Wind Turbine Control - PDF Free Download

Wind Turbine Control W. E. Leithead University of Strathclyde, Glasgow Supergen Student Workshop 1

Outline 1. Introduction 2. Control Basics 3. General Control Objectives 4. Constant Speed Pitch Regulated WT s 5. Variable Speed Stall Regulated WT s 6. Variable Speed Pitch Regulated WT s 7. Conclusion Reproduced with permission of EWEA Supergen Student Workshop 2

Introduction Supervisory control Oversees total operation of wind turbine including start-up/shutdown safety of turbine operation fault handling data collection Focus Operational control Continuously adjusts dynamic state of wind turbine cause the operating point to track the on-design trajectory minimise the off-design fluctuations Supergen Student Workshop 3

Introduction Wind Turbine Types Stall regulated constant speed Pitch regulated constant speed Stall regulated variable speed Pitch regulated variable speed 24 th Supergen Student Workshop 4

Introduction Constant wind speed curves 24 th Supergen Student Workshop 5

Introduction Stall regulated constant speed Torque [Nm] 2.5 3 x 106 Rated power 2 1.5 11 m/s 12 m/s 10 m/s 1 0.5 4 m/s 0 Beginning of Stall 5 m/s 6 m/s 7 m/s 8 m/s 9 m/s 96% 97% 98% 99% 99% 98% 97% 96% -0.5 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Rotor Speed [rad/s] 24 th Supergen Student Workshop 6

Introduction Pitch regulated constant speed Torque [Nm] 2.5 3 x 106 Rated power 2 1.5 11 m/s 12 m/s 10 m/s 1 0.5 4 m/s 0 Beginning of Stall 5 m/s 6 m/s 7 m/s 8 m/s 9 m/s 96% 97% 98% 99% 99% 98% 97% 96% -0.5 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Rotor Speed [rad/s] 24 th Supergen Student Workshop 7

Introduction Stall regulated variable speed Torque [Nm] 2.5 3 x 106 Rated power 2 1.5 11 m/s 12 m/s 10 m/s 1 0.5 4 m/s 0 Beginning of Stall 5 m/s 6 m/s 7 m/s 8 m/s 9 m/s 96% 97% 98% 99% 99% 98% 97% 96% -0.5 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Rotor Speed [rad/s] 24 th Supergen Student Workshop 8

Introduction Pitch regulated variable speed Torque [Nm] pitching Rotor Speed [rad/s] 24 th Supergen Student Workshop 10

Introduction Control Design Task: Reproduced with permission of BWEA Changed with the technology Related Activities Model development and validation Dynamic analysis Supergen Student Workshop 11

Introduction Control design task Define operational strategy different control modes Implementation issues Ensure smooth switching between control modes controller start-up and shut-down Within each mode cater for aerodynamic nonlinearity actuator constraints Design linear control law for each mode Supergen Student Workshop 12

Linear Control Basics Feedback systems transfer functions Setpoint (e.g. Desired Rotor speed) + - Controller System Output (e.g. Rotor Speed) Closed loop system stability is required Output will asymptotically converge to setpoint Supergen Student Workshop 13

Linear Control Basics Transfer functions Transfer functions model the dynamics bs + bs +... + b s+ bm G( s) = ; m n as + as + + a s+ a m m 1 0 1 m 1 n n 1 0 1... n 1 Roots of the denominator are the poles. Unstable poles have negative real parts. Roots of the numerator are the zeros. Non-minimum phase zeros have negative real parts. n Gs () = 1 s 1 unstable ( s 1) Gs () = non-minimum 2 2s + 3s+ 1 phase Supergen Student Workshop 14

Linear Control Basics Dynamics represented by transfer function G(s) Gs () = 1 s=jω G( jω) = 1 s + 1 jω + 1 Horizontal axis: log 10 (frequency in rad/s) Vertical axis (top): 20log 10 ( G(jω) ) Vertical axis (bottom): Arg(G(jω)) magnitude [db] phase [deg] 0-20 -40 10-2 10-1 10 0 10 1 10 2 0-50 -100 10-2 10-1 10 0 10 1 10 2 Supergen Student Workshop frequency [rad/s] gain phase 15

