Design and Analysis of a Model Predictive Unified Power Flow Controller (MPUPFC) for Power System Stability Assessment

Transcription

1 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol:1 No:04 3 Design and Analysis of a Model Predictie Unified Power Flow Controller (MPUPFC) for Power System Stability Assessment Md.Shoiib Shahriar, Md.Ashik Ahmed and Md.Shahid Ullah Abstract This paper addresses model predictie controller (MPC) as an effectie solution for improing the oscillations in a single machine infinite bus (SMIB) power system connected with a FACTS deice, unified power flow controller (UPFC). UPFC is mainly used in the transmission systems which can control the power flow by controlling the oltage magnitude, phase angle and impedance. And as a controller, MPC, not only proides the optimal control inputs, but also predicts the system model outputs which enable it to reach the desired goal. So, model predictie unified power flow controller (MPUPFC), a combination of UPFC and MPC along with proper system model parameters can proide a satisfactory performance in damping out the system oscillations making the system stable. Simulation is done inmatlab. Response is shown for different states controlling 4 different control signals of UPFC. Index Term Power system stability, FACTS, system model, UPFC, MPC. I INTRODUCTION Power system oscillations are an ineitable phenomenon of the system. Though it starts with normal small changes in system loads, it can turn into a disaster following a large disturbance. Faults and weak protectie relaying operation can cause the oscillation to collapse the system [1]. In order to damp these power system oscillations, different deices and control methods are used []. Power system stabilizer (PSS) has been used for years for this purpose as an economical and effectie solution. But, excessie ariation in oltage profile as well as the lack of control oer three phase large disturbances at generator terminals causes the demand of Md.Shoiib Shahriar Departmnet of Electrrical and Electronics Engineering, Islamic uniersuty of Technology (IUT)Board Bazar 1704,Gazipur Shoibee05@gmail.com Md.Ashik Ahmed Departmnet of Electrrical and Electronics Engineering, Islamic uniersuty of Technology (IUT)Board Bazar 1704,Gazipur ashikhmd@yahoo.com Md.Shahid Ullah Departmnet of Electrrical and Electronics Engineering, Islamic uniersuty of Technology (IUT)Board Bazar 1704,Gazipur msullah@iut-dhaka.edu finding out a better solution to this problem [3]. FACTS technology is the newest way of improing power system operation controllability and power transfer limits which has been added in the stream with the progress in the field of power electronics deices. FACTS deices can cause a substantial increase in power transfer limits during steady state operation [3-4].Among the FACTS deices, UPFC is the one haing ery attractie and effectie features. It is capable of proiding simultaneous control of oltage magnitude and actie and reactie power flows, in adaptie fashion. It has the ability to control the power flow in transmission line, improe the transient stability, mitigate system oscillation and proide oltage support [1, 5]. A number of researches had been done to find out the control schemes for performing the oscillation-damping task of UPFC. Huang et al. [6] attempted to design a conentional fixed-parameter lead-lag controller for a UPFC installed in the tie line of a two area system to damp the inter area mode of oscillation. Wang and Swift [7] deeloped a unified Fillips- Heffron model for a power system equipped with a SVC, a TCSC and a TCPS. Chen et al. [8] used an output feedback controller designed by simulated annealing (SA) for TCSC to improe power system low frequency oscillations. Mok et al. [9] considered the design of an adaptie fuzzy logic controller for the samepurpose. Dash et al. [10] suggested the use of a radial basis function NN for a UPFC to enhance system damping performance. Among the controllers which are used to control the FACTS deices, model predictie controller (MPC) has got a wide range of attractie and ersatile features. Now a day, this controller is widely used in the field of industry as it has the ability to implement constraints in control process system. A good oeriew of industrial linear MPC techniques can be found in [11]. In this paper, model predictie Controller (MPC) has been chosen to control UPFC. Attractie features of these two tools jointly proide a ery satisfactory solution to the system stability. System model of SMIB system along with UPFC is controlled here with MPC for four different control signals of UPFC. Impact of the system for different combinations of control signals is also inestigated.

