Iterative Learning Control for Smart Rotors in Wind turbines First Results

Transcription

1 Iterative Learning Control for Smart Rotors in Wind turbines First Results Owen Tutty 1, Mark Blackwell 2, Eric Rogers 3, Richard Sandberg 1 1 Engineering and the Environment University of Southampton 2 Vestas 3 Electronics and Computer Science University of Southampton

2 General Comments Interested in dynamic control (of the turbine in operation) of wind turbines not supervisory control (fault tolerance etc), e.g. modern variable speed pitch controlled turbines.

3 General Comments There are many (often conflicting) aspects to wind turbine control: Power Regulation: maximum energy extraction. Speed Regulation: Noise restrictions limit the tip speed to about 80 m/sec. Load Mitigation: ensure safe operation by limiting the forces.

4 Control Actuators

5 Control Actuators Two major control systems: Blade Pitch Control: change blade orientation to change the aerodynamic forces collective and full span. Generator Torque Control: use a power electronics convertor to give control over the generator torque.

6 Power Curve

7 Smart Rotor Control Overall Aim: To improve the aerodynamic effectiveness and hence energy production of wind turbines there is currently research into to the inclusion of smart devices in rotor blades in conjunction with collective and individual pitch control. Objective: Significant reduction of blade loads by spanwise load-distributed load control devices. Fast local active load control is possible. Active feedback control based on local measurements.

8 Smart Rotor Control

9 Motivation

10 Motivation Turbines are becoming very large -5MV turbine, 126m diameter.reduction in blade loads also reduces load on other components, e.g. tower and drive train.

11 Loads Turbulence

12 Loads Wind Shear

13 Loads Tower Shadow

14 Aerodynamic Load Control Devices Flaps

15 Aerodynamic Load Control Devices Adaptive Geometry Microtabs

16 Aerodynamic Load Control Devices Active Twist Material up to here kindly supplied by Matthew Lachner, University of Massachuetts, Amherst.

17 Control Design Specifications Wind turbines blades are subjected to fluctuating aerodynamic forces involving both deterministic and stochastic elements. The most obvious stochastic component comes from the variable nature of the wind, which varies in both frequency and magnitude, producing a variation in aerodynamic load which passes through the turbine system. Deterministic components include the effects of the atmospheric boundary layer, stator-rotor interaction and yaw misalignment. Both types of disturbance create loads that require management.

18 Control Design Specifications Blades are relatively flexible structures, and changing blade loads will change the blade position relative to the oncoming wind, and therefore the aerodynamic loading, thus compounding the complexity of the aeroelastic system. Wind turbine load control basically involves modifying the lift on the blades. There are four main ways of achieving this: varying the blade incidence angle (variable pitch and/or predetermined blade twist), flow velocity (variable rotor speed), blade size (variable blade length) or modifying the blade section aerodynamics (active flow control). This work is concerned with the last of these, in particular, damping fluctuations in the lift using circulation control, as a model of a blade equipped with a smart rotor.

19 Control Design Specifications Wind turbines operate in the atmospheric boundary layer where there is a non-zero shear profile and a regular variation in wind speed past the blade throughout a cycle, even in reasonably steady, non-gusting, conditions. Thus the flow past the blade will contain a oscillatory component. This will be more pronounced towards the tip of the blade, where the speed differential will be greatest. Further, in a wind farm, a turbine may be downstream of others, which can also add an oscillatory component to the flow.

20 Flow Model Unsteady flow conditions (relative to the blade) will cause cyclic loads on the blade, in particular in the lift, which will in turn affect the performance of the turbine. Deterministic disturbances such as repetitive oscillations tend to be easier to mitigate against as their period and magnitude can be relatively easily estimated from other turbine data, such as rotor speed, diameter etc. However, there is also a need to reduce the load due to peak/extreme events, particularly those that threaten the structural integrity of the turbine. Thus a control system should aim to reduce both the underlying level of disturbance and the peak load.

21 Flow Model The airfoil used in this study is an NREL S825. This was chosen as it resembles blade sections used in wind turbines. 0.2 y x

22 Flow Model Non-dimensional form using the mean free stream velocity V and the chord (length) of the airfoil H as reference values is used Hence v = V v = V (v x, v y ) are the velocity components in x = Hx = H(x, y), where the asterisk denotes a dimensional quantity. Time is non-dimensionalized using H/V so that t = H V t. The lift on and airfoil/wing section comes primarily from the pressure exerted by the fluid on the surface of the airfoil and inviscid flow is assumed. Inviscid flow no viscosity viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress (water low, honey high).