Linear Control Basics Stability margins Phase and gain margins positive closed loop stable Magnitude (db) 10 5 0-5 -10-15 -20 360 Bode Diagram Bode plot for open-loop Gain Margin Phase (deg) 270 180 Phase Margin 90 10-2 10-1 10 0 10 1 Frequency (rad/sec) Supergen Student Workshop 16

Linear Control Basics Design trade-off Maximum phase loss possible is 180 degrees Improvements to all aspects of performance costs phase Zero sum game Supergen Student Workshop 17

Linear Control Basics Delay Delay of τ seconds has transfer function Gs () s e τ = s=jω G( jω) = j e τω Gain = 1 Phase = -τ ω Does nothing other than lose phase Performance inevitably lost Supergen Student Workshop 18

Linear Control Basics Non-minimum phase zero Gs () = ( s 1) s + s+ 2 (2 3 1) has non-minimum phase zero at 1rad/s ( s 1) ( s+ 1) (1 s) = + + + + + 2 2 (2s 3s 1) (2s 3s 1) (1 s) (1 s) 2 and e (1 + s) s Non-minimum phase zero is similar to a delay 1.2 1 0.8 Step Response Again, performance inevitably lost Amplitude 0.6 0.4 0.2 0-0.2 0 2 4 6 8 10 12 14 16 18 Time (sec) Supergen Student Workshop 19

Linear Control Basics Crossover frequency 20 Bode Diagram Magnitude (db) 10 0-10 -20-30 -40 0 crossover frequency Phase (deg) -45-90 -135-180 10-2 10-1 10 0 10 1 Frequency (rad/sec) Performance improves with crossover frequency of open-loop Bode plot Supergen Student Workshop 20

Linear Control Basics Poles and zeros Crossover frequency is bounded below by any unstable pole Crossover frequency is bounded above by any non-minimum phase zero Unstable poles and non-minimum phase zeros impose absolute bounds on performance Supergen Student Workshop 21

Linear Control Basics Sensitivity function Operating strategy Wind speed setpoint disturbance + Controller Plant output - measurement noise Feedback causes the output to track the input What does it do for the wind speed disturbances? Supergen Student Workshop 22

Linear Control Basics Sensitivity function The transfer function between the disturbance and the output is the sensitivity function Magnitude (db) Phase (deg) 20 10 0-10 -20-30 -40 0-45 -90-135 Bode Diagram Bode plot gain for openloop transfer function crossover frequency Magnitude (db) Phase (deg) Bode Diagram 5 0-5 -10-15 -20 90 60 30 Bode plot gain sensitivity function -180 0 10-2 10-1 10 0 10 1 10-2 10-1 10 0 10 1 Frequency (rad/sec) Frequency (rad/sec) The sensitivity function is negative when the openloop is positive and vice versa Supergen Student Workshop 23

Linear Control Basics Sensitivity function disturbance Gain << 0dB Magnitude (db) 5 0-5 -10-15 -20 90 Bode Diagram Phase (deg) 60 Disturbance 30at frequencies below crossover is attenuated 0 Disturbance 10at frequencies -2 10 above crossover -1 10 is enhanced 0 10 1 Frequency (rad/sec) Supergen Student Workshop 24

Linear Control Basics Wind turbine control Wind turbine control is a disturbance rejection problem There are many disturbance above crossover, the spectral peaks at nω and dynamic mode frequencies The dynamics have non-minimum phase zeros For some strategies have unstable poles Supergen Student Workshop 25

General Control Objectives Smooth Generated Power Alleviate Loads Provide Damping Maximise Energy Capture Not all apply to all types of turbines Supergen Student Workshop 26

General Control Objectives Historically, control objectives changed from simply limiting power fluctuations to: Drive-train load alleviation Power quality control Maximising energy capture Dynamic mode damping Avoidance of enhancing structural loads Actuator activity reduction Supergen Student Workshop 27

