Session 5 Wind Turbine Scaling and Control W. E. Leithead

Transcription

1 SUPERGEN Wind Wind Energy Technology Session 5 Wind Turbine Scaling and Control W. E. Leithead Supergen 2 nd Training Seminar 24 th /25 th March 2011

2 Wind Turbine Scaling and Control Outline Introduction How big will wind turbines be? Central controller and size Load imbalance reduction Conclusion 2

3 Introduction???

4 Introduction Over the last 20 years there has been an almost exponential growth in the size of wind turbines. In offshore machines, the trend is towards bigger machines with taller towers. Does this trend have any consequences for the controller and visa versa. 4

5 Introduction Conventional scenario Variable speed pitch regulated wind turbine Above rated operation Pitch control of rotor/generator speed 5

6 Torque (Nm) Introduction x m/s % 97% 10 m /s 98% 2 9 m /s 99% 8.85 m/s m /s 1 6 m /s 7 m /s % 98% 97% 96% 0.5 Beginning 5 of m Stall /s 4.64 m/s 4 m /s Rotor Speed (rad/s) Typical operating strategy 6

7 How big will wind turbines be? Drivers for Up-scaling Utilities like power in multi-megawatt scale units. In a wind farm, a number of infrastructure items reduce in cost per MW of installed capacity, the larger the capacity of the wind turbine units. Larger turbines can often use land and wind more effectively. In public funding of wind energy, size has tended to be regarded as a metric of technology progress. 7

8 max take off weight [t] How big will wind turbines be? Growth in the aircraft industry year 8

9 nameplate rating [kw] How big will wind turbines be? Growth in the wind industry System re-design from 1000 blade to grid connection Low cost 100 Low maintenance Ultra high reliability Full-scale 10demonstrator year 9

10 How big will wind turbines be? Is there a limit to size? What influences it? Basic scaling laws rated power scales as square of length scale strength scales as square of length scale mass scales as cube of length scale inertia scales as fifth power of length scale Materials limit ultimate structural feasibility Are these scaling laws seen in wind turbines? 10

11 mass of 3 blades, M [t] How big will wind turbines be? Blade Mass Scaling RE power 5MW M = D Siemens 3.6MW Multibrid M5000 Enercon E diameter D [m] Improvement in technology disguises true scaling 11

12 shaft mass [kg] How big will wind turbines be? Shaft Mass Scaling M s = D rotor diameter [m] 12

13 normalised mass [kg] How big will wind turbines be? Hub mass scaling M hub = x diameter [m] 13

14 tower mass, Mt [kg] normalised tower mass, Mtn [t] How big will wind turbines be? Tower mass Normalised tower mass Mt = D R 2 = diameter, D [m] 100 Mtn = D R 2 = diameter, D [m] 14

15 How big will wind turbines be? Adverse scaling effects are evident but not as bad as expected This is due to technology advance To see full effect would need today s technology to be applied to smaller turbines Are these adverse scaling effects affecting the price of wind turbines? 15

16 specific cost [$/kw] How big will wind turbines be? Scaling of turbine price/kw land based designs offshore, higher tip speed designs diameter [m] 16

17 specific cost, C [ /kw] How big will wind turbines be? Scaling of turbine price/kw C = D diameter, D [m] 17

18 How big will wind turbines be? Minimum cost of turbine has been reached. Minimum cost of energy occurs at bigger size due to balance of plant costs installation operation and maintenance grid connection For onshore wind turbines, the minimum cost of energy is achieved with turbines between 3MW and 3.5MW For offshore wind turbines, the minimum cost of energy is achieved with turbines between 9MW and 10MW 18

19 Central controller and size V T A Aerodynamics Drivetrain R T G g b Actuator b d Controller V Wind speed R g Rotor speed Generator speed T A T G b d b Aerodynamic torque Generator torque demand Demanded pitch angle Blade pitch angle 19

20 Central controller and size Above rated speed control loop Assume T G constant Simple model Controller Actuator b Drive-train R Drive-train dynamics are influenced by structural dynamics 2 modes for the tower 2 modes for the blades 20

21 Central controller and size Dynamics from pitch demand to generator speed. blade flap frequency tower frequency blade edge frequency 21

