Design of Robust UPFC Controller Using Η Control Theory in Electric Power System

Transcription

1 American Journal of Applied Sciences 5 (8): , 8 ISSN Science Publications Design of Robust UPFC Controller Using Η Control heory in lectric Power System Seyed Abbas aher, Shahabeddin Akbari,Ali Abdolalipour and Reza Hematti Department of lectrical ngineering, University of ashan, ashan, Iran Abstract: An industrial plant, such a power system, always contains parametric uncertainties. In the design of a controller the uncertainties have to be considered. Otherwise, if the real plant differs from the assumed plant model, a controller, designed based on classical controller design approaches, may not ensure the stability of the overall system. In this paper design of robust control for the UPFC controllers including power - flow and DC voltage regulator, using a Η loop-shaping design via a normalized coprime factorization approach, where loop-shape refers to magnitude of the loop transfer function L = G as function of frequency is presented. As an example, we have designed a case for the system to compare the proposed method with a conventional method (classical P-I controller). AS the results of the linear and nonlinear simulations, the validity of the proposed method has been confirmed. ey words: Unified Power Flow Controller (UPFC); Flexible AC ransmission Systems (FACS); power system oscillation; Η loop-shaping INRODUCION he Flexible AC ransmission Systems (FACS) based on power electronics offer an opportunity to enhance controllability, stability, and power transfer capability of AC transmission systems []. he Unified Power Flow Controller (UPFC), which is the most versatile FACS device, has the capabilities of controlling power flow in the transmission line, improving the transient stability, mitigating system oscillation and providing voltage support [-4]. PID is the most commonly used control algorithm in the process industry. Also, this technique is used to control the FACS devices [5]. However, the nonlinear nature of well as the uncertainties that exist in the system make it difficult to design an effective controller for the FACS that guarantees fast and stable regulation under all operating conditions. A major source of difficulty is that open-loop plant may change. In particular, inaccuracy in plant may cause problems because the plant is part of the feedback loop. o deal with such a problem, instead of using a single model plant, an uncertain model should be considered. his problem has led to the study of applying adaptive controllers for instance [6, 7], nonlinear controllers for instance [8] in the power system stability control. Also, during past decade, the Η optimal robust control design has received increasing attention in power systems. Most of above methods have been applied in power systems and some of these efforts have contributed to the design of supplementary control for SVC using mixed sensitivity [9], applying µ-synthesis for SVC in order to voltage control design [] and supplementary control design for SVC and SACOM []. For many control problems, a design procedure is required that offers more flexibility than mixed sensitivity, but should not be as complicated as µ-synthesis and should not be limited in its application like LR procedures. he Η loop-shaping design is such a controller procedure, used to design a robust controller for FACS control to improve the system damping []. In this paper as an example, a Single Machine Infinite Bus (SMIB) power system installed with a UPFC is considered for case study and Η loop-shaping method is used to design a robust controller for UPFC controller including power-flow and DC-voltage regulator in this system. o show influence of proposed method, the proposed method is compared to conventional method (the parameters of conventional P-I controller are optimized using genetic algorithm). As the validity of the proposed method has been confirmed by linear and nonlinear time domain simulation results. MARIALS AND MHODS Figure shows a SMIB system equipped with a UPFC. he UPFC consists of an xcitation ransformer (), a Boosting ransformer (B), two three-phase GO based voltage source converters Corresponding Author: Seyed Abbas aher, Depatment of lectrical ngineering, University of ashan, ashan, Iran 98

