© Journal of Hydrocarbons Mines and Environmental Research http://jhmer.univ-rennes1.fr
Volume 2, Issue 1, June 2011, 13-18
Variable speed doubly fed induction generators power control with wind turbine maximum power point tracking Saïd Drid *, Abdesslem Makouf and Mohamed-Saïd Naït-Saïd L.S.P.I.E Laboratory, Electrical Engineering Department, University of Batna, Rue M.E.H Boukhlof, Algeria Received: 06 July2011
Accepted after revision: 11 August 2011
Published online: 13 August 2011
Abstract: This paper deals with a control intended for doubly fed induction generator. A simple method of tracking the maximum power points and forcing the system to operate close to these points is presented. The created decoupling control between active and reactive stator power allows keeping the power factor close to unity. The power controllers are designed from the Lyapunov theory. The asymptotic stability of the overall system is theoretically proven and simulation results confirm the feasibility and the effectiveness of the proposed control. Keywords: doubly fed induction generator wind power, wind turbine, Lyapunov method, decoupling control, variable speed, method of tracking the maximum power points. Commande de puissance d’un générateur double alimenté à vitesse variable avec poursuite de la puissance maximale de la turbine éolienne Résumé : Cet article traite la commande d’un générateur asynchrone double alimenté entraîné par une turbine éolienne. Une méthode simple de poursuite de la puissance maximale est présentée. Le découplage entre la puissance active et réactive du stator permet de garder le facteur de puissance près de l'unité. Les contrôleurs de puissance sont conçus selon la théorie de Lyapunov. La stabilité asymptotique du système global est théoriquement prouvée et les résultats de la simulation confirment l'efficacité de la commande proposée. Mots clés: générateur asynchrone double alimenté, énergie éolienne, turbine, méthode de Lyapunov, commande découplée, vitesse variable, méthode simple de poursuite de la puissance maximale.
1. Introduction Wind energy is one of the most rapidly growing sources of electricity generation all over the world. At the beginning of 2004, the total installed capacity of Wind Energy all over the world reached 39 GW with an annual growth rate of about 30% (Ackermann, 2005). It is predicted that 12% of the total world electricity demands will be supplied from wind energy by 2020 (Millais and Teske, 2005). It is recognized as being a means ecological and economic to produce electricity. At the same time, there was a fast development relating the wind turbine technology (Ekanayake et al., 2003; Datta and Ranganathan, 2002; Tapia et al., 2003). In the area of wind power generation systems, where the input power varies considerably, variable-speed generation (VSG) is more interesting than fixed-speed systems. In these systems, a maximum power point tracker (MPPT) adjusts a system quantity to maximize turbine power output (Wang and Chang 2004; Huynh and Cho, 1996). The generator that operates directly at the variable speed drive is extremely attractive. This is possible particularity for small machines where the rotor speed * Corresponding author:
[email protected] (S. Drid) ISSN: 2107-6502
is high. The direct drive eliminates the mechanical gear altogether. This, result in multiple benefits like: lower weight, reduced noise and vibration and lower power losses by several percent (Drid et al., 2009 and Miller et al., 1997). This can be carried out using the synchronous generators provided that a static frequency converter is used to connect the machine to the grid. Another solution uses a double fed induction generator (DFIG) where the rotor is fed by a variable ac voltage sources which can be controlled in frequencies according to variable speed of the rotor shaft due to the variation of speed wind. Then the electric power at constant frequency is simply provided from the stator of the machine. Consequently, the use of the DFIG can give the increasing attention for the wind power generation. Particularly, the DFIG advantage is that the rotor is controlled from a reduced power converter, while the simpler vector control can be utilized to control the stator power-factor and the power flow. Capacities to produce electricity with power-factors close to unit which would reduce the system cost comparatively to using the condensers (Drid et al., 2006; Datta and Ranganathan, 2002; Leithead et al., 1995) The main objective of this paper is the power control of the doubly fed induction wind turbine generator
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(DFIWTG) using Lyapunov (Khalil, 1996) and the 3. Dfig modeling maximization of the wind power capture with unknown Its dynamic model expressed in the synchronous turbine power coefficient characteristics. reference frame is given by the following equations. Voltage equations: di s di + M. r + jL s ωs i s + jMωs i r dt dt di s di r ur = R r i r + L r +M + jL r ωr i r + jMωr i s dt dt us = R s i s + L s
where: γ4 =
γ1 =
(1)
1 M M ; γ2 = ; γ3 = ; and σTs σTs L r σTrL s
1 . σTr
The electromagnetic torque is: Fig. 1. Turbine powers various speed characteristics for different wind speeds, with indication of the maximum power tracking curve. Les caractéristiques puissance-vitesse de rotation pour différentes vitesses du vent, avec indication de la puissance maximum.
