Design of Sliding Mode Stabilizer for Wind Turbine Generator using Dynamic Compensation Observer Technique

Transcription

1 Proceedings of the 6th WSES International Conference on Power Systes, Lisbon, Portugal, Septeber -4, 6 84 Design of Sliding Mode Stabilizer for Wind urbine Generator using Dynaic Copensation Observer echnique ISSRCHI NGMROO Sirindhorn International Institute of echnology haasat University, Bangkok HILND bstract: - sliding ode stabilizer design for enhanceent of the dynaic stability of a wind turbine generator supplying an infinite bus is presented. he dynaic copensation observer technique is applied to design the hyperplane in a sliding ode control. he salient feature of this technique is that only output inforation can be used as a feedback signal of a controller. In addition, this technique provides a systeatic approach to obtain the control design specification, a robustness against syste paraeter variations as well as various loading conditions, and an enhanceent of syste dynaic perforance against disturbances. Siulation study reveals that the proposed controller is not only able to dap power oscillations due to wind gust disturbances, but also very robust against various loading conditions and variations of syste paraeters. Key-Words: - Power syste dynaic stability, Sliding ode control, Wind turbine generator, Dynaic copensation observer Introduction he developent of wind energy technology is growing rapidly throughout the world. s the oil price keeps increasing and the power deand also continues to rise, wind energy sees to becoe a new aspect to solve these probles. Wind energy provides any advantages to power syste as it is a clean energy and it does not require a ajor redesign of the existing power syste. However, the fluctuating nature of wind as well as the new generator types that are used in wind turbines, are the challenges that power syste engineers encounters []. One of the areas that has been paid attentions by any researchers is the dynaic stability of the wind turbine generators [-3]. he iportant aspect of the dynaic perforance of the wind turbine generator is its effect on the dynaic stability of the syste to which it is connected. he wind power generation unit should not contribute the dynaic instability of the power syste. o iprove syste dynaic stability, any control theories have been adopted to design of power syste stabilizers for a wind turbine syste such as a proportional integral controller [4], a variable-structure stabilizer [5], etc. ong these schees, a sliding ode control is one of advanced design ethods. It offers the satisfactory attenuation perforance against disturbance as well as the high robustness to a power syste under various operating conditions and syste uncertainties [6-7]. Nevertheless, the sliding ode controller is constructed by a state feedback control schee. ccordingly, it is not easy to ipleent in practical syste. Besides, the difficulty of switching gain setting in a hyperplane design is also an inevitable proble. o overcoe these probles, a new technique for sliding ode control design is highly expected. With the syste where only output inforation of syste is available, a hyperplane design based on a dynaic copensation observer [7] is applied to design a sliding ode stabilizer for a wind turbine generator in this paper. he ain feature of this technique is that only output inforation can be used as a feedback signal of a controller. dditionally, the syste robustness against various uncertainties such as syste paraeter variations, generating and loading conditions etc., can be guaranteed. Siulation studies in a single wind turbine generator infinite bus syste insist that the proposed sliding ode control is not erely capable of daping low frequency oscillations, but also very robust to syste uncertainties. Syste Modeling G Wind urbine Generator v t ransission Line E Infinite Bus Fig. Single wind turbine generator infinite bus.

2 Proceedings of the 6th WSES International Conference on Power Systes, Lisbon, Portugal, Septeber -4, 6 85 V gust ω 377 δ P K Ms D s Load Loop y Sliding Mode Control Dynaic Copensation u = -K c z-ky (6) u K 4 K K 5 z u K v R S E Interaction Coefficients s K E s E sk 3 do K 3 K 6 E q v t Reduced-order Observer () v 3 K F s E fd s F Excitation Loop Fig. Block diagra of a linearized power syste odel with a dynaic copensation controller. V K V K δ δ τ P ζ τ P θ θ θ K ω τ P ω Fig.3 Block diagra of a pitch change regulation. wind turbine generator connected to an infinite bus [5] as shown in Fig. is used as a studied syste. he linearized odel of power syste can be depicted in Fig.. he block diagra of a pitch change regulation is shown in Fig. 3. Noenclatures are given by δ - Rotor angle ω - Electrical speed - Mechanical input torque xe - ransission line ipedance D - Daping constant of the generator M - Inertia constant of the generator - ie constant of the aplifier E - Field voltage fd Eq - ransient EMF in q -axis KF - Stabilizer gain KE - Exciter gain E - ie constant of the exciter K - plifier gain F - ie constant of the stabilizer loop - Open circuit field tie constant do V - Wind speed θ - Blade pitch angle d KV = - Coefficient of torque fro wind dv speed d K θ = - Coefficient of torque fro pitch dθ angle d K ω = - Coefficient of torque fro rotational dω speed Kω, Kv, Kδ - Pitch angle regulation constants ζ - Daping ratio τ P - ctuator tie constant K K - Syste constants 6