2 v t I t x t v o i x i tl i B m δ V dc x mb x B δ B Am. J. Applied Sci., 5 (8): , 8 v B x BV Fig. : SMIB power system equipped with UPFC (VSCs) and a DC link capacitors. he four input control signals to the UPFC are m, m B,, and B, where, m is the excitation amplitude modulation ratio, m B is the boosting amplitude modulation ratio, is the excitation phase angle and B is the boosting phase angle. Non-Linear Dynamic Model: By applying Park s transformation and neglecting the resistance and transients of the and B transformers, the UPFC can be modeled as [3-5] : m cosδvdc vtd x i d v = tq x i q m sin δvdc mb cosδbvdc vbtd x i B Bd v = x i m sin δ v Btq B Bq B B dc 3m id v = [cosδ sin δ ] i dc 4C dc 3m i B Bd [cos δb sin δb ] 4C dc i Bq q v b () () (3) Where, v, i, V Bt and i B are the excitation voltage, excitation current, boosting voltage, and boosting current, respectively; c dc and v dc are the DC link capacitance and voltage, respectively. he nonlinear model of the SMIB system as shown in Fig. is described by:. ω = (P P D ω) / M. m δ = ω ( ω) = ( )/ q q fd do e (4) (5) (6) 98 Where,. = ( (V V ))/ fd fd a ref t a ( ) P = V I V I ; = X X I e td td tq tq q qe d d td V = V jv ;V = X I ;V = X I t td tq td q tq tq q d td Itd = Itld Id I Bd;Itq = Itlq Iq IBq x mevdc Itld = Id cosδ Vb cosδ X X X x m V I = I sin δ V sin δ e dc tlq q b X X X (x x x ) x m V I = V cosδ cosδ dt BB b3 dt B dc d b B x (x x x ) m V cos BB dt BB b e dc δ (x x x ) x m V I V sin sin dt BB a3 qt B dc q = b δ δb xq x q (x qt x BBx a ) mevdc sin δ xq (x x x ) x m V I = V cosδ cosδ b3 b b B dc Bd b B x xb xxb mevdc q cosδ (xa3x x b) xa mbvdc I = V sin δ sin δ x x Bq b B q q (xa x x a ) mevdc sin xq δ x = X X ; x = X X ; x d t d q q t ds = X x ; x = X x d qs q (7) (x X x X ) x x x = ; x = ; x = ; qs q q q a a a3 X X X (x X x X ) x x x = ; x = ; x = ds d d d b b b3 X X X x x x x = ( x x x x ); x BB d d d BB ds q X x BBxqx = ( x x q x BBx qs ) X he equation for real power balance between the series and shunt converters is given by: Re(V I V I ) = B B (8) Power system linearised model: A linear dynamic model is obtained by linearising the nonlinear model round an operating condition. he linearised model of power system as shown in Fig. is given as follows:

3 Am. J. Applied Sci., 5 (8): , 8 δ = ω ω ω = ( Pe D ω) / M (9) () P e P m MS D w S / / q q fd do = ( ) / () pu 4 5 pd = A fd fd V A A () / q 6 / 3 S do ka S a V ref / dc 7 8 q 9 dc ce v = δ v m δ m δ cδe cb B cδb B (3) U cu 8 S 9 qu V dc qd vu vd Where, P = δ v m / e q pd dc pe δ m δ pδe pb B pδb B V = δ v m / t 5 6 q vd dc ve δ m δ vδe vb B vδb B / / q 4 3 q qd dc qe = δ v m δ m δ qδe qb B qδb B, 9, pu, qu and vu are linearization constants. he state-space model of power system is given by: x = Ax Bu (4) Where, the state vector x, control vector u, A and B are: x = [ δ ω v ] q fd dc B B u = [ m δ m δ ] he block diagram of the linearised dynamic model of the SMIB power system with UPFC is shown in Fig.. Η Loop-shaping design: he adopted control method is based on Η robust stabilization combined with classical Loop-shaping, where loop-shape refers to the magnitude of the loop transfer function L = G as a function of frequency. It is essentially a tow-step procedure, where in the first step; the singular values of the open-loop plant are shaped by pre and post compensators. In the second step, the resulting shaped plant is robustly stabilized with respect to coprime factor uncertainty using Η optimization. An important advantage is that no problem-dependent uncertainty modeling, or weight selection, is required in this second step [6]. he stabilization of a plant G is considered, that has a normalized left coprime factorization as follows [6] : 98 Fig. : linearised dynamic model of the SMIB power system with UPFC w pd M M M 4 3 qd A = / / / / do do do do A5 A6 A vd A A A A pe p e pb δ pδb M M M M qe q δe qb qδb B = / / / / do do do do A vc A vδe A vb A vδb A A A A ce c δe cb c δb hat has a normalized left coprime factorization as follows: G = M (5) A perturbed plant model G d can then be written as: 7 G = (M ) (N ) p M N (6) Where M and N represent the uncertainty in the nominal plant model G. he objective of robust stabilization is to stabilize a family of perturbed plants defined by: { [ ] } G = (M ) (N ) : ε p M N N M (7) Where ε> is then the stability margin. For the perturbed feedback system of Fig. 3, the stability

