Advanced Control of a DFIG-based Wind Power Plant for Frequency Regulation Mohamed Nadour*, Ahmed Essadki, Mohammed Fdaili Tamou Nasser Research Centre of Engineering and Health Sciences and Technologies (STIS), High Normal School of Technical Education (ENSET), Mohammed V University. Rabat, Morocco [email protected], [email protected], [email protected] Research Centre of Engineering and Health Sciences and Technologies (STIS), Higher National School of Computer Science and Systems Analysis (ENSIAS), Mohammed V University Rabat, Morocco. [email protected] Abstract—the expansion of renewable power penetration in the power system has given rise to many concerns in terms of frequency stability. Since unlike the conventional synchronous generators, these intermittent energy sources do not inherently undertake frequency regulation. For instance, The Doubly-fed induction generator (DFIG) based wind power plants have a destitute response to frequency deviations, being that its rotational speed is almost totally disassociated from the grid frequency. Another point is that significant wind power penetration leads to the retirement of many conventional power plant. Which lowers the power system’s total inertia and the power reserves that are normally needed to preserve the frequency within an adequate range of variation. Therefore, this paper proposes an advanced control strategy that allows of the DFIG based wind energy conversion system to provide, at the event of frequency excursion, an inertial support for the power system through a simultaneous use of the kinetic energy reserved in the turbine rotating masses and a portion of the energy reserved in the DC-link capacitor. A case of four synchronous generators SGs connected with a DFIG bases wind farm WF considering a sudden frequency disturbance has been studied using Matlab/Simulink to validate the capability of the suggested control strategy. Keywords- Wind Turbine; DFIG; Frequency control; MPPT; Backstepping; DC-link. I. INTRODUCTION In last few decades, thanks to the recent development in the field of power electronics, machines and systems control, wind power generation has experienced a significant growth compared to others renewables energy conversions systems. However, as this type of power generation continue flourishing worldwide and as we keep on increasing its power penetration in the system, the electrical network will have to face multiple stability challenges, such as frequency excursions. Since, unlike the conventional synchronous generators that are naturally designed to provide a response to frequency deviations (a release or absorption of kinetic energy) [1]. The wind energy conversion system does not possess this inherited response to help the system in arresting the frequency decay, being that its 978-1-5386-7850-3/19/$31.00 ©2019 IEEE rotational speed is almost totally dissociated from the frequency of the network by the presence of the power electronic interface that is normally controlled only to ensure a maximum wind power extraction. Moreover, an increase of the wind power penetration will minimize the total equivalent inertia of the power system by leading to the withdrawal of more and more traditional generation plants. Which actually present the units that are taking almost all the responsibility in maintaining the frequency within an acceptable range of a very small variation. This problem is recognized and significantly discussed over the past few years. Some works have proposed the utilization of the turbine kinetic energy to support the system in frequency regulation during transient [2]. While others, have suggested operating the wind turbine following a de-loaded operation characteristic instead of the maximum power point tracking MPPT characteristic [3]. In order to create a certain power reserve, using either the pitch or the mechanical speed control, which can automatically be activated to support the system right after the detection of a frequency deviation. However, this strategy lowers noticeably the energy yield, which may require monetary compensation for the wind power plant owner. Moreover, [4] have proposed a coordinated control strategy using both of the previous methods to enhance the WT response to frequency excursions. This paper, proposes an advanced (rotor and grid side RSC GSC converters) control strategies of the DFIG bases wind turbine. Allowing the system to provide an artificial inertial support to the power system at the event of a frequency deviation, by a simultaneous release of the kinetic energy store in the turbine rotating masses and a portion of the energy stored in the DC-link capacitor with respect to some system stability concerns. The case of four synchronous generation units (representing the electrical grid) connected to a DFIG based wind farm considering a sudden change in the load, hence, frequency disturbance is studied. The simulation results in Matlab/Simulink environment show the validity of the suggested control strategy in terms of tracking behavior and supporting the system during transient by bringing the minimum frequency up to a level where we have a 0% wind power penetration in the system. Section II gives a description of the aerodynamic model of the wind turbine and the DFIG. In section III and IV, the operation and control of wind turbine presenting both inertial support (KE and DC-link) strategies . Section V, simulation results are presented and discussed. Then, the conclusion. Figure 1. Studied System II. DYNAMIC MODEL OF THE SYSTEM A. Wind Turbine Model The aerodynamic power extracted by the wind turbine can be expressed as follows [5]: 1 (1) Pa = C p ( λ, β ) ⋅ Pwind = ⋅ C p ( λ, β ) ⋅ ρ Sv3w 2 With, S the surface of the area swept by the rotor blades, being the air density, v the wind velocity and is the wind turbine power coefficient, it is a proportion of the angle of blades and λ the tip speed ratio given by the following formula: R ⋅ Ωt λ= vw (2) The power coefficient has been approached in this work by[6]: B2 0.0035 ⋅ B2 − C p = B1 λ + 0.008β β3 + 1 B5 0.0035 ⋅ B5 ⋅ exp − λ + β 0.008 β3 + 1 − B3β − B4 + B6 λ is obtained from P ρ Sv3 , Ca = a = C p ( λ, β ) ⋅ Ωt 2Ω t (3) by: (4) Neglecting the energy losses. The gearbox that is placed to adapt the mechanical speed of the turbine’s rotor to that of the generator can be modelled using G a gain ratio as follows: Ωmec = G ⋅ Ωt Ca = G ⋅ Cg Finally, the fundamental equation of dynamics: B. DFIG Modelling The DFIG based wind turbine is most popular application among the wind energy conversion technologies. That is due to its high-energy conversion efficiency, small power electronic interface that carried only a third of the DFIG rated power, wider range of operation, which means a low mechanical stress, and a separately and easily controllable active and reactive power. It is basically an induction generator, with stator windings directly linked network, and rotor windings linked through a back-toback converter that consists of a two converters (one on the rotor side RSC and the other on the grid side GSC) parted by a DClink capacitor Fig.1. The DFIG model can be determined using the following dynamic equations [7]: dΨsd Vsd = −Rs × isd + dt −ωs ×Ψsq dΨsq Vsq = −Rs × isq + dt + ωs ×Ψsd V = −R × i + dϕrd −ω ×Ψ r rd r rq rd dt V = −R × i + dϕrq + ω ×Ψ r rq r rd rq dt Ψsd = −Ls × isd − M × ird Ψsq = −Ls × isq − M × irq (7) Ψrd = −Lr × ird − M × isd Ψrq = −Lr × irq − M × isq Where, , , , , , are respectively the stator and the rotor currents (A), voltages (A), and fluxes (Wb). , (rad/s) being the angular speeds of the rotating fields associated to the are the stator and rotor stator and the rotor. , , , inductances and resistances, is the mutual inductance. The active Ps and reactive Qs powers as well as electromagnetic torque can be given by, with p being the pair of poles: B = 0.5109 , B = 116 , B = 0.4 , B = 5 , B = 21 and B = 0.0068. The aerodynamic torque dΩmec = Cg − Cem − f ⋅Ωmec , (6) dt J is the generator inertia, f the coefficient that represents the frictions, Cg the mechanical torque of the turbine and Cem is the electromagnetic torque of the doubly fed induction generator. J (5) ( ( Ps = Re {vsis } = vsdisd + vsqisq Qs = Im {vsis } = vsqisd − vsdisq III. ) ) Cem = p M Ψsqird −Ψsdirq (9) Ls ( ) BACKSTEPPING CONTROL OF THE DFIG A. RSC control using backstepping By neglecting the stator DFIG resistance Rs, which is an acceptable assumption for high and medium induction machines [5] and aligning the stator flux on the d axis of the park reference frame (such that sd= s and sq=0) we can achieve an separate control over Ps and Qs. Accordingly, the DFIG model it becomes approximately dissociated in two subsystems and can now be represented as differential equations, such that [5]: MVs • M Ps = − vs L Δ (Vrq + R r Irq + gωs ΔI rd − g L ) s s • MV 1 s I rq = − Δ (Vrq + R r I rq + gωs ΔI rd − g L ) s z1 = Ps (10) • M Qs = − vs L Δ (Vrd + R r Ird − gωs ΔIrq ) s • 1 Ird = − (Vrq + R r I rd − gωs ΔIrq ) Δ z 2 = Qs (11) M2 ) Ls In order to improve and the performance of the overall system and the stability against parametric uncertainties, a backstepping control approach was used. This control methodology that is based on Lyapunov second method (which is a powerful tool used to pronounce on dynamic systems stability), it allows the decomposition of nonlinear complex control scheme into smaller steps, using the so-called virtual control. So that every step produces a reference for the following one. The block diagram of the RSC control design is shown in Fig. 2. The blocks ‘‘Irq-c computation’’ and ‘‘Ird-c computation’’ provides the currents of the rotor references (the virtual control variables) via a feedback control of the the active and the reactive powers Eq.12. Where: Δ = L r σ = (L r − Ls Δ Irq −ref = v s MR r Ls Δ Ird −ref = v MR s r • 1 Ps −ref + k1 ⋅ e1 − Rr vs M Vrq + gωs Δ ⋅ Ird − g Ls (12) • 1 Vrd − gωs Δ ⋅ Irq Qs −ref + k3 ⋅ e3 − Rr ( ) Where ki are the backstepping setting coefficient and ei the errors variables. Moreover, ‘‘Vrq-c computation’’ and ‘‘Vrd-c computation’’ blocks generate the actual control variables via the rotor currents feedback control (13). • vs MRr v M e1 Δ− Rr Irq + gωs ΔIrd + g s Vrq−C = −k2e2 − Irq−ref − Δ L Ls s (13) • vs MRr Vrd−C = −k4e4 − Ird−ref − L Δ e3 Δ− ( Rr Ird − gωs ΔIrd ) s B. GSC control using backstepping The GSC control scheme is based on voltages orientation such that (Vsd=0 and Vsq=Vs). The active and reactive power traded through the RL filter Figure 1. can be represented as differential equations such that [8]: vs • P t = L (Vtq − R t I tq − L t ω s ⋅ I td − Vs ) t 1 • I tq = L (Vtq − R t I fq − L t ωs ⋅ I fd − Vs ) t z1 = Pt vs • (Vtd − R t I td + L t ωs I tq ) Q t = Lt 1 • I tq = L (Vtd − R t I td + L t ωs I tq ) t z 2 = Q t (14) (15) The block diagram of the GSC control design is shown in Fig 3. The control scheme has four blocks. Two blocks ‘‘Itq-c computation’’ and ‘‘Itd-s computation’’ provides respectively the rotor currents references components (known in backstepping theory as virtual control variables) via feedback control of the filter’s active Pt and reactive Qt powers Eq. 16. In addition, another two blocks ‘‘Vrq-c computation’’ and ‘‘Vrd-c computation’’ that generate the actual control variables (voltages) via the rotor currents feedback control Eq.17. 1 Lt • Itq −ref = − Pt −ref − k1e1 + Vtq − Lf ωs Itd − vs R V t s 1 Lt • Itq −ref = R V − Qt − ref − k 3e3 + Vtd − Lt ωs Itq t s ( ) ( ) • vs Vtq−C = −k2e2 − Itq−ref + e1 Lt − Rt Itq + Lt ωs Itd + vs L t • vs Vtd−C = −k4e4 − Itd−ref + L e3 Lt − Rt Itd − Lt ωs Itq t ( ( Figure 4. RSC control Figure 5. GSC control (16) ) ) (17) IV. SYNTHETIC INERTIA During normal operation, the wind turbine operate in order to produce the maximum power from the wind velocity (using traditional MPPT algorithms), which makes it insensitive to frequency deviations due to the rapid responses of the power electronic interface. Moreover, DC-link is normally controlled to maintain a constant voltage between the armatures of the capacitor. Thus, conventional DFIG-based wind turbine does not have any response during a frequency disturbance [2]. A. Inertial support from the WT kinetic energy This additional control loop sets the active power reference for the RSC Figure 4, it allows the DFIG based wind turbine to provide an inertial active power support for the power system for a short term duration, at the event of frequency excursion. It consists on customizing the electromagnetic torque reference as function of the derivative of the measured frequency f (also known as the rate of change of frequency ROCOF). For instance, when the frequency drops, the torque set point rises causing a deceleration of the mechanical speed of the wind turbine, hence, the extraction of a part of the kinetic energy reserved in the rotating masses. The new reference of the power can be written as follow[9][2]: PWT −ref = ΔPin + PMPPT (18) Where, PMPPT is the maximum extractible power from the wind (using MPPT algorithm), ΔPin the inertial support using the additional control loop and PWT-ref is the new active power reference for the DFIG based wind turbine. Moreover, the response of the artificial inertial control loop is chosen equivalent to that of a traditional generator given by (19). df pu ΔP = 2Hsyn ⋅ f pu (19) dt Hence: df pu ΔPin = 2Hin ⋅ f pu (20) dt The previous equation represent the amount the released kinetic energy. Where, fpu is the system frequency per-unit and Hin is the wind turbine inertia constant given by the [1]: Hin = 1 JΩ2nominal 2 Pnomin al (21) From (20) we can determine the new set point of the electromagnetic point Figure. 6, which is proportional to the derivative of the frequency (ROCOF) such that: ΔCem−in = 2H ⋅ f pu df pu 1 dt Ωm −pu (22) Ti is a time constant chosen depending on the performance of the equipment about 100ms [high]. Figure 6. Block diagram of the WT inertial support B. Inertia support from the DC-link This control loop provides the reference of the active power for the GSC Figure 6. Neglecting the energy losses, the DC-link voltage reflects the balance between the power transmitted through the GSC to the grid Pgsc and the power injected to the RSC PRSC.[8]. dU (t) d 1 PC = PGSC − PRSC = Cpu .Udc (t) = Cpu .Udc (t) dc (24) dt 2 dt Where PC is the active power stored in the DC capacitor and: 2 C VDC − no min al Cpu = (25) S Where Cp.u is the per-unit total capacitance and S is the rated (power system based). Using the same analogy as for the inertial support from the wind turbine kinetic energy, the inertial support using the DC-link voltage is chosen to emulate the response of a traditional synchronous generators given by Eq.19 such that: dfpu dU (t) (26) Cpu .Udc (t) dc = 2HDC ⋅ f pu dt dt HDC is the artificial inertia constant provided by the capacitor. If we integrate in both side of (26), we have: 2 − Udc0 ) =H ( ) Cpu ⋅ Udc0 ⋅ ΔUdc = 2HDC ⋅ fpu0 ⋅Δfpu (23) A phase locked loop synchronization is used to estimate the electrical network frequency. A low pass filter is used to minimize the noises impact Figure 6. With Ki is the parameter that determines the desired quantity if the additional power and 2 dc 2 2 (27) DC ⋅ f pu − f pu0 2 Where f0 and Udc0 are the per unit nominal Dc-bus voltage and nominal frequency respectively. For stability reasons, the DCbus voltage will be maintained within a range of a small variation, we set the constraint such as ±0.1pu. Moreover, a linearization of (27) around its equilibrium point leads to: Cpu Thus: Cem−ref = Cem− MPPT + ΔCem−in (U (28) From (28) we can determine the additional control loop: Udc = KDC ⋅ Δfpu + Udc0 With: (29) ( KDC = ( 2HDC ⋅ f0 ) Cpu ⋅ Udc0 ) (30) Where, KDC is the parameter that determines the quantity of power discharged from the DC-link with respect to the stability constraint. Note that, the installation of a super capacitor can significantly improve the inertial response from the DC link using the same control principle. The block diagram of the inertia support is illustrated in Fig 7. leads to a deceleration mechanical speed as shown in Fig 8. Allowing the DFIG based wind turbine to rise the production by extracting a part of the kinetic energy reseved in the turbine rotating masses Fig 9. The additional power will help the system in contacting the frequency deviation during transient. At the steady state, the frequency stabilizes (note that the system is operating with only primary frequency regulation and without an automatic generation control AGC), and the active power return to its reference. Figure 7. Block diagram of the DC-link inertial support V. SIMULATION RESULTS To examine the performance of the additional control strategy, a small power system was simulated. Which contains static loads, four conventional synchronous generators, and DFIG-based wind power farm. Each generator has a power rating S, an inertia constant H and a droop coefficient R. All the generators are represented by a single equivalent generator driven by the mechanical outputs of the individual turbines, and assumed to be operating with primary frequency regulation and without the secondary frequency controller, such that: nH 0S0 1 − L p = H eq 1 − L p H sys = nS 0 R eq R0 R sys = R eq = = n ⋅ 1 − Lp 1 − Lp ( ) ( ( ) ( ) Figure 9. Active power generated by the DFIG-based wind turbine 1.1 Fault 1.05 1 0.95 0.9 (24) ) 0.85 0.8 0 10 20 30 40 50 60 Time (seconds) Figure 10. DC-link voltage Where, Lp % is the wind power penetration. The studied system (with characteristics presented in Appendix) and its control using backstepping strategy was simulated in Matlab/Simulink environment. the simulation is run with a constant wind profile that varies of 9 m/s for a 50 sec duration. To evaluate the frequency response characteristic of the isolated power system, a step perturbation in load of 0.1pu is applied at 10sec. Moreover, at the event of the frequency deviation, the DClink voltage reference decreases to extract a portion of the energy stored in the capacitor Figure 10. The good choice of the parameter KDC allows the voltage to remain within its limitation. Figure 8. Rotational speed of the DFIG Figure 11. Network frequency for different wind power penetration WPP with and without the frequency dependent active power support from the WF. At the presence of the fault at t=10sec, the electromagnetic set point increases by the quantity determined by Eq.22 proportional to the derivative of the measured frequency. Which Figure 11 shows the maximum short term frequency deviation from its rated value for various wind power penetration WPP levels. It can be observed from the simulation that the grid frequency nadir is of a deeper value in the case of 30% wind power penetration with a wind farm WF that does not contribute with its active power in frequency control. On the other hand, with the proposed control schemes, for different wind power penetration the active power support from the WF helps bringing the minimum frequency (after the fault) up to the level of 0% wind penetration. Moreover, with a higher wind power penetration WPP, the grid frequency nadir is of a narrower value, which demonstrate the effectiveness of the additional control loop in arresting the frequency decay. • DFIG Parameters Rated Power 1.6Mw, Grid rated voltage Vs=690; fs= 50 Hz, Pole pair p=2, Stator & rotor resistances =12mΩ, Stator & rotor inductance =13.7mH, =21mΩ, =13.6mH, Mutual Inductance M=13.5mH. ACKNOWLEDGMENT Reactive power (Var) The help of the (CNRST)" "National Center for Scientific and Technical Research’’ is gratefully acknowledged. REFERENCES [1] Figure 11. Total reactive active Finally, Fig 12 shows the total reactive power (Q=Qs+Qr) control. Which is maintained in this work equal to zero for a unity power factor at the point of common coupling. VI. [3] CONCLUSION This work presents an additional control loop using backstepping applied to a DFIG-based wind turbine to enhance its capability to participate in frequency regulation. The control strategy consists on providing an inertial support to the power system through a simultaneous release of the kinetic energy reserved in the turbine rotating masses and a portion of the energy reserved in the DC-link capacitor of the back to back converter. Simulation shows capability of the control strategy in terms of dynamic behaviour, and the enhancement of ability of wind turbine in providing frequency regulation and Bringing the frequency nadir (in the fault case) up to level of 0% wind power penetration in the power system APPENDIX • [2] [4] [5] [6] [7] Wind Turbine Parameters The blades radius R=35m, [8] Maximum power coefficient Cpmax=0.435, Gearbox gain G=50. Moment of inertia J=200 kg/m2. Damping coefficient f=0.017 N.m.s/rd. Density of air =1.2 kg/m3. [9] R. Chakib, M. 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