Ce =
[ ]
PM ℑm φs φr* σL sL r
and its associated Power equations is:
{ } { }
2. Wind and wind turbine modeling
Ps = ℜe us .is*
The wind model is based on a conventional Weibull Q = ℑm u .i * s s s probability distribution function of the wind speed. Several models for power production capability of wind 4. Control strategy turbines have been developed and can be found throughout the bibliography (Miller et al., 1997; Tanaka di s = λ u r + fd ,q et al., 1997; Leithead et al., 1995). The mechanical From Eq. (1) we can write: dt power, captured by a wind turbine, depends on its power coefficient given for a wind velocity v and can be where: represented by: 1 Pmec = C p ρπR 2 v 3 2
(1)
(2)
(3)
(4)
fd =
L L ω − M 2 ωr 1 1 M i rd u sd − i sd + ( s r s )i sq + ωi rq − σL s σTs σL s L r σL s Tr
fq =
L L ω − M 2 ωr 1 1 M u sq − i sq − ( s r s )i sq − ωi rd − i rq σL s σTs σL s L r σL s Tr
where ρ and R correspond to the air density and the radius of the turbine propeller, respectively. The power M coefficient can be described as the portion of mechanical where, λ = − σ .L s .L r power extracted from the total power available from the wind, and it is unique for each turbine. This Cp power coefficient is generally defined as a function of the tip- Stator Voltage constraint speed-ratio λ which, in turn, is given by: For computing simplicity, let us consider the stator voltage constraint given as follows in dq-axis. ωR (2) λ= v ⎧usq = us (5) where ω correspond to the speed of the wind turbine. ⎨u = 0 ⎩ sd The power generated by any wind turbine shall have the characteristics shown similar to what is shown in Fig. 1. We can see that the maximum power and the rotating speed which can be extracted from a wind turbine vary Power law control with the wind speed. Hence the speed of the turbine Separating the real-part and the imaginary-part of Eq. should be set at any point on the line of optimal power. (4), one will have: J. hydrocarb. mines environ. res., ISSN: 2107-6502, Volume 2, Issue 1, June 2011, 13-18
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⎧ di sd ⎪⎪ dt = fd + λ u rd ⎨ di ⎪ sq = f + λ u q rq ⎪⎩ dt
(6)
The active and reactive powers, according to (5), are given respectively as: Ps = us .i sq
(7)
Q s = us .i sd
1 1 (Ps − Psref ) 2 + (Q s − Q sref ) 2 > 0 2 2
be used: the gradient method, the estimate method or reconstitution, and geometrical or heuristic methods. If the aerofoil is well-known the MPPT implementation on DSP is easier by reconstruction method. But in our case the aerofoil is not known; to make converge the power at the optimal point, the rules to be established depend on the variations of turbine power: ∆Pt = Pt (k ) − Pt (k − 1)
(8)
(14)
The principle thus consists in increasing or decreasing the stator power reference with a quite selected step. Psref (k ) = Psref (k − 1) ± ∆Ps
Let us formulate a Lyapunov function as follows: V1 =
15
(15)
The rules can be summarized below for a constant speed of wind for example: ∆Pt > 0 Increase Psref
Its derivative function is: & & & = (P − P )(P& − P& V 1 s s sref sref ) + (Q s − Q sref )(Q s − Q sref )
(9)
∆Pt < 0 Decrease Psref
The power reference is updated by the MPPT controller at every time step h. The above mentioned actions bring the operating point toward Pt_max (turbine power) by increasing or decreasing the stator power reference stepV&1 = ( Ps − Psref )(u s f q + λ .u s u rq − P&sref ) (10) by-step. This tracking methodology in the control + (Qs − Q sref )(u s f d + λ.u s u rd − Q& sref ) scheme is called the perturbation and observation method (P&O) method. (Huynh and Cho, 1996; Wang Ex(10) can become negative definite, if we define the and Chang, 2004). following control law: Substituting Eq. (6) and Eq. (7) in Eq. (9) gives:
1 ⎧ & ⎪u rd = λ.u ( −u s fd + Q sref − K 2 (Q s − Q sref )) ⎪ s (11) ⎨ ⎪u rq = 1 ( −u s fq + P& sref − K 1 (Ps − Psref )) ⎪⎩ λ.u s
Indeed, Eq. (11) replaced in Eq. (10) gives the required result as: 2 & = − K ( P − P )2 − K ( Q − Q V 1 1 s 2 s sref sref ) < 0
(12)
where; K1 > 0 and K2 > 0 Then Eq.(12) is asymptotically stable. Hence, using the Lyapunov theorem (Khalil, 1996), one can conclude Fig. 2. that: ⎧lim( P − P ) = 0 s sref ⎪⎪ t → +∞ ⎨ ⎪lim( Q s − Q sref ) = 0 ⎪⎩ t → +∞
(13)
The MPPT control Algorithm. L’algorithme de commande MPPT.
A flowchart of the P&O method is illustrated in Fig. 2, which shows how the operating point moves toward the maximum power point, periodically increasing or decreasing the stator power references by comparing power quantities between the present state and the past history turbine power.
MPPT Control Strategy For operating at variable speed in order to recover the maximum of power of the turbine several techniques can J. hydrocarb. mines environ. res., ISSN: 2107-6502, Volume 2, Issue 1, June 2011, 13-18
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Fig. 3. The MPPT control Algorithm. L’algorithme de commande MPPT.
5. Simulation tests Fig. 3 illustrates a general block diagram of the suggested DFIG control scheme. As it is shown, one can see that the stator powers are controlled. Note that the placement of the estimator-block which estimate from the armatures terminal measurements, first the stator voltage in term of modulus and position, respectively us, ρs and ρr, and second the feedback functions fd, fq.
Simulation results The obtained results are organized according to the following specifications. The Figs. 5 and 6 present the turbine speed and the active power reference profiles resulting of the MPPT and injected into the grid. Figs. 7 and 8 present the machine powers errors versus time from where one can clearly observe the performed tracking of the designed control. Figs. 9 and 10 present respectively current and voltage inside rotor with weak magnitudes due to the control of slip power. Fig. 11 presents the stator current.
Timetable reference profiles The machine and wind turbine data are given in Appendix 1. In order to validate our approach, the digital simulation has been realized using the general blockdiagram specified by the Fig. 3. Assume to have a timetable of different operating conditions illustrated by the basic profiles defined in Fig. 4. The reactive power is fixed at 0 VAR.
Fig. 5.
Speed turbine according to the MPPT. Turbine de vitesse suivant l’algorithme MPPT.
Fig. 4.
Variable wind speed profiles.
The Fig. 12 presents Wind turbine output power characteristics with MPP tracking process. For a variable wind Fig. 12 shows an operation with optimum capacity. We note oscillations around the optimal points as in Fig. 6.
Profils de vitesse du vent.
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Fig. 6. Stator active power injected in the grid according to the MPPT.
Fig. 9.
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Rotor current response. Réponse du courant rotorique.
Puissance active du stator injectée dans le réseau suivant l’algorithme MPPT.
Fig. 7.
Stator active power error. Erreur de la puissance active du stator.
Fig. 8.