4 Am. J. Applied Sci., 5 (8): , 8 N M N M Fig. 3: Η robust stabilization problem Fig. 4: shaped plant and controller property is Robust if and only if, the nominal feedback system is stable and: ( ) γ = I G M I ε (8) he lowest achievable value of y and corresponding maximum stability margin ε are given by: [ ] Z γ = ε = { N M } = ( ρ(x )) / / min MAX H z (9) Where. H denotes the Hankel norm, p denotes radius (maximum eigenvalue), and for a minimal stat space realization (A, B, C, D) of G, Z and X are the unique positive definite solution to the algebraic Riccati equations: ( ) ( ) Z : A BS D C Z Z A BS D C = ZC R CZ BS B ( ) ( ) X : A BS D C X X A BS D C XBS B X C R C = Where R = I DD and S = I D D. A controller, which guarantees that I G M I ( ) For a specified y > y is given by: () () A BF γ L ZC C DF γ L ZC = B X D () γ ( ) ( ) ( ) he controller design procedure can be summarized as follows. Loop Shaping: Using pre- and post compensators W and W, the singular values of the plant are shaped to give a desired open loop shape as shown in Fig. 4. Some trial and error is involved Here W is usually chosen as a constant. W contains dynamic shaping. Integral action for low frequency performance, phaseadvance for reducing the roll-off rates at crossover, and phase-lag to increase the roll-off rates at high frequencies, should all be placed in W if desired. he weights should be chosen so that no unstable hidden modes are created in G s. Robust Stabilization: Robustly stabilize the shaped plant G s. First, calculate the maximum stability margin max </y min. If the margin is too small, max <.5, return to step and adjust the weight. Otherwise, select y>y min by about % and synthesis a suboptimal controller using (). When max >.5 (respectively, y min <4) the design is usually successful. A small value of max indicates that the chosen singular value loop shapes are incompatible with robust stability requirements. he loop shape does not change much following robust stabilization if y is small [6-7]. If all the specification is not met: Return to step and make further modification to the weights. Reduce the order of controller: Check the frequency response plot of s-red against that of s. Final feedback controller : his is achieved by combining s-red with the shaping function W and W such that = W s-red W. UPFC CONROLLRS Where F = S ( D C B X) and L = ( γ )I ZX. It is important to emphasizes that, since y min is he UPFC control system comprises following computed from (9) and an explicit solution has been controllers: derived by solving just two Riccati equations and the y Power flow controller iteration needed to solve them, the general Η problem DC voltage regulator controller has been avoided [ 6-7]. Power system oscillation-damping controller 983

5 Am. J. Applied Sci., 5 (8): , 8 Pe ref P e k pp k pi s m B - Singular Values power flow ω Fig. 5: Power flow controller with damping controller V dcref V dc Fig. 6: DC voltage regulator P m P e dδ dt Ms DC k s Fig. 7: ransfer function block diagram of the UPFC based damping controller Power flow and DC voltage regulator controllers: he UPFC is installed in one of the two lines of the SMIB system. Figure 5 shows the transfer function of the power flow controller. he power flow controller regulates the power flow on this line. k pp and k pi are the proportional and integral gain of the power flow controller. he real power output of the shunt converter must be equal to the real power input of the series converter or vice versa. In order to maintain the power balance between the two converters, a DC-voltage regulator is incorporated. DC-voltage is regulated by modulating the phase angle of the shunt converter voltage. A P-I type DC-voltage regulator is considered Fig. 6. k dp and k di are the proportional and integral gain of the DC-voltage regulator. Power system oscillation-damping controller: A damping controller is provided to improve the damping of power system oscillations. his controller may be considered as a lead-lag compensator [8-9] or a fuzzy controller block. However an electrical torque in phase with the speed deviation is to be produced in order to improve damping of the system oscillation. he transfer function block diagram of the damping controller is shown in Fig. 7. It comprises gain block, signal-washout block and lead-lag compensator. k dp s di s w s s w δ Singular Values Fig. 8: Singular values of open loop of Power flow controller Singular Fig. 9: Singular values of open loop of DC voltage regulator Frequency (rad/sec) Singular Frequency dalta CONROLLR DSIGN USING Η HORY Due to system parameters are given in Appendix, the initial d-q axes voltage, current components and torque angle are computed for the nominal operating condition as follows: =.396 pu; =.953 pu d d q V = pu; V = pu I =.437 pu;i =.66 pu; δ = 5.6 q Design of UPFC controller: he UPFC power-flow and DC voltage regulator are designed independently. Based on the procedures explained in section 4, the following controller design results are obtained. First, the singular values of the open loop are calculated and B 984

