Wind_Energy_Essentials_Lecture 8

Wind_Energy_Essentials_Lecture 8 - 11/9/2010 Wind Turbine...

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Unformatted text preview: 11/9/2010 Wind Turbine Modeling and Control EE5940: October 28, 2010 Peter Seiler, Ahmet Arda Ozdemir, Gary J. Balas, Mihailo R. Jovanovic Outline • Introduction to Feedback Control • Wind Turbines – Modeling – Control – Fault Detection • Future Research Directions 1 11/9/2010 What is control? • The idea of feedback • Open vs. closed loop systems • Block diagrams – a useful abstraction • Current status The Idea of Feedback • Feedback – Compare the actual result with the desired result – Take actions based on difference • Feedback - also called closed loop control • Feedforward or open loop control – Make a plan and execute it 2 11/9/2010 Open vs. Closed Loop Control • Simplistic analysis based on static models • Process model: • Open loop control: • Closed loop control: • Also important to consider dynamics Properties of Feedback • • • • Reduces effects of process disturbances Makes system insensitive to process variations Stabilizes an unstable system Creates well defined relations between signals • Warning! Risk for instability 3 11/9/2010 Feedback: Examples • Operational amplifier • Maneuverable aircraft • Cruise control Negative Feedback Amplifier Harold Black, 1927 • Novel technique for correcting instability and distortion in amplification of communication signals: negative feedback • Typically: gain determined only by passive components! 4 11/9/2010 Maneuverable Aircraft • Design unstable aircraft for increased maneuverability • Use control to stabilize the aircraft during flight Automotive Cruise Control Objective: Use the engine throttle to track a desired speed specified by the driver. User interface Vehicle 5 11/9/2010 Block Diagrams • • • • Capture the essence Hide the rest Abstraction Also some limitations • Block diagrams: similarity between different types of control systems Open Loop • Open Loop: Compute an engine throttle angle based on the desired velocity. • Issue: Incomplete knowledge of the car dynamics – Uncertain mass, e.g. different #’s of passengers – Varying environment conditions, e.g. hills and wind – Imprecise models for complex effects, e.g. engine dynamics and tire forces. Slope of Road / Uncertain Mass Desired Velocity Controller Throttle Command Velocity Car 6 11/9/2010 Closed Loop • Closed Loop: Update the throttle command based on a measurement of the current vehicle speed. • Feedback is the basic principle used to control the system despite our incomplete knowledge. • The use of feedback involves tradeoffs – Stability, robustness, noise rejection Slope of Road / Uncertain Mass Desired Velocity Error Controller Throttle Command Velocity Car Feedback Path Cruise Control Block Diagram Slope of Road / Uncertain Mass Desired Velocity Error Throttle Cmd. Controller Actuator Car Sensor Measured Velocity 7 11/9/2010 Reference Command Slope of Road / Uncertain Mass Desired Velocity Throttle Error Cmd. Controller Actuator Car Sensor Measured Velocity The reference (desired velocity) is the desired condition for the system. Embedded Processor Slope of Road / Uncertain Mass Desired Velocity Error Throttle Cmd. Controller Actuator Car Sensor Measured Velocity The algorithm computations are are done on an embedded processor. 8 11/9/2010 Plant Slope of Road / Uncertain Mass Desired Velocity Throttle Error Cmd. Controller Actuator Car Sensor Measured Velocity The plant (car) is the system being controlled. Actuator Slope of Road / Uncertain Mass Desired Velocity Error Throttle Cmd. Controller Actuator Car Sensor Measured Velocity The actuator (throttle motor) is a device used to control the plant. 9 11/9/2010 Sensor Slope of Road / Uncertain Mass Desired Velocity Throttle Error Cmd. Controller Actuator Car Sensor Measured Velocity The sensor (wheel speed sensor) is a device used to measure the behavior of the plant. Uncertainties/Disturbances Slope of Road / Uncertain Mass Desired Velocity Error Throttle Cmd. Controller Actuator Car Sensor Measured Velocity 10 11/9/2010 Control Design Slope of Road / Uncertain Mass Desired Velocity Error Throttle Cmd. Controller Actuator Car Sensor Measured Velocity • Objective: Maintain the desired velocity • Considerations: – – – – Transient response (rise time, overshoot) Changes in desired velocity Driver comfort (control effort) Disturbances, model uncertainty, sensor noise Control Design Slope of Road / Uncertain Mass Desired Velocity Error Throttle Cmd. Controller Actuator Car Sensor Measured Velocity • Design Process 1. 