Control Optimization of a Renewable Energy Park with Energy Storage - - PowerPoint PPT Presentation

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Control Optimization of a Renewable Energy Park with Energy Storage - - PowerPoint PPT Presentation

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Control Optimization of a Renewable Energy Park with Energy Storage and Distribution Network Nicol` o Gionfra Supervisors: Guillaume Sandou, Houria

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works

Control Optimization of a Renewable Energy Park with Energy Storage and Distribution Network

Nicol`

  • Gionfra

Supervisors: Guillaume Sandou, Houria Siguerdidjane EDF actors: Damien Faille, Philippe Loevenbruck

22nd of September 2016

3rd Scientific Day of RISEGrid

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works

Table of contents

1 Objectives 2 Wind Turbine

Model and Classic Mode of Operation Wind Turbine Control Objectives FL + MPC Simulations

3 Wind Farm Power Maximization

Wake Effect Power Maximization Simulations

4 Conclusions and Future Works

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works

Objectives

Grid Constraints Active power constraints, as curtailment. Frequency and voltage primary control. Artificial inertia. Power Maximization Coupling effects between WTs, such as wake effect. Mechanical Stress Minimization of mechanical stress and maintenance.

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Model and Classic Mode of Operation

Wind Turbine Model

Two-mass model

      ˙ ωr ˙ ωg ˙ δ ˙ ϑ ˙ Tg       =       

1 Jr Pr(ωr,ϑ,v) ωr

− Ds

Jr ωr + Ds Jrng ωg − Ks Jr δ Ds Jgng ωr − Ds Jgn2

g ωg +

Ks Jgng δ − 1 Jg Tg

ωr − 1

ng ωg

− 1

τϑ ϑ + 1 τϑ ϑr

− 1

τT Tg + 1 τT Tg,r

      

where Pr = ωrTr = 1

2 ρπR2v3Cp (λ, ϑ), and λ = ωr

v

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Model and Classic Mode of Operation

Classic Mode of Operation

MPPT control at low wind speed, with constant ϑ. Power Limiting (PL) at high wind speed, by acting on ϑ. Tipically two loops of PI control: ωr controlled via Tg,r, and by inverting the static relation in the figure. Power limiting via ϑ, only activated when necessary.

Power curves for for ϑ = 1◦ and parametric wind. 5 / 24

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Wind Turbine Control Objectives

Control Objectives

Main objective

Track a general power reference P∗

e (·) satisfying

0 ≤ P∗

e (t) ≤ min(PMPPT, Pe,n)

∀t ≥ 0, given by an upper control level for: Wind farm power maximization. Downward active power reserve. Temporary maximum deliverable power constraints.

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Wind Turbine Control Objectives

Choice of a Particular Reference

For a given P∗

e there might exist

multiple state choices to achieve it: space

State choice that maximizes the stored kinetic energy

(ω∗

r , ϑ∗) = arg max ωr ,ϑ ωr

subject to P∗

e = Pr(ωr, ϑ, v)

ωr,min ≤ ωr ≤ ωr,n ϑmin ≤ ϑ ≤ ϑmax

So that we get:

∆Wk ∼ = 1 2Jr(ω2

r,up − ω2 r,MPPT) 7 / 24

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works FL + MPC

Feedback Linearization Step

Main steps

Choice of the change of coordinates (considering the output y = ωr): ξ = col(ωr ˙ ωr ωg δ Tg) Non linearities are concentrated in: ˙ ξ2 = α(ξ, ϑ, v, ˙ v) + A2ξ + β(ξ, ϑ, v)ϑr Choice of feedback linearizing input: ϑr,FL ϑr = 1 β(ξ, ϑ, v)(−α(ξ, ϑ, v, ˙ v) + vϑ) where vϑ is left as a degree of freedom.

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works FL + MPC

Feedback Linearization Step

Main steps

Choice of the change of coordinates (considering the output y = ωr): ξ = col(ωr ˙ ωr ωg δ Tg) Non linearities are concentrated in: ˙ ξ2 = α(ξ, ϑ, v, ˙ v) + A2ξ + β(ξ, ϑ, v)ϑr Choice of feedback linearizing input: ϑr,FL ϑr = 1 β(ξ, ϑ, v)(−α(ξ, ϑ, v, ˙ v) + vϑ) where vϑ is left as a degree of freedom.

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works FL + MPC

Feedback Linearization Step

Main steps

Choice of the change of coordinates (considering the output y = ωr): ξ = col(ωr ˙ ωr ωg δ Tg) Non linearities are concentrated in: ˙ ξ2 = α(ξ, ϑ, v, ˙ v) + A2ξ + β(ξ, ϑ, v)ϑr Choice of feedback linearizing input: ϑr,FL ϑr = 1 β(ξ, ϑ, v)(−α(ξ, ϑ, v, ˙ v) + vϑ) where vϑ is left as a degree of freedom.

