Optimised Aerodynamics and Control by Nonlinear Model based Predictive Control

1. Optimised Aerodynamics and Control by Nonlinear Model based Predictive Control By: Jan Schuurmans (DotX Control Solutions BV) Eelco Nederkoorn (DotX Control Solutions BV) Stoyan Kanev (Energy research Centre Netherlands) Robert Rutteman (XEMC-Darwind) Eric Nguyen (Mitsubishi Power Systems Europe)

2. Introduction • Commercial WTB controllers: PID loops • However, PID is not optimal for: • nonlinear dynamics • interactions • handling of constraints relevant for wind turbines !

3. Introduction • Conclusions on (N)MPC so far: • hardly performs better than PID • major benefits with preview wind information • more computational load • However, conclusions were based on simulations with simplified models (not aero-elastic models) • Definition of the problem (in this presentation): Can NMPC offer advantages (when used in wind turbine design)?

4. NMPC controller: overview measured signals Observer Internal Model control signals (u) state (x) Control model Prediction optimization variables (c) constraints Optimization setpoints

5. NMPC controller (Internal model) • Internal model defines: • state derivatives (dx/dt) • cost function output (y) • soft limits (on output) • Cost function:

6. NMPC controller (Internal model) Cost output definition: y = gen_speed – setpoint power – setpoint tower top speed soft limit on gen_speed soft limit on tower top position

7. Soft limit value 0 gen_speed max value NMPC controller (Internal model) Soft limit definition:

8. NMPC controller (Observer) • generator speed and power: measured • wind speed: Nonlinear Leunberger observer • tower top position and speed: linear Leunberger observer convergence speed is exponential and adjustable

9. u most common parameterisation in (N)MPC c3 c2 c1 c0 time u u(t) = c0 + c1 exp(-a t) time t=0 NMPC controller (Control Model)

10. NMPC controller (Predictions) • Predictions are obtained by forward simulation • ‘initial’ state from Observer and measurements • wind speed: • here: assumed to be constant in future • (with gust detection: from detector) • (with LIDAR: from wind speed ahead of turbine)

11. NMPC controller (Optimization) • Optimization problem, to be solved each sample: • Find vector c that minimises J, subject to nonlinear model and input constraints • input constraints: • absolute • rate

12. NMPC controller (Practical issues) • Practical problems with NMPC: • how to filter ‘noise’? • how to obtain robust stability? • common filtering approach: task for Observer • Simply filter feedback signals? Phase lag causes stability issues • Extended Kalman filter? Issues with stability/reliability

13. NMPC controller (Practical issues) • Common robust stability approach: use observer and/or weight matrices as ‘tuning knobs’ • What we use: for both filtering and robust stability, we use novel method (for which patent application is written)

14. Case study (DLC 1.5 simulation) Hub wind NMPC soft limits Tower bottom load Collective pitch NMPC Conventional grid loss

15. Conclusions • Yes, NMPC has advantages (over PID) • Why? • more power output due to better load reduction • NMPC reduces fatigue loads due to: • model based approach • ability to distribute input constraints optimally • NMPC reduces ultimate loads due to: • ability to handle output constraints • ability to accurately simulate loads with nonlinear model

16. Acknowledgement Thanks to Dutch Ministry of Economic Affairs for financial support!