system performs better if MPC isOperating condition: Pe = 0.8 pu,Q=.1670pu , Vb = 1allowed to operate with multiple control signals ofpu, Vt = 1 puUPFC. Impact of MPC as MIMO plant is thusDC link parameter: VDC = 2 pu, CDC = 1.2 puevident. Best solution of stability analysis for theREFERENCE[1] Shayeghi H. - Jalilizadeh S. - Shayanfar H. -[6] Qin S.J. and Badgwell T.A. An overview ofSafari A. : Simultaneous coordinated designing of industrial model predictive control technology, In F.UPFC and PSS output feedback controllers using Allgower and A. Zheng, editors, Fifth InternationalPSO, Journal of ELECTRICAL ENGINEERING, Conference on Chemical Process Control CPC V,VOL. 60, NO. 4, 2009, 177184pages 232256. American Institute of Chemical Engineers, 1996.[2] Anderson P. 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