General Control Objectives The increasing size of machines is driving control development directions. More demands are placed on the control system at the same time as low frequency dynamic issues have greater importance. Control systems are now being required to regulate some fatigue related dynamic loads Of strong interest are the tower loads. The larger the wind turbine the greater the requirements Must be achieved without compromising turbine performance Must be achieved without increasing pitch activity Supergen Student Workshop 28

General Control Objectives Control Actions: Stall regulated constant speed WT s No active control Pitch regulated constant speed WT s Blade pitch Stall regulated variable speed WT s Generator reaction torque Pitch regulated variable speed WT s Blade pitch Generator reaction torque Supergen Student Workshop 29

Pitch Regulated Constant Speed WT s Supergen Student Workshop 30

Pitch Regulated Constant Speed WT s Typical machine rating (1990) 300kW Below Rated Operation: No Control Above Rated Operation: Blade Pitch Control Objectives Maintain Constant Power Wind Speed Disturbance Rejection Avoid Increasing Tower/Blade Load Measurement Generated power Supergen Student Workshop 31

Pitch Regulated Constant Speed WT s Above rated control: Basically PI augmented by filters at np and 2nP Major issues are nonlinear: Switching between above and below rated WT Dynamics vary strongly with operating point Actuator saturation The nonlinear issues drive the performance Only look at second in detail Supergen Student Workshop 32

Pitch Regulated Constant Speed WT s Nonlinear dynamics: The important nonlinearity is the aerodynamic torque Wind speed Pitch Pitch Aero Rotor demand angle torque Speed actuator aerodynamics drive-train Supergen Student Workshop 33

Pitch Regulated Constant Speed WT s To operate at rated power, there is a pitch angle,, for each wind speed,. υ β0 0 β 0 υ 0 Linearising the aerodynamics at (, ). Is gain-scheduling appropriate? Schedule on wind speed or pitch angle? Supergen Student Workshop 34

Pitch Regulated Constant Speed WT s The aerodynamic gain has a large range Varies rapidly as the wind speed varies A priori it s not appropriate to gain-schedule Aerodynamic gain Supergen Student Workshop 35

Pitch Regulated Constant Speed WT s Since the aerodynamic torque is constant along the locus of operating points, its partial derivatives are related by: δt dβ ( υ0) δt ( β0, υ0) = ( β0, υ0) δυ dυ δβ ( h( β ) g( υ)) It follows that is constant on the locus of operating points provided f and g satisfy dh δt dg δt = ( βυ, υ) = ( βυ, υ) dβ δβ dυ δυ Supergen Student Workshop 36

Pitch Regulated Constant Speed WT s Hence locally to the locus of operating points T ( β, υ) τ ( ε) ε = h( β ) g( υ) dτ dε for some function τ(ε) such that τ(0)=t 0 and ( 0) = 1 Supergen Student Workshop 37

Pitch Regulated Constant Speed WT s Since ( pdt) y = = 1 y h h ( y) pdt Global scheduling is achieved provided the integrator is placed after the scheduled gain Supergen Student Workshop 38

Pitch Regulated Constant Speed WT s Typical power time histories for a 300 kw machine at 16 m/s mean wind speed 7 Power (kw) gain before integrator gain after integrator 10 2 6 5 4 3 2 1 0 20 40 60 80 100 Time (s) Supergen Student Workshop 39

Pitch Regulated Constant Speed WT s Structure of controller that deals with all three nonlinear issues. Supergen Student Workshop 40

Pitch Regulated Constant Speed WT s Supergen Student Workshop 41

Pitch Regulated Constant Speed WT s Nonlinear control: Sensitivity of the aerodynamic torque to changes in pitch increases faster than to changes in wind speed Increase bandwidth with wind speed Rate of change wrt wind speed Rate of change wrt pitch angle Supergen Student Workshop 42

Pitch Regulated Constant Speed WT s Nonlinear control: It is the fatigue loads on the drive-train that need alleviating Extreme loads do most damage Alter the distribution of the load transients by pulling in the tails Supergen Student Workshop 43

Pitch Regulated Constant Speed WT s Nonlinear control: Two-bladed WT Extreme loads Linear control Nonlinear control Supergen Student Workshop 44