Fig. 10. Rotor voltage response. Réponse de la tension rotorique.
Stator reactive power error. Erreur de la puissance réactive du stator.
Fig. 11. Stator current response. Réponse du courant statorique.
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Fig. 12. Wind turbine power according to MPP tracking process. Puissance de turbine de vent suivant l’algorithme MPPT
6. Conclusion In this paper, a control approach of a doubly fed induction generator grid-connected wind energy conversion system, incorporating a maximum power point tracker (MPPT) for dynamic power control has been presented. The obtained results demonstrate that the proposed DFIG system control operating at the variable speed may be considered as an interesting way for problems solution in renewable energy area.
References Ackermann, T., 2005. Historical Development and Current Status of Wind Power, in: John Wiley and Sons (Eds), Wind Power in Power Systems, 7-23. Datta, R., Ranganathan, V.T., 2002. Variable-Speed Wind Power Generation Using Doubly Fed Wound Rotor Induction Machine -A Comparison With Alternative Schemes. IEEE Transaction on energy conversion, 17 (3), 414-421. Drid, S. Naït-Saïd, M.S., Makouf, A., Tadjine, M., 2009. The Doubly Fed Induction Generator Robust Vector Control based on Lyapunov Method. Transactions on Systems, Signals and Devices, Issues on Power Electrical Systems, 4 (2), 237-250. Drid, S., Naït-Saïd, M.S., Makouf, A., Tadjine, M., 2006. Doubly fed induction generator modeling and scalar controlled for supplying an isolated site. Journal of Electrical Systems, 2 (2), 103-115. Ekanayake, J.B., Holdsworth, L., Wu, X.G., d Jenkins, N., 2003. Dynamic Modeling of Doubly Fed Induction Generator Wind Turbines. IEEE Transaction on Power system, 18 (2), 803-809. Huynh, P., Cho B.H., 1996. Design and analysis of a
Microprocessor Controlled Peak-power-Tracking System. IEEE Transaction Aerospace and Electronic Systems, 32 (1), 182–190. Khalil, H., 1996. Lyapunov-Based Design, in: Prentice Hall (Eds.), Nonlinear systems, Upper Saddle River, 577-640. Leithead, W.E., Rogers, M.C.M., Leith, D.J., Connor, B., 1995. Progress in control of wind turbines. 3rd Europe. Contr. Conf., Rome, Italy, 1556–1561. Millais, C., Teske, S., 2005. WIND FORCE 12. A blueprint to achieve 12% of the world's electricity from wind power by 2020. Renewable Energy House, 1-52. Miller, A., Muljadi, E,. Zinger, D., 1997. A variable speed wind turbine power control. IEEE Transaction Energy Conversion, 12 (2), 181–186. Tanaka, T., Toumiya, T., Suzuki, T., 1997. Output control by hill-climbing method for a small scale wind power generating system. Renewable Energy, 12 (4), 387–400. Tapia, A., Tapia, G., Ostolaza, J. X., Sáenz, J. R., 2003. Modeling and Control of a Wind Turbine Driven Doubly Fed Induction Generator. IEEE Transaction on energy conversion, 18 (2), 194-204. Wang, Q., Chang L., 2004., An Intelligent Maximum Power Extraction Algorithm for Inverter Based Variable Speed Wind Turbine Systems. IEEE Transaction Power Electronics, 19 (5), 242-1249.
Appendix The Induction motor with wound rotor data: Rated values: 4 kW ; 220/380 V-50 Hz ; 15/8.6 A Parameters: Rs (Stator resistance): 1.2 Ω Rr (Rotor resistance) 1.8 Ω Ls (Stator inductance) : 0.158 Henry Lr (Rotor inductance): 0.156 Henry M (Mutual inductance): 0.15 Henry J (Rotor inertia): 0.07 kg.m2 ff (Friction coefficient) : 0.00 I.S. Wind turbine data : Wind turbine Type : horizontal axis Rotor diameter : 4000 mm Blade numbers: 3 Rotation : Free (360°) Maximum power : 4 kW
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