2. 3. 4. 5. Model the system: Differential equations Design the controller: PID control is a basic technique Analyze and simulate: Theory + MATLAB Implement the controller and experiment Iterate 11 11/9/2010 Proportional-Integral-Derivative (PID) Control velocity (mph) 65 e(t) vd(t) 55 Past Present Future time (sec) Amazing Property Of Integral Action • Integral control • Assume: there is a steady-state • Then: • Proof: • Impossible unless 12 11/9/2010 Advanced Control Design • Observer-based design • MIMO • Robust • Nonlinear • Adaptive • Distributed Feedback Control of Wind Turbines • Increase captured power • Reduce structural loads • Sequence operation modes • Fault detection and diagnostics 13 11/9/2010 Wind Turbine Modeling • Focus on modeling of an individual turbine – Ignore aerodynamic interactions between turbines in a wind farm • Tradeoff between model fidelity and complexity • Reasonably accurate models of low complexity are most useful for control design Available Wind Power • Available Power: – – – – Pwind = 1 ρAv 3 2 2 1 Kinetic energy density: 2 ρv Volume flow across rotor in time dt: Avdt Energy flow across rotor in time dt: dE = 1 ρAv 3 ( Avdt ) 2 Pwind = dE/dt vdt ( ) v R ω A= πR2 14 11/9/2010 Aerodynamic Efficiency, Cp • Cp := Pcaptured Pwind = C p (β , λ ) – β=Collective blade pitch ωR – λ=Tip speed ratio = v • Cp does not account for losses in gearbox, power electronics, etc • Cp shown for Controls Advanced Research Turbine (CART) at NREL – 600kW, R=21.7m Figure from: K. Johnson, L. Pao, M. Balas, and L. Fingersh, Control of Variable Speed Wind Turbines, IEEE Control Systems Magazine, June 2006 Betz’ Law • Betz’ Limit (1919): C p , Betz = 16 ≈ 0.593 27 • Derived for axial, incompressible flow • Ref: Burton, et. al, Wind Energy Handbook, 2001 A Figure from Wikipedia Entry on Betz’ Law 15 11/9/2010 Betz’ Law: Proof Sketch • Ref: Burton, et. al, Wind Energy Handbook, 2001 • Show by conservation of mass and energy balances that wind speed at rotor = (v1 + v2)/2 2 • Extracted Power = Av ⋅ 1 ρ v12 − v2 = 1 ρAv13 1 + v2 − 2 4 v1 ( ) ( ( ) −( ) ) v2 2 v1 v2 3 v1 • Power coefficient is maximized when v2/v1 = 1/3 and maximal value is Cp = 16/27 Figure from Wikipedia Entry on Betz’ Law Rigid Body Model • Simple model for a variable speed turbine & Jω = τ a − τ g ω, τa τg = • where – J:= rotor + drivetrain inertia – τg:= generator torque P – τa= aerodynamic torque = captured ω ρAv 3C p ( β , λ ) 2ω • Model derived from Newton’s second law • Actuators: β and τg • Sensor: ω 16 11/9/2010 Rigid Body Model • The rigid body model is simple but it neglects or simplifies important details – Flexible modes: drivetrain, blade and towerbending – Turbine aerodynamics • Drivetrain flexibility and tower fore/aft modes are important in the control law design – These modes can be excited by control actions – Excitation of these modes can cause drivertrain and/or tower failure – Higher fidelity, but more complex models can be constructed that include these two modes. Fatigue, Aerodynamics, Structures and Turbulence (FAST) • “Medium” complexity nonlinear simulation code – AeroDyn: Aerodynamics modeled using bladeelement/momentum theory rather than CFD – Main degrees of freedom: Rotor position, nacelle yaw, drivetrain flexibility, tower fore/aft and side/side bending, blade flapwise and edgewise bending • Software is freely available: – http://wind.nrel.gov/designcodes/simulators/fast/ – Jonkman and Buhl, FAST User’s Guide, 2005 17 11/9/2010 FAST: Additional Features • Model parameters for: – Onshore: 1.5MW WindPACT horizontal-axis wind turbine – Offshore: 5MW turbine • Simulink interface • Postprocessors, e.g. Crunch for fatigue analysis • Ability to remove DOF for simpler models • Ability to linearize model FAST Simulation Result Blade loads for steady wind speed (Rotor Speed = 2.15 rad/s, Generator Torque = 8377Nm, Wind = 18m/s, Vertical Wind Shear Coef.