2 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol:1 No:04 33 I. SYSTEM DYNAMIC MODEL The power system [1] that is studied in this paper consists of a synchronous generator connected to transmission lines and an infinite bus ia two transformers.the UPFC consists of an excitation transformer (ET), a boosting transformer (BT)and twothree-phase GTO based oltage source conerters (VSCs); which are connected to each other with a common dc link capacitor [1]. Fig. 1 shows a SMIB system equipped with an UPFC. The four input control signals to the UPFC are m E, m B, δ E, and δ B. Where, m E is the excitation amplitude modulation ratio, m B is the boosting amplitude modulation ratio, δ E is the excitation phase angle, and δ B is the boosting phase angle. angle and speed, respectiely; E q,e fd, and the generator internal, field and terminal oltages, respectiely; T do the open circuit field time constant; x d andx d the d-axis reactance, d-axis transient reactance respectiely; K A and T A the exciter gain and time constant, respectiely; V ref the reference oltage; and u PSS the PSS control signal. By applying Park s transformation and neglecting the resistance and transients of the ET and BT transformers, the UPFC can be modeled by the following equations (5-7): Etd Etq i [ o x E x E 0 ] Ed i Eq m cos + m sin m cos + m sin E E dc E E dc (5) B B dc Btd [ o x B i x B 0 ] Bd Btq i (6) Bq B B dc 3m E 3m B dc (cos EiEd sin EiEq ) (cos BiBd sin BiBq ) 4C 4C dc dc Fig. 1. SMIB power system equipped with UPFC In stability and control studies of power system oscillations, the linearized model can be used. In this paper dynamic model of the system for small signal stability improement is used. Nominal parameters used for system modeling are gien in Appendix-I. The nonlinear model of the SMIB system of Fig 1 can be expressed by the following differential equations (1-4) [1]: (1) base ( 1) 1 [ Pm Pe D ( 1)] () H ' 1 ' ' E q ' [ E fd Eq ( xd xd ) id ] (3) Tdo 1 E fd K A(( Vref U pss ) E fd ) T (4) A Where Pm and Peare the input and output power, respectiely. Pe did qiq, t d q d q q q iq lq, x i x i i, E ' x ' i, i i i, i i i d Ed Bd q Eq Bq q q d d Where M and D the inertia constant and damping coefficient, respectiely; ω base the synchronousspeed; δ and ω the rotor (7) Where, Et, i E, Bt, andi B are the excitation oltage, excitation current, boosting oltage, and boosting current, respectiely; C dc and dc are the DC link capacitance and oltage.the relations of excitation and boosting transformers parameters and line currents can be written as: x m Sin x x m Sin i BB E ' E E dc Bd de ( Cos B B dc ) Ed x q x x b d d d m Cos x x E E dc Bq qe m Sin i - ( Sin B B dc ) Eq x x b q q x m Sin x x m Sin i E E ' E E dc de dt ( Cos B B dc ) Bd x q x x b d d d m Cos x x E E dc qe qt m Cos i ( Sin B B dc ) Bq x x b q q Where, X E and X B are the ET and BT reactance, respectiely. By combining and linearizing the equations (1-7) state space equations of system will be obtained which are present in state space represented equation (8). In this process there are 8 constants denoted by k are being used. X = AΔX + BΔU. (1) Where the state ector ΔXand control ector ΔUare ΔX = [ΔδΔωΔE q ΔE fd ΔV dc ] T ΔU = [ΔU pss Δm E Δδ E Δm B Δδ B ] T

