Recent Developments of Electrical Drives - Part 40 pot

III-2.3. Maximum Wind Power Control in Wind Diesel System 391 E CC and E CD design the electromotive force when the battery is completely charged and discharged respectively. The battery is represented by avoltage source in serieswith a resistanceand capacitance. The internal resistance, R bat , is assumed to be constant and the internal voltage, E bat , varies with state of charge. The internal terminal voltage, V s , in discharge and charge operations, is given respectively by [14]: V s = E bat − I bat R bat (23) V s = E bat + I bat R bat (24) I bat is the battery current. In steady state, the terminal voltage of the capacitance is negligible. In our case the battery current will have two different expressions: I discharge = E bat 2R bat − 1 2  E 2 bat R 2 bat − 4P out R bat (25) I charge =− E bat 2R bat + 1 2  E 2 bat R 2 bat + 4P out R bat (26) P out is the power delivered or received by the batter y. The state of charge of the battery may be calculated by: C SOC discharge = η disch C cap ∗ 3600  t t=0 I discharge dt (27) C SOC charge = η ch C cap ∗ 3600  t t=0 I charge dt (28) C cap is the capacity of the battery in Ampere-hours and (η disch , η ch ) are efficiency factors of discharge and charge operations respectively. The C soc can have a value between 0% and 100%. The 0% corresponds to a fully dis- charged state and 100% correspond to a fully charged state. Control strategy Unfortunately, the wind energy is not completely predictable and it fluctuates rapidly. As a result it is difficult to balance the system. For efficient capture of wind power, turbine torque or turbine speed should be controlled to follow the optimal tip-speed-ratio (TSR). Our study is based on the current control of the wind generator (Fig. 1). Assuming that the permanent magnet generator torque is proportional to the machine cur rent, the control structure allows the torque and rotational speed to be controlled. The reference current of the wind generator rectified current is calculated for steady state points where the turbine torque and the generator torques are equals. J dω dt = T t − T g (29) 392 El Mokadem et al. 0 10 20 30 40 50 60 0 50 100 150 200 250 300 Torque (Nm) Shaft speed (rd/s) v 1 < v 2 < v 3 < v 4 v 1 v 2 v 3 v 4 A C D B ORC Figure 4. Wind turbine torque characteristics. J is the inertia in kgm 2 . T g = KI (30) K is a constant, it depends on generator characteristics. I = T t K (31) If the turbine torque changes when the wind speed increases, the system will be able to accelerate more quickly to the next steady state which corresponds to the maximum power points tracking (MPPT) (Fig. 4). We can see that the optimal operating points are different for every wind speed v i . Consequently, the wind maximum power transfer is ensured by the operations points following thecurvecontrolled with MPPT unit (Fig. 5). In ourapproach,the MPPT function is realized by a step down converter. In order to control the diesel generator, we have considered two possibilities. For the first case, we assume that the diesel generator operates at constant power and constant speed. In this case, the diesel generator is started on when the terminal voltage of batteries falls bellow a minimum value E batmin and the wind power is not sufficient to supply the load. The diesel engine should be started to re-charge the battery and supply the load. In the contrary case, if the terminal voltage of batteries exceeds a maximum value E batmax and the wind power is sufficient to supply the load, the diesel generator is slow down. The second possibility: the diesel generator is controlled using the power-speed charac- teristics. A power sensor detects the load power and produces reference correction speed that is compared to actual speed signal. A speed controller provides signal for adjustment of the fuel injection unit, feeding the engine prime mover [16]. III-2.3. Maximum Wind Power Control in Wind Diesel System 393 0 10 20 30 40 50 60 0 3000 4000 5000 6000 7000 8000 Power (W) Shaft speed (rd/s) v 1 v 2 v 3 v 4 A C D B ORC 2000 1000 v 1 < v 2 < v 3 < v 4 Figure 5. Wind turbine power characteristics. Desired speed ω max ω min P min P max Estimated power Figure 6. Speed vs. power characteristics. Actual speed is adjusted according to the power required by the load in steady state operation (Fig. 6). The speed