1. Raja M. Imran, D. M. Akbar Hussain and Mohsen Soltani
DAC with LQR Control Design for Pitch Regulated Variable Speed Wind Turbine
Raja M. Imran, D. M. Akbar Hussain and Mohsen Soltani
Department of Energy Technology, Aalborg University, Denmark
ABSTRACT
METHODS
DISCUSSION
We have used step wind to analyze the controller performance and then we have tested this controller with turbulent wind. This paper has presented a DAC controller design methodology with optimal control theory and its mathematical modeling. State feedback matrix is calculated for the using LQR. We have generated two-mass state space model of wind turbine for above rated wind speed and then DAC controller is implemented in MATLAB/Simulink. We have tuned PI controller for robust performance to mitigate the effect of disturbance and used MATLAB to tune it properly for optimum performance. Disturbance feedback matrix is calculated to mitigate effect of wind on the plant and make system disturbance free and to get better estimation of the wind speed. We have compared the results for a step wind and then for the turbulent wind. Results for step shows that there is less overshoot and better settling time of the proposed controller as compared to PID. Then results with turbulent wind shows less fluctuation in generator speed which will result stability of output power and less fatigue of drive train to increase its life time. The performance analysis of the system shows that our proposed controller have better power regulation and less fatigue of drive train as compared to PID controller for 5MW wind turbine in the presence of actuator dynamics.
Disturbance Accommodation Control (DAC) is used to model and simulate a system with known disturbance wave- form. This paper presents a control scheme to mitigate the effect of disturbances by using collective pitch control for the above-rated wind speed (Region III) for a variable speed wind turbine. We have used Linear Quadratic Regulator (LQR) to obtain full state feedback gain, disturbance feedback gain is calculated independently and then estimator gain is achieved by pole-placement technique in the DAC augmented plant model. The reduced order model (two-mass model) of wind turbine is used and 5MW National Renewable Energy Laboratory (NREL) wind turbine is used in this research. We have shown comparison of results relating to pitch angle, drive train torsion and generator speed obtained by a PID controller and DAC. Simulations are performed in MATLAB/Simulink. The results are compared with PID controller for a step wind and also for turbulent wind disturbance. DAC method shows better regulation in output power and less fatigue of drive train in the presence of pitch actuator limits. Proposed controller tested on wind turbine shows better robustness and stability as compared to PID.
DAC is a control scheme to augment the known waveform disturbance with the states of the system, so that it becomes a part of the exogenous system.
Disturbance feedback is used with state feedback to mitigate the effect of the disturbance. State space model of plant is of the form
State space model of the disturbance waveform is
Simulink model of the DAC augmented plant is shown in Fig.2
INTRODUCTION
RESULTS
REFERENCES
Classical control based on Proportional-Integral-Derivative (PID) controller discussed in [1], [2] and[3].
[4] and [5] have used expert PID controller for better performance and to reduce vibration generated during its operation.
LQG techniques is discussed in [6] and used on wind turbine to multiple objectives in [7], [8], [9], [10] .
Periodic Disturbance Accommodation control techniques is discussed in [11] to reduce load.
In this paper, DAC control scheme is designed to reduce disturbance effect in above rated wind speed for 5MW NREL wind turbine. We have used optimal control theory to design full state feedback gain in the presence of actuator dynamics and also disturbance feedback gain is calculated independently. Pole-placement technique is used to estimate plant states as well as disturbance states from the disturbance accommodated model of the system. Reduced order two-mass model of wind turbine is used and then its linearized three- state model is generated at an operating point for the plant for above-rated wind speed. We have done simulation in MATLAB/ Simulink and finally results are analyzed in the presence of the pitch actuator dynamics.
Wind turbine is a complex nonlinear system but here we are using its reduced order two-mass model. Aerodynamic power available on the swept area of wind turbine rotor is given by
We have used 5MW wind turbine as research object .
Step response comparison of the system for DAC and PID is
[1] M.M. Hand, and M.J. Balas, “Systematic Approach for PID Controller Design for Pitch-Regulated Variable-Speed Wind Turbines,” In Proc. ASME Wind Energy Symposium, Reno, Nevada, January,1998.