3 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol:1 No:04 34 Where 0 b K1 D K K pd 0 M M M M K4 K3 1 Kqd A 0 T ' d0 T ' d 0 T ' d0 T ' d0 K K5 K K6 1 K K 0 TA TA TA TA K7 0 K8 0 K9 And A A A d K K K K 0 M M M M K K K K B 0 T ' T ' T ' T ' KA K K K K K K K K TA TA TA TA TA 0 Kce Kcde Kcb Kcdb III. pe pde pb pdb qe qde qb qdb d0 d0 d0 d0 A e A de A b A db DAMPING CONTROL The unique feature of MPC which has made it different from other controllers is the ability to predict the future response of the plant.at each control interal an MPC algorithm attempts to optimize future plant behaior by computing a sequence of future manipulated ariable adjustments [13]. Figure shows the basic principle of MPC. Prediction horizon (TP) is the time range which, future system outputs are predicted in it. Control horizon (Tc) is the time steps number that input control sequence calculations for the prediction horizon are done [13].In this plant model, alue of prediction horizon is taken 10 and control horizon is. MPC approach can be expressed considering the following finite horizon cost function [15] H1 rh J ( x,[ u ( t),..., u ( t)]) h( x ( u), u( t)) g( xt HT ( u)) t 0 H1 t it i i1 wheret is the current time; H is the length of the optimization horizon; ΔT is the sample period. If i > 0,then xt ( u) denotes the controlled trajectory at i T time t it from x t under piecewise controls H u [ u ( t),..., u ( t)] U ; h is the running cost; 0 i1 and g is the terminal cost. We assume that h is nonnegatie function and g satisfies g( x) x xeq for all x, where x eq is somedesired equilibrium and α>0 is some positie constant.that is, g is an upward function whose lowest point is at the Fig.. Principle of model predictie control Based on measurements obtained at time t, the controller predicts the future dynamic behaior of the system oer a prediction horizon Tpand determines the input oer a control horizon Tc such that a predetermined open-loop performance can be achieed. Ifthere were no disturbances and no modelplant mismatch, and ifthe optimization problem could be soled for infinite horizons, then one could apply the input function found at time t=0 to the system for all times t 0. Howeer, this is not possible in general. Due to disturbances and model-plant mismatch, the true system behaior is different from the predicted behaior. In order to incorporate some feedback mechanism, the open-loop manipulated input function obtained will be implemented only until the next measurement becomes aailable. Using the new measurement at time t+, the whole procedure will be repeated to find a new input function with the control and prediction horizons moing forward [14]. system equilibrium. Thiscondition on g(.) ensures that the control design attempts to reach the system equilibrium. Fig 3 shows a complete block representation of UPFC connected SMIB system controlled with MPC. y ref y x Linearized System Model x Ax Bu Fig 3: Block diagram of MPC with UPFC connected plant. u y

4 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol:1 No:04 35 IV. SIMULATION RESULTS A disturbance of pulse type signal is gien in the system s ΔP e. Disturbance duration (period) is 0.1 sec, disturbance amplitude (size) is 1 unit and disturbance occurring time is 1 sec. Response of MPC on proposed model is obsered for states δ and ω. Indiidual effects of 4 different control signalsm E, δ E, m B and δ B on system states are obsered first in figure (4-7) Fig. 4. Responses for control signal m Efor states (i) δ, (ii) ω Fig. 5. Responses for control signal m Bfor states (i) δ, (ii) ω Fig. 6.Responses for control signal δ Efor states (i) δ, (ii) ω Fig. 7. Responses for control signal δ Bfor states (i) δ, (ii) ω

5 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol:1 No:04 36 It has been seen that δ E (Fig. 6) and δ B (Fig. 7) gie the worse response. They can bring stability only in state ω, but takes a long time which is not desired. Control signal m E (Fig. 4) also doesn t hae a good response characteristics. It can stable state ω at a time of around 5 seconds but can t stable state δ. Among the four signals, m B gies the best output making both the states stable at a reasonable time of below 6 seconds (Fig. 5). As, MPC is a MIMO supported controller, so responses will be obsered now for control signals two at a time. Fie different combinations of two control signals are obsered in this paper in fig (8-1). Fig. 8. Responses for control signal m B and m E together for states (i) δ, (ii) ω Fig. 9. Responses for control signal δ B and δ E together for states (i) δ, (ii) ω Fig. 10. Responses for control signal m E and δ E together for states (i) δ, (ii) ω Fig. 11. Responses for control signal m B and δ B together for states (i) δ, (ii) ω