is relatively low when power demand is not important. When the load power increases, the diesel governor controls the speed evolution according to the linear law designed for this purpose (Fig. 6). Simulation results The complete model of thesystemhasbeenimplemented on Matlab-Simulink environment. In our study, we have used the wind speed profile depicted in Fig. 2. According to Figs. 7 and 8, we can see that the wind turbine operates at its most efficient operating points for different values of wind speed. Fig. 9 presents the outputcurrent of the wind generator. We can conclude that thecurrent follows well the reference generated according to the MPPT law. 394 El Mokadem et al. 7000 6000 5000 4000 3000 2000 1000 0 0 5 10 15 20 25 30 35 Shaft speed (rd/s) Power (W) Figure 7. Simulation of the maximum regime characteristics (MPPT) for a given wind turbine. 150 100 50 0 0 5 10 15 20 25 30 35 Shaft speed (rd/s) Torque (Nm) 250 200 Figure 8. Simulation of the torque characteristics for a given wind turbine. Fig. 10 presents the diesel generator speed and its reference. This reference is a function of the power required by the load and the wind fluctuations. Because of the diesel engine inertia, the diesel generator speed cannot follow the dynamics of this reference. Conclusion The purpose of our work is to study and develop a maximum wind power control using torque characteristic for a wind diesel system with battery storage. III-2.3. Maximum Wind Power Control in Wind Diesel System 395 wind generator rectified current references current 0 0 24 6 810 12 14 16 18 20 5 10 15 20 25 30 35 Current (A) Time (s) Figure 9. Wind generator rectified current of the wind generator and its reference. Estimated reference speed Actual speed Time (s) 0 24 6 810 12 14 16 18 20 0 20 40 60 80 100 120 Speed(rd/s) Figure 10. Diesel generator speed and its reference. Our study is based on the current control of the wind generator. We have assumed that the permanent magnet generator torque is proportional to the machine current; the control structure allows the torque and rotational speed to be controlled. Moreover, the dieselgeneratorpower contributionisafunction of the wind power and the load variations. When wind resource is not abundant, the diesel is started on to supply the load, the excess of energy could be dissipated by the dump load. Also, when it is necessary, the batteries take over to supply the load. 396 El Mokadem et al. We have point outthat this control strategy, basedon the maximum power point tracking, could ensure the maximum conversion of the wind power. References [1] C.V. Nayar, S.J. Philips, W.L. James, T.L. Pryor, D. Remer, Novel wind/diesel/battery hybrid energy system, Solar Energy, Vol. 51, No. 1, pp. 65–78, 1993. [2] K.B. Saulnier, R. Reid, “Mod´elisation, simulation et r´egulation d’un r´eseau Eolien/Diesel autonome”, Rapport IREQ4340, Institut de Recherche de l’Hydro-Quebec Varennes, P.Q., 1989, Qu´ebec. [3] R.B. Chedid, S.H. Karaki, C. El-Chamali, Adaptive fuzzy control for wind-diesel weak power systems, IEEE Trans. Energy Convers., Vol. 15, No. 1, pp. 71–78, 2000. [4] C. Nichita, D. Luca, B. Dakyo, E. Ceanga, Large band simulation of the wind speed for real time wind turbine simulators, IEEE Trans. Energy Convers., Vol.17,No.4,pp.523–530,2002. [5] M. El Mokadem, N. Nichita, G. Barakat, B. Dakyo, “Control Strategy for Stand Alone Wind- Diesel Hybrid System Using a Wind Speed Model”, Electrimacs Proceeding CD-ROM, Mon- treal, 2002. [6] M. El Mokadem, “Structure d’un conditioneur depuissance pour un syst`eme ´eolien-diesel”, JCGE’03 Proceedings CD-ROM, Saint-Nazaire, June 2003. [7] C. Nichita, “Etude et d´eveloppement de structures et lois de commande num´eriques pour la simulation en temps r´eel d’actionneurs. Application `alar´ealisation d’un simulateur d’a´erog´en´erateur de 3 kW”, Th`ese de Doctorat, Universit´e du Havre, 1995. [8] D. Le Gourieres, Energie ´eolienne, th´eorie, conception et calcul pratique des installations, Eyrolles, Paris, France, 1982. [9] J.F. Walker, N. Jenkins, Wind Energy Technology, John Wiley & Sons, Inc., Chichester, UK, 1997. [10] L.L. Freris, Wind Energy Conversion System, England: Prentice Hall International Ltd., 1990. [11] M.J. Ryan, R.D. Lorenz, “A Novel Controls-Oriented Model of a PM Generator with Diode Bridge Output”, Proceedings EPE, Trondheim, 1997, pp. 1.324–1.329. [12] M.N. