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 Siguerdidjane EDF actors: Damien Faille, Philippe Loevenbruck 22 nd of September 2016 3 rd Scientific Day of RISEGrid 1 / 24
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 2 / 24
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. 3 / 24
Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Model and Classic Mode of Operation Wind Turbine Model Two-mass model P r ( ω r ,ϑ, v ) 1 − D s J r n g ω g − K s D s J r ω r + J r δ ω r ˙ J r ω r J g n g δ − 1 D s D s K s ω g ˙ J g n g ω r − g ω g + J g T g J g n 2 ˙ δ ω r − 1 = n g ω g ˙ ϑ − 1 1 τ ϑ ϑ + τ ϑ ϑ r ˙ T g − 1 1 τ T T g + τ T T g , r 2 ρπ R 2 v 3 C p ( λ, ϑ ) , and λ = ω r where P r = ω r T r = 1 v 4 / 24
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: ω r controlled via T g , r , and by inverting the static relation in the figure. Power curves for for ϑ = 1 ◦ and parametric wind. Power limiting via ϑ , only activated when necessary. 5 / 24
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 ( P MPPT , P e , n ) ∀ t ≥ 0, given by an upper control level for: Wind farm power maximization. Downward active power reserve. Temporary maximum deliverable power constraints. 6 / 24
Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Wind Turbine Control Objectives Choice of a Particular Reference State choice that maximizes For a given P ∗ e there might exist the stored kinetic energy multiple state choices to achieve it: space ( ω ∗ r , ϑ ∗ ) = arg max ω r ,ϑ ω r subject to P ∗ e = P r ( ω r , ϑ, v ) ω r , min ≤ ω r ≤ ω r , n ϑ min ≤ ϑ ≤ ϑ max So that we get: = 1 ∆ W k ∼ 2 J r ( ω 2 r , up − ω 2 r , MPPT ) 7 / 24
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 = ω r ): ξ = col ( ω r ω r ˙ ω g δ T g ) Non linearities are concentrated in: ˙ ξ 2 = α ( ξ, ϑ, v , ˙ v ) + A 2 ξ + β ( ξ, ϑ, v ) ϑ r Choice of feedback linearizing input: 1 ϑ r , FL � ϑ r = β ( ξ, ϑ, v )( − α ( ξ, ϑ, v , ˙ v ) + v ϑ ) where v ϑ is left as a degree of freedom. 8 / 24
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 = ω r ): ξ = col ( ω r ω r ˙ ω g δ T g ) Non linearities are concentrated in: ˙ ξ 2 = α ( ξ, ϑ, v , ˙ v ) + A 2 ξ + β ( ξ, ϑ, v ) ϑ r Choice of feedback linearizing input: 1 ϑ r , FL � ϑ r = β ( ξ, ϑ, v )( − α ( ξ, ϑ, v , ˙ v ) + v ϑ ) where v ϑ is left as a degree of freedom. 9 / 24
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 = ω r ): ξ = col ( ω r ω r ˙ ω g δ T g ) Non linearities are concentrated in: ˙ ξ 2 = α ( ξ, ϑ, v , ˙ v ) + A 2 ξ + β ( ξ, ϑ, v ) ϑ r Choice of feedback linearizing input: 1 ϑ r , FL � ϑ r = β ( ξ, ϑ, v )( − α ( ξ, ϑ, v , ˙ v ) + v ϑ ) where v ϑ is left as a degree of freedom. 10 / 24
Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works FL + MPC Feedback Linearization step Linearized system ˙ T g , r ] ⊤ ξ = A ξ + B [ v ϑ 0 1 0 0 0 0 0 a 2 , 1 0 a 2 , 3 a 2 , 4 a 2 , 5 D s − D s K s − 1 1 0 0 � � v ϑ n 2 0 0 n g J g g J g n g J g J g = ξ + − 1 T g , r 0 0 1 0 0 0 1 n g 0 − 1 τ T 0 0 0 0 τ T 11 / 24
Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works FL + MPC Avoiding Singular Points In our system: Proposition β ( · ) = L g L r − 1 h ( · ) , which is, for f Consider a SISO system of the form the points of functioning of interest, negative and whose � x = f ( x ) + g ( x ) u , ˙ x ( 0 ) = x 0 domain is connected . y = h ( x ) where x ∈ Ω ⊆ R n . Then L g L r − 1 h ( x ( t )) � = 0 ∀ t ≥ 0 iff f The system relative degree in x 0 is well-defined and equal to r ≤ n. Λ : set of ( λ, ϑ ) s.t. β ( λ, ϑ ) < 0 sign ( L g L r − 1 h ( x ( t ))) = f sign ( L g L r − 1 h ( x 0 )) ∀ t ≥ 0 . Hence: we aim to constrain the f trajectory to lie in Λ . 12 / 24
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 : N h − 1 � � ˜ R ∆ + � ˜ ξ ( k ) � 2 u MPC ( k ) � 2 R + � ∆ u MPC ( k ) � 2 ξ ( N h ) � 2 min Q ξ + � ˜ P { u MPC } k = 1 subject to ˙ • discretization of ξ = A ξ + Bu MPC , ξ ( 0 ) = ξ ( j ) • β ( ξ, ϑ, v ) < 0 • ϑ min ≤ ϑ r , FL ≤ ϑ max • 0 ≤ ω r T g , and other system constraints Note: constraints are linearized at each j to make the problem convex , (quadratic). where ˜ ξ � ξ − ξ ref , ˜ u MPC � u MPC − u MPC , ref , u MPC � col ( v ϑ T g , r ) . 13 / 24
Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works FL + MPC Overall Controller space space where y = col ( ω r ω g ϑ T g ) 14 / 24
Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Simulations MPPT and Power Limiting 15 / 24
Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Simulations De-loaded Mode 16 / 24
Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Simulations Montecarlo Simulation 100 simulations on a 600 s time basis. We let D s , K s , J r , J g 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. 17 / 24
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 α i � ( u i − u R ) / u i , ( u i : wind sufficiently far from the rotor plane, u R : wind behind it) : P i � 1 2 ρπ R 2 u 3 i 4 α i ( 1 − α i ) 2 η from which: α Betz � arg max α i P i u i is also function of the upwind turbines operating conditions: u i = u ∞ ( 1 − δ ¯ u i ) �� u 2 δ ¯ u i = δ ¯ ij j ∈ M i where δ ¯ u ij = f wake ( d ij , r ij , R , α j ) 18 / 24
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 α i � ( u i − u R ) / u i , ( u i : wind sufficiently far from the rotor plane, u R : wind behind it) : P i � 1 2 ρπ R 2 u 3 i 4 α i ( 1 − α i ) 2 η from which: α Betz � arg max α i P i u i is also function of the upwind turbines operating conditions: u i = u ∞ ( 1 − δ ¯ u i ) �� u 2 δ ¯ u i = δ ¯ ij j ∈ M i where δ ¯ u ij = f wake ( d ij , r ij , R , α j ) 19 / 24
Objectives Wind Turbine Wind Farm Power Maximization Conclusions and Future Works Power Maximization Static Optimization Optimization problem N 1 α ∗ = arg i ( α , u ∞ , ϑ W ) C p ( α i ) η � 2 ρπ R 2 u 3 max ( α 1 ,...,α N ) i = 1 subject to 0 ≤ α i ≤ α Betz i = 1 , . . . , N So, the optimal power reference for turbine i : C p ( α ∗ i ) η P ∗ i = P MPPT , i C p ( ω r , MPPT , i , ϑ MPPT , i , u i ) 20 / 24
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: 21 / 24
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