Structural Analysis and Design of STATCOM s Integrator Anti Windup Based Synchronous PI Controller

Transcription

1 Structural Analysis and Design of STATCOM s Integrator Anti Windup Based Synchronous PI Controller Aman Ganesh Department of Electrical Engineering MMU, Mullana Ambala, India Ratna Dahiya Department of Electrical Engineering NIT Kurukshetra Kurukshetra, India G.K. Singh Department of Electrical Engineering IIT Roorkee Roorkee, India Abstract STATCOM is usually installed to a power system that has a poor power factor and often poor voltage regulation. During the normal or steady state operation of the power system the STATCOM injects reactive power in order to maintain the desired voltage profile. It is customary for the STATCOM to have a safety margin in terms of reactive power, so that it responds to different faults and loading conditions. In this paper integrator anti windup based synchronous PI controller is proposed that brings the change in the dynamics of the STATCOM control loop in order to provide better voltage regulation by using less reactive power from the device safety margins while responding to different faults and loading conditions. Keywords-component; STATCOM, PI controller, integrator anti windup, voltage regulation T I. INTRODUCTION HE static synchronous compensator (STATCOM), a shunt connected FATCS device, finds its application in transmission and distribution networks, which under steady state condition can control the voltage and the reactive power exchange with the network at the point of connection to the power system i.e. the point of common coupling (PCC) and is also capable of improving the damping of power system during dynamic and transient disturbances []. To effectively improve STATCOM performance, researchers have mainly concentrated on its topology and control strategy. Either voltage source inverter [2]-[8] or current source inverter [9]- [2] are used to modulate the reactive power output of the STATCOM. Proportional-integral (PI) controllers of the STATCOM have been designed as regulators for ac system voltage, the dc voltage and the current regulators. Satisfactory dynamic responses have been reported for the STATCOM with these PI controllers. In the fixed gain PI controller [4]-[5], the controllers gain for the STATCOM are usually designed based on a linearized system equation for the system under a nominal load condition. These controller gains remained fixed in daily operation of the STATCOM. However, the performance of the PI controller can be largely affected by a change in the operating condition of the power system or its topology. The situation can be greatly affected or worsened as the complexities of the power system to which the STATCOM is connected increases. It is found that a linear controller fine tuned for a certain operating condition is not able to effectively damp out the oscillation in the power system [3]. A typical double loop PI control strategy along with fuzzy controllers was proposed [4]-[5] in which the outer loop framed the desired active and reactive current commands for maintaining the voltage at the PCC and to compensate for the STATCOM losses and the inner loop realized the control of the inverter current with zero steady state errors. The strategy involved the tuning of the PI controllers, but because of the coupling relationship between the active current and the reactive current it was hard to maintain the voltage at the PCC with small effects on the dc-link voltage. The decoupled controls of d- and q-axis currents and voltages have been proposed to regulate the dc capacitor voltage and the ac system voltage, respectively, in STATCOM controller design [6]-[7]. But under the condition of sudden changes in load, generation or transmission system configuration due to fault or switching; the control error becomes so large that the integrator of the controller saturates. The integrator being an unstable system may then integrate to a very large value, thus arises the phenomenon of integrator windup. The previous studies have not dealt with the winding up phenomena although nonlinear control strategies are widely used via the feedback path by the linearized model. Fuzzy systems have been extensively used in power system application for identification, modeling and control [3]-[4], [6]-[9]. In this paper synchronous transfer function based control strategy using integrator anti windup is employed because unlike the conventional PI controllers or controllers using artificial intelligence techniques the proposed scheme is cheap, reliable and has better uncertainty tolerance. The paper is organized in five sections.