6 Am. J. Applied Sci., 5 (8): , 8 plotted in Fig. 8. After trial and error, W and W for power flow controller are chosen: S.6 W = 5.5 S(S.8S 8) W = For DC voltage regulator, the same procedure is followed. he singular values of the open loop are calculated and plotted in Fig. 9. W and W for DC voltage regulator are chosen: structure of UPFC based damping controller is shown in Fig. 7. It consists of gain, signal washout and phase compensator blocks. he parameters of the damping controller are obtained using the phase compensation technique. he detailed Step-by-step procedure for computing the parameters of the damping controllers using phase compensation technique is given [6, 7]. Damping controller m B was designed and obtained as follows (wash-out block is considered). Power flow controller damping with damping ratio of.5, 5(S ) W = S(S 5) W = he variable ( min ) is the inverse of the magnitude of coprime uncertainty, which can be tolerated before getting instability. min > should be as small as possible, and usually requires that min is less than a value of 4 [6-7]. By applying this, min =.34 for power flow controller and min =.336 for the DC voltage regulator are obtained. In order to show influence of Η loop-shaping method, the proposed method is compared to conventional method. In conventional method, the parameters of the power-flow controller (k pp and k pi ) are optimized using genetic algorithm []. Optimum values of the proportional and integral gain settings of the power-flow controller are obtained as k pp = and k pi =.35. he parameters of DC voltage regulator are now optimized using genetic algorithm. When the parameters of power-flow controller are set at their optimum values. he optimum gain setting of P-I type DC voltage regulator are k dp =.5 and k di =.35. Using a commercially available software package [], two controllers satisfying design objectives are obtained. For easy implementation, the order has been reduced by model reduction technique. he transfer functions of the controllers are: S.44S 7.43S 35.6S.43S.9874 PF = S 6.4S 8.69S 4.6S 7.367S.6474S S 65.8S 355.6S 373S 5. VDC = S.47S.55S 59.8S 9.48S ( ) ( s.) ( s 4.5) s s damping controller = RSULS AND DISCUSSION In order to examine the robustness of the UPFC power-flow and DC voltage regulator controller in the presence of wide variation in loading condition (three cases), the system load is varied over a wide range. Dynamic responses are obtained for the following three typical loading conditions for Peref =.pu and =.pu Case a: P =.8pu, Q = 5 pu (nominal load) Case b: P =. pu, Q =. pu (heavy load) Case c: P =. pu, Q =.85 pu (very heavy load) he performance of the designed Η -UPFC and classic-upfc controllers with damping controller m B after sudden change in reference power on transmission line, reference mechanical power and reference voltage are shown in Figs. to 5. It can be observed from these figures, which the proposed controller designed (Η -UPFC) significantly damp power system oscillations compared to conventional (classical P-I) UPFC controllers (C-UPFC). In order to investigate the performance of the proposed controller and the system behavior under large disturbances and various operating conditions, a transitory 3-phase fault of 5- ms duration at the generator terminals is considered. Dynamic performance is obtained using the non-linear model under the system of the nominal and heavy loading condition with Η -based and optimal settings of the UPFC controllers (Power-flow controller, DC-voltage regulator and damping controller). Figure 6 shows the power system responses under the above operation condition. It can be observed from this figure, which the proposed controller designed significantly damp power system oscillations compared to conventional Design of PSS: he damping controllers are designed to produce an electrical torque in phase with the speed deviation according to phase compensation method. he four control parameters of the UPFC (m B, m, δ B and δ ) can be modulated in order to produce the damping torque. In this paper m B is modulated in order to damping controller design. he speed deviation ω is considered as the input to the damping controllers. he (classical P-I) UPFC controllers (C-UPFC). 985 m

7 Am. J. Applied Sci., 5 (8): , 8. x -4 x Pe W Fig. : Dynamic responses at operating point (Nominal loading) during step change in P eref =. pu; Solid (Η ) and Dashed (Classical a) Power flow deviation on line b) DC- voltage deviation c) Speed deviation...8 x 8 6 x -4 Pe W Fig. : Dynamic responses at operating point (Heavy loading) during step change in P eref =. pu; Solid (Η ) and Dashed (Classical) a) Power flow deviation on line b) DC- voltage deviation c) Speed deviation x x Pe.6 4 W Fig. : Dynamic responses at operating point 3 (Very heavy loading) during step change in P eref =. pu; Solid (Η ) and Dashed (Classical a) Power flow deviation on line b) DC- voltage deviation c) Speed deviation CONCLUSION In this paper, the design of robust controller based on Η theory with application to an UPFC has been carried out for power system. he performance of the controller has been evaluated in comparison with conventional UPFC by linear and nonlinear time domain simulations. he following issues have been addressed: representation of non-linear characteristics of the system by uncertainty model principle. 986

