A turbine interaction model for choosing operating points in wind farms

Transcription

1 A turbine interaction model for choosing operating points in wind farms Daria Madjidian and Anders Rantzer Dept. of Automatic Control Lund University

2 Outline Motivation Modeling Examples Summary

3 Motivation wind dir Each turbine extracting power emits a wake characterized by: mean wind speed deficit increased turbulence levels

4 Motivation Aerodynamic coupling results in reduced mean wind speeds, and increased levels of turbulence. This implies Loss of power production Increased maintenance cost Can we mitigate these effects by coordinating the turbines?

5 Previous work Wake models are abundant in the literature. Field models Kinematic models Roughness models Not all have been investigated. The ones that have are not suitable for control purposes.

6 Turbine Model C P curve β = 0 β = 2 β = 4 β = 6 β = 8 C P 0.3 P wind F T P ext λ β = 0 β = 2 β = 4 β = 6 β = 8 CT curve C T λ P wind = ρ 2 πr2 v 3 P ext =C P (λ, β)p wind λ= F T = ρ 2 πr2 C T (λ, β)v 2 Rω r v

7 Wake mechanisms The trust coefficient,c T, determines the momentum extracted from the flow. It is thus directly linked to the wind speed deficit. Added turbulence is mainly shear generated. Turbulence levels are thus directly linked toc T. Deficit and turbulence added by upwind turbines decrease with distance. Deficit and turbulence added by upwind turbines increase with the thrust coefficient.

8 Turbine interaction v 1 v 2 v 3 v N 1 v N v... v 2 =(1 k 1 C T1 ) v where0<k 2 <k 1 <1. v 3 =(1 k 2 C T1 ) v, ifturbine2off

9 Turbine interaction v 1 v 2 v 3 v N 1 v N v... v 2 =(1 k 1 C T1 ) v v 3 =(1 k 2 C T1 ) v, ifturbine2off where0<k 2 <k 1 <1. v 3 =(1 k 1 C T2 k 2 C T1 ) v, whenturbine2on

10 Turbine interaction v 1 v 2 v 3 v N 1 v N v... v 2 =(1 k 1 C T1 ) v v 3 =(1 k 2 C T1 ) v, ifturbine2off where0<k 2 <k 1 <1. v 3 =(1 k 1 C T2 k 2 C T1 ) v, whenturbine2on v n+1 =(1 k 1 C Tn k 2 C Tn 1 k n C T1 ) v

11 Turbine interaction v 1 v 2 v 3 v N 1 v N v... If the deficit decays exponentially with distance: k=k 1, k i =k i the model can be rewritten recursively: For more flexibility: deficit {}}{ v n+1 =v n +(1 k) ( v v n ) k vc Tn v n+1 =v n +k ( v v n ) k vc }{{} Tn }{{} recovery effect of neighbor

12 Turbine interaction Wind speed fluctuations (turbulence) can be handled in a similar way. Resulting model: v n+1 =v n +k (v v n ) kvc Tn, v 1 =v σ n+1 =(1+ c v (v v n)+cc Tn )σ, σ 1 = σ P n+1 = ρ 2 πr2 C Pn v 3 n+1 where 0<k<k 1 and c>0,c >0

13 Examples We will use NREL 5 MW turbine models, equipped with an internal controller acting on power reference,u. 6 Power curve NREL 5 MW turbine P max 5 4 Power [MW] wind speed [m/s]

14 Examples We will use NREL 5 MW turbine models, equipped with an internal controller acting on power reference,u. 6 Power curve NREL 5 MW turbine P max 5 4 Power [MW] wind speed [m/s] Defines a map:(u,v) (C T,C P )

15 Examples: Wind conditions Incoming wind speed 11 m/s,k=0.1,k = Available power Pa [MW] turbine number 11 wind speeds 10.5 wind speed [m/s] turbine number

16 Example 1: Maximize Farm Power v 1 v 2 v 3 v N 1 v N v... Given v, maximize extracted power in row of turbines. where max u n,v n subject to N n=1 P n v n+1 =v n +k ( v v n ) k vc Tn (u n,v n ), v 1 = v P n = ρ 2 πr2 C P (u n,v n )v 3 n

17 Result N=10 gives a 3.0% increase in power. 5 Available power and power extracted Pa turbine number 1.1 Portion of available power extracted u/pa turbine number

18 Example 2: Different farm sizes Increase in total power [%] Number of turbines Relative increase in total power production increases when the row becomes larger.

19 Example 3: Interesting effect Experiment: Let each turbine extract max. Decrease power in turbine 1 by0.5 MW, while keeping power production at other turbines Available and produced power C T Pa [MW] Thrust coefficient

20 Example 3: Interesting effect Experiment: Let each turbine extract max. Decrease power in turbine 1 by0.5 MW, while keeping power production at other turbines Available and produced power C T Pa [MW] Thrust coefficient

21 Example 3: Interesting effect Experiment: Let each turbine extract max. Decrease power in turbine 1 by0.5 MW, while keeping power production at other turbines Available and produced power C T Pa [MW] Thrust coefficient

22 Example 3: Interesting effect Experiment: Let each turbine extract max. Decrease power in turbine 1 by0.5 MW, while keeping power production at other turbines Available and produced power C T Pa [MW] Thrust coefficient

23 Example 3: Interesting effect Experiment: Let each turbine extract max. Decrease power in turbine 1 by0.5 MW, while keeping power production at other turbines. Snowball effect Available and produced power C T Pa [MW] Thrust coefficient

24 Summary Developed a model for aerodynamic turbine interaction: The model has a simple intuitive structure, and the parameters have a clear interpretation. The model points to an interesting effect as well as the possibility of a substantial power increase. Future/ongoing work. Experiments for model validation. How should turbines be coordinated for optimal performance? Extension to more complicated wind farm topologies, such as grids.

25 Thank you for your attention......questions?