22 Central controller and size The models have been validated against both measured data and aero-elastic simulations 22

23 Digression: Linear control basics Transfer functions Transfer functions model the dynamics b s b s... b s bm Gs ; m n a s a s a s a m m1 0 1 m1 n n n1 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 Gs () ( s 1) 2 2s 3s1 non-minimum phase 23

24 phase [deg] magnitude [db] Digression: Linear control basics Dynamics represented by transfer function G(s) Gs () 1 s=jω G( j) 1 s 1 j 1 Horizontal axis: log 10 (frequency in rad/s) Vertical axis (top): 20log 10 ( G(jω) ) Vertical axis (bottom): Arg(G(jω)) frequency [rad/s] gain phase 24

25 Phase (deg) Magnitude (db) Digression: Linear control basics Stability margins Phase and gain margins positive closed loop stable Bode Diagram Bode plot for open-loop Gain Margin Phase Margin Frequency (rad/sec) 25

26 Digression: Linear control basics Design trade-off Maximum phase loss possible is 180 degrees Improvements to all aspects of performance costs phase Zero sum game 26

27 Digression: Linear control basics Delay Delay of t seconds has transfer function G() s s e t s=jω G( j) j e t Gain = 1 Phase = -t Does nothing other than lose phase Performance inevitably lost 27

28 Amplitude Gs () ( s 1) 2 (2s 3s1) Digression: Linear control basics ( s 1) ( s 1) (1 s) 2 2 (2s 3s 1) (2s 3s 1) (1 s) Non-minimum phase zero has non-minimum phase zero at 1rad/s and (1 s) e (1 s) 2s Non-minimum phase zero is similar to a delay Step Response 0.4 Again, performance inevitably lost Time (sec) 28

29 Phase (deg) Magnitude (db) Digression: Linear control basics 20 Crossover frequency Bode Diagram crossove r frequenc y Frequency (rad/sec) Performance improves with crossover frequency of open-loop Bode plot 29

30 Digression: 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 30

31 Central controller and size Dynamics from pitch demand to generator speed. Non minimum phase zeros Non minimum phase zeros 31

32 Central controller and size The dynamics from pitch demand to generator speed have pairs of RHPZs First pair is induced by the rotor dynamics Second pair is induced by the tower dynamics 32

33 Central controller and size RHPZs for a 3MW wind turbine 33

34 Central controller and size Zeros due to rotor dynamics 34

35 Central controller and size RHPZs for a 5MW wind turbine 35

36 Central controller and size Zeros due to rotor dynamics 36

37 Central controller and size To match wind speed characteristics, crossover frequency needs to be 1rad/s RHPZs limit crossover frequency achievable by controller Can it be achieved? Depends on phase and gain margins 37

38 Central controller and size Control limitations Ideal open-loop L(s) Near crossover frequency, c, gain ~ ( a / s) k 38

39 Central controller and size Explicitly separate the non-minimum phase terms L( s) L ( s) L ( s) MP NMP Minimum phase component in vicinity of the crossover frequency is L ( s) ( a / s) MP Non-minimum phase component is Blaschke product L NMP 2 2 ( s 2 zs z ) ( s) 2 2 ( s 2 s ) z k z ;

40 Relation between ( c / z ) and PM is Denote positive solution by Relation for ( p / z ), where p is phase crossover frequency Denote positive solution by 2 2) / (1 ; 0 1 ) tan( 2 2 PM k c z c c z c ), ( PM k c 2 2) / (1 ; 0 1 ) tan( 2 2 k p z p p z p p (k) 40 Central controller and size

41 Central controller and size Relation between p, c, and GM is Hence p 20k log 10 GM c p c c p ( k) ( GM / 20k ) ( k, PM ) 10 Given PM and GM, solve for k ( k, PM ) c z c is the maximum possible crossover frequency 41

42 Central controller and size Apply to the 3MW and 5MW machines 3MW has tower frequency 2.6rad/s 5MW has tower frequency 2.0rad/s Rated wind speed are roughly 12m/s Greatest controller crossover frequency is required just above rated wind speed 42

43 Central controller and size With a GM of 10dB and a PM of 60deg 3MW, c =0.65rad/s at 12m/s c =1.04rad/s at 25m/s 5MW, c =0.27rad/s at 12m/s c =0.49rad/s at 25m/s With a GM of 6dB and a PM of 45deg 3MW, c =1.0rad/s at 12m/s 5MW, c =0.43rad/s at 12m/s 43