8 Pe Am. J. Applied Sci., 5 (8): , Fig. 3: Dynamic responses at operating point (Nominal loading) during step change in m =. pu; Solid (Η ) and Dashed (Classical a) Power flow deviation on line b) DC- voltage deviation c) Speed deviation Pe x Fig. 4: Dynamic responses at operating point (Heavy loading) during step change in m =. pu; Solid (Η ) and Dashed (Classical a) Power flow deviation on line b) DC- voltage deviation c) Speed deviation W W x Pe W x Fig. 5: Dynamic responses at operating point 3 (Very heavy loading) during step change in m =. pu; Solid (Η ) and Dashed (Classical a) Power flow deviation on line b) DC- voltage deviation c) Speed deviation selection of appropriate weighting functions based on the control system objectives, and: verification of the Η controller design by time domain simulations under various operating conditions. he main conclusions are: he robust controller can improve the damping of power system oscillation. 987 he non-linear characteristics of the system can easily by incorporated into the controller design by suitable selection of weighting functions. he results of these studies show that the proposed controller design using Η method compared to conventional method, has an excellent capability in damping of power system oscillations.

9 t(sec) Am. J. Applied Sci., 5 (8): , t(sec) Fig. 6: Speed deviation for a transitory 3-phase fault at the generator terminals, Solid (Η -based) and Dashed (Classical) a) For 5ms duration at operating point b) For ms duration at operating point c) For ms duration at operating point t(sec) Performance of damping controllers under large perturbations show the superiority of proposed Η -based controller over its conventional counterpart. Also, effectiveness of the proposed control strategy in damping the local low frequency oscillations with UPFC is confirmed. APPNDIX he nominal parameters and operating condition of the system are given below: Generat M = 8 MJ/M do = 5.44 S d = lpu or sec X q =.6 P.U X d =.3 pu D = xcitation system α = α =.5 sec ransformers X t =. pu X =. pu X B =. pu ransmission line X = pu X =.3 pu Operating condition P =.8pu Q =.5pu V t =.3 pu DC link parameter V DC = pu C DC = 3pu UPFC parameter m B =.4 δ B = δ = 6.9 m =.33 RFRNCS. Hingorani N.G. and L. Gyugui,. Understanding FACS, I Press, New York.. Gyugyi L. and C.D. Schauder, 995. he unified power flow controller: a new approach to power transmission control, ieee trans. pwrd, (): Gyugyi L., 99, Unified power flow control concept for flexible ac transmission systems, iee proceedings-c, 39(4): Al-Awami A.., Y.L. Abdel-Magid and M.A. Abido, 7. A Particle-Swarm-Based Approach of Power System Stability nhancement with UPFC, lec. Power and nergy Systems, 9: Liou.L. and Y.Y. Hsu, 986. Damping of generator oscillation using svc, ieee trans. aero. electron. sys., (5): Liou.L. and Y.Y. Hsu, 99. Damping of generator oscillation using an adaptive static var compensator, ieee trans. pwrs, 7(): Smith J.R., D.A. Pierre, A.D. Rudberg, I. Sadighi and A.P. Johnson, 989. an enhanced lq adaptive var unit controller for power system damping, ieee trans. PWRS, 4(): Ni Y., L. Jiao, S. Chen and B. Zhang, 998. Application of a nonlinear pid controller on statcom with a differential tracker, international conference on energy management and power delivery, empd-98, New York: Zhao Q., J. Jiang, 995. Robust SVC Controller Design for Improving Power System Damping, I PWRS, (4): Parniani M., M.R. Iravani, 998. Optimal Robust Control Design of SVC, I Proc.-C, 5(3): 37.. Farsangi M.M., Y.H. Song, Y.Z. Sun,. supplementary control design of svc and statcom using Η optimal robust control, international conference electric utility deregulation and restructuring and power technologies, drpt, city university london, uk. pp: Farsangi M.M., Y.H. Song, W.L. Fang and X.F. Wang,. Robust FACS Control Design Using the H Loop-Shaping Method, I Proc.-C, 49(3): Nabavi A., M.R. Iravani, 996. Steady-state and dynamic models of UPFC for power sys. studies, I rans. PWRS, (4): Wang H.F., 999. Damping function of UPFC, I Proc.-C, Vol. 46, No. : Wang H.F., 999. Application of modeling UPFC into multi-machine power systems, I Proc.-C, 46(3):

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