Pitch Regulated Constant Speed WT s Nonlinear control: Three-bladed WT Extreme loads Linear control Nonlinear control Supergen Student Workshop 45

Stall Regulated Constant Speed WT s Supergen Student Workshop 46

Stall Regulated Constant Speed WT s Above/Below Rated Operation: Generator reaction torque control Objective Increase drive-train damping Measurement Generator speed Below Rated Operation: Objective Maximise energy capture Above Rated Operation: Objective Power/torque regulation by stalling Supergen Student Workshop 47

Stall Regulated Constant Speed WT s Strategy below rated Supergen Student Workshop 48

Stall Regulated Constant Speed WT s Strategies above rated Supergen Student Workshop 49

Stall Regulated Constant Speed WT s Control drivers: Choose strategy defining a curve to be tracked Dynamics are strongly nonlinear Above rated, curve dependent unstable pole and non-minimum phase zero 0.3r/s and 2.5r/s Switching between modes Supergen Student Workshop 50

Stall Regulated Constant Speed WT s Performance 400 350 300 250 200 150 100 50 0-50 Power Power (kw) 4.25 8.25 12.25 16.25 20.25 24.25 28.25 32.25 wind speed (rad/s) 90 80 70 60 50 40 30 20 10 Torque 0 Low-speed shaft torque (knm) 4.25 8.25 12.25 16.25 20.25 24.25 28.25 32.25 wind speed (rad/s) Supergen Student Workshop 51

Pitch Regulated Variable Speed WT s Reproduced with permission of EWEA Supergen Student Workshop 52

Pitch Regulated Variable Speed WT s Typical machine rating (2005) 1-2MW Below Rated Operation: Same as stall regulated variable speed WT Above Rated Operation: Blade Pitch Control Generator Reaction Torque Control Objectives Maintain Constant Power Maintain Constant Speed Measurement Generator speed Supergen Student Workshop 53

Pitch Regulated Variable Speed WT s Very Large WTs 5MW With the increase in size, wind turbines are more flexible: structural issues important Bigger blades and tower place structural modes at lower frequencies Basic control strategies remain, but fatigue reduction must be added onto the control objectives Control strategies to reduce tower and blade fatigue is currently an active field of research Fatigue of production cases account for the 89% of the relative damage on the tower Supergen Student Workshop 54

Pitch Regulated Variable Speed WT s 13 m/s 22 m/s Dynamics: pitch angle to generator speed 3MW WT Supergen Student Workshop 55

Pitch Regulated Variable Speed WT s The tower fatigue might be reduced by a tower acceleration feedback loop. Feedback loop acts on fore-and-aft tower mode Supergen Student Workshop 56

Pitch Regulated Variable Speed WT s 22 m/s 16 m/s Dynamics: pitch angle to tower speed 3MW WT Supergen Student Workshop 57

Pitch Regulated Variable Speed WT s Proportional control is sometimes not very successful With TFL No TFL Problem is the interaction with the blade flap mode Supergen Student Workshop 58

Pitch Regulated Variable Speed WT s Instead localise the feedback Supergen Student Workshop 59

Pitch Regulated Variable Speed WT s Much more effective With TFL No TFL Supergen Student Workshop 60

Pitch Regulated Variable Speed WT s Above approach can reduce the tower fatigue by 5% to 8% More advanced control can reduce the tower fatique by 12% to 18% Measured as 20 year lifetime equivalent fatigue loads Supergen Student Workshop 61

Pitch Regulated Variable Speed WT s Rotor Load Imbalance Reduction 20 x 10 6 5MW Supergen exemplar wind turbine Collective, Stationary hub My [Nm] 1P IA, Stationary hub My [Nm] 1P+2P IA, Stationary hub My [Nm] 15 10 --- [Nm] 5 0-5 50 100 150 200 250 300 350 400 450 500 550 Time (s) Hub bending moment (nodding, stationary motion) Supergen Student Workshop 62

Concluding Remarks Reproduced with permission of EWEA Supergen Student Workshop 63