[2] E.A. Bossanyi, “The design of closed loop controllers for wind turbines,” Wind Energy 2000; 3:
[3] E. A. Bossanyi, “Wind Turbine Control for Load Reduction,” Wind Energy 2003; 6:
[4] Y. Xingjia, L. Yangming, X. Zuoxia, and Z. Chunming, “Active Vibration Control Strategy based on Expert PID Pitch control of Variable Speed Wind Turbine,” In Proc Int. Conf. Electrical Machines and Systems, Oct
[5] X. Anjun, X. Hao, H. Shuju, and X. Honghua, “Pitch Control of Large Scale Wind Turbine Based on Expert PID Control,” In Proc. Int. Conf. Electronics, Communications and Control, 9-11 Sept
[6] B.D.O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods. New Jersey: Prentice-Hall, 1989.
[7] Y. Xingjia, G. Changchun,X. Zuoxia, L. Yan, L.Shu, and W. Xiaodong, “Pitch Regulated LQG Controller Design for Variable Speed Wind Turbine,” In Proc. Int. Conf. Mechatronics and Automation, 9-12 Aug
[8] A. Kalbat, “Linear Quadratic Gaussian (LQG) control of Wind turbines,” In Proc. 3rd Int. Conf. on Electric Power and Energy Conversion Systems (EPECS), 2-4 Oct
[9] A.D. Wright., “Modern Control Design for Flexible Wind Turbines,“ NREL Report No. TP , Golden, CO: National Renewable Energy Laboratory, 2004.
[10] Raja M. Imran, D. M. Akbar Hussain and Zhe Chen, “LQG Controller Design for Pitch Regulated Variable Speed Wind Turbine,” In Proc. Of IEEE Int. Energy Conference (ENERGYCON), Dubrovnik, Croatia, May, 2014.
[11] K.A. Stol, and M.J. Balas, “Periodic Disturbance Accomodation Control of blade load mitigation in WT,” Journal of Solar Energy Engineering, vol. 125, no. 379, 2003.
[12] K.A. Stol, “Disturbance Tracking and Blade Load Control of Wind Turbines in Variable-Speed Operations,” In Proc. of ASME Wind Energy Symposium, Reno, Nevada, 6-9 Jan
[13] J. Li, H. Xu, L. Zhang, Zhuying, Shuju, and Hu, “Disturbance Accommodating LQR Method Based Pitch Control Strategy for wind turbines,” In Proc. 2nd Int. Symposium on Intelligent Information Technology
Application, Dec
[14] J. Jonkman, S. Butterfield, W. Musial, and G. Scott,”Definition of a 5-MW Reference Wind Turbine for Offshore System Development”, Technical Report NREL/TP ,February 2009.
[15] M.N. Soltani, T. Knudsen, M. Svenstrup, R. Wisniewski, P. Brath, R. Ortega, and K. Johnson, “Estimation of Rotor Effective Wind Speed:A Comparison,” IEEE Transactions on Control Systems Technology, Vol. 21, No. 4, July 2013.
Comparison of the results for the turbulent wind is
We have tuned PI controller to reduce the effect of wind disturbance at the output and its optimum parameters values are Kp = −0.40 and Ki = −0.15. Simulations are performed in MATLAB/Simulink with the actuator dynamics which include pitch angle saturation and rate limit as mentioned in [14]. We have compared PI controller with DAC for step wind. Drive train torsion, input pitch angle and generator speed step response are shown in Fig. 3, Fig. 4 and Fig. 5 respectively. Then we have applied the turbulent wind as shown in Fig. 6 to the system and compared the results with PI controller. Results of the drive train torsion, pitch angle and generator speed are shown in Fig. 7, Fig. 8 and Fig. 9 respectively for the turbulent wind. It can be seen that our proposed controller shows less fluctuation in generator speed and less fatigue on drive train as compared to PI controller.
Drive train is transmission system which convert low rotational speed to high rotational speed to drive the generator as shown in Fig. 1. Its dynamics can be represented by the following differential equations and discussed in [10], [15].