Energy Based Methods in Wind Turbine Control CeSOS Highlights and AMOS Visions
Morten D. Pedersen ∗,†,‡
†
∗ Department of Engineering Cybernetics, NTNU Nowitech - Norwegian Research Centre for Offshore Wind Technology ‡ Centre for Ships and Ocean Structures (CeSOS)
June 7, 2013
Morten D. Pedersen (NTNU)
June 7, 2013
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This talk
1
Background
2
Understanding the Wind Turbine
3
Nonlinear Turbine Modeling
4
Passivity Based Control
5
Implementation Challenges
Morten D. Pedersen (NTNU)
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Background
The Problem Previously stable wind turbine systems began exhibiting resonant behavior when put on a floating base. This was quickly determined to be a control problem, caused by the new dynamics in floating operation.a The problem manifests for high wind speeds, when the turbine is in power limiting mode. a Bjørn Skaare, Tor David Hanson, and Finn Gunnar Nielsen. “Importance of control strategies on fatigue life of floating wind turbines”. In: ASME. 2007.
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Region
P I
II
III
Rated Power
V∞ Cut-in
Rated wind speed
Cut-out
Wind Speed
Turbine control 101 The turbine works in two distinct regions: 1
Power optimizing mode, V∞ < Vrated : Torque control is used to optimize power absorption.
2
Power limiting mode, power.
Morten D. Pedersen (NTNU)
V∞ > Vrated : Pitch control is used to limit the absorbed
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Key relations Steady state integrated power and thrust in coefficient form: P
=
T
=
1 3 ρACP (λ, β)v∞ 2 1 2 ρACT (λ, β)v∞ 2
λ , ΩR/v∞ : Tip speed ratio Morten D. Pedersen (NTNU)
(Power) (Thrust) β: Pitch angle June 7, 2013
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Understanding the Wind Turbine
Model Based Control The first, and perhaps most critical step in control design, is modeling the plant. The model dictates the applicable control methods. A good model aids physical insight.
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State of the Art
ogstad, P.E. Eriksen / Renewable Energy 50 (2013) 325e333
using LES with or was simulated m a conventional ed in a domain he effects of the ng body forces. no LES.
a
vil and Transport The performance lastic code called ethod predicts CP e loadings, but is evelopment. The omassen BEM.
b
ShePer-Åge has used the Krogstad and Pål Egil actuator CP wakedisk. development for a model easurements repp. 325–333 ere performed in wind tunnel using tower were not Morten D. Pedersen (NTNU)
Eriksen. “Blind test calculations of the performance and wind turbine”. In: Renewable Energy 50 (2013),
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State of the Art
Facts of Life Aerodynamics is not an exact science. There are still no reliable means of calculating wind turbine performance accurately. More complicated 6= better. Model inaccuracies must be expected.
Morten D. Pedersen (NTNU)
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Nonlinear Turbine Modeling
Wake
Induction
Wind +
− Lifting theory
Forces
− Motion
Structure
Present approach Apply first principles throughout Keep the model analytical, keep it simple! Respect the natural modular structure of the wind turbine
Morten D. Pedersen (NTNU)
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Nonlinear Turbine Modeling
Γ v∞
u
w
Morten D. Pedersen (NTNU)
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Ω r
VN
Γ
Ωr Γ U
VN LT
β + θ(r)
L
Ωr
LN
Lifting theory L = ρU × Γ
Morten D. Pedersen (NTNU)
− Kutta Joukowski Lift Theorem
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1.5
1
a
0.5
0
Experiment 4(1−a+dg)a 4|1−a|a 4(1−a)a
−0.5 −1
−0.5
0
0.5 Ct
1
1.5
2
Dynamic wake model 2ρAR w˙ + 2ρAg(v∞ , w)w = T
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Model Axial subsystem equations
J 0 0
˙ 0 0 0 1 1 Ω ρA −1 0 0 2ρAR 0 w˙ + Γ 2π 0 m −1 0 0 x¨ c|Ω| 0 0 Ω 2ρAg(v∞ , w) 0 w + + 0 0 0 d x˙
Ω w x˙ 0 v∞ τ ρA 0 − 0 0 =Γ 2π kx 0 0
where: ˙ − s2 RΩβ] Γ = 2πR[s1 (v∞ − w − x)
Note Full 6DOF model in Morten D Pedersen and Thor I Fossen. “Efficient Nonlinear Wind-Turbine Modeling For Control Applications”. In: Proceedings: MATHMOD 2012 Preprint Volume, Vienna University of Technology (2012)
Morten D. Pedersen (NTNU)
June 7, 2013
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Axial subsystem equations
J 0 0
˙ 0 0 0 1 1 Ω ρA −1 0 0 2ρAR 0 w˙ + Γ 2π 0 m −1 0 0 x¨ c|Ω| 0 0 Ω 2ρAg(v∞ , w) 0 w + + 0 0 0 d x˙
Ω w x˙ v∞ τ 0 ρA 0 − 0 0 =Γ 2π kx 0 0
where: ˙ − s2 RΩβ] Γ = 2πR[s1 (v∞ − w − x)
Interesting properties The model embeds classical aerodynamic momentum theory. The control signal works through the circulation intensity Γ in a non affine fashion. Pitch control β cannot supply damping, due to skew symmetry! Rather than damping, there is energy transfer.