44 Central controller and size A bandwidth of 1rad/s is unachievable with a GM of 10dB and a PM of 60deg For the 3MW machine, a bandwidth of 1rad/s is achievable with a GM of 6dB and a PM of 45deg For the 5MW machine, a bandwidth of only 0.5rad/s is achievable Detailed design of controllers agreed with the above predictions 44

45 Central controller and size Tower and rotor induce RHPZs in the drive-train dynamics Attainable controller performance is restricted by these RHPZs The rotor induced RHPZs cause greater reduction in performance than the tower RHPZs Attainable controller performance degrades with increasing size of wind turbine Will this limit turbine size? 45

46 Central controller and size Tower + speed control Speed reference Tower+speed Pitch Turbine Tower acceleration controller Torque Dynamics Generator speed 46

47 Phase (deg) Magnitude (db) Central controller and size 50 Bode Diagram From: GSpRef To: Out(1) PCC (Basic) - (16m/s) SISO (Basic) - (16m/s) Frequency (rad/sec) Non- minimum phase zeros removed dynamic 47

48 Central controller and size Above rated controller Tower Damper Speed reference - Speed Controller Torque reference + + Pitch Turbine Dynamics Tower acceleration Generator speed Drive-train Damper 48

49 Spectra (Nm 2 /rad) Cumulative spectra (Nm 2 ) Central controller and size x Life-time equivalent load reductions 10% - 15% SISO(Basic)_14m/s_Tower My [0] [Nm] SISO(Basic+TFL)_14m/s_Tower My [0] [Nm] PCC(Basic+TFL)_14m/s_Tower My [0] [Nm] 3 Improvement of tower feedback loop 50% - 100% Frequency (rad/s) Tower base bending moments 49

50 Central controller and size Single Blade Control reference inputs central controller b d actuator + control actuator + control M 1 b 1 M 2 b 2 turbine dynamics rotor speed g actuator + control M 3 b 3 50

51 Load imbalance reduction Blade loads have a strong azimuth angle dependence Cause: Rotational sampling of the uneven wind-field Deterministic components tower shadow, wind sheer Stochastic components turbulence Concentrated at multiples of rotor speed W 0 51

52 Load imbalance reduction 1Ω o 2Ωo Edge frequency 3Ω o 52

53 Load imbalance reduction Applied Supergen Exemplar 2MW wind turbine Supergen Exemplar 5MW wind turbine Performance assessed for reduction Blade root bending moment Hub unbalanced load in rotating rotor frame Hub unbalanced loads in stationary frame Strong dependence of machine size 53

54 Load imbalance reduction The 2MW Supergen machine has following characteristics: Nominal Rotor Diameter: 75 m Tower height: m Cut-in wind speed: 4 m/s Cut-out wind speed: 25 m/s Out-of-plane 1-st mode frequency: 6.65 rad/s In-plane 1-st mode frequency: 9.96 rad/s Tower 1-st Fore-aft mode: 2.54 rad/s Tower 1-st Side-side mode: 2.53 rad/s Nominal rotor speed is rad/s. May

55 --- [Nm] PSD (Nm 2 /rad) Cumulative PSD (Nm 2 ) Load imbalance reduction 2MW Supergen exemplar wind turbine x 10 6 x Collective Pitch: Blade 1 My [1.25] [Nm] IA, Design 1: Blade 1 My [1.25] [Nm] IA, Design 2: Blade 1 My [1.25] [Nm] Collective Pitch: Blade 1 My [1.25] [Nm] IA, Design 1: Blade 1 My [1.25] [Nm] IA, Design 2: Blade 1 My [1.25] [Nm] Time (s) Frequency (rad/s) Out-of-plane blade root bending moment 1.4 May

56 --- [Nm] PSD (Nm 2 /rad) Cumulative PSD (Nm 2 ) Load imbalance reduction 2MW Supergen exemplar wind turbine x 10 6 x Collective, Rotating hub My [Nm] IA, Des.1, Rotating hub My [Nm] IA, Des.2, Rotating hub My [Nm] -1.5 sim3_powprod10a_stationary hub My [Nm] sim2_powprod10a_stationary hub My [Nm] sim1_powprod_cc10a_stationary hub My [Nm] Time (s) Frequency (rad/s) Hub bending moment (nodding rotating coordinates) May

