ISA Transactions 53 (2014) 827–833
Contents lists available at ScienceDirect
ISA Transactions journal homepage: www.elsevier.com/locate/isatrans
Research Article
Second-order sliding mode control for DFIG-based wind turbines fault ride-through capability enhancement Mohamed Benbouzid a,n, Brice Beltran a, Yassine Amirat b, Gang Yao c, Jingang Han c, Hervé Mangel a a
University of Brest, EA 4325 LBMS, Rue de Kergoat, CS 93837, 29238 Brest Cedex 03, France ISEN, EA 4325 LBMS, 20, Rue Cuirassé Bretagne, 29200 Brest, France c Shanghai Maritime University, Department of Electrical Automation, 201306 Shanghai, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 6 December 2013 Received in revised form 10 January 2014 Accepted 23 January 2014 Available online 13 February 2014 This paper was recommended for publication by Dr. Jeff Pieper.
This paper deals with the fault ride-through capability assessment of a doubly fed induction generatorbased wind turbine using a high-order sliding mode control. Indeed, it has been recently suggested that sliding mode control is a solution of choice to the fault ride-through problem. In this context, this paper proposes a second-order sliding mode as an improved solution that handle the classical sliding mode chattering problem. Indeed, the main and attractive features of high-order sliding modes are robustness against external disturbances, the grids faults in particular, and chattering-free behavior (no extra mechanical stress on the wind turbine drive train). Simulations using the NREL FAST code on a 1.5-MW wind turbine are carried out to evaluate ridethrough performance of the proposed high-order sliding mode control strategy in case of grid frequency variations and unbalanced voltage sags. & 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Keywords: Wind turbine Doubly fed induction generator Fault-ride through Second-order sliding mode
1. Introduction An increasing number of power system operators have implemented technical standards known as grid codes that wind turbines must meet when connecting to the grid [1,2]. Generally, these grid codes requirements cover many topics such as voltage operating range, power factor regulation, frequency operating range, grid support capability, and low fault ride-through capability. Indeed, grid codes dictate FRT requirements. LVRT capability is considered to be the biggest challenge in wind turbines design and manufacturing technology [3]. LVRT requires wind turbines to remain connected to the grid in the presence of grid voltage sags. The DFIG is one of the most frequently deployed large gridconnected wind turbines. Indeed, when compared with the full-scale power converter WT concept, the DFIG offers some advantages, such as reduced inverter and output filter costs due to low rotor- and grid-side power conversion ratings (25–30%) [4]. However, DFIG-based WTs are very sensitive to grid disturbances, especially to voltage dips [5].
n
Corresponding author. E-mail addresses: [email protected] (M. Benbouzid), [email protected] (B. Beltran), [email protected] (Y. Amirat), [email protected] (G. Yao), [email protected] (J. Han), [email protected] (H. Mangel).
In this context, this paper proposes to address the FRT problems using a so-called active method achieving FRT with no additional devices. The goal is to control rotor voltages and currents, to reduce the rotor overvoltages and/or overcurrents, and therefore avoid the crowbar use/activation in order to keep full DFIG control at all times to meet the FRT requirements. The implementation of classical flux-oriented vector control techniques (PI controllers) has been proven to work well for the accomplishment of the initial grid code requirements [6–9]. But, this kind of control could be easily saturated when dealing with substantial sag. Moreover, it is sensitive to the generator parameters and other phenomena such as disturbances and unmodeled dynamics [10,11]. In particular, [10] gives a critical review of control methods for LVRT compliance with DFIG. This state-of-theart review suggests the need of robust and nonlinear controller. A robust one has been proposed in [12], claiming full control in all LVRT cases. However, this was achieved with an oversized converter to accommodate rotor overvoltages and full rotor current control. It is therefore suggested that sliding mode control is a solution of choice to the FRT problem [13]. Therefore and in this particular context, this paper proposes the use of high-order sliding mode control as an improved solution that handles the classical sliding mode chattering problem and particularly avoids using additional devices and converter oversizing. Indeed, the main and attractive features of HOSMs are robustness against
0019-0578/$ - see front matter & 2014 ISA. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.isatra.2014.01.006
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M. Benbouzid et al. / ISA Transactions 53 (2014) 827–833
Nomenclature WT DFIG FRT LVRT HOSM SOSM MPPT v ρ R Pa Ta λ Cp(λ) ω
wind turbine doubly fed induction generator fault ride-through low-voltage ride-through high-order sliding mode second-order sliding mode maximum power point tracking wind speed (m/s) air density (kg/m3) rotor radius (m) aerodynamic power (W) aerodynamic torque (Nm) tip speed ratio power coefficient wind turbine rotor speed (rad/s)
external disturbances (grid faults) and chattering-free behavior (no extra mechanical stress on the drive train) [14–16]. The proposed control strategy combines an MPPT using a second-order sliding mode for the DFIG control [17,18]. The proposed work is based on [17,18] philosophy (high-order sliding mode). In the case of [18], the control is on the turbine with a specific controller. In the case of [17], the control is on the DFIG as in this paper. However, this paper contribution is on the design of the second-order sliding mode controller based on the supertwisting algorithm that takes into account grid disturbances, in addition to the optimal power extraction [19]. This strategy presents attractive features such as chatteringfree behavior, finite reaching time, robustness and unmodeled dynamics (generator and turbine). To check the overall control strategy ride-through performance, simulations using the NREL FAST code on a 1.5-MW wind turbine are carried out in case of grid frequency variations and unbalanced voltage sags.
2. Grid-code requirements Grid-code requirements typically refer to large wind farms connected to the transmission system, rather than smaller stations connected to the distribution network. These new grid codes stipulate that wind farms should contribute to power system control (frequency and also voltage), much as the conventional power stations, and emphasize wind farm behavior in case of abnormal operating conditions of the network (such as in case of voltage dips). The most common requirements include FRT capability, extended system voltage and frequency variation limits, active power regulation, and frequency control, as well as reactive power/power factor and voltage regulation capabilities [1,2]. Grid codes main requirements regarding the addressed faults are given below. 2.1. Frequency operating range Wind power plants are required to run continuously within typical grid frequency variations between 49.5 Hz and 50.5 Hz. Fig. 1 gives an example of frequency–grid voltage variations [1]. 2.2. Low voltage ride-through Grid codes invariably require that large wind farms must withstand voltage sags down to a certain percentage of the nominal voltage and for a specified duration. Such constraints are known as LVRT requirements. They are described by a voltage versus time
Tg J K d, q s, (r) V (I) P (Q) ϕ Tem R L (M)
s
θr ωr (ωs) s p
generator electromagnetic torque (Nm) turbine total inertia (kg m2) turbine total external damping (Nm/rad s) synchronous reference frame index stator (rotor) index voltage (current) active (reactive) power flux electromagnetic torque resistance inductance (mutual inductance) leakage coefficient, s ¼1 – M2/LsLr rotor position angular speed (synchronous speed) slip pole pair number
characteristic, denoting the minimum required immunity of the wind power station to the system voltage sags (Fig. 2) [1].
3. Wind turbine modeling The wind turbine modeling is inspired from [17]. In the following, the wind turbine components models are briefly described. 3.1. Turbine model In this case, the aerodynamic power captured by the wind turbine is given by 1 P a ¼ πρR2 C p ðλÞv3 2
ð1Þ
where λ¼
Rω v
ð2Þ
The rotor power (aerodynamic power) is also defined by P a ¼ ωT a
ð3Þ
The following simplified model is adopted for the turbine (drive train) for control purposes. _ ¼ T a Kω T g Jω
ð4Þ
3.2. DFIG model The control system is usually defined in the synchronous d q frame fixed to either the stator voltage or the stator flux. For the proposed control strategy, the generator dynamic model written in a synchronously rotating frame d q is given by 8 dϕsd > > > V sd ¼ Rs I sd þ dt ωs ϕsq > > dϕ > > > V sq ¼ Rs I sq þ dtsq þωs ϕsd > > > > > V rd ¼ Rr I rd þ dϕdtrd ωr ϕrq > > > > > > V ¼ R I þ dϕrq þ ω ϕ < rq r rq r rd dt ð5Þ ϕ ¼ L I þ MI > s sd rd sd > > > > ϕsq ¼ Ls I sq þ MI rq > > > > > ϕrd ¼ Lr I rd þMI sd > > > > > ϕrq ¼ Lr I rq þ MI sq > > > > : T em ¼ pMðI I sq I rq I Þ rd sd
M. Benbouzid et al. / ISA Transactions 53 (2014) 827–833
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Fig. 1. Frequency–voltage variations ranges [© Nordel] [1].
Fig. 2. LVRT requirements for different countries [1].