23 Flow Model The incoming flow is assumed to be oscillatory, but with added disturbance in the form of vortices that are convected with the flow. The vortices interact with each other and with the airfoil so that the system is non-linear. Devices such as trailing edge flaps and microtabs operate by generating circulation (vorticity) in the region of the trailing edge of the blade, thereby directly affecting the lift on the blade. In the CFD model, the flow at the trailing edge of the airfoil is manipulated to model these devices and thereby provide the actuation for the control system.

24 Flow Model The effectiveness of the control system is assessed with a 2-norm measure of the disturbance, which relates to the fatigue load, and an -norm, which measures the reduction in the peak disturbance. In simple terms, vorticity is the tendency for elements of the fluid to "spin." In formal terms, vorticity can be related to the amount of "circulation" or "rotation" (or more strictly, the local angular rate of rotation) in a fluid.

25 Flow Model The base flow consists of the free-stream velocity V 0 (t) = (V 0x (t), 0) and the velocity field generated by the vortex and source panels v p (x, t) = (v px, v py ), the latter including the effects of the actuation. In addition, disturbances are introduced into the flow in the form of discrete vortices. The Euler equations governing two-dimensional inviscid incompressible flow can be written in vorticity form as Dω Dt = ω t + v ω x x + v ω y y = 0 (1) where ω = v y x v x v y (2)

26 Oscillatory Flow Consider the case with no vortices so that the variation in the lift comes from that in the free stream velocity, and the aim is to damp this fluctuation. The flow past the airfoil is assumed to be periodic with velocity V 0x = 1 + A sin(2πt/t) (3) where A is the amplitude of the oscillation T its period. A time step of t = is used, with amplitude A = 1 10, and a period of T = 1 4. Since there are no vortices in the flow, the problem is linear in the unknowns (the vortex and source panel strengths). At each step the latest values are used to update the control input.

27 Oscillatory Flow Cnsider P-type ILC of the form u k = u k 1 + µe k 1 (4) where u k is the control input for step k, and E k is the error for step k given by E k = L k L r (5) where L k is the lift at step k and L r is the target value for the lift, obtained by taking A = 0 in (3). Figure 1 shows the control input u k and the error E k for the controller (4) with µ = 20. Also shown is the error with no control.

28 k E 0 0 u t Figure 1: Controller (4) with µ = 20. Blue, error E k with no control (u k = 0). Red, error E k with control. Green, control input u k.

29 Oscillatory Flow A better result is obtained with a larger gain of µ = 50, although, early in the run, there is short term high frequency (time step) fluctuation in the solution. Taking a gain much larger gain causes the scheme to become unstable. The flow has a forced oscillatory component, the effect of which on the lift is only partially damped. This operates over N c steps where N c = T/ t. Label the cycles as j, j = 0, 1,..., and the step within a cycle as k c, k c = 0, 1,..., N c 1, so that k = jn c + k c. Consider phase-lead ILC of the form u kc j = u kc j 1 + µekc+ j 1 (6)

30 Oscillatory Flow Control Taking = 0 with µ = 10 produces a stable algorithm, with the disturbance decaying to zero and the actuation taking a periodic form, as can be seen in Figures 2 and 3, which show values early in the simulation, and Figure 4 which shows the error at larger times. However, this is not the case for both larger and smaller values of. With = 4 a small, high frequency oscillation, which is growing by t = 3, can be seen in the error.

31 Oscillatory Flow Control k 0.05 E t Figure 2: Error E k for controller (6) with µ = 10 and = 1 (red), = 4 (green), and = 0 (blue).

32 Oscillatory Flow Control k u t Figure 3: Control input u k for controller (6) with µ = 5 and = 1 (red), = 4 (green), and = 0 (blue).

33 Oscillatory Flow Control k 0 E t Figure 4: Error E k for controller (6) with µ = 10 and = 0.

34 Oscillatory Flow Control As the problem is linear, the stability of the control can be investigated directly. In this case, as the only vorticity in the flow field is bound to the surface in the vortex panels, the lift may be calculated directly from L = V 0x Γ, where Γ is the circulation, i.e. the sum of the bound vorticity on the surface, given by Γ = N i=1 λ i i. Hence Γ = A V 0x + B u (7) and L = A V 2 0x B V 0x u (8)

35 Oscillatory Flow Control In discrete form L kc j = A(V kc 0x )2 B V kc 0x ukc j (9) Therefore Ej kc = A (V kc 0x )2 B V 0xj u kc j L r = A (V kc 0x )2 B V 0x u kc j 1 L r µb V kc 0x Ekc+ j 1 = E kc j 1 µb Vkc 0x Ekc+ j 1 Hence Ej kc E kc j 1 E kc+ = 1 µb V kc j 1 0x E kc j 1 (10)

36 Oscillatory Flow Control For = 0, the control will be stable if 0 < µb V kc 0x < 2, but the error will decay monotonically only if 0 < µb V kc 0x 1. The error changes sign throughout the cycle, so that stability cannot be guaranteed for any other value of. A comparison of the Error E k for the different controllers is shown next, showing the superior performance of the ILC control. µ = 10 will be used for the ILC control as it provides good attenuation of the error but with a allowance for non-linear effects.

37 Oscillatory Flow Control k 0.05 E t Figure 5: The error E k for controller (4) with µ = 20 (red) and (4) with µ = 50 (green), and controller (6) with µ = 10 and = 0 (blue).

38 Control with Vortical Disturbances Consider the flow with an oscillatory free stream with A = 0.1 and T = 0.25, as above, and with two vortices introduced into the flow upstream of the airfoil, one with strength Γ 1 = 1 10 placed at x v1 = ( 15, 0.25) and the other also with strength Γ 2 = 1 10 but at x v2 = ( 9, 0.35) at the start of the simulation (t = 0). With these starting values, vortex 1 will pass above the airfoil and vortex 2 below it, generating a significant disturbance in the lift in addition to that from the oscillation in the free stream velocity. Next figure shows the error for this flow with no control for the time that the vortices are passing the airfoil. In addition to the oscillation in lift arising from the free stream, large disturbances are generated by the vortices.

39 Control with Vortical Disturbances k E t Figure 6: The error E k for oscillatory flow past the airfoil with two vortices with no control.

40 Control with Vortical Disturbances The ILC controller (6) with = 0 and µ = 10 and a target value of the lift for undisturbed flow (L r = 0.379) was applied to this flow. This suppressed most of the effect of the oscillation in the free stream, but not the disturbance due to the vortices. 0.1 k E t Figure 7: The error E k for oscillatory flow past the airfoil with two vortices and the controller (6) with = 0 and µ = 10.

41 Control with Vortical Disturbances and Alternative control law. û kc j = u kc j 1 + µ 0E kc+ j 1 (11) ū k = ū k 1 + µ 1 E k 1 (12) u kc j = û kc j + ū k (13)

42 Control with Vortical Disturbances The oscillatory component of the fluctuation has been almost completely eliminated, while the disturbance from the vortices has been heavily damped k E Figure 8: The error E k for oscillatory flow past the airfoil with two vortices and the controller (11) (13) with µ 0 = 10, = 0 and µ 1 = 20. t

43 Control with Vortical Disturbances The control input u k closely tracks the lift for the uncontrolled flow, generating a counterbalancing force to the inherent fluctuation in the lift. Increasing the values of the gains above these values did not significantly affect the performance of the controller, and these values will be used below.

44 Control with Vortical Disturbances Performance Two measures have been used to estimate the degree of damping, a 2-norm with [ 1 L 2 = T 1 T 0 and a -norm with T1 T 0 L = max k ] 1 (L(t) L r ) 2 2 dt L k L r In general terms, L 2 can be thought of as measuring the fatigue load, and L the peak load on the blade. The integration for L 2 was performed from T 0 = 5, which allows the controller to settle, to T 1 = 25, when both vortices have passed the airfoil.

45 Control with Vortical Disturbances Performance The table gives the values of L 2 and L for various cases referred to explicitly here. The table also gives the ratio of the measures for controlled versus uncontrolled flow, and lists the relevant figures for each case. For the current case (case 1), the two term ILC produces a reduction of two orders of magnitude in L 2, and a value of L less than 4% of that for the uncontrolled flow.

46 Control with Vortical Disturbances Performance Table: Error norms for selected cases. case/figs norm no control control ratio 100 1: L L L L : L L : L L : L L : L L

47 Conclusions Promising initial results but much yet to do. Other work advocates identifying a model Verhaegen (Delft). In all cases short of experimentation, the question of examining performance arises. This would mean including the controller in the CFD code. This method advocates design directly based on the CFD generated data.