A novel control structure for wind turbine with synchronous generator for tower load reduction

Transcription

1 mme.modares.ac.ir * 2 2 imani@um.ac.ir *. () : : : A novel control structure for wind turbine with synchronous generator for tower load reduction Arash Hatami, Behnam MoetakefImani * Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran * P.O.B , Mashhad, Iran, imani@um.ac.ir ARTICLEINFORMATION ABSTRACT OriginalResearchPaper ReceivedJune26 Accepted24September26 Available Online 26 October 26 Keywords: Multivariable adaptive control Wind turbine simulator Mechanical load reduction Nonlinear model [2]. 66 The attenuation of mechanical load is one of the most effective approaches in wind turbine components cost reduction, and improving the control system reduces mechanical loads with minimum effort. In modern wind turbines, electricallyexcited synchronous generators are mostly applied in directdrive structure. In current research, generator field voltage along with the blade pitch angle is employed for tower load reduction in a novel multivariableadaptive control structure. The controller is designed based on the extracted model with aerodynamic, vibratory and electrical interactions. The centralized multivariable structure is chosen to simultaneously reduce rotor speed fluctuations and tower vibrations. Since the nonlinear wind turbine model is complex, the controller is designed via optimization process. The nonlinear aerodynamic behavior of blades influences the closedloop performance in different operating condition; therefore controller is adapted to the condition by employing gainscheduling method. The effects of signal noise, digital control and higherorder dynamics of electrical system might defect the closedloop stability. The designed controller is implemented on a wind turbine simulator which includes the previouslymentioned effects. By comparing the performance of the multivariable adaptive controller with a two inputone output multivariable controller, it is proven that the mechanical loads acting on tower have been greatly decreased...[]. Pleasecitethisarticleusing: : A. Hatami, B. MoetakefImani, A novel control structure for wind turbine with synchronous generator for tower load reduction, Modares Mechanical Engineering, Vol. 6, No., pp. 4553, 26 (in Persian)

2 ProportionalIntegralDifferentiator (PID) 6 Hardware In the Loop (HIL). [3].. [3,2]..[5,4]. [6]. [7]. [8]. 2.. [8,7] [9]... 3 ).. 4 Linear Quadratic Gaussian (LQG) 2 Linear Quadratic Regulator (LQR) 3 Electrically Excited Synchronous Generator (EESG) 4 foreaft

3 C q = =5 = =5 =2 = Fig. 2 Torque coefficient versus tip speed ratio for various pitch angle 2 C T Fig. 3 Thrust coefficient versus tip speed ratio for various pitch angle 3 Table Natural frequencies of tower in Hz ) = =5 = =5 =2 =25 Fig. 4 Four mode shapes of tower with concentrated tip mass 4 Fig. Interaction of aerodynamic, mechanical and electrical subsystems of wind turbine 2 [] (2) (). (3) = (, ) 2 = (, ) (2) 2 (3) = 3 2. () (4) + = = +, = +. (5)... [2,] 4 (4) (5)

4 Fig. 5 Block diagram of wind turbine nonlinear model with flexible tower 5 :[9,8] [2] ) ( ). ( ) (2).. 2 decentralize 3 centralize.[3] [4] = (6) [6,5] + = (6) (7) (7) 32 [7]. (8). () (9)..56 = [ ] (8).29 = (9) ( +.7).25( +.73) = () sideside

5 max( ) min( ) <.2, =,2,, 3) (2) (4). = / (4) (6) (5)..[8] = + + = + + (5) (6). 9. (7) PID gains (deg) Fig. 7 Pitch control gains as functions of pitch angle 7 3 gainscheduling k p k i k d Fig. 6 Closedloop nonlinear block diagram for wind turbine 6.. [22,2] () () = + + () (3) (2) 2 [23] 2 = ( ) < max( ) < 7, =,2,,.3 < min( ), =,2,,. < max( ) <.5, =,2,,. (2) 3) 3) 3) 2norm 2 norm

6 .[24] [2725] Fig. 9 Concentrated multivariable control structure 9 imaginary axis (rad/s) real axis (rad/s) Fig. Closedloop poles in splane Dapming ratio (%) V w to r V w to dx tip /dt V (m/s) w Fig. The variation of closedloop poles damping ratio with respect to wind speed (deg) V w (m/s) Fig. 8 Pitch angle variation above the rated wind speed for stable operation 8. (8) = + = [ ], = [ ], = (7) (8) (9).. (2) (2) = = + = = = + (22) 9) 9) 9) 9) 9) + + = 9) = (2) = + ( + ) + (2) = 22) = ( ) 22) = ( + ) 22) (23). () (). = = ( ) (24) (23) (24)... splane

7 [2] r (rpm) [28] % Fig. 3 Rotor speed via and controllers 3 dx tip /dt (mm/s) Fig. 4 Tower top velocity via and controllers 4. (). (4) (3 ) (2 ) 2 (6 ) (5) Table 2 Test setup components properties (deg) Fig. 5 Pitch angle via and controllers 5 2 Duty cycle Fig. 2 Test setup structure 2 MultiInput SingleOutput ()

8 (kgm 2 s ) (kgm 2 s ) (kgm 2 s ) (kgs ) (Ndeg ) (kgms 2 ) (Nsm ) (Nsrad ) (Av ) (rads N m ) (ms N ) (As) (m) (kgm 2 ) (kgm 2 ) (kgm 2 ) (kgs 2 ) (kgm 2 s 2 A ) (kg) (m) (m) (kgm 2 s 2 ) (kgm 2 s 2 ) (s) (v) (ms ) (m) (ms ) (ms 2 ) (deg) (deg) (kgm 3 ) (Nmdeg ) (Ns) (Nmsrad ) (rad/s) 8 V f (v) Fig. 6 Excitation voltage via and controllers x tip (mm) Fig. 7 Tower top displacement via and controllers 7 3 Table 3 Comparison of the multivariable controllers performance %

