Scheduled Model Predictive Control of Wind turbines in Above Rated Wind Avishek Kumar Dr Karl Stol Department of Mechanical Engineering

2 Overview BackgroundObjectives Control Design Overview of MPC techniques Overview of MPC techniques Modelling Modelling Applied Controllers Applied ControllersResultsConclusions

3 BACKGROUND

4 Horizontal Axis Wind Turbines Source: US Department of Energy

5 Control Objectives Speed control Maintain rated rotor speed in above rated winds Maintain rated rotor speed in above rated winds Load control Oscillations occur in the Low Speed Shaft (LSS) Oscillations occur in the Low Speed Shaft (LSS) Reduce loads in LSS Reduce loads in LSS

6 Turbine Nonlinearities

7 Model Predictive Control Choose the control input trajectory that will minimize a cost function over the prediction horizon H p Example:

8 Why MPC? Accommodate disturbances MIMOConstraints Many cost functions Can extend to nonlinear systems

9 Current State of MPC for Wind Turbines MPC using linear models of turbine (LMPC) Lacks ability to deal with system nonlinearities Lacks ability to deal with system nonlinearities MPC using nonlinear models of turbine Difficult to increase order of model as explicit nonlinear equations become very complex Difficult to increase order of model as explicit nonlinear equations become very complex Computationally expensive Computationally expensive

10 Bridging the Gap Scheduled MPC (SMPC) Uses a network of linear models easily obtained from linearization codes (FAST) Optimization remains convex for each controller Controllers can be specifically tuned at various operating points to operate with different aims

11 Objectives Create Scheduled MPC for speed and LSS load regulation in above rated winds Simulate nonlinear controller in Region 3 using high order model Compare performance of nonlinear and linear controllers Tower and blade load mitigation not considered at this stage

12 MPC OVERVIEW

13 Constrained Linear Quadratic Regulator Up till now, MPC has been posed as a finite horizon problem For better performance set up MPC as an infinite horizon problem This allows LQR control with constraints

14 Infinite Horizon Cost Function for CLQR

15 Constrained Linear Quadratic Regulator Design a LQR for the linear system giving predictions:

16 Constrained Linear Quadratic Regulator Create a MPC to calculate perturbations c about control input given by the LQR only over H p so constraints are met

17 CLQR Minimization

18 CLQR Block Diagram

19 Scheduled MPC Create a network of MPCs at enough operating points to capture nonlinearities of system Tune each controller for the region it operates in Weight the outputs of each controller based on scheduling variable

20 SMPC Block Diagram

21 Model FAST model of Controls Advanced Research Turbine (CART) at NWTC 600kW Variable-Speed Variable-Pitch 2 Bladed

22 Linear Model for Control Design/Disturbance Estimation

23 Nonlinear Model for EKF (7) where

24 WIND TURBINE CONTROL DESIGN

25 Baseline Controllers GSPI

26 Baseline Controllers CLQR

27 Scheduled MPC Linearization Point 123 Wind Speed (V i 0 ) 14ms -1 18ms -1 22ms -1 Blade Pitch2.2°11.1°16.1° Generator Torque 3524Nm Rotor Speed41.7rpm

28 Scheduled MPC

29 Scheduled MPC

30 Simulations Simulations conducted in MATLAB/Simulink with FAST model Active DOF Blade flap (modes 1 and 2) Blade flap (modes 1 and 2) Blade Edgewise Blade Edgewise Teeter Teeter Tower fore-aft (mode 1 and 2) Tower fore-aft (mode 1 and 2) Drivetrain Drivetrain Generator Generator Tower side-side Tower side-side

31 Wind Inputs 15ms -1 5% turbulence intensity 18ms -1 5% turbulence intensity 22ms -1 5% turbulence intensity 18ms -1 15% turbulence intensity

32 Performance Criteria Rotor Speed RMS Error Low Speed Shaft Damage Equivalent Load RMS Pitch Acceleration

33 Tuning Each SMPC controller tuned to have same speed control as GSPI in respective low turbulence wind Each SMPC controller tuned to have same LSS load control as CLQR in respective low turbulence wind

34 RESULTS

35 Constraints

36 Speed Control

37 LSS DEL

38 Pitch Acceleration

39 Conclusions SMPC can successfully control a turbine in above rated wind conditions SMPC has ability to control MIMO systems with multiple control objectives SMPC adjusts to the system nonlinearities SMPC satisfies input constraints Each controller in the SMPC network can be finely tuned to achieve the required performance in its region of operation

40 Future Work Add individual blade pitch control Increase control objectives to include tower and blade loads Quantify computational requirements Compare with NMPC Use of more advanced disturbance prediction models

Questions?

42 Nonlinear Model (7) where

43 Extended Kalman Filter FL design needs accurate wind speed estimate Extended Kalman Filter (EKF) is a nonlinear state estimator Sub optimal Linearizes the system model each time step, then estimates states like a linear Kalman Filter

44 Choosing Hp