6 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol:1 No:04 37 Fig. 1. Responses for control signal m B and δ E together for states (i) δ, (ii) ω Obsering the combined effect of two different control signals, it has been found that the responses are significantly improed for eery cases than applying them indiidually. Among the 5 combinations, combination of m E and δ E proides the worst response (Fig. 10). It can t make any of the states stable. δ B -δ E combination brings stability in eery states but takes a long period of time (10 secs.) to bring stability in δ (Fig. 9). Combination of m B -δ B (Fig. 11), m E -m B (Fig. 8)and m B -δ E (Fig. 1) show the best responses here making both the states stable within a short time of 3.5 seconds. V. CONCLUSIONS In this paper, by linearizing and combining the equations of SMIB power system and UPFC, a complete state space model was presented to study the oscillations. Effect for model predictie controller for stability analysis is obsered then for different states of the system model. Different combinations and indiidual impacts of four different control signals of UPFC are analyzed. It has been found that the best solution of stability analysis for the proposed model is the use of MPC with multiple control signals of UPFC at a time. APPENDIX The parameters used in system model: Generator: M = 8 MJ/MVA, T d0 = s,d = 0,X q = 0.6 pu, X d = 1.0 pu, X d = 0.3 pu Transformers: X T = 0.1 pu, X E = 0.1 pu, X B = 0.1 pu Transmission line : XL = 0.1 pu Operating condition: Pe = 0.8 pu,q=.1670pu, Vb = 1 pu, Vt = 1 pu DC link parameter: V DC = pu, C DC = 1. pu REFERENCE 1. Shayeghi H. - Jalilizadeh S. - Shayanfar H. - Safari A. : Simultaneous coordinated designing of UPFC and PSS output feedback controllers using PSO, Journal of ELECTRICAL ENGINEERING, VOL. 60, NO. 4, 009, Anderson P. M. - Fouad A.A., Power System Control and Stability : Ames, IA: Iowa State Uni.Press, Keri A. J. F. Lombard X. Edris A. A. : Unified power flow controller: modeling and analysis, IEEE Transaction on Power Deliery 14 No. (1999), [4] Hingorani N. G. Gyugyi L. : Understanding FACTS: concepts andtechnology of flexible AC transmission systems, Wiley-IEEE Press, Hingorani N. G. Gyugyi L. : Understanding FACTS: concepts and technology of flexible AC transmission systems, Wiley-IEEE Press, Tambey N. - Kothari M.L. : Unified power flow controller based damping controllers for damping low frequency oscillations in a power system, IEE Proc. on Generation, Transmission and Distribution, Vol. 150, No. (003), Huang Z. Nil Y, et al. : Control strategy and case study, IEEE trans Power System 000;15(): Wang H.F. Swift F.J. : An unified model for the analysis of FACTS deices in damping power system oscillations part I: Single machine infinite bus power systems, IEEE Trans Power Delier 1997; 1: Chen X.R Pahalawaththa. N.C Annakkage U. D - Cumble C. S : Design of decentralized output feedback TCSC damping controllers by using simulated annealing, IEE Proc. on Generation, Transmission and Distribution 145 No. 5 (1998), T. K. Mok, Y. Ni, and F. F. Wu, Design of fuzzy damping controller of UPFC through genetic 10. algorithm, IEEE Power Eng. Society Summer Meeting, ol. 3, pp , July 16 0, Dash P. K. - Mishra S. Panda G : A radial basis function neural network controller for UPFC, IEEE Trans. Power Systems, ol. 15, no. 4, pp , Noember Qin S.J. and Badgwell T.A. An oeriew of industrial model predictie control technology, In F. Allg ower and A. Zheng, editors, Fifth International Conference on Chemical Process Control CPC V, pages American Institute of Chemical Engineers, Al-Awami A. T. - Abdel-Magid Y. L. - Abido M. A. : Simultaneous Stabilization of Power System 14. Using UPFC-Based Controllers, Electric Power Components and Systems, 34: , Ahmadzade B. Shahgholian G. - MogharrabTehrani F. Mahdaian M. : Model Predictie control to improe power system oscillations of SMIB with Fuzzy logic controller. 16. Allg ower F, Badgwell T.A, Qin J.S, Rawlings J.B and Wright S. J. Nonlinear predictie control and moing horizon estimation An introductory oeriew, In P. M. Frank, editor, Adances in Control, Highlightsof ECC 99, pages Springer, Ford J.J. - Ledwich G. - Dong Z.Y : Efficient and robust model predictie control for first swing transient stability of power systems using flexible AC transmission systems deices, IET Generation, Transmission & Distribution Receied on 6th September 007.