Morten D. Pedersen (NTNU)
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Validation - 5MW Ref. NREL FAST 6
6
5
x 10
8
x 10
5 6 T[N]
P[W]
4 3
4
2 2
NREL FAST LOM
1 0
0
5
10 15 V∞[m/s]
20
0
25
0
5
10 15 V∞[m/s]
20
25
20
25
6
25
0 Ω β
−0.5 dP/dβ [W/deg]
Ω[rpm], β[deg]
20 15 10
−1 −1.5
5
−2
0
−2.5
0
x 10
10
20 V∞[m/s]
30
dP/dβ: Frozen wake dP/dβ: Quasistatic 5
10 15 β [deg]
J Jonkman. Fast theory manual. Tech. rep. NREL/TP-500-32449. Golden, CO: National Renewable Energy Laboratory (to be published), 2009 Morten D. Pedersen (NTNU)
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Validation - Tjæreborg Turbine experimental data
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Passivity Based Control
u
h1
y
h2
u
h1 +
y
h2 u −
h1
y
h2 Why Passivity Based Control? The chosen model is posed on a form ideal for PBC PBC treats the model on a system level. Powerful interconnection properties may be established.
Morten D. Pedersen (NTNU)
June 7, 2013
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Fundamental feedback structure of the Wind Turbine ρA 2π Γ
Hw w v∞ + − vT −
c|Ω| Q −
−
1 Js
Ω
T
τ (Ω)
u
Hs 1 Morten D. Pedersen (NTNU)
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Passivity properties ρA 2π Γ
Hw w v∞
+ − vT −
c|Ω| Q −
−
1 Js
τ (Ω)
u
Hs 1
Ω
T
Substructure Wake Rotor below rated Rotor above rated
Passive Passive Passive Inconclusive
X X X X
Observations If the rotor subsystem could be made passive, overall passivity of the system would follow. Many controllers will inadvertently cause passivity violation under certain operating conditions above rated power. Attempts to damp the system may have undesired side effects. Energy is simply moved to a different subsystem. Morten D. Pedersen (NTNU)
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A note on torque control 6
5
6
x 10
8
P [W]
2
4 2
1 0
Const. tor. Const. pwr.
6
3
g
τ [N ⋅ m]
4
x 10
0
0.5
1 Ω [rad/s]
1.5
2
0
0
0.5
1 Ω [rad/s]
1.5
2
Torque control Optimizing : τ (Ω) = bΩ2 Limiting : τ (Ω) = P/Ω Soft Limiting : τ (Ω) = P/Ωr = k (More stable)
Morten D. Pedersen (NTNU)
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Application of PBC ρA 2π Γ
u
1 Js
−
y
Ω
τ (Ω) 1
Some Physics 1 2 ˙ = Ω ρA Γu − Ωτ (Ω) = uy − P JΩ ⇒ V˙ = JΩΩ 2 2π "Perfect control" by input cancellation: V =
Γ=
τ (Ω) 2π u ρA
..is destabilizing because of incremental passivity violation: y0 + δy =
Morten D. Pedersen (NTNU)
ρA P P P ΓΩ = ' − 2 δu 2π u0 + δu u0 u0
⇒ δy = −
P δu u02 June 7, 2013
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Application of PBC
ρA 2π Γ
u
1 Js
−
Ω
y
τ (Ω) 1
Solution Perfect control = Instability We make V selectively absorb energy from the substructure. An energy management compromise is made
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Application of PBC
x[m]
8 6
[rad/s]
4 2000
3000
4000
5000
6000
3000
4000
5000
6000
3000
4000
5000
1.3 1.25 1.2 2000 6
x 10 P[w]
5.2 5 4.8 2000 Morten D. Pedersen (NTNU)
6000 June 7, 2013
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Implementation Challenges
A reliable wind speed estimate is critical The unknown wind speed is the dominant variable for the wind turbine. Direct anemometer measurements are unreliable due to turbulence. Metmast measurements are made untenable due to spacial separation. There is no "wind speed", rather a wind field. Morten D. Pedersen (NTNU)
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The estimation problem is tricky ˙ ' −τ (Ω) + ρAR(s1 V 2 − s2 RΩβV ) JΩ The unmeasured flow velocity acts as: Unknown forcing Unknown input gain & Unknown parameter
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References
Bjørn Skaare, Tor David Hanson, and Finn Gunnar Nielsen. “Importance of control strategies on fatigue life of floating wind turbines”. In: ASME. 2007 Per-Åge Krogstad and Pål Egil Eriksen. “Blind test calculations of the performance and wake development for a model wind turbine”. In: Renewable Energy 50 (2013), pp. 325–333 Morten D Pedersen and Thor I Fossen. “Efficient Nonlinear Wind-Turbine Modeling For Control Applications”. In: Proceedings: MATHMOD 2012 Preprint Volume, Vienna University of Technology (2012)
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