For simplification purposes, the q-axis is aligned with the stator voltage and the stator resistance is neglected. These will lead to 8 dϕsd dIrd > ¼ s1Lr V rd Rr I rd þsωs sLr I rq M > L dt dt > s > < dIrq ¼ s1Lr V rq Rr I rq sωs sLr I rd sωs M Ls ϕsd dt > > > > T ¼ pM ϕ I : em
Ls
ð6Þ
sd rq
4. DFIG-based wind turbine control 4.1. MPPT strategy
with C p max 1 k ¼ πρR5 3 2 λopt Details about the adopted strategy are given in [17]. 4.2. HOSM control strategy The DFIG-based WT control objective is to optimize the extracted power by tracking the optimal torque Topt (7). The control is a compromise between conversion efficiency and torque oscillation smoothing. The reactive power is expressed as follows. Q s ¼ V sq I sd V sd I sq
The control objective is to optimize the capture wind energy by tracking the optimal torque Topt. T opt ¼ kω2
ð7Þ
ð8Þ
Adapting (8) to our hypotheses, it comes then Qs ¼
V s ϕs V s M I Ls rd Ls
ð9Þ
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M. Benbouzid et al. / ISA Transactions 53 (2014) 827–833
As the stator reactive power reference is zero, then ϕs ¼ (
Vs Vs -I rd_ref ¼ ωs ωs M
ð10Þ
Let us consider the following tracking errors. eIrd ¼ I rd I rd_ref
ð11Þ
eT em ¼ T em T ref Then we will have 8 dϕsd > < e_ Ird ¼ s1Lr V rd Rr I rd þ gωs Lr sI rq M _I rd_ref Ls dt > : e_ T em ¼ psLML ϕs V rq Rr I rq gωs Lr sird s r M gωs ϕsd T_ ref Ls
:
ð12Þ
If we define the G1 and G2 functions as follows. 8 dϕsd > _I rd_ref < G1 ¼ s1Lr gωs sLr I rq M Ls dt _ > : G2 ¼ psLMs Lr ϕs gωs sLr I rd gωs M Ls ϕsd T ref Thus we have 8 _ 1 1 Rr _I < e€ Ird ¼ s1L V_ rd þ G rd s Lr r _ 2 þp : e€ Γ ¼ p M ϕ V_ rq þ G em
s Ls Lr s
_
sLs Lr ϕs Rr I rq M
ð13Þ
Now, lets us consider the following second-order sliding mode controller based on the supertwisting algorithm [17–19]. 8 1 > V rq ¼ y1 þ B1 eT em 2 SgnðeT em Þ þ s1Lr Rr I rd > > > > < y_ 1 ¼ þB2 SgnðeT Þ em ð14Þ 1 M > 2 > ¼ y B e V 3 I rd SgnðeI rd Þ psLs Lr ϕs Rr I rq rd > 2 > > : y_ ¼ B Sgnðe Þ I rd 4 2 where y1 and y2 are intermediate variables and represent the control error integral.
Fig. 3. The proposed FRT control structure.
Fig. 4. 1.5-MW wind turbine illustration.
Fig. 5. Wind speed profile.
M. Benbouzid et al. / ISA Transactions 53 (2014) 827–833
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Fig. 6. FAST wind turbine block.
Fig. 8. Grid voltage.
The above proposed second-order sliding mode control strategy for a DFIG-based WT is illustrated by Fig. 3.
5. Simulations using FAST code
Fig. 7. Simulink model.
To ensure the sliding manifolds convergence to zero in finite times, the gains B1, B2, B3, and B4 can be chosen as follows [19,20] 8 _ > G1 o Φ1 > > > > > > 4Φ ðB þ Φ Þ 2 > < B1 4psLMs Lr ϕs Φ1 ; B2 Z s2 L12 ðB1 Φ1 Þ r 1 1 ð15Þ _ > > o Φ G 2 2 > > > > > > B3 4 Φ2 ; B4 2 Z 4Φ22ðB3 þ Φ2 Þ : s Lr
s2 Lr ðB3 Φ2 Þ
In this context, it can be asserted that there exist finite times tTem and tIrd leading to (16). This means that the control objective is achieved. ( I rd_ref ¼ I rd ; 8 t 4 t Ird ð16Þ T ref ¼ T em ; 8 t 4 t T em
Simulation using FAST with Matlab-Simulinks has been carried out on the NREL WP 1.5-MW wind turbine (Fig. 4) using turbulent FAST wind data shown by Fig. 5 [21]. The wind turbine, the DFIG ratings, and control parameters are given in the Appendix. An interface has been developed between FAST and MatlabSimulinks enabling users to implement advanced turbine controls in Simulink convenient block diagram form (Fig. 6). Hence, electrical model (DFIG, grid, control system, etc.) designed in the Simulink environment is simulated while making use of the complete nonlinear aerodynamic wind turbine motion equations available in FAST (Fig. 7). 5.1. Frequency variation The proposed SOSM-based FRT strategy will be first tested regarding a frequency variation. Indeed, the studied case is a frequency fall from 50 to 48 Hz as illustrated by Fig. 8. This case corresponds to a power generation loss that could lead to a rapid decrease of the grid frequency. The FRT performances are illustrated by Fig. 9. It clearly shows that the frequency fall has practically no effect on the torque. This is confirmed by the quadratic error shown by Fig. 10. Obviously, a good tolerance is achieved for this type of fault. To assess the FRT capability enhancement of the proposed SOSM control approach, it has been compared to a classical PI
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M. Benbouzid et al. / ISA Transactions 53 (2014) 827–833
control approach [22,23]. The achieved results as shown by Figs. 11 and 12 clearly confirm the superiority of a high-order sliding mode approach over more classical control approaches. It should be noticed that the SOSM control approach achieves the same quadratic error as a classical first-order sliding mode control.
by Fig. 17. This figure clearly shows that PI control achieves poorer LVRT performances. If the FRT performances were similar in case of frequency variation, Fig. 18 shows the superiority of a high-order mode control over a first-one in case of unbalanced voltage sags.
5.2. Unbalanced voltage sags When unbalanced sags occur (Fig. 13), very high current, torque, and power oscillations appear at double of the electrical frequency, forcing a disconnection. The LVRT performances are illustrated by Fig. 14 where an almost constant torque is achieved. Good tracking performances are also achieved in terms of DFIG rotor current (Fig. 15). Faulttolerance performances are also confirmed by the quadratic error shown by Fig. 16. To assess the LVRT capability enhancement of the proposed SOSM control approach, it has also been compared to the same classical PI control approach. The achieved results are illustrated
Fig. 9. Torque tracking performance during frequency variation: reference (green) and real (blue). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Fig. 12. Quadratic error between the reference torque and the PI control-based one (frequency variation).
Fig. 13. Grid voltage.
Fig. 10. Quadratic error between the reference torque and the SOSM control-based one (frequency variation).
Fig. 14. Torque tracking performance during unbalanced voltage sags: reference (blue) and real (green). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Fig. 11. Torque: reference (green) and real (blue). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Fig. 15. Current Ird tracking performance during unbalanced voltage sags: reference (blue) and real (green). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
M. Benbouzid et al. / ISA Transactions 53 (2014) 827–833
Hub height Rated power Turbine total inertia
833
84.3 m 1.5 MW 4.4532 105 kg m2
Simulated DFIG parameters Rs ¼0.005 Ω, Ls ¼0.407 mH, Rr ¼ 0.0089 Ω, Lr ¼0.299 mH, M¼0.0016 mH, p ¼2 Control parameters B1 ¼10, B2 ¼20,000, B3 ¼7, B4 ¼500 Fig. 16. Quadratic error between the reference torque and the SOSM control-based one (voltage sags).
References
Fig. 17. Quadratic error between the reference torque and the PI control-based one (voltage sags).
Fig. 18. Quadratic error between the reference torque and the first-order sliding mode control-based one (voltage sags).
6. Conclusion This paper dealt with a second-order sliding mode control of a doubly fed induction-based wind turbine for fault ride through. The SOSM-based FRT strategy has been tested regarding grid frequency variations and unbalanced voltage sags on a 1.5-MW three-blade wind turbine using the NREL wind turbine simulator FAST. The achieved results show promising successful ride-through performances over well-known PI-based control and even over classical sliding mode control (first-order). It should be particularly mentioned that the proposed SOSM control approach does not need any specific adjustments to fault ride-through purposes. Appendix A. Simulated wind turbine characteristics.
Number of blades Rotor diameter
3 70 m
[1] Mohseni M, Islam SM. Review of international grid codes for wind power integration: diversity, technology and a case for global standard. Renew Sustain Energy Rev 2012;16(August (6)):3876–90. [2] Tsili M, Papathanassiou S. A review of grid code technical requirements for wind farms. IET Renew Power Gener 2009;3(September (3)):308–32. [3] Yingcheng X, Nengling T. Review of contribution to frequency control through variable speed wind turbine. Renew Energy 2011;36(June (6)):1671–7. [4] Liserre M, Cardenas R, Molinas M, Rodriguez J. Overview of multi-MW wind turbines and wind parks. IEEE Trans Ind. Electron. 2011;58(April (4)):1081–95. [5] Jadhav HT, Roy R. A comprehensive review on the grid integration of doubly fed induction generator. Int J Electr Power Energy Syst 2013;49(July):8–18. [6] Yang L, Xu Z, Ostergaard J, Dong ZY, Wong KP. Advanced control strategy of DFIG wind turbines for power system fault ride through. IEEE. Trans Power Syst 2012;27(May (2)):713–22. [7] Abdelli R, Rekioua D, Rekioua T, Tounzi A. Improved direct torque control of an induction generator used in a wind conversion system connected to the grid. ISA Trans 2013;52(July (4)):525–38. [8] Khezami N, Benhadj Braiek N, Guillaud X. Wind turbine power tracking using an improved multimodel quadratic approach. ISA Trans 2010;49(July (3)):326–34. [9] Leon AE, Mauricio JM, Solsona JA. Fault ride-through enhancement of DFIGbased wind generation considering unbalanced and distorted conditions. IEEE. Trans Energy Convers 2012;27(September (3)):775–83. [10] Cardenas R, Pena R, Alepuz S, Asher G. Overview of control systems for the operation of DFIGs in wind energy applications. IEEE Trans Ind Electron 2013;60(July(7)):2776–98. [11] Long T, Shao S, Li CY, Chun-Yin E, Abdi, McMahon RA. Crowbarless fault ridethrough of the brushless doubly fed induction generator in a wind turbine under symmetrical voltage dips. IEEE Trans Ind Electron 2013;60(July (7)):2833–41. [12] Phan VT, Lee HH. Improved predictive current control for unbalanced standalone doubly-fed induction generator-based wind power systems. IET Electric Power Appl 2011;5(3):275–2875. [13] Martinez MI, Tapia G, Susperregui A, Camblong H. Sliding-mode control for DFIG rotor- and grid-side converters under unbalanced and harmonically distorted grid voltage. IEEE Trans Energy Convers 2012;27(June (2)):328–39. [14] Eker I. Second-order sliding mode control with experimental application. ISA Trans 2010;49(July (3)):394–405. [15] Benbouzid, MEH, Beltran, B, Amirat, Y, Yao, G., Han, J and Mangel, H., Highorder sliding mode control for DFIG-based wind turbine fault ride-through. In: Proceedings of the 2013 IEEE IECON, Vienna (Austria); November 2013. p. 1–5. [16] Benbouzid MEH, Beltran B, Ezzat M, Breton S. DFIG driven wind turbine grid fault-tolerance using high-order sliding mode control. Int Rev Model Simul 2013;6(February (1)):29–32. [17] Beltran B, Benbouzid MEH, Ahmed-Ali T. Second-order sliding mode control of a doubly fed induction generator driven wind turbine. IEEE Trans Energy Convers 2012;27(June (2)):261–9. [18] Beltran B, Ahmed-Ali T, Benbouzid MEH. High-order sliding mode control of variable speed wind turbines. IEEE Trans Ind Electron 2009;56(September (9)):3314–21. [19] Levant A, Alelishvili L. Integral high-order sliding modes. IEEE Trans Autom Control 2007;52(July (7)):1278–82. [20] Khalil HK. Nonlinear systems. New York: McMillan; 1992 ([chapter 14]). [21] 〈http://wind.nrel.gov/designcodes/simulators/fast/〉. [22] Hu J, Xu H, He Y. Coordinated control of DFIG's RSC and GSC under generalized unbalanced and distorted grid voltage conditions. IEEE Trans Ind Electron 2013;60(July (7)):2808–19. [23] Hu J, Xu H, He Y. Integrated modeling and enhanced control of DFIG under unbalanced and distorted grid voltage conditions. IEEE Trans Energy Convers 2012;27(September (3)):725–36.
Contents lists available at ScienceDirect
ISA Transactions journal homepage: www.elsevier.com/locate/isatrans
Research Article
Second-order sliding mode control for DFIG-based wind turbines fault ride-through capability enhancement Mohamed Benbouzid a,n, Brice Beltran a, Yassine Amirat b, Gang Yao c, Jingang Han c, Hervé Mangel a a
University of Brest, EA 4325 LBMS, Rue de Kergoat, CS 93837, 29238 Brest Cedex 03, France ISEN, EA 4325 LBMS, 20, Rue Cuirassé Bretagne, 29200 Brest, France c Shanghai Maritime University, Department of Electrical Automation, 201306 Shanghai, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 6 December 2013 Received in revised form 10 January 2014 Accepted 23 January 2014 Available online 13 February 2014 This paper was recommended for publication by Dr. Jeff Pieper.
This paper deals with the fault ride-through capability assessment of a doubly fed induction generatorbased wind turbine using a high-order sliding mode control. Indeed, it has been recently suggested that sliding mode control is a solution of choice to the fault ride-through problem. In this context, this paper proposes a second-order sliding mode as an improved solution that handle the classical sliding mode chattering problem. Indeed, the main and attractive features of high-order sliding modes are robustness against external disturbances, the grids faults in particular, and chattering-free behavior (no extra mechanical stress on the wind turbine drive train). Simulations using the NREL FAST code on a 1.5-MW wind turbine are carried out to evaluate ridethrough performance of the proposed high-order sliding mode control strategy in case of grid frequency variations and unbalanced voltage sags. & 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Keywords: Wind turbine Doubly fed induction generator Fault-ride through Second-order sliding mode
1. Introduction An increasing number of power system operators have implemented technical standards known as grid codes that wind turbines must meet when connecting to the grid [1,2]. Generally, these grid codes requirements cover many topics such as voltage operating range, power factor regulation, frequency operating range, grid support capability, and low fault ride-through capability. Indeed, grid codes dictate FRT requirements. LVRT capability is considered to be the biggest challenge in wind turbines design and manufacturing technology [3]. LVRT requires wind turbines to remain connected to the grid in the presence of grid voltage sags. The DFIG is one of the most frequently deployed large gridconnected wind turbines. Indeed, when compared with the full-scale power converter WT concept, the DFIG offers some advantages, such as reduced inverter and output filter costs due to low rotor- and grid-side power conversion ratings (25–30%) [4]. However, DFIG-based WTs are very sensitive to grid disturbances, especially to voltage dips [5].
n
Corresponding author. E-mail addresses: [email protected] (M. Benbouzid), [email protected] (B. Beltran), [email protected] (Y. Amirat), [email protected] (G. Yao), [email protected] (J. Han), [email protected] (H. Mangel).