=0.2) 18 11/9/2010 Wind Turbine Models • Linearization—Used to obtain simpler models • Steady state oscillations (prev. slide) means we obtain periodic models • Several methods to obtain good time LTI models Linearization Methods • • • • Point linearizations (FAST [1]) Averaging (FAST [1], Stol, K., 2001 [2]) Floquet Theorem (Stol, K., Balas, M., Bir, G. 2002 [3]) Multiblade Coordinate Transformation (Bir, G. 2008 [4], MBC3 [5]) 1. 2. 3. 4. 5. Jonkman , J. M., Buhl J. M. L., FAST User’s Guide, National Renewable Energy Laboratory, Golden, Colorado (2005). Stol, K., Dynamics modeling and periodic control of horizontal-axis wind turbines, Ph.D. thesis, University of Colorado at Boulder (2001). Stol, K., Balas, M., Bir, G., Floquet Modal Analysis of a Teetered-Rotor Wind Turbine, Transactions of the ASME (2002) Bir, G.,Multi-blade coordinate transformation and its applications to wind turbine analysis. AIAA– 2008–1300 (2008) Bir, G., User’s Guide to MBC3, National Renewable Energy Laboratory, Golden, Colorado (2008). 19 11/9/2010 Comparison of Nonlinear and Linear Models Blade tip response to 0.01 deg pitch angle perturbation (Simulations on reduced 5 DOF models: Tower 1st Fore-Aft Bending, Rotor Position, Blade 1st Flapwise Bending) Wind Turbine Control • Control strategies depend on the wind conditions • Wind Turbine Control – – – – Supervisory Control and Mode Logic Yaw Control Power capture at low wind speeds Rated power + Load reduction at high wind speeds • References – K. Johnson, L. Pao, M. Balas, and L. Fingersh, Control of Variable Speed Wind Turbines, IEEE Control Systems Mag., June 2006. – T. Burton, D. Sharpe, N. Jenkins, E. Bossanyi, Wind Energy Handbook, Chapter 8: The Controller, 2001. – J. Laks, L. Pao, and A. Wright, Control of Wind Turbines: Past, Present and Future, American Control Conference, 2009. 20 11/9/2010 System Components Figure from the US DOE Power vs. Wind Characteristics Pwind Region 3: Rated Power+ Load Reduction Region 2: Maximize Power Cut-in Cut-out Plot based on Clipper Liberty C100 2.5MW turbine (R=50m, Vcutin = 4m/s, Vcutout = 25m/s) assuming Cp,max = 0.4 21 11/9/2010 Supervisory Control • Supervisory control switches turbine between modes based on wind conditions, startup, and emergency stops • Logic for Clipper’s Liberty Wind Turbines: – Slide 27 of September 9 talk by Steve Owens shows the operating states for Clipper’s Liberty Turbines – Turbine cut-in at 4m/s based on 10min average – Turbine cut-out at 25m/s based on 10min average Yaw Control • Yaw rotor into wind in both regions 2 and 3 • Yaw dynamics are slow due to large nacelle mass Wind Heading Yaw Cmd. Measured Yaw Angle Error PID Actuator Yaw Dyn. Sensor 22 11/9/2010 Region 2 Control • Objective: Maximize power capture by holding β=βopt (constant) and using τg to track λopt Figure from: K. Johnson, L. Pao, M. Balas, and L. Fingersh, Control of Variable Speed Wind Turbines, IEEE Control Systems Mag., June 2006 Region 2: Possible Control Strategy • Compute desired rotor speed using the optimal tip speed ratio (TSR) and measured wind speed. ωdes = λopt v R • Issues: – Shadowing effects corrupt wind speed measurement – Uncertainty in power coefficient model Measured Wind Speed TSR Relation Optimal TSR βopt Desired Rotor Speed Error PID τg Turbine wind Measured Rotor Speed 23 11/9/2010 Region 2: Standard Controller • Control Law τ g = Kω 2 3C where K = 1 ρAR λ 2 p ,max 3 max – Ref: Johnson, et al, 2006 Control System Mag. – For typical operating conditions, convergence to optimal power capture in steady state – Only requires rotor speed sensor – Control law still depends on uncertain power coefficient model. Adaptive laws have been developed. βopt Kω2 ω wind Measured Rotor Speed Turbine τg Region 3 Control • Objective: Maintain rated power • Holding τg = τrated (constant) and using β=βopt to track ωrated • Ref: J. Laks, L. Pao, and A. Wright, Control of Wind Turbines: Past, Present and Future, American Control Conference, 2009. wind Rated Rotor Speed Error PID τg βcmd Turbine Measured Rotor Speed 24 11/9/2010 Region 3 Control • Issues: – Excitation of flexible modes, e.g. Tower fore/aft – Loads on blades due to wind gusts • Advanced control methods – Reduce tower fore/aft with notch filters and/or accelerometer measurements in the nacelle – Use individual blade pitch control to reduce bending on each blade – Reduce drivetrain vibrations by adding a small generator torque ripple computed by