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13Статья поступила в редакцию 13.02.11. Ред. рег. № 936 The article has entered in publishing office 13.02.11. Ed. reg. No. 936
УДК 621.311.24
ПРЯМОЕ УПРАВЛЕНИЕ МОЩНОСТЬЮ АСИНХРОННОГО ГЕНЕРАТОРА ДВОЙНОГО ПИТАНИЯ (АГДП) ВЕТРОТУРБИНЫ
М. Безза, Б-Эль-Муссаоу
ЛИИА&ТИ
Электротехнический отдел научно-технического факультета Мохаммедия - Морокко E-mail: [email protected]
Заключение совета рецензентов: 20.02.11 Заключение совета экспертов: 24.02.11 Принято к публикации: 27.02.11
В работе описана работа регуляторов Гистерезис, основанных на прямом управлении мощностью (ПУМ), применяемых для асинхронных генераторов двойного питания (АГДП). Получено развязанное активное и реактивное управление мощностью статоров. Характеристики и параметры надежности этой стратегии прямого управления мощностью изучаются с помощью MATLAB/SIMULINK.
Ключевые слова: прямое управление мощностью, контроллер Гистерезис, асинхронный генератор двойного питания, ветряная энергия.
DIRECT POWER CONTROL FOR DFIG WIND GENERATOR M. Bezza, B-El-Moussaoui
LEEA&TI Electrical Engineering Department Scientific and Technical Faculty Mohammedia - MOROCCO E-mail: [email protected]
Referred: 20.02.11 Expertise: 24.02.11 Accepted: 27.02.11
In this paper Hysterisis regulators based direct power control DPC applied for doubly fed induction generator DFIG is presented. De-coupled active and reactive stator powers regulation is achieved. The performances and the parameter reliability of this direct power control strategy are studied by simulation with MATLAB/SIMULINK.
Keywords: DPC, Hysterisis controller, DFIG, wind-energy.
Nomenclature:
d-q Park's frame index
фа (resp. q) Direct (resp. quadrature) component
ф5 (resp. r) Stator's (resp. rotor's) variable or parameter
Фге£ Reference order value
Фп! Initail value
Фйп Final value
V Voltage
I Current
ф Flux
P, Q Active, reactive power
R Resistance
P Pole pair number
L, M Phase and mutual inductance
n Mechanical rotor speed
f Friction coefficient
J Rotor inertia
ro Angular frequency of electrical network
Angular rotor frequency rosi Slip frequency
5 Angle bettwen stator and rotor flux Introduction
Wind energy is the fastest growing power generation technology in the world. According to [1], accumulated wind power capacity of the world pass from 130 GW to 220 GW between 2010 and 2014. The squirrel cage induction machine working at fixed speed and for insular power system is classically used for its weak cost and its simplicity of construction and maintenance [2]. But when it is connected to a fixed frequency network, the totality of the power is not extracted because its low sliding, and a capacitor bank designed to compensate reactive power consumption [2, 3].
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Recently these drawbacks can remediate by doubly fed induction generator DFIG operating in variable speed fixed frequency VSFF systems [4].
A DFIG consists of a wound rotor induction generator with the stator windings directly connected to a three-phase power grid and with the rotor winding mounted to a bidirectional back-to-back IGBT frequency converter [5]. A schematic diagram of a variable-speed wind turbine system with a DFIG is shown in Fig. 1. Rotor side converter RSC and the grid side converter GSC are in 2030% apparent power size [1, 3, 6]. The controller of the utility side converter regulates the voltage across the DC link for power transmission to the grid. The RSC regulates the electro-magnetic torque or active power and supplies some of the reactive power [4, 7].
Рис. 1. Ветряная турбина, запитываемая от асинхронного
генератора двойного питания (АГДП) Fig. 1. Wind-turbine driven doubly-fed induction generator (DFIG)
Рис. 2. Система отчета Парка Fig. 2. Park's reference frame
Equations of stator voltage components:
d ф
Vqs = RslqS +~JL +Ш S Ф ds .
qs S qS
dt
Equations of rotor voltage components:
d ф
= R/ +—q- + ф_ ;
qr r qr
dt
V. = R I. + ^_ш ф .
dr r dr dt rTqr
Equations of stator and rotor flux components:
Ф ás = LsIds + MIdr
Ф = LI + MI ;
qr r qr qs >
Ф.Г = LrIár + MI s ;
A new Grid Code Requirements (GCR) of wind generation systems are increasingly demanding due to the high penetration [8]. Controlling independently stator's active and reactive powers can satisfy one among this. We focuse this study on new control for RSC, alternative to the classical field-oriented control (FOC). The FOC has a complex control structure that consists of a current controller, a power controller and frame transformations. The performance of the FOC depends highly on parameter variations of the rotor and stator resistances and the inductances [5, 9].
