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IJASCSE, VOL 1, ISSUE 4, 2012 Dec. 31 Performance analysis of a model predictive unified power flow controller (MPUPFC) as a solution of power system stability Md. Shoaib Shahriar1, Md. Saiful Islam2, B. M. Ruhul Amin3 1 School of Engineering and Computer Science (SECS), Independent University Bangladesh (IUB), Bashundhara R/A, Baridhara, Dhaka, Bangladesh. 2 Department of Electrical and Electronic Engineering, Islamic University of Technology (IUT), BoardBazar, Gazipur-1704, Bangladesh. 3 Department 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 of controller (MPC) as a powerful solution for providing simultaneous control of voltage magnitude improving the stability of an FACTS device like and active and reactive power flows, in adaptive unified power flow controller (UPFC) connected fashion. It has the ability to control the power flow in single 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 voltage which can control the power flow by controlling support [1, 4]. the voltage magnitude, phase angle and A number of researches had been done to find out the impedance. 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 which predicts the system model outputs which enable it are used to control the FACTS devices, model to reach the desired goal. So, model predictive predictive controller (MPC) has got a wide range of unified power flow controller (MPUPFC), a attractive and versatile features. Now a day, this combination of UPFC and MPC along with controller is widely used in the field of industry as it proper system model parameters can provide a satisfactory performance in damping out the has the ability to implement constraints in control system oscillations making the system stable. process system. A good overview of industrial linear Simulation 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) has control signals of UPFC operating individually been chosen to control UPFC. Attractive features of and combining 2 at a time. these two tools jointly provide a very satisfactory solution to the system stability. System model of Keywords— Power system stability, system model, SMIB system along with UPFC is controlled here UPFC, FACTS, MPC. with MPC for four different control signals of UPFC. Impact of the system for different combinations of I. INTRODUCTION control signals is also investigated. Power system oscillations are an inevitable phenomenon of the system. Faults and weak protective relaying operation can cause the oscillation II.SYSTEM DYNAMIC MODEL to collapse the system [1]. In order to damp these power system oscillations, different devices and The power system [8] that is studied in this paper control methods are used [2]. FACTS technology is consists of a synchronous generator connected to the newest way of improving power system operation transmission lines and an infinite bus via two transformers. The UPFC consists of an excitation controllability and power transfer limits which has transformer (ET), a boosting transformer (BT), two been added in the stream with the progress in the three-phase GTO based voltage source converters field of power electronics devices. FACTS devices (VSCs); which are connected to each other with a can cause a substantial increase in power transfer common dc link capacitor [1]. limits during steady state operation [3]. Among the Fig. 1 shows a SMIB system equipped with an FACTS devices, UPFC is the one having very UPFC. The four input control signals to the UPFC www.ijascse.in Page 56 IJASCSE, VOL 1, ISSUE 4, 2012 Dec. 31 are mE, mB, δE, and δB. Where, mE is the excitation By applying Park’s transformation and neglecting the amplitude modulation ratio, resistance and transients of the ET and BT mB is the boosting amplitude modulation ratio, transformers, the UPFC can be modeled by the δE is the excitation phase angle, and following equations (5-7): δB 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 2 Fig 1: SMIB power system equipped with UPFC …… (6) 3mE 3m In stability and control studies of power system vdc (cos E iEd sin E iEq ) B (cos BiBd sin BiBq ) 4Cdc 4Cdc oscillations, the linearized model can be used. In this paper 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 boosting current, respectively; Cdc and vdc are the DC link The nonlinear model of the SMIB system of Fig 1 capacitance and voltage. can be expressed by the following differential equations (1-4) [8]: By combining and linearizing the equations (1-7) base ( 1) … … … … … … … … (1) state space equations of system will be obtained which are present in equations (8). In this process 1 [ Pm Pe D( 1)] … … … … (2) there are 28 constants denoted by k are being used. 2H = AΔX + BΔU ………………. (8) 1 where the state vector ΔX and control vector ΔU are Eq ' [ E fd Eq ( xd xd )id ] … … … (3) ' ' ' ΔX = [Δδ Δω ΔEʹq ΔEfd ΔVdc]T Tdo ΔU = [ΔUpss ΔmE ΔδE ΔmB ΔδB]T 1 E fd K A ((Vref v U pss ) E fd ) … (4) Where TA where Pm and Pe are the input and output power, 0 b 0 0 0 respectively. P vd id vqiq , vt e v 2 d v 2 q , K1 D K2 0 K pd M M vd xqiq xq iiq ilq , vq Eq ' xd ' id , M M K qd K K3 1 A 4 0 id iEd iBd , iq iEq iBq , T 'd 0 T 'd 0 T 'd 0 T 'd 0 M and D the inertia constant and damping K A K5 0 K A K6 1 K K A vd coefficient, respectively; ωbase the synchronous speed; TA TA TA TA δ and ω the rotor angle and speed, respectively; E′q , K7 0 K8 0 K9 Efd, and v the generator internal, field and terminal voltages, respectively; T′do the open circuit field time constant; xd and x′d the d-axis reactance, d-axis transient reactance respectively; KA and TA the exciter gain and time constant, respectively; Vref the reference voltage; and uPSS the PSS control signal. and www.ijascse.in Page 57 IJASCSE, VOL 1, ISSUE 4, 2012 Dec. 31 0 0 0 0 0 prediction horizon is infinite, one could apply the K pe K pde K pb K pdb control strategy found at current time k for all times. 0 However, due to the disturbances, model-plant M M M M mismatch and finite prediction horizon, the true K qe K qde K qb K qdb B 0 system behavior is different from the predicted T 'd 0 T 'd 0 T 'd 0 T '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 vde K A K vb K 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 ce K cde K cb K cdb entire computation is repeated [10]. III. DAMPING CONTROL MPC approach can be expressed considering the The unique feature of MPC which has made it following finite horizon cost function [10] H 1 J ( 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 rh predict the future response of the plant. At each control interval an MPC algorithm attempts to i 1 optimize future plant behavior by computing a sequence 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; ΔT 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 controls future system outputs are predicted in it. Control horizon (Tc) is the time steps number that input control 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 of and 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 xeq 2. for all x, where xeq is some desired equilibrium and Set-point α>0 is some positive constant. That is, g is an past future trajectory ‘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 of Inputs UPFC connected SMIB system controlled with MPC. k k+1 k+Hc k+Hp Input horizon A,B Linearized System Model Output horizon x Ax Bu y - Fig 2: The receding horizon principle of model + x Quadratic Programming u y Power System (SMIB) (QP) Problem predictive control yref Plant Cost Function and At a current instant k, the MPC solves an Constraints Equation optimization problem over a finite prediction horizon MPC [k , k H P ] with respect to a predetermined objective function such that the predicted state Fig 3: Block diagram representation of UPFC ˆ ˆ variable x or output y can optimally stay close to a connected SMIB system controlled with MPC reference trajectory. The control is computed over a The UPFC connected SMIB power system plant is control horizon [k , k H C ] , which is smaller than connected here with the MPC block. The output of the prediction horizon ( H C H P ). If there were no the plant (y) enters into the summing junction where it has been compared with the reference value (yref). disturbances, no model-plant mismatch and the Subtracted result (∆y) goes into the MPC block. The www.ijascse.in Page 58 IJASCSE, VOL 1, ISSUE 4, 2012 Dec. 31 information about the plant (system matrix A,B) are v xtE vEt vBt vb xBV already given to the MPC block. So, the linearized iB xB system model of the plant gives the future output (u) it VSC E VSC B iE BT with the help of Quadratic Programming (QP) function of MPC and proper constraints of the MPC xE block. Predicted output of the controller, u enters into ET the plant and creates the next result y′. Thus the loop vdc will continue until it reaches the desired reference trajectory of the plant. mE E mB B Figure 4 show