2 The first section introduces the literature and the objective of the paper. The generalized structure & its classical mathematical implementation are explained in the second section. The third section gives the insight of the design of decoupled current controller, cross coupling controller, integrator wind up controller. The simulation results are summed up in the fourth section. The conclusion is drawn in the last section q v q (t) (t) V V (t) II. v(t) v d (t) ( t ) d STATCOM STRUCTURE STATCOM is a voltage source inverter connected in shunt to the system (or grid) at the point of common coupling (PCC). The principle action of the STATCOM is to control the voltage source inverter in such a way so as to make it deliver the reactive and harmonic currents demanded by the load so that the grid has to supply only the active current which is in phase with the grid voltage. In this process a small amount of real power will be absorbed from the grid practically to compensate for the energy losses in the system. For this the STATCOM has to compute the reactive and harmonic current absorbed by the load and has a control strategy which makes the controller to follow the reference and ultimately this is achieved with the help of the voltage source inverter. For a three phase balanced system of grid voltage, with the help of Clarke transformation and Park transformation the voltage space vector v s in synchronous coordinates can be expressed as v s = v dq e jθ = v α + jv β () Figure (a) represents the voltage space vector v s rotating in the coordinate frame a frequency ω. wt Voltage Space Vector Current Space Vector Reactive Power Q (a) (b) (c) Voltage Space Vector ( Direct axis) Active Power P Current Space Vecto Quadrature axis Figure. (a) Space vector representation in coordinate frame, (b) voltage and current space vector and (c) decomposition of space vector. The space vector using () can alternatively be represented as v s = 3 2 V m e j ωt π 2 (2) Figure (b) depicts the grid voltage and line current space vectors in the α-β frame. The current space vector has two components, figure (c), one in phase with the (grid) voltage space vector and another lagging the voltage space vector by π/2. Unit vectors (3) referred in terms of sine and cosine vectors are generated by transforming the grid voltage to α-β plane they are used to track the angle between the voltage and the current vector cos θ = V α V sin θ = V β V = sin ωt (3.) = cos ωt (3.2) Now under the consideration of the sudden load change or under the transient effect of fault occurrence the frequency of the system will change hence the reference current generation will be affected this is represented by the set of the following equations where ω represents the fundamental grid frequency and ω i represents the arbitrary frequency of load current. The transformation of the current to the d-q axis using ()-(3) is i d iq = 3 I 2 m cos ω i ω. t φ 3 I 2 m sin ω i ω. t φ (4) Sinusoidal variations are shown by equation (4) because of the frequency difference. Thus the harmonics will appear as ripples in the d and q axis. Blocked dc component in d-axis and entire q axis current will be taken as reference for composite compensation. The voltage source inverter output of the STATCOM on the ac side and the dc side in the dq frame is represented as v d = Ri d + L di d ωli q + v in (5.) v q = Ri q + L di q + ωli d + v in (5.2) C d u dc = 3 2 S di d + S q i q (5.3) The above equation represents voltage references v d and v q obtained from the current reference represented by (4) to facilitate the voltage source inverter. Considering the above MIMO system and using the above set as combination of two SISO systems the identical d-axis (as is q-axis) the transfer function obtained is III. i d s = v d s R+sL DESIGNING THE CURRENT CONTROLLER A. Transfer Fuction of the Voltage Source Controller For the conventional STATCOM using Clarke and Park transformations, the current measurements are transformed to DC quantities, then, a simple PI controller is implemented for the obtained transfer function. For proper synchronization the impedance too has to be represented in synchronous frame. If y s is a general space vector with θ=ωt, its transformation in synchronous coordinates is y dq = y s e jθ (7) The time derivative of (7) is transformed as (notations, derivative operation p=d/) dy s = d ejθ y dq = e jθ jωy dq + dy dq (6) = e jθ (p + jω)y dq (8) In the Laplace domain, the following substitution is made as s s+jω. This implies that the complex impedance of an inductor in synchronous coordinates is represented as Z s = s + jω L (9) So the modified identical d-axis (as is q-axis) transfer function in reference to (6) obtained is i d s = v d s R+sL+jωL () Now the aim is to find the synchronous coordinate equation for this (5) has to be modified (notations, x = x dq = x d + jx q, E = v dq, v = v indq ) L di = E R + jωl i v (.) 2

