Scheduled Model Predictive Control of Wind turbines in Above Rated Wind
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Scheduled Model Predictive Scheduled Model Predictive Control of Wind turbines in Control of Wind turbines in
Above Rated WindAbove Rated Wind
Avishek KumarDr Karl Stol
Department of Mechanical Engineering
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OverviewOverview
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BACKGROUNDBACKGROUND
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Horizontal Axis Wind TurbinesHorizontal Axis Wind Turbines
Source: US Department of Energy
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Control ObjectivesControl ObjectivesSpeed controlSpeed control Maintain rated rotor speed in above rated Maintain rated rotor speed in above rated
windswinds
Load controlLoad control Oscillations occur in the Low Speed Shaft Oscillations occur in the Low Speed Shaft
(LSS)(LSS) Reduce loads in LSSReduce loads in LSS
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Turbine NonlinearitiesTurbine Nonlinearities
),(21
432 xCVRP pwrr
w
rr
VR
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Model Predictive ControlModel Predictive ControlChoose the control input trajectory that will Choose the control input trajectory that will minimize a cost function over the minimize a cost function over the prediction horizon prediction horizon HHpp
Example:Example:
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Why MPC?Why MPC?Accommodate disturbancesAccommodate disturbances
MIMOMIMO
ConstraintsConstraints
Many cost functionsMany cost functions
Can extend to nonlinear systemsCan extend to nonlinear systems
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Current State of MPC for Current State of MPC for Wind TurbinesWind Turbines
MPC using linear models of turbine (LMPC)MPC using linear models of turbine (LMPC) Lacks ability to deal with system nonlinearitiesLacks ability to deal with system nonlinearities
MPC using nonlinear models of turbineMPC using nonlinear models of turbine Difficult to increase order of model as explicit Difficult to increase order of model as explicit
nonlinear equations become very complexnonlinear equations become very complex Computationally expensiveComputationally expensive
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Bridging the GapBridging the Gap
Scheduled MPC (SMPC)Scheduled MPC (SMPC)
Uses a network of linear models easily obtained Uses a network of linear models easily obtained from linearization codes (FAST)from linearization codes (FAST)
Optimization remains convex for each controllerOptimization remains convex for each controller
Controllers can be specifically tuned at various Controllers can be specifically tuned at various operating points to operate with different aimsoperating points to operate with different aims
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ObjectivesObjectives
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MPC OVERVIEWMPC OVERVIEW
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Constrained Linear Constrained Linear Quadratic RegulatorQuadratic Regulator
Up till now, MPC has been posed as a Up till now, MPC has been posed as a finite horizonfinite horizon problem problem
For better performance set up MPC as an For better performance set up MPC as an infinite infinite horizon problemhorizon problem
This allows LQR control with constraintsThis allows LQR control with constraints
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Infinite Horizon Cost Function for Infinite Horizon Cost Function for CLQRCLQR
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Constrained Linear Constrained Linear Quadratic RegulatorQuadratic Regulator
Design a LQR for the linear system giving Design a LQR for the linear system giving predictions:predictions:
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Constrained Linear Constrained Linear Quadratic RegulatorQuadratic Regulator
Create a MPC to calculate perturbations Create a MPC to calculate perturbations cc about control input given by the LQR about control input given by the LQR onlyonly over over HHp p so constraints are met so constraints are met
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CLQR MinimizationCLQR Minimization
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CLQR Block DiagramCLQR Block Diagram
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Scheduled MPCScheduled MPCCreate a network of MPCs at enough Create a network of MPCs at enough operating points to capture nonlinearities operating points to capture nonlinearities of systemof system
Tune each controller for the region it Tune each controller for the region it operates inoperates in
Weight the outputs of each controller Weight the outputs of each controller based on scheduling variablebased on scheduling variable
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SMPC Block DiagramSMPC Block Diagram
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ModelModel
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Linear Model for Control Linear Model for Control Design/Disturbance EstimationDesign/Disturbance Estimation
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Speed Wind
errorpower Integralratepitch Blade
pitch BladeTorqueGenerator
rate twist DrivetrainspeedRotor
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Nonlinear Model for EKFNonlinear Model for EKF(7)where
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WIND TURBINE CONTROL WIND TURBINE CONTROL DESIGNDESIGN
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Baseline ControllersBaseline ControllersGSPIGSPI
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Baseline ControllersBaseline ControllersCLQRCLQR
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Scheduled MPCScheduled MPCLinearization
Point 1 2 3
Wind Speed (Vi0)
14ms-1 18ms-1 22ms-1
Blade Pitch 2.2° 11.1° 16.1°
Generator Torque 3524Nm 3524Nm 3524Nm
Rotor Speed 41.7rpm 41.7rpm 41.7rpm
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Scheduled MPCScheduled MPC
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Scheduled MPCScheduled MPCV̂
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SimulationsSimulationsSimulations conducted in MATLAB/Simulink with Simulations conducted in MATLAB/Simulink with FAST modelFAST modelActive DOFActive DOF Blade flap (modes 1 and 2)Blade flap (modes 1 and 2) Blade EdgewiseBlade Edgewise TeeterTeeter Tower fore-aft (mode 1 and 2)Tower fore-aft (mode 1 and 2) DrivetrainDrivetrain GeneratorGenerator Tower side-sideTower side-side
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Wind InputsWind Inputs
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Performance CriteriaPerformance Criteria
Rotor Speed RMS ErrorRotor Speed RMS Error
Low Speed Shaft Damage Equivalent LoadLow Speed Shaft Damage Equivalent Load
RMS Pitch AccelerationRMS Pitch Acceleration
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TuningTuningEach SMPC controller tuned to have same Each SMPC controller tuned to have same speed control as GSPI in respective low speed control as GSPI in respective low turbulence windturbulence wind
Each SMPC controller tuned to have same Each SMPC controller tuned to have same LSS load control as CLQR in respective LSS load control as CLQR in respective low turbulence windlow turbulence wind
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RESULTSRESULTS
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ConstraintsConstraints
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Speed ControlSpeed Control
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LSS DELLSS DEL
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Pitch AccelerationPitch Acceleration
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ConclusionsConclusions
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Future WorkFuture Work
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Questions?Questions?
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Nonlinear ModelNonlinear Model(7)where
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Extended Kalman FilterExtended Kalman FilterFL design needs FL design needs accurate accurate wind speed wind speed estimateestimateExtended Kalman Filter (EKF) is a Extended Kalman Filter (EKF) is a nonlinear state estimatornonlinear state estimatorSub optimalSub optimalLinearizes the system model each time Linearizes the system model each time step, then estimates states like a linear step, then estimates states like a linear Kalman FilterKalman Filter
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Choosing HpChoosing Hp