9 of cantilever beams under linrearly varying axial load carrying an eccentric end rigid body, Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No., pp. 89, 23. [3] A. D. Wright, Modern control design for flexible wind turbines, NREL, USA, pp. 5762, 24. [4] D. A. Spera, Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering, Second Edition, pp , New York: ASME press, 29. [5] A. Kumar, K. Stol, Simulating feedback linearization control of wind turbines using highorder models, Wind Energy, Vol. 3, No. 5, pp , 2. [6] F. D. Bianchi, H. D. Battista, R. J. Mantz, Wind Turbine Control Systems: Principles, Modelling and Gain Scheduling Design, First Edition, pp. 4243, Germany: SpringerVerlag, 27. [7] P.C. Krause, O. Wasynczuk, S. D. Sudhoff, Analysis of Electric Machinery and Drive Systems, Second Edition, pp. 9255, New Jersey: IEEE press, 22. [8] A. K. Sedigh, B. Moaveni, Control Configuration Selection for Multivariable Plants, First Edition, pp. 2, Berlin: Springer Verlag, 29. [9] S. Skogestad, I. Postlethwaite, Multivaraible Feedback Control: Analysis and Design, Second Edition, pp , Chichester: John Wiley & Sons, 25. [2] A. K. Sedigh, Analysis and Design of Multivariable Control Systems, Second Edition, pp , Tehran: KNUT press, 2. (in Persian) [2] M. Maureen Hand, M. J. Balas, Systematic controller design methodology for variablespeed wind turbines, NREL, USA, pp. 45, 22. [22] M. H. Hansen, A. Hansen, T. J. Larsen, S. Oye, P. Sorensen, P. Fuglsang, Control design for a pitchregulated variable speed wind turbine, Riso, Denmark, pp. 47, 25. [23] K. Zhou, J. C. Doyle, Essentials of Robust Control, First Edition, pp. 24, New Jersey: Prentice Hall, 999. [24] J.S. Shamma, M. Athans, Models analysis of gain scheduled control for nonlinear plants, IEEE Transactions on Automatic Control, Vol. 35, No. 8, pp , 99. [25] R. Bajpai, M. Goyal, R. Gupta, Modeling and control of variable speed wind turbine using laboratory simulator, Journal of Renewable and Sustainable Energy, Vol. 7, No. 5, pp. 5327, 25. [26] A. Sajadi, L. Roslaniec, M. Klos, P. Biczel, K.A. Loparo, An emulator for fixed pitch wind turbine studies, Renewable Energy, Vol. 87, No., pp. 3942, 26. [27] M. Monfared, H. M. Kojabadi, H. Rastegar, Static and dynamic wind turbine simulator using a converter controlled dc motor, Renewable Energy, Vol. 33, No. 5, pp. 9693, 28. [28] T. Burton, D. Sharpe, N. Jenkins, E. Bossanyi, Wind Energy Handbook, First Edition, pp , England: John Wiley & Sons, 2. (rad/s) 9 [] H. Moradtabrizi, A. Nejat, Aerodynamic design and optimization of a megawatt wind turbine blade based on blade element momentum theory, Modares Mechanical Engineering, Vol. 5, No., pp , 25. (in Persian) [2] V. Fazlollahi, M. Taghizadeh, Modeling and design of dynamic state feedback controller with wind speed estimator, in variable speed wind turbines, Modares Mechanical Engineering, Vol. 6, No. 4, pp. 3637, 26. (in Persian) [3] B. Boukezzar, L. Lupu, H. Siguerdidjane, M. Hand, Multivariable control strategy for variable speed variable pitch wind turbines, Renewable Energy, Vol. 32, No. 8, pp , 27. [4] M. H. Giahi, A. Jafarian Dehkordi, FSI simulation of a small size horizontal axis wind turbine to investigate the effects of blade thickness and mmaterial on blade deformation, Modares Mechanical Engineering, Vol. 5, No. 5, pp. 4552, 25. (in Persian) [5] H. Moeenfard, B. Moetakef Imani, M. Davoudi, A. Rahimzadeh, Dynamic instability in tapered beams under wind excitation, Modares Mechanical Engineering, Vol. 5, No. 3, pp. 536, 25. (in Persian) [6] J. Licari, C. E UgaldeLoo, J. Liang, J. Ekanayake, N. Jenkins, Torsional damping considering both shaft and blade flexibilities, Wind Engineering, Vol. 36, No. 2, pp. 895, 22. [7] M. Geyler, P. Caselitz, Robust multivariable pitch control design for load reduction on large wind turbines, Journal of Solar Energy Engineering, Vol. 3, No. 3, pp. 2, 28. [8] J. Genov, B. Gilev, Y. Slavchev, G. Venkov, Modeling and control of wind turbine tower vibrarions, AIP Conference Proceeding 293, Bulgaria: AIP Publishing, pp. 338, 2. [9] M. Soltani, R. Wisniewski, P. Brath, S. Boyd, Load reduction of wind turbines using receding horizon control, IEEE International Conference on Control Applications (CCA), Denver: IEEE Publication, pp , 2. [] M. O. L. Hansen, Aerodynamics of Wind Turbines, Second Edition, pp. 274, London: Earthscan, 28. [] W. H. Liu, C. C. Huang, Free vibration of restrained beam carrying concentrated massed, Journal of Sound and Vibration, Vol. 23, No., pp. 342, 988. [2]S. A. Mousavi Lajimi, G. R. Heppler, Free vibration and buckling