filtering the rotor speed measurement. Individual Pitch Control Ref: A. Ozdemir, P. Seiler, G. Balas, Effects of Disturbance Augmented Control Design for Wind Turbines, Submitted to Journal of Mechatronics 25 11/9/2010 Results Under Steady Wind 1% Turbulent Wind 26 11/9/2010 5% Turbulent Wind 5% Turbulent Wind 27 11/9/2010 Fault Detection and Diagnostics • Reduce downtimes • Reduce maintenance costs • Prevent catastrophic failures Benchmark Problem • Benchmark problem given by: – Fault Tolerant Control of Wind Turbines – a benchmark model, Odgaard, P.F., Stoustrup, J., and Kinnaert, M. (2009) [5] • A generic 4.8MW turbine model with realistic sensor configuration • Faults in the sensing, actuation and drivetrain systems [5] Odgaard, P.F., Stoustrup, J., and Kinnaert, M. (2009). Fault tolerant control of wind turbines - a benchmark model. In Proceedings of Fault Detection, Supervision and Safety of Technical Processes. 28 11/9/2010 Sensor Configuration Sensor Rotor Speed Generator Speed Generator Torque Generator Power i-th Blade Pitch Angle Wind Speed Configuration Dual redundant Dual redundant Single string Single string Dual redundant Single string • Measurement challenges: – Noisy rotor speed measurements – Wind speed measurement with high bias • 3 types of faults: – Sensor bias, scale factor, frozen sensor Faults Fault No 1 2 3 4 5 Fault β 1_m1=β 1_m1+5 Description (deg) Pitch Sensor Bias Pitch Sensor Scale Factor (deg) Pitch Sensor Bias Rotor Speed Sensor Frozen Simultaneous Rotor and Generator Speed Sensor Scale Factor β 2_m2=1.2 β 2_m2 β 3_m1=β 3_m1+10 r_m1=1.4 r_m2=1.1 g_m2=0.9 rad/s r_m2 g_m2 Fault No 6 7 8 9 Description Pitch Actuator 2 Hydraulic Failure Pitch Actuator 3 Air in Oil Generator Inner Control Loop Failure Increased Drivetrain Friction due to Wear Effect Slow Response Slow Response Gen. Torque Bias Lower Efficiency 29 11/9/2010 Fault Detection Requirements Fault No 1-5 6 7 8 9 Detection Time Requirement 10 Ts 8 Ts 600 Ts 5 Ts No Detection Time Constraints Ts: Sensor sampling time 0.01s • False alarm rate must be less than 1/105 Ts • False alarms must be cleared in 3 Ts Approach Fault Detection Residual Generation Physical Redundancy: Sensor Fault Detection Parity Equations: Actuator Fault Detection Kalman Filtering: Sensor Fault Diagnosis Signal Processing: Filtering Noisy Residuals Decisioning Up/Down Counters 30 11/9/2010 Wind Disturbance • 100 simulations wind different noise seeds Response to Blade Pitch Sensor Fault 31 11/9/2010 Simulation Results Fault No 1 2 3 4 5 6 7 8 9 Detection Time 3 Ts 819.4 Ts 3 Ts 12.4 Ts 187.4 Ts r_m2 2 Ts g_m2 5050 Ts 1573 Ts 1 Ts N/A False Alarm Rate 0.091/105 0.046/105 0.046/105 0.068/105 0.159/105 0 0.182/105 0.022/105 0 N/A Missed Detection 0 0 0 0 0 0 0 0 0 100 False Alarm Clearance Time 2.9 Ts 2.3 Ts 2.4 Ts 18.8 Ts 17.5 Ts 0 3.9 Ts 3.2 Ts 0 N/A Sensor Faults Pitch Act. Faults Generator F. Drivetrain F. Failed Design Specifications • Fault 2: Pitch angle sensor scale factor can only be detected in Region 3 • Fault 4 and 5: Rotor speed sensor faults – Std. deviation of noise on rotor speed measurement is about 10% of rated rotor speed – High order, low pass filtering results in slow detections • Fault 6 and 7: Pitch actuator faults – Turbine needs to be in Region 3 – Controllers must generate commands at mid-frequency range • Fault 9: Drivetrain efficiency drop by 5% – Wind speed measurement has a bias about 10-15% of the measurement 32 11/9/2010 Research Problems • Modeling – Development of low-fidelity, control oriented models for turbine interactions in a wind farm – Impact of modeling errors on turbine energy production. • Estimation and Control – Benefits/cost of sharing wind measurements across a wind farm with individual wind turbines. – Impact of additional sensors/actuators that provide the most performance improvement for the least increase in cost. – Application of aeroservoelastic control techniques to increase energy capture by enabling operation at higher wind speeds – Adaptation of wind turbine control algorithms to account for aging, degradation, seasonal change, etc. • Fault Detection and Isolation – Application of fault detection and isolation to enhance reliability, longevity while reducing operating cost of large wind turbines. 33 ...
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