AIAA Aerospace Sciences Meeting 2009 Adaptive Control of a Utility-Scale Wind Turbine Operating in Region 3 Susan A. Frost Intelligent Systems Division NASA Ames Research Center Susan.A.Frost[at]nasa.gov Mark J. Balas Wind Energy Research Center (WERC) University of Wyoming Mbalas[at]uwyo.edu Alan D. Wright National Wind Technology Center National Renewable Energy Laboratory Alan_Wright[at]nrel.gov research on acknowledge coauthors National Wind Technology Center Golden, Colorado

Outline Utility-Scale Wind Turbines Adaptive Control Theory Region 3 Adaptive Pitch Controller Controls Advanced Research Turbine (CART) Simulation Results Conclusions click on RIGHT after CART

Utility-Scale Horizontal Axis Wind Turbine Utility-Scale HAWT’s Rotor Diameter: 40-95 m Onshore 90-114 m Offshore Tower: 25-180 meters Capacity: 0.1-3 MW Onshore 3-6 MW Offshore Start up wind speed: 4-5 mps Max operating wind speed ~16 mps Low speed shaft: 30-60 RPM High speed shaft: 1000-1800 RPM WT manufactures are undoubtedly building larger wind turbines Image: NWTC

Operating Regions Control Goals: Maximize power generation in Region 2 Maintain rated power in Region 3

Pitch-Controlled Wind Turbines Region 2: Control generator torque to yield optimum power Hold blade pitch constant Region 3: Control blade pitch to maintain constant rotor speed Generator torque held constant like this picture b/c of people in tower

Wind Turbine Actuation Blade Pitch Nacelle Yaw Generator Torque collective pitch control Pitch Actuators Control Actions

Adaptive Control in Wind Turbines Adaptive Control = uses output of Plant to determine control inputs Good for poorly modeled plants with uncertain operating environments Requires less modeling of turbine & its operating conditions Can reduce controller design & verification time since less tuning required than for PID Changes to existing turbine may require no controller modification Adaptive vs PID

Direct Adaptive Control Direct Model Reference Adaptive Control (DMRAC) with Rejection of Persistent Disturbances Plant is linear time-invariant (LTI) where x is plant state, u is control input, y is sensor output, uD is disturbance input Disturbance input vector, uD, comes from a Disturbance Generator: See: Johnson,C.D., 1976. where zD is disturbance state

Disturbance Generator Disturbances are of known form, but unknown amplitude Ex: Step disturbance: Ex: Sinusoidal disturbance: Convenient form of Disturbance Generator:

Reference Model Output Tracking Known Reference Model: Reference model parameters are known Plant parameters are unknown Control Objective: Cause Plant output y to asymptotically track Reference Model output ym Need to show error goes to zero and gains are bounded LOOK at AUDIENCE!! Output error: Adaptive Control Law: See: Wen, Balas, JMAA, 1989 Fuentes, Balas, JMAA, 2000.

Ideal Trajectories & Model Matching Conditions Define ideal trajectories for plant: Matching conditions are necessary and sufficient for existence of ideal trajectories where Model Matching Conditions are obtained by substituting ideal trajectories into above: If CB>0, then solutions to matching conditions exist Solutions to matching conditions must exist for analysis purposes, BUT they don’t need to be known for adaptive controller design!

Adaptive Controller Analysis State tracking error: Ideal output error: For analysis, form: Using the above definitions and adaptive control law: Substitute into equation for to obtain: where is the vector of available information

Adaptive Gain Laws Form the Tracking Error System: where is the vector of available information Specify the Adaptive Gain Laws: where is an arbitrary, positive definite matrix. The Adaptive Gain Laws can be written as: The adaptive gain laws are chosen to be simple and effective For Closed-Loop Stability Analysis, see: Frost, Balas, Wright, IJRNC (2009)

Closed-Loop Stability Result Theorem: Suppose the following are true: All um are bounded (i.e., all eigenvalues of Fm are in the closed left-half plane and any eigenvalues on the jω-axis are simple); The reference model, is stable; is bounded (i.e., all eigenvalues of F are in the closed left-half plane and any eigenvalues on the jω-axis are simple); (A,B,C) is Almost Strict Positive Real (ASPR) (i.e. and the open-loop transfer function is minimum phase) Then the adaptive gains are bounded, and asymptotic tracking occurs, i.e. Don’t know where the gains are bounded

Adaptive Pitch Control in Region 3 Objective: Regulate generator speed in Region 3 and reject step disturbances Controller designed w/ extended DMRAC approach to collectively pitch blades & hold generator torque constant Region 3 operation requires regulation, so no reference model is used, i.e. and are identically zero Disturbance can be modeled by a step function of unknown amplitude, so Adaptive control law: Several papers published demonstrating that changes in wind speed across the rotor surface are well modeled by step functions Note: not considering wind shear