3 R + sl + jωl i = E v (.2) i = E v R+sL+jωL And the system transfer function G s is given by G s = i v = R+sL+jωL B. Cross Coupling Cancellation (.3) (2) The first step in the controller design is to cancel the cross coupling initiated by the term jωli (since multiplication by j maps the d axis on q axis and vice versa). With the accurate estimation of L this can be achieved. L is estimated for L. A PI current controller traces the performance for the coupled system described by equations v d and v q. For high performance and accuracy current tracking we need to cancel this cross coupling. Selecting v as () and estimating the value of E as E we have v = v + E jωli (3) If L = L and E = E, then i = v R+sL (4) With G (s) the decoupled system transfer function from v to i we have G s = i = (5) v R+sL C. Controller Transfer Function Based on Model Control theory [2] for controller design, for which the resulting controller becomes directly parameterized in terms of the plant model parameters and the desired closed loop bandwih. For the transfer function defined by (5) the generalized controller transfer function will be of the type G i s = α n s+α n α n G s (s) (6) G i (s), hence is a low pass filter with bandwih α and G s (s) is the estimation of the plant and n is the order of G. For this a PI controller is enough G i s = k p + k i (7) s Estimating (6) in terms of (7) the obtained PI coefficients are k p = αl and k i = αr For this inner current control loop, the bandwih α is selected smaller than a decade below the sampling frequency. D. Decoupled Current Control In order to establish the decoupled current control continue with equation (). We define I, complex integrator state variable as di = ε, we have v = E k p ε k i I jωli (8.) v = E d + je q k p εd + jεq k i I d + ji q jωl i d + ji q (8.2) The reference voltage is then computed by writing the real and the imaginary part v d = Ed k p εd k i i d + ωli q (9.) v q = Eq k p εq k i i q + ωli d (9.2) i d and i q determines the active and reactive power flow. E. Integrator Anti Windup Scheme For large step variation of the d-current, the controller might demand a too large voltage. Considering v as the reference voltage, the PI controller output is expressed as: v t = k p ε t + k i I(t), where di = ε (2) The phenomenon of integrator windup is introduced by the integrator part of the PI controller once v becomes limited. An integrator windup generally manifests itself by an overshoot (to the step response). In order to avoid windup, the integrator part I should not be updated with too large error ε. The integrator is fed with another error ε, so thatv = v. v t = k p ε t + k i I t (2) Then by writing the difference v v the error is ε = ε + v v (22) k p For the decoupled controller (9) can be expressed as v dq = E dq k p ε dq k i i dq + ωli d + ωli q (23) Now we call v, the value of v dq after some saturation is expressed as v dq = E dq k p ε dq k i i dq + ωli d + ωli q (24) By writing the differencev dq v, the error ε dq : fed to the controller is A. Test Model Bus Bus 9 Bus 6 ε dq = εdq + v dq v k p (25) IV. Bus 2 RESULTS AND DISCUSSION In order to verify the correctness and effectiveness of the control strategy and to verify the performance of the proposed scheme, the MatLab simulations were carried out. The simulation parameters are given in the appendix. The paper uses the proposed theory for a 2 bus benchmark power system [5] with a STATCOM shown in fig. 2. The uncompensated system has low voltages at buses 4 and 5. Infinte Bus Bus Bus 2 M M Bus 5 Gen 2 Gen 4 Bus 7 Bus 8 Bus 4 (PCC) Bus 3 STATCOM Figure 2. IEEE 2 bus benchmark system Bus Gen 3 M 3

4 Vm (pu) Vm (pu) Q (MVAR) Q (MVAR) P (MW) P (MW) Iq (p.u.) Iq (pu) B. Simulation Result The system objective is maintain the reactive current component against the reference under normal and fault conditions and as described earlier maintaining the voltage profile and controlling the MVAR supply. Simulations are carried out to validate that the effectiveness of the proposed controller against STATCOM without integrator anti windup. To analyze system performance and reactive power support under critical conditions a general Z-fault (LG, 2L-G and 3L- G) is applied to the middle of the parallel transmission lines connecting the STATCOM to the generator at t=.4s for ms (6 cycles) and the bus is loaded with switch capacitive and inductive load form t=.25 to.75 with a span switching of point twenty five. The controller gains for all of the three cases were kept same and constant. The STATCOM operates in the reactive current reference control mode. Figure 3(a), 4(a) and 5(a) shows the reactive current generation and tracking. Better results are obtained using integrator anti windup (IAW). The dynamic stability of the power system can be improved by the active VAR compensator with suitable.4.2 Iq Tracking genertaed Iq tracked Iq genertaed Iq tracked Iq.4.2 Iq Tracking genertaed Iq tracked Iq genertaed Iq tracked Iq (a) Reference Current tracking (a) Reference current tracking Active Power Active Power (b) Active power oscillation (b) Active Power oscillation 5 Reactive Power Supplied(pu) 5 Reactive Power Supplied(pu) (c) Injected reactive power (c) Injected reactive power.2. Voltage(pu).2 Voltage(pu) (d) Voltage at PCC Figure 3. Case I: under LG fault.9 (d) Voltage at PCC Figure 4. Case II: under 2L-G fault 4