3 Proceedings of the 6th WSES International Conference on Power Systes, Lisbon, Portugal, Septeber -4, 6 86 he state equation of a linearized syste in Fig. can be expressed as where () 3 x = x Bu 4 x = δ ω Eq Efd vr v3 θ θ K KK F B = F 377 K K D K ω M M M = K 4 do K3do do SE K E E K θ M = E KK5 KK6 KK5KF KK6KF 3 = F F Kδ Kω τp τp K KF KKF 4 F = F ζ τ P τp he output y is δ ω E q δ E fd = ω vr v3 θ θ () 3 Design of Sliding Mode Stabilizer using Dynaic Copensation Observer he design of a sliding ode stabilizer based on a dynaic copensation observer [7] is divided into ain parts; the syste atrix partition and the hyperplane gains design. s deonstrated in Fig., the speed deviation ω which is an output signal fro the syste is used as a feedback signal of the sliding ode stabilizer and a reduced-order observer, to generate a control signal u. his signal is used to stabilize the syste. 3. he partition of syste atrix he state equations () and () are expressed as x = x Bu (3) y = Cx (4) n n where, R n is a syste atrix, B R is an p n input atrix, C R n is an output atrix, x R is the state variables, u R is a control signal and p y R is an output signal with p< n. Fro (3), the syste atrix is split into the following n where R divided into = (5) ( ) ( n ). his sub-block can be = (6)

4 Proceedings of the 6th WSES International Conference on Power Systes, Lisbon, Portugal, Septeber -4, 6 87 Define r to be a diension of and r >. hen, R r r, ( n p r) ( n p r) R and ( p ) ( n p r R ). Divide the subatrices and as = and = ( n r) where R, split and into = ( n p r) ( p ) R ( n p r) ( p ), 3 (7) and = (8) ( n : n) (: r) ( n : n) ( r : n p) where R, R, ( n : n) ( n p : n ) 3 R ( n : n) ( n : n) and R. Finally, define = and C = [( p ) ( n p r) I( p ) ] (9) he pair (, ) is controllable and the triple (,, C ) is stabilizable with respect to output feedback. s a result, the original systes (3) and (4) are reduced to the fictitious systes as x = x u () y = C x () he systes () and () are used to design sliding ode control. he signal y is an actual output feedback fro the syste which will be used as an input for the controller and the observer as depicted in Fig.. 3. Design of copensator variables and hyperplane gains he design of dynaic copensator variables and hyperplane gains can be explained as follows: ) Specify a new daping ratio (ζ ) and a new real part of the eigenvalue corresponding to the power oscillation ode. ( n p r) ( p ) ) Define a gain atrix L R so that L is stable. Select L = p where p is a ( n p r) vector representing the desired poles of L. he values of p is usually real negative values. Define p as a ( n r) vector representing the desired poles of [ K K ]. he values of p ay be real negative nubers. djust p to obtain [ K K] by using a pole placeent ethod. 3) Define the reduced-order observer [8] for the syste in () and () as z = Hz D y D u () he copensator variables in () are obtained fro H = L (3) D = L L L (4) D = L (5) ( ) he state feedback law is provided by u = K z K K L y = K z Ky (6) ( ) C where the hyperplane gains K and K are given by K = K KL (7) KC = K (8) 4 Siulation Study Based on syste paraeters [5], the operating point selected for the dynaic copensation design is ( PQ, ) = (.,.3) pu. he syste atrix and the input atrix B are given as =, =, =, C