the circuital representation of UPFC connected SMIB system controlled with MPC which MPC Controller is actually the modification of Fig 1. Four control signals of UPFC (mE, mB, δE, and δB) are Change in speed or power output entering into the UPFC connected SMIB plant Fig 4: Circuital representation of UPFC connected through MPC. Thus MPC is connected with the SMIB system controlled with MPC (modification of system 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 system’s ΔPe. Disturbance duration (period) is 0.1 sec, different states ∆δ, ∆ω, ∆E′q and ∆Efd. Individual effects disturbance amplitude (size) is 1 unit and disturbance of 4 different control signals mE, δE, mB and δB 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) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd Fig 6: Responses for control signal mB for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd www.ijascse.in Page 59 IJASCSE, VOL 1, ISSUE 4, 2012 Dec. 31 Fig 7: Responses for control signal δE for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd Fig 8: Responses for control signal δB for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd It has been seen that mE (Fig. 5) and δE (Fig. 7) give the worse applications involve plants having multiple inputs and outputs. response. They can bring stability only in state ∆ω. Control Here, combination of different control signals of UPFC is now signal δB also doesn’t have a good response characteristics applied 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 making Then, the responses are observed for different combinations of all the 4 states stable at a reasonable time of below 6 seconds control 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 to provide support to the MIMO plants. Most MPC toolbox www.ijascse.in Page 60 IJASCSE, VOL 1, ISSUE 4, 2012 Dec. 31 Fig 9: Responses for control signal mB and mE together for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd Fig 10: Responses for control signal δB and δE together for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd Fig 11: Responses for control signal mB and δB together for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd Fig 12: Responses for control signal mB and δE together for states (i) ∆δ, (ii) ∆ω, (iii) ∆E′q,and (iv) ∆Efd www.ijascse.in Page 61 IJASCSE, VOL 1, ISSUE 4, 2012 Dec. 31 Observing the combined effect of two different time to settle ∆δ (Fig. 10). But the other 4 states are control signals, it has been found that the responses settled down within 3 seconds. Combination of mB-δB are significantly improved for every case than (Fig. 11), mE-mB (Fig. 9) and mB-δE (Fig. 12) show applying them individually. Among the 5 the best responses here making all the 5 states stable combinations, combination of δE and δB takes a long within a short time of 3 seconds. CONCLUSION proposed model is the use of MPC with four control In this paper by linearizing and combining the signals of UPFC at a time. equations of single machine infinite bus power system and unified power flow controller, a complete Appendix: state space model of SMIB power system including UPFC was presented. Effect for model predictive The parameters used in system model: controller for stability analysis is observed then for Generator: M = 8 MJ/MVA, T′d0 = 5.044 s, D = different states of the system model. Different 0 , Xq = 0.6 pu, Xd = 1.0 pu, X´d = 0.3 pu combinations and individual impacts of four different Transformers: XT = 0.1 pu, XE = 0.1 pu, XB = 0.1 pu control signals of UPFC are analyzed. It has been Transmission line : XL = 0.1 pu found that the system performs better if MPC is Operating condition: Pe = 0.8 pu,Q=.1670pu , Vb = 1 allowed to operate with multiple control signals of pu, Vt = 1 pu UPFC. Impact of MPC as MIMO plant is thus DC link parameter: VDC = 2 pu, CDC = 1.2 pu evident. Best solution of stability analysis for the REFERENCE [1] Shayeghi H. - Jalilizadeh S. - Shayanfar H. - [6] Qin S.J. and Badgwell T.A. “An overview of Safari A. : “Simultaneous coordinated designing of industrial model predictive control technology”, In F. UPFC and PSS output feedback controllers using Allg¨ower and A. Zheng, editors, Fifth International PSO”, Journal of ELECTRICAL ENGINEERING, Conference on Chemical Process Control – CPC V, VOL. 60, NO. 4, 2009, 177–184 pages 232–256. American Institute of Chemical Engineers, 1996. [2] Anderson P. 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