Adaptive Pitch Control Law The adaptive collective pitch control law is given by: Adaptive controller gains were tuned to minimize generator speed error while keeping the blade pitch rate in a range similar to baseline PI controller’s The actual values of the gains used in the adaptive controller were: and

Controls Advanced Research Turbine (CART) NWTC, Golden, Colorado

CART Specifications CART Specifications Low-speed Shaft High-speed Shaft Tower Nacelle Generator Gearbox Blade Hub Rotor CART Specifications Variable-speed, two-bladed, teetered, upwind, active-yaw Rotor Diameter: 43.3 m Hub Height: 36.6 m Rated electrical power: 600 kW at 42 RPM in region 3 Region 3 Rated generator speed: 1800 RPM Power electronics command constant generator torque Blade pitch rate limit: ±18 deg/sec Baseline PI Pitch Controller utility scale, but small blade pitch rate limit +-18 baseline pi pitch controller for region 3 control

FAST Simulator for CART FAST= Fatigue, Aerodynamics, Structures, and Turbulence Aeroelastic simulator capable of predicting extreme and fatigue loads of HAWTs AeroDyn subroutine package (Windward Engineering) generates aerodynamic forces along turbine blades Turbine modeled as combination of rigid and flexible bodies Versatile high fidelity simulation of CART with controller included in the loop with switches for DOFs, etc. Good folks at NREL developed a high fidelity simulator of the CART Uses Kane’s method to set up equations of motion

Simulink Model of Adaptive Pitch Controller Look at audience

Simulation Conditions Simulation time: 0-100 seconds Integration step size: 0.006 seconds Generator DOF switch on All other DOF switches turned off Wind turbine had fixed yaw with no yaw control Aerodynamic forces were calculated during runs Two types of wind inflow: step and turbulent wind These are the simulation conditions

Step Wind Inflow – Generator Speed Errors time scale starts at 20 secs after transients Pitch Controller Normalized Generator Error Baseline PI 0.0922 RPM Adaptive 0.0479 RPM Generator Speed Errors Relative difference: 48% Normalized Generator Speed Errors for Step Wind

Step Wind: Pitch Angle Rate Baseline PI Controller Pitch Rate Adaptive Controller Pitch Rate

Turbulent Wind Inflow – Generator Speed Errors Pitch Controller Normalized Generator Error Baseline PI 0.2435 RPM Adaptive 0.0781 RPM Relative difference: 68% Normalized Generator Speed Errors for Turbulent Wind

Turbulent Wind: Pitch Angle Rate adaptive controller is much quicker to respond to the changes in the wind so more pitch activity Baseline PI Controller Pitch Rate Adaptive Controller Pitch Rate

Robustness to Modeling Errors Turbulent Wind Inflow Generator speed errors with 5% perturbation in chord length Generator speed errors with 15% perturbation in aerodynamic twist

Operation with Flexible Modes Enabled Turbulent Wind Inflow Generator errors when drive train rotational flexibility DOF switch is turned on   Generator errors when drive train rotational flexibility, first fore-aft tower bending-mode, and first side-to-side tower bending-mode DOF switches are turned on

Conclusions & Future Work Adaptive controller was easy & quick to design Adaptive controller showed improved generator speed regulation when compared with baseline PI controller Pitch rate was comparable for both controllers with step wind Both controllers performed in robust manner under parameter variations Future work Investigate parameter modifications which would require redesign of PI controller, but no change to adaptive controller Incorporate a tracking model representing an ideal wind turbine to be used in design of adaptive controller Apply adaptive control to Region 2 and 2.5 Test adaptive controller on CART

References Johnson, C.D. Theory of disturbance-accommodating controllers. Control & Dynamic Systems, Advances in Theory and Applications, Leondes, CT. ed. Academic Press: New York, 1976; 12: 387-489. Wen, J.T, Balas, M.J. Robust adaptive control in Hilbert space. Journal of Mathematical Analysis and Application 1989; 143(1): 1-26. Fuentes, R.J., Balas, M.J. Direct adaptive rejection of persistent disturbances. Journal of Mathematical Analysis and Applications 2000; 251(1): 28-39. Frost, S.A., Balas, M.J., Wright, A.D., Direct adaptive control of a utility-scale wind turbine for speed regulation, International Journal of Robust and Nonlinear Control, 2009, 19(1): 59-71, DOI: 10.1002/rnc.1329. Fingersh, L.J., Johnson, K.E. Baseline results and future plans for the NREL Controls Advance Research Turbine. Proceedings of the 23rd AIAA Aerospace Sciences Meeting and Exhibit Wind Energy Symposium 2004; 87-93.