57 --- [Nm] Load imbalance reduction x MW Supergen exemplar wind turbine Collective Control, Stationary hub My [Nm] IA, Design 1, Stationary hub My [Nm] IA, Design 2, Stationary hub My [Nm] Time (s) Hub bending moment (nodding, stationary motion) May

58 Load imbalance reduction 2MW Supergen exemplar wind turbine Blade 1 Mx Blade 1 My Blade 2 Mx Blade 2 My Blade 3 Mx Blade 3 My 1P D(%) P + 2P D(%) Blade root bending moment reduction Rotating hub Mx Rotating hub My Rotating hub Mz Tower Mx Tower My 1P D(%) P D(%) P + 2P D(%) P + 2P D(%) Hub moments (rotating) reduction Tower moments reduction May

59 Load imbalance reduction The 5MW Supergen machine has following characteristics: Nominal Rotor Diameter: 126 m Tower height: 87.6 m Cut-in wind speed: 4 m/s Cut-out wind speed: 25 m/s Out-of-plane 1-st mode frequency: 4.57 rad/s In-plane 1-st mode frequency: 7.00 rad/s Tower 1-st Fore-aft mode: 1.75 rad/s Tower 1-st Side-side mode: 1.75 rad/s Nominal rotor speed is rad/s. May

60 --- [Nm] PSD (Nm 2 /rad) Cumulative PSD (Nm 2 ) Load imbalance reduction 5MW Supergen exemplar wind turbine x 10 6 x Collective Pitch: Blade 1 My [1.5] [Nm] 1P+2P IA: Blade 1 My [1.5] [Nm] Time (s) Colelctive Pitch: Blade 1 My [1.5] [Nm] 1P IA: Blade 1 My [1.5] [Nm] 1P+2P IA: Blade 1 My [1.5] [Nm] Frequency (rad/s) Out-of-plane blade root bending moment May

61 --- [Nm] PSD (Nm 2 /rad) Cumulative PSD (Nm 2 ) Load imbalance reduction 5MW Supergen exemplar wind turbine 1 x 10 7 x Collective Pitch: Rotating hub My [Nm] 1P IA: Rotating hub My [Nm] 1P+2P IA: Rotating hub My [Nm] Collective Pitch: Rotating hub My [Nm] 1P+2P IA: Rotating hub My [Nm] Time (s) Frequency (rad/s) 0 Hub bending moment (nodding rotating coordinates) May

62 --- [Nm] Load imbalance reduction 5MW Supergen exemplar wind turbine x Collective, Stationary hub My [Nm] 1P IA, Stationary hub My [Nm] 1P+2P IA, Stationary hub My [Nm] Time (s) May 2009 Hub bending moment (nodding, stationary motion) 62

63 Load imbalance reduction 5MW Supergen exemplar wind turbine % Blade lifetime fatigue reduction Collective 1P+2P IA 1P+2P IA all May

64 Load imbalance reduction 5MW Supergen exemplar wind turbine 49.25% hub lifetime fatigue reduction (rotating) Collective 1P+2P IA 1P+2P IA all

65 Load imbalance reduction 5MW Supergen exemplar wind turbine % hub lifetime fatigue reduction (stationary) Collective 1P+2P IA 1P+2P IA all May

66 Load imbalance reduction 5MW Supergen exemplar wind turbine Blade 1 Mx Blade 1 My Blade 2 Mx Blade 2 My Blade 3 Mx Blade 3 My 1P D(%) P + 2P D(%) 1P + 2P all D(%) Blade root bending moment reduction Rotating hub Mx Rotating hub My Rotating hub Mz Tower Mx Tower My 1P D(%) P D(%) P + 2P D(%) P + 2P D(%) P + 2P all D(%) P + 2P all D(%) Hub moments (rotating) reduction May 2009 Tower moments reduction 66

67 Load imbalance reduction Load reductions greatly increased when change from 2MW to 5MW machine MW, 1P 2MW, D1 5MW, 1+2P, all 2MW, D1 2MW, D2 5MW, 1P 5MW, 1+2P 5MW, 1+2P, all May

68 Conclusion Turbines are going to become even bigger Control will be a key enabling technology To enable operation of the turbines within design operating envelope To reduce load imbalances Next generation controllers will need to reduce loads even more 68

69 Thank you! Consortium 69