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works FL + MPC

Feedback Linearization step

Linearized system

˙ ξ = Aξ + B[vϑ Tg,r]⊤ =            1 a2,1 a2,3 a2,4 a2,5 Ds ngJg − Ds n2

gJg

Ks ngJg − 1 Jg 1 − 1 ng − 1 τT            ξ +        1 1 τT       

  • vϑ

Tg,r

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works FL + MPC

Avoiding Singular Points

Proposition

Consider a SISO system of the form

  • ˙

x = f (x) + g(x)u, x(0) = x0 y = h(x) where x ∈ Ω ⊆ Rn. Then LgLr−1

f

h(x(t)) = 0 ∀t ≥ 0 iff The system relative degree in x0 is well-defined and equal to r ≤ n. sign(LgLr−1

f

h(x(t))) = sign(LgLr−1

f

h(x0)) ∀t ≥ 0.

In our system: β(·) = LgLr−1

f

h(·), which is, for the points of functioning of interest, negative and whose domain is connected.

Λ: set of (λ, ϑ) s.t. β(λ, ϑ) < 0

Hence: we aim to constrain the trajectory to lie in Λ.

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works FL + MPC

MPC Step

Optimization problem

At each time step j, MPC solves the following problem P: min

{uMPC } Nh−1

  • k=1

˜ ξ(k)2

Qξ + ˜

uMPC(k)2

R + ∆uMPC(k)2 R∆ + ˜

ξ(Nh)2

P

subject to

  • discretization of

˙ ξ = Aξ + BuMPC, ξ(0) = ξ(j)

  • β(ξ, ϑ, v) < 0
  • ϑmin ≤ ϑr,FL ≤ ϑmax
  • 0 ≤ ωrTg

, and other system constraints

Note: constraints are linearized at each j to make the problem convex, (quadratic). where ˜ ξ ξ − ξref , ˜ uMPC uMPC − uMPC,ref , uMPC col(vϑ Tg,r).

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works FL + MPC

Overall Controller

space space

where y = col(ωr ωg ϑ Tg)

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Simulations

MPPT and Power Limiting

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Simulations

De-loaded Mode

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Simulations

Montecarlo Simulation

100 simulations on a 600 s time basis. We let Ds, Ks, Jr, Jg span an interval of ± 20 % of their nominal value, according to a uniform distribution of probability. The system is excited by a wind speed signal whose average is 12 m/s.

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Wake Effect

Wake Model

Aerodynamic coupling among turbines

Turbine i power can be expressed as a function of αi (ui − uR)/ui,

(ui: wind sufficiently far from the rotor plane, uR: wind behind it):

Pi 1 2ρπR2u3

i 4αi(1−αi)2η

from which: αBetz arg maxαi Pi ui is also function of the upwind turbines operating conditions: ui = u∞(1 − δ¯ ui) δ¯ ui =

  • j∈Mi

δ¯ u2

ij

where δ¯ uij = fwake(dij, rij, R, αj)

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Wake Effect

Wake Model

Aerodynamic coupling among turbines

Turbine i power can be expressed as a function of αi (ui − uR)/ui,

(ui: wind sufficiently far from the rotor plane, uR: wind behind it):

Pi 1 2ρπR2u3

i 4αi(1−αi)2η

from which: αBetz arg maxαi Pi ui is also function of the upwind turbines operating conditions: ui = u∞(1 − δ¯ ui) δ¯ ui =

  • j∈Mi

δ¯ u2

ij

where δ¯ uij = fwake(dij, rij, R, αj)

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Power Maximization

Static Optimization

Optimization problem

α∗ = arg max

(α1,...,αN) N

  • i=1

1 2ρπR2u3

i (α, u∞, ϑW )Cp(αi)η

subject to 0 ≤ αi ≤ αBetz i = 1, . . . , N

So, the optimal power reference for turbine i: P∗

i = PMPPT,i

Cp(α∗

i )η

Cp(ωr,MPPT,i, ϑMPPT,i, ui)

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Simulations

An example

Expected gain from static optimization: ∼ 9 %.

Simulation considering the dynamics of the controlled turbines:

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works

Wind Turbine Level

Conclusions

The proposed control enables tracking of a general power reference. It allows to control a wind turbine in the whole operating envelope. Montecarlo simulation showed a certain inherent degree of robustness.

Future Works

Stability conditions for the MPC step: error boundedness and recursive feasibility. Application for mechanical stress reduction via Individual Pitch Control.

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works

Wind Farm Level

Conclusions

Hierarchical control for wind farm power maximization under wake effect. The power gain consolidates the need for wake consideration for farms of a certain amount of turbines.

Future Works

Introduction of feedback at the highest control level. Distributed intelligence to take into account the system dynamics for power maximization. Distributed algorithm for optimization and control without the need for a centralized controller.

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Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works

Thanks for your attention!

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