5 Vm (pu) Q (MW) P (MW) Iq (pu) control scheme. Where the compensator injects/withdraws reactive power into the network in response to the oscillation in active power (or load angle) refer figures: 3(b), 4(b) and 5(b). During the time when the transmission line active power (load angle) is increasing, reactive power injection (figure 3(c), 4(c) and 5(c)) into the network causes an increase in PCC voltage which opposes the change in active power as is clear from figures: 3(d), 4(d) and 5(d) Iq Tracking genertaed Iq tracked Iq genertaed Iq tracked Iq It can be seen that the proposed control scheme successfully improves the voltage profile. The amount of injected power depends upon the severity of the fault and P and Q loading. All this is attributed to the change in control scheme V. CONCLUSION In this paper PI controller based on synchronous frame transfer function with integrator anti windup is proposed for evaluating the control parameters of the STATCOM used for improvement in the voltage profile connected to a benchmark power system. The obtained result demonstrates that how by bring the change in the structure and dynamics of control loop STATCOM is able to provide good voltage regulation using less reactive power, while responding to different faults and loading conditions (a) (b) (c) Reference current generation Active power oscillation (d) Active Power Reactive Power Supplied(pu) Injected reactive power Voltage at PCC Figure 5. Case III: under 3L-G fault Voltage(pu).86 REFRENCES [] C. Schauder and H. Mehta, Vector analysis and control of advanced staticvar compensators, Proc. Inst. Elect. Eng. C, vol. 4, no. 4, pp [2] N. G. Hingorani and L. Gyugyi, Understanding FACTS Concepts and Technology of Flexible AC Transmission Systems. New Jersey: IEEE Press, 999, pp [3] Wood Alan R. and Osauskas Chris M., A linear frequency domain model of a STATCOM, IEEE Transaction on Power Delivery, vol. 9, no. 3, pp. 4-48, July 24. [4] K. Acharya, S. K. Mazumder, and I. Basu, Reaching criterion of a threephase voltage-source inverter operating with passive and nonlinear loads and its impact on global stability, IEEE Trans. Ind. Electron., vol. 55, no. 4, pp , Apr. 28. [5] Soto Diego and Pena Ruben, Nonlinear control strategies for cascaded multilevel STATCOMs, IEEE Transaction on Power Delivery, vol. 9, no. 4, pp , Oct. 24. [6] B. S. Chen and Y. Y. Hsu, A minimal harmonic controller for a STATCOM, IEEE Trans. Ind. Electron., vol. 55, no. 2, pp , Feb. 28. [7] B. S. Chen and Y. Y. Hsu, An analytical approach to harmonic analysis and controller design of a STATCOM, IEEE Trans. Power Del., vol. 22, no., pp , Jan. 27. [8] B. K. Lee and M. Ehsani, A simplified functional simulation model for three-phase voltage-source inverter using switching function concept, IEEE Trans. Ind. Electron., vol. 48, no. 2, pp , Apr. 2. [9] Y. and Kazerani, decoupled state feedback control of CSI based STATCOM, in Proceedings of 32nd Annual North American Power Symposium., vol. 2, pp. -8, Oct. 2. [] J. R. Espinoza, G. Joos, J. I. Guzman, L. A. Moran, and R. P. Burgos, Selective harmonic elimination and current/voltage control in current/ voltage-source topologies: A unified approach, IEEE Trans. Ind. Electron., vol. 48, no., pp. 7 8, Feb. 2. [] Ye Yang, Kazerani Mehrdad and Quintana Victor H., Current source convereter based STATCOM: modeling and control, IEEE Transaction on Power Delivery, vol. 2, no. 2, pp , April 25. [2] Y. W. Li, Control and resonance damping of voltage-source and currentsource converters with LC filters, IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 5 52, May 29. [3] S. Mohagheghi, G. K. Venayagamoorthy, and R. G. Harley, Optimal neuro-fuzzy external controller for a static compensator in a 2-bus benchmark power system, IEEE Trans. Power Del., vol. 22, no. 4, pp , Oct. 27. [4] S. Mohagheghi, R. G. Harley, and G. K. Venayagamoorthy, An adaptive Mamdani fuzzy logic based controller for STATCOM in a multimachine power system, in Proc. ISAP, Nov. 25, pp [5] S. Mohagheghi, Adaptive crictic designs based neurocontrollers for local and wide area control of a multimachine power system with a static 5

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