In this context, this paper proposes to address the FRT problems using a so-called active method achieving FRT with no additional devices. The goal is to control rotor voltages and currents, to reduce the rotor overvoltages and/or overcurrents, and therefore avoid the crowbar use/activation in order to keep full DFIG control at all times to meet the FRT requirements. The implementation of classical flux-oriented vector control techniques (PI controllers) has been proven to work well for the accomplishment of the initial grid code requirements [6–9]. But, this kind of control could be easily saturated when dealing with substantial sag. Moreover, it is sensitive to the generator parameters and other phenomena such as disturbances and unmodeled dynamics [10,11]. In particular, [10] gives a critical review of control methods for LVRT compliance with DFIG. This state-of-theart review suggests the need of robust and nonlinear controller. A robust one has been proposed in [12], claiming full control in all LVRT cases. However, this was achieved with an oversized converter to accommodate rotor overvoltages and full rotor current control. It is therefore suggested that sliding mode control is a solution of choice to the FRT problem [13]. Therefore and in this particular context, this paper proposes the use of high-order sliding mode control as an improved solution that handles the classical sliding mode chattering problem and particularly avoids using additional devices and converter oversizing. Indeed, the main and attractive features of HOSMs are robustness against
0019-0578/$ - see front matter & 2014 ISA. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.isatra.2014.01.006
828
M. Benbouzid et al. / ISA Transactions 53 (2014) 827–833
Nomenclature WT DFIG FRT LVRT HOSM SOSM MPPT v ρ R Pa Ta λ Cp(λ) ω
wind turbine doubly fed induction generator fault ride-through low-voltage ride-through high-order sliding mode second-order sliding mode maximum power point tracking wind speed (m/s) air density (kg/m3) rotor radius (m) aerodynamic power (W) aerodynamic torque (Nm) tip speed ratio power coefficient wind turbine rotor speed (rad/s)
external disturbances (grid faults) and chattering-free behavior (no extra mechanical stress on the drive train) [14–16]. The proposed control strategy combines an MPPT using a second-order sliding mode for the DFIG control [17,18]. The proposed work is based on [17,18] philosophy (high-order sliding mode). In the case of [18], the control is on the turbine with a specific controller. In the case of [17], the control is on the DFIG as in this paper. However, this paper contribution is on the design of the second-order sliding mode controller based on the supertwisting algorithm that takes into account grid disturbances, in addition to the optimal power extraction [19]. This strategy presents attractive features such as chatteringfree behavior, finite reaching time, robustness and unmodeled dynamics (generator and turbine). To check the overall control strategy ride-through performance, simulations using the NREL FAST code on a 1.5-MW wind turbine are carried out in case of grid frequency variations and unbalanced voltage sags.
2. Grid-code requirements Grid-code requirements typically refer to large wind farms connected to the transmission system, rather than smaller stations connected to the distribution network. These new grid codes stipulate that wind farms should contribute to power system control (frequency and also voltage), much as the conventional power stations, and emphasize wind farm behavior in case of abnormal operating conditions of the network (such as in case of voltage dips). The most common requirements include FRT capability, extended system voltage and frequency variation limits, active power regulation, and frequency control, as well as reactive power/power factor and voltage regulation capabilities [1,2]. Grid codes main requirements regarding the addressed faults are given below. 2.1. Frequency operating range Wind power plants are required to run continuously within typical grid frequency variations between 49.5 Hz and 50.5 Hz. Fig. 1 gives an example of frequency–grid voltage variations [1]. 2.2. Low voltage ride-through Grid codes invariably require that large wind farms must withstand voltage sags down to a certain percentage of the nominal voltage and for a specified duration. Such constraints are known as LVRT requirements. They are described by a voltage versus time
Tg J K d, q s, (r) V (I) P (Q) ϕ Tem R L (M)
s
θr ωr (ωs) s p
generator electromagnetic torque (Nm) turbine total inertia (kg m2) turbine total external damping (Nm/rad s) synchronous reference frame index stator (rotor) index voltage (current) active (reactive) power flux electromagnetic torque resistance inductance (mutual inductance) leakage coefficient, s ¼1 – M2/LsLr rotor position angular speed (synchronous speed) slip pole pair number
characteristic, denoting the minimum required immunity of the wind power station to the system voltage sags (Fig. 2) [1].
3. Wind turbine modeling The wind turbine modeling is inspired from [17]. In the following, the wind turbine components models are briefly described. 3.1. Turbine model In this case, the aerodynamic power captured by the wind turbine is given by 1 P a ¼ πρR2 C p ðλÞv3 2
ð1Þ
where λ¼
Rω v
ð2Þ
The rotor power (aerodynamic power) is also defined by P a ¼ ωT a
ð3Þ
The following simplified model is adopted for the turbine (drive train) for control purposes. _ ¼ T a Kω T g Jω
ð4Þ
3.2. DFIG model The control system is usually defined in the synchronous d q frame fixed to either the stator voltage or the stator flux. For the proposed control strategy, the generator dynamic model written in a synchronously rotating frame d q is given by 8 dϕsd > > > V sd ¼ Rs I sd þ dt ωs ϕsq > > dϕ > > > V sq ¼ Rs I sq þ dtsq þωs ϕsd > > > > > V rd ¼ Rr I rd þ dϕdtrd ωr ϕrq > > > > > > V ¼ R I þ dϕrq þ ω ϕ < rq r rq r rd dt ð5Þ ϕ ¼ L I þ MI > s sd rd sd > > > > ϕsq ¼ Ls I sq þ MI rq > > > > > ϕrd ¼ Lr I rd þMI sd > > > > > ϕrq ¼ Lr I rq þ MI sq > > > > : T em ¼ pMðI I sq I rq I Þ rd sd
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Fig. 1. Frequency–voltage variations ranges [© Nordel] [1].
Fig. 2. LVRT requirements for different countries [1].
For simplification purposes, the q-axis is aligned with the stator voltage and the stator resistance is neglected. These will lead to 8 dϕsd dIrd > ¼ s1Lr V rd Rr I rd þsωs sLr I rq M > L dt dt > s > < dIrq ¼ s1Lr V rq Rr I rq sωs sLr I rd sωs M Ls ϕsd dt > > > > T ¼ pM ϕ I : em
Ls
ð6Þ
sd rq
4. DFIG-based wind turbine control 4.1. MPPT strategy
with C p max 1 k ¼ πρR5 3 2 λopt Details about the adopted strategy are given in [17]. 4.2. HOSM control strategy The DFIG-based WT control objective is to optimize the extracted power by tracking the optimal torque Topt (7). The control is a compromise between conversion efficiency and torque oscillation smoothing. The reactive power is expressed as follows. Q s ¼ V sq I sd V sd I sq
The control objective is to optimize the capture wind energy by tracking the optimal torque Topt. T opt ¼ kω2
ð7Þ
ð8Þ
Adapting (8) to our hypotheses, it comes then Qs ¼
V s ϕs V s M I Ls rd Ls
ð9Þ
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As the stator reactive power reference is zero, then ϕs ¼ (
Vs Vs -I rd_ref ¼ ωs ωs M
ð10Þ
Let us consider the following tracking errors. eIrd ¼ I rd I rd_ref
ð11Þ
eT em ¼ T em T ref Then we will have 8 dϕsd > < e_ Ird ¼ s1Lr V rd Rr I rd þ gωs Lr sI rq M _I rd_ref Ls dt > : e_ T em ¼ psLML ϕs V rq Rr I rq gωs Lr sird s r M gωs ϕsd T_ ref Ls
:
ð12Þ
If we define the G1 and G2 functions as follows. 8 dϕsd > _I rd_ref < G1 ¼ s1Lr gωs sLr I rq M Ls dt _ > : G2 ¼ psLMs Lr ϕs gωs sLr I rd gωs M Ls ϕsd T ref Thus we have 8 _ 1 1 Rr _I < e€ Ird ¼ s1L V_ rd þ G rd s Lr r _ 2 þp : e€ Γ ¼ p M ϕ V_ rq þ G em
s Ls Lr s
_
sLs Lr ϕs Rr I rq M
ð13Þ
Now, lets us consider the following second-order sliding mode controller based on the supertwisting algorithm [17–19]. 8 1 > V rq ¼ y1 þ B1 eT em 2 SgnðeT em Þ þ s1Lr Rr I rd > > > > < y_ 1 ¼ þB2 SgnðeT Þ em ð14Þ 1 M > 2 > ¼ y B e V 3 I rd SgnðeI rd Þ psLs Lr ϕs Rr I rq rd > 2 > > : y_ ¼ B Sgnðe Þ I rd 4 2 where y1 and y2 are intermediate variables and represent the control error integral.
Fig. 3. The proposed FRT control structure.
Fig. 4. 1.5-MW wind turbine illustration.
Fig. 5. Wind speed profile.
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Fig. 6. FAST wind turbine block.
Fig. 8. Grid voltage.
The above proposed second-order sliding mode control strategy for a DFIG-based WT is illustrated by Fig. 3.
5. Simulations using FAST code
Fig. 7. Simulink model.
To ensure the sliding manifolds convergence to zero in finite times, the gains B1, B2, B3, and B4 can be chosen as follows [19,20] 8 _ > G1 o Φ1 > > > > > > 4Φ ðB þ Φ Þ 2 > < B1 4psLMs Lr ϕs Φ1 ; B2 Z s2 L12 ðB1 Φ1 Þ r 1 1 ð15Þ _ > > o Φ G 2 2 > > > > > > B3 4 Φ2 ; B4 2 Z 4Φ22ðB3 þ Φ2 Þ : s Lr
s2 Lr ðB3 Φ2 Þ
In this context, it can be asserted that there exist finite times tTem and tIrd leading to (16). This means that the control objective is achieved. ( I rd_ref ¼ I rd ; 8 t 4 t Ird ð16Þ T ref ¼ T em ; 8 t 4 t T em
Simulation using FAST with Matlab-Simulinks has been carried out on the NREL WP 1.5-MW wind turbine (Fig. 4) using turbulent FAST wind data shown by Fig. 5 [21]. The wind turbine, the DFIG ratings, and control parameters are given in the Appendix. An interface has been developed between FAST and MatlabSimulinks enabling users to implement advanced turbine controls in Simulink convenient block diagram form (Fig. 6). Hence, electrical model (DFIG, grid, control system, etc.) designed in the Simulink environment is simulated while making use of the complete nonlinear aerodynamic wind turbine motion equations available in FAST (Fig. 7). 5.1. Frequency variation The proposed SOSM-based FRT strategy will be first tested regarding a frequency variation. Indeed, the studied case is a frequency fall from 50 to 48 Hz as illustrated by Fig. 8. This case corresponds to a power generation loss that could lead to a rapid decrease of the grid frequency. The FRT performances are illustrated by Fig. 9. It clearly shows that the frequency fall has practically no effect on the torque. This is confirmed by the quadratic error shown by Fig. 10. Obviously, a good tolerance is achieved for this type of fault. To assess the FRT capability enhancement of the proposed SOSM control approach, it has been compared to a classical PI
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control approach [22,23]. The achieved results as shown by Figs. 11 and 12 clearly confirm the superiority of a high-order sliding mode approach over more classical control approaches. It should be noticed that the SOSM control approach achieves the same quadratic error as a classical first-order sliding mode control.
by Fig. 17. This figure clearly shows that PI control achieves poorer LVRT performances. If the FRT performances were similar in case of frequency variation, Fig. 18 shows the superiority of a high-order mode control over a first-one in case of unbalanced voltage sags.
5.2. Unbalanced voltage sags When unbalanced sags occur (Fig. 13), very high current, torque, and power oscillations appear at double of the electrical frequency, forcing a disconnection. The LVRT performances are illustrated by Fig. 14 where an almost constant torque is achieved. Good tracking performances are also achieved in terms of DFIG rotor current (Fig. 15). Faulttolerance performances are also confirmed by the quadratic error shown by Fig. 16. To assess the LVRT capability enhancement of the proposed SOSM control approach, it has also been compared to the same classical PI control approach. The achieved results are illustrated
Fig. 9. Torque tracking performance during frequency variation: reference (green) and real (blue). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Fig. 12. Quadratic error between the reference torque and the PI control-based one (frequency variation).
Fig. 13. Grid voltage.
Fig. 10. Quadratic error between the reference torque and the SOSM control-based one (frequency variation).
Fig. 14. Torque tracking performance during unbalanced voltage sags: reference (blue) and real (green). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Fig. 11. Torque: reference (green) and real (blue). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Fig. 15. Current Ird tracking performance during unbalanced voltage sags: reference (blue) and real (green). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
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Hub height Rated power Turbine total inertia
833
84.3 m 1.5 MW 4.4532 105 kg m2
Simulated DFIG parameters Rs ¼0.005 Ω, Ls ¼0.407 mH, Rr ¼ 0.0089 Ω, Lr ¼0.299 mH, M¼0.0016 mH, p ¼2 Control parameters B1 ¼10, B2 ¼20,000, B3 ¼7, B4 ¼500 Fig. 16. Quadratic error between the reference torque and the SOSM control-based one (voltage sags).
References
Fig. 17. Quadratic error between the reference torque and the PI control-based one (voltage sags).
Fig. 18. Quadratic error between the reference torque and the first-order sliding mode control-based one (voltage sags).
6. Conclusion This paper dealt with a second-order sliding mode control of a doubly fed induction-based wind turbine for fault ride through. The SOSM-based FRT strategy has been tested regarding grid frequency variations and unbalanced voltage sags on a 1.5-MW three-blade wind turbine using the NREL wind turbine simulator FAST. The achieved results show promising successful ride-through performances over well-known PI-based control and even over classical sliding mode control (first-order). It should be particularly mentioned that the proposed SOSM control approach does not need any specific adjustments to fault ride-through purposes. Appendix A. Simulated wind turbine characteristics.
Number of blades Rotor diameter
3 70 m
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