Predictive Control Strategy for DFIG Wind Turbines with Maximum Power Point Tracking Using Multilevel Converters

Transcription

1 Predictive Control Strategy for DFIG Wind Turbines with Maximum Power Point Tracking Using Multilevel Converters José Sayritupac 1, Eduardo Albánez 1, Johnny Rengifo 1, José Aller 1,2 and José Restrepo 1,2 1 Universidad Simón Bolívar - Caracas - Venezuela 2 Universidad Politécnica Salesiana - Cuenca - Ecuador June 2, 215

2 Abstract This paper proposes a control scheme for a wind turbine using a DFIG electromechanical converter, implemented through an NPC three-level back to back converter A predictive direct power control (DPC) strategy drives the grid-side converter, to maintain the DC bus reference voltage A predictive direct torque control (DTC) strategy drives the machine-rotor-side converter, to control the power extraction, the power factor and balancing of the DC bus capacitors

3 Wind energy conversion systems WECS m g Figure: WECS using a DFIG drives by a 3 level B2B converter

4 Wind energy conversion systems Wind speed and Wind Turbine Wind speed A wind speed measurement that includes wind gust and a wind ramp and provides a global scenario suitable to analyze the energy conversion system dynamics and the performance of the control strategies

5 Wind energy conversion systems Wind speed and Wind Turbine Wind turbine model The torque developed by the turbine rotor is T m = P m ω t = ρav 3 2ω t C p (Λ, θ p, ) Cp Λ θ p, Figure: C p vs λ curves (Turbine Power coefficient-tip speed ratio)

6 Wind energy conversion systems Doubly Fed Induction Generator DFIG I The fixed stator reference frame αβ space vector model of the induction machine is v s = R s i s + L s p i s + L sr p i s r v s r = R r i s r + L sr p i s + L r p i s r jn p ω m (L sr i s + L r i s r ) J pω m = T e T m = n p L sr ( i s r i s ) T m pθ e = n p ω m

7 Wind energy conversion systems Doubly Fed Induction Generator DFIG II The space-vector transformation used in this paper is, 2 ( ) x = x a + x b e j 2π 3 + xc e j 4π 3 = x α + jx β 3 The transformation to refer to the rotor variables to the frame of reference fixed in the stator is, x s r = x r e jθe

8 Wind energy conversion systems Multilevel Back to Back Converter Multilevel Back to Back Converter I Each inverter generates 3 3 = 27 different valid voltage space vectors in the αβ reference frame Figure: Three level NPC back to back

9 Wind energy conversion systems Multilevel Back to Back Converter Multilevel Back to Back Converter II The NPC topology requires to keep the voltage on each capacitor equal, but these voltages are affected by the connectivity states The strategy for balance operation consists in controlling the neutral voltage v n around zero volts pv n = 1 C m={a,b,c} S gm i gm S rm i rm

10 Control Strategies Predictive direct power control Predictive DPC I The algorithm computes the optimum voltage space vector that satisfies the active and reactive power references This formulation is based on computing the optimum trajectory using Lagrange operator s k = p k + j q k = s,k T s ( ) vsys,k+1 v g,k L g s,k = v sys,k i g + v sys,k+1 T s L g ( v sys,k R g i g,k )

11 Control Strategies Predictive direct power control Predictive DPC II Given an active and reactive power references, the errors are defined as, ɛ k = ɛ p,k + jɛ q,k = (p ref,k+1 p k ) + j (q ref,k+1 q k ) The cost function Ψ 1 follows as, Ψ 1 = ρ p (ɛ p,k p k ) 2 + ρ q (ɛ q,k q k ) 2

12 Control Strategies Predictive Direct Torque Control Predictive DTC I The predictive strategy is based on applying the optimal rotor voltage space vector v r that best accomplishes the following targets: Maximize the energy harvested from wind MPPT algorithm Control the stator power factor PI controller to set λ r Balance each capacitor voltage of the DC bus redundant v r

13 Control Strategies Predictive Direct Torque Control Predictive DTC II The discrete form of the electric torque differential is, T e,k = f 1 ( v s,k, v r,k, i s,k, i r,k, ω m,k ) For the magnitude of the rotor linkage λ r,k = f 2 ( λr,k, v r,k, i r,k ) Finally, the change of the neutral voltage of the DC bus is, v n,k = f 3 ( ig{abc},k, i r{abc},k, S g{abc},k, S r{abc},k )

14 Control Strategies Predictive Direct Torque Control Predictive DTC III The electric torque, rotor flux and neutral point voltage errors are defined as, ɛ T = T ref T e,k ; ɛ λ = λ ref λ r,k ; ɛv = v ref v n,k The cost function Ψ 2 is, Ψ 2 = ρ T (ɛ T,k T e,k ) 2 + ρ λ (ɛ λ,k λ r,k ) ρ v (ɛ v,k v n,k ) 2

15 Control Strategies Maximun Power Point Trancking MPPT I The wind turbine has an optimum operating point (C p opt, λ opt ) for a given pitch angle θ p, and wind speed V Pt (pu) m/s 7 m/s 9 m/s 11 m/s 13 m/s MPPT ω t (pu) Figure: WT power extraction vs ω t, for a fixed pitch angle.

16 Simulations Results Results: Case of study The system dynamics are studied within a 5 s window of incident wind speed Psys (pu) time (s) incident wind rated speed V (m/s) Figure: Active power delivered and incident wind speed

17 Simulations Results Results:Turbine power and power coefficient Effect of the pitch angle control over the turbine power Pt (pu) Cp time (s) Figure: Turbine power and power coefficient

18 Simulations Results Results:DC bus voltages vn vc1 vc time (s) Figure: Capacitors and neutral DC voltages

19 Simulations Results Results: Mechanical angular speed ωm (pu) time (s) Figure: Turbine speed

20 Simulations Results Results: Stator current is (pu) time (s) Is(jω) (db) f (Hz) Figure: Detail of stator phase current Figure: Frequency spectrum of the stator current

21 Simulations Results Results: Power factor and sensitivity analysis Mean Median Standard deviation (a) Power factor results R s R r L σs L σr L sr +2% % % (b) Torque ripple σ T under parameters uncertainty

22 Conclusions Conclusions I A DFIG-based WECS has been simulated, using a detailed model of the turbine operating under demanding wind speed conditions The proposed DTC strategy has proven to be effective, Fast tracking MPPT reference that maximizes the harvesting of the wind energy The reactive power requirements were reduced by keeping the power factor close to unity Balancing the voltage of the back to back converter DC bus capacitors

23 Conclusions Conclusions II The proposed control technique was tested for machine-parameters detuning, revealing a main dependence with the mutual inductance. In spite of this, the sensitivity analysis showed the robustness of the DTC under this operating condition.