The main objective of this work was to develop a direct controlling stator's active and reactive powers by two Hysteresis regulators. In this method we estimate Ps, Qs and 5 angle between stator and rotor flux with only stator voltages and currents, then we don't use a sensor for rotor current. Thus a system reliability and maintenance cost are improving.
Simulations results are given and discussed with MATLAB/SIMULINK to validate the proposed control strategy for10 kW DFIG wind generator.
Modeling of the DFIG
In the rotating field reference frame (Fig. 2) the model of the wound-rotor induction machine is given by the following equations [2, 5].
= LsIqs + MIqr .
Mechanical equation:
c. = + +f a.
Stator active and reactive expression:
*=
(á^ás + Vqs^qs
Q = — (v L - v^i ).
s qs ds ds qs
DPC by hysterisis controllers
The Direct Power Control is based on the same control principles as the Direct Torque Control technique. The unique difference is the directly controlled variables. In the case of the DTC, the electromagnetic torque and the rotor flux are directly controlled while in the DPC, the stator active and reactive power [6, 10].
The studied system can be shown on Fig. 3.
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Рис. 3. Принципиальная схема предлагаемого ПУМ для системы АГДП Fig. 3. Schematic diagram of the proposed DPC for a DFIG System
First of all, the relation of the stator active and reactive power on the stator and rotor fluxes is deduced:
D 3 M i i • 0
P, =--юtфtфг sino;
s 2 nLL s s r
Qs =
3 ^ 2 gL„
M
. -фr cos8
Ффп
ф . . + f Vdt
T rini J r
Considering the voltage vector constant during the application time T:
6 r = 6 . . + V T
T rjtn T rtnt r
These facts are graphically shown in Fig. 4. The application of a sufficiently large constant voltage vector in the rotor, produces simultaneously an increase of 5 and the rotor flux space vector amplitude [6].
Considering that the stator flux space vector amplitude is constant, the stator active and reactive powers only depend on the relative angle between the fluxes 5 and the rotor flux space vector amplitude. Since the stator flux space vector rotates at constant speed, any of the eight voltage vectors of the two level converter will produce a 5 angle variation.
Рис. 4. Влияние вектора напряжения статора и ротора на потоки статора и ротора Fig. 4. Stator and rotor voltage vector effect on the stator and rotor fluxes
Fig. 5 shows an increase of the terms Фrcos5 and Ф^т5 due to the effect of the active voltage vector V6. These increases produce an active power increase and a reactive power decrease. In first sector Fig. 6 summarizes effect of voltage vectors on the stator powers.
being 5 the angle between the stator and the rotor flux space vectors. The voltage dropped in the stator resistance has been neglected. The stator active and reactive power can be controlled by modifying the relative angle between the rotor and stator flux space vectors and their amplitudes.
Neglecting the dropping voltage due to the rotor resistance, the rotor flux space vector time evolution in the rotor reference frame, can be calculated by means of the following expression:
Рис. 5. Влияние вектора напряжения V6 на активную и реактивную мощность Fig. 5. Effect of V6 voltage vector, on the active and reactive power
Рис. 6. Векторы напряжения и их влияние на активную и реактивную мощность статора Fig. 6. Voltage vectors and their effect on the stator active and reactive power
International Scientific Journal for Alternative Energy and Ecology № 1 (93) 2011
© Scientific Technical Centre «TATA», 2011
On the other hand, the angle 5 between the rotor and the stator flux space vectors can be expressed as a function of the active and reactive power:
8 = tan
P
M 3 M V2 - Q
. 2 aLsLr ffl,
Рис. 7. Отклик Qs для Qsref Fig. 7. Qs response for a steps of Qsref
Рис. 8. Отклик Ps для Qsref Fig. 8. Ps response for a steps of Qsref
Case b:
We maintain Qsref at 7 kVAR and two steps for Psref are introduced at t = 2 s (from -7.5 kW to 10 W) and (from -10 kW to 6 kW) at t = 4 s.
Then we can deduce rotor flux position by know the one of stator flux, and we don't use a sensor for a current rotor.
Simulations
So as to really evaluate the performances of this direct regulation strategy of active and reactive power stator, we test the responses in following cases:
Case a:
We applicate an reactive power steps from 8 kVAR to 6.5 kVAR at t = 2.5 s and from 6.5 kVAR to 7.5 kVAR at t = 4 s (Psref = 7.5 kW).
-5000 -6000 -7000 -8000 -Э000 ■10000
-11000
Ps(W)
tO)
1.5
2.5
3.5
4.5
Рис. 9. Отклик Ps для Psref Fig. 9. Ps response for steps of Psref
Рис. 10. Отклик Qs для Psref Fig. 10. Qs response for a steps of Psref
Case c:
In the third case, we varying Rs of ±50% at t = 2s and
t = 4s (Psref = -8.5 kW; Qsref = 7 kVA)
Rs
0.5K.S
tú)
2.5
3.5
4.5
Рис. 11. Изменения Rs Fig. 11. Rs variations
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Рис. 12. Отклик Ps для изменений Rs Fig. 12. Ps response for variations of Rs
Рис. 13. Отклик Qs для изменений Rs Fig. 13. Qs response for variations of Rs
3. Arnaud Davigny Participation aux services système de fermes d'éoliennes à vitesse variable. Thèse de doctorat université des sciences et technologies de Lille décembre 2007.
4. Forchetti D., Garcia G., Valla M.I. Vector control strategy for a doubly-fed stand-alone induction generator // Industrial Electronics Society, IEEE 2002 28th Annual Conference of the IEEE journal, Vol. 2, pp. 0_1-VI, 2002.
5. Sung-Tak Jou, Sol-Bin Lee, Yong-Bae Park, and Kyo-Beum Lee. Direct Power Control of a DFIG in Wind Turbines to Improve Dynamic Responses // Journal of power electronics vol. 9, no. 5, september 2009. P. 781-790.
6. Abad biain G. Predictive direct control techniques of DFIG for wind energy generation applications. PhD thesis Faculty of Engineering Mondragon Unibertsitatea julio 2008.
7. Hui J. An Adaptive Control Algorithm for Maximum Power Point Tracking for Wind Energy Conversion Systems. Thesis of Master of Science Queen's UniversityKingston, Ontario, Canada December 2008.
8. Arbi J. et al. "Control of a DFIG-based wind system in presence of large grid faults: analysis of voltage ride through capability". 9th international conference. Electrical power quality and utilisation Barcelona October 2007.
9. Salloum G. Contribution à la commande robuste de la MADA. Thése de doctorat de l'INP Toulouse Mars 2007.
10. Pena R., Clare C.J., Asher G.M. Doubly fed induction generator using back-to-back PWM converters and its application to variable speed wind-energy generation // IEE Proc. Electr. Power Appl., Vol. 143, No. 3, May 1996.
Conclusion
After introducing the mathematical model of the DFIG, we have presented a direct stator active and reactive powers control .angular rotor flux position is estimated without a sensor for rotor current. Independently active and reactive powers control is verified and robust to parameters variation of the machine as confirmed by the resulting simulations. However the DPC controller presents the drawback mainly active and reactive ripples.
References
1. Gabriele Michalke. Variable Speed Wind Turbines - Modelling, Control, and Impact on Power Systems PhD thesis Universtat Darmstat, 2008.
2. Belfedal C. et al. Comparison of PI and Direct Power Control with SVM of Doubly Fed Induction Generator // Journal of electrical & electronics engineering. 2008. Vol. 8, No. 2. P. 633-641. Istanbul university.
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Appendix: DFIG-parameters
PN = 10 kW
VN = 220V/380V-50Hz
IN = 15/8.6 A
nN = 1440 rpm
P = 2
RS = 1.2 П
Rr = 1.8 П
LS = 0.155 H
Lr = 0.1568 H
M = 0.15H
J = 0.2 Kg m2
f = 0.001 Nmsrd'
International Scientific Journal for Alternative Energy and Ecology № 1 (93) 2011
© Scientific Technical Centre «TATA», 2011