5 Proceedings of the 6th WSES International Conference on Power Systes, Lisbon, Portugal, Septeber -4, = [ 6 ] B = (9) Fro section 3., n= 8, =, p= and r = 5 are obtained. he eigenvalues corresponding to the electroechanical oscillation ode are.735 ±.9i which are unstable. In order to acquire syste stability, the new real part and the new daping ratio of these eigenvalues are specified at.9 and.57, respectively. s a result, the atrices and are calculated as 6 = and = () o reach the desired specifications above, the value p is adjusted to be 75 and [ K K] are deterined as [.5 5], respectively. he hyperplane gains are calculated as K = and K =.5 () ccording to equation (), the actual output signal y is as follow [ ] δ ω = () ω Consequently, the eigenvalues and daping ratios of the syste with and without stabilizer are given in able. he designed specifications are et. able Syste eigenvalues Without stabilizer.735 ±.9i ( ζ =.38 ) C With sliding ode stabilizer.94±.34i ( ζ =.57 ) In order to exaine the perforance of the dynaic copensation controller, the syste shown in Fig. was disturbed by the pseudo-typical wind gust of the for V gust π t = G( cos ) (3) where < t <, = 4 and G = 7.5%. Fig. 4 shows the wind gust which is siulated to the syste under three various conditions. Besides, the effect of wind turbine syste the designed sliding ode stabilizer is copared to that of the Variable Structure Stabilizer (VSS) [5]. Vgust, pu tie, s Fig.4 Wind gust disturbance. 4. t the noral operating point he power syste operates at P =. pu, Q =.3 pu, the field tie constant do =.94 sec,and the transission line X e =.3 pu. he speed deviation responses of the syste with and without controllers are illustrated in Fig.5. he response without controller is unstable whereas the response of the syste with both VSS and sliding ode stabilizer is well daped. 4. With the changes in reactive power and field tie constant In this situation, reactive power and field tie constant are reduced to be Q =.5 pu, do = sec, respectively. he responses of generator speed deviation are shown in Fig.6. It can be seen that the aplitude of the response with the sliding ode stabilizer is lower than that with the VSS. he VSS is sensitive to these paraeter variations. 4.3 t light loading with a decreased field tie constant Under this condition, real power, reactive power, and field tie constant are set at P =. pu Q =.6 pu

6 Proceedings of the 6th WSES International Conference on Power Systes, Lisbon, Portugal, Septeber -4, 6 89 ω, pu.5 x No control VSS Dynaic copensation tie, s Fig.5 Speed deviation response at operating point. ω, pu 5 x VSS Dynaic copensation tie, s Fig.6 Speed deviation response with decreases in reactive power and field tie constant. ω, pu.5 x VSS Dynaic copensation tie, s Fig.7 Speed deviation response at light loading. and do =. sec, respectively. s deonstrated in Fig.7, it is clear that the speed deviation response by VSS controller is poorly daped, the oscillation is uch severe than that of the sliding ode stabilizer. he VSS controller is very sensitive to syste paraeter variations. On the other hand, the proposed sliding ode stabilizer is very robust to this operating condition. It is able to dap speed oscillation significantly and rapidly. hese siulation results confir that the robustness of the proposed sliding ode stabilizer is uch superior to that of the VSS [5]. 5 Conclusion In this paper, the dynaic copensation observer technique has been applied to design a sliding ode stabilizer for the wind turbine syste. he ain advantage of this ethod is that only output inforation is required as a feedback signal of the controller. Moreover, this technique provides a systeatic design to achieve the design specification, robustness against syste paraeter variations, and an enhanceent of syste dynaic perforance. Siulation results against the variety of loading conditions and syste paraeters under the wind gust disturbance indicate that the sliding ode stabilizer provides higher effectiveness and superior robustness than the variable structure stabilizer. In the future work, the effectiveness of the proposed stabilizer will be investigated under ore severe, continuous and rando wind gusts, various syste paraeter variations etc. References: []. ckerann, Wind Power in Power Systes, John Wiley & Sons, Ltd, 5. [] E.N. Hinrichsen and P.J. Nolan, Dynaics and stability of wind turbine generators, IEEE rans. Power pparatus Syste, Vol., 98, pp [3] C.C. Johnson and R.. Sith, Dynaics of wind generators on electric utility networks, IEEE rans. on erospace Electron and Syste, Vol., 976, pp [4].S. Bhatti,.. F. l-dei and N. K. Bansal, Load frequency control of isolated wind diesel hybrid power systes, Energy Conversion and Manageent, Vol. 39, No.9, 997, pp [5] Y.L. bdel-magid, Z.M. l-haouz, J.M. Bakhashwain, variable-structure stabilizer for wind turbine generators, Electric Power Systes Research, Vol. 33, 995, pp [6] U. Itkis, Control systes of variable structure, Wiley, New York, 976. [7] C. Edward and S.K. Spurgeon, Sliding Mode Control: heory and pplication, aylor and Francis, , ch.5. [8] K. Ogata, Modern Control Engineering, Prentice -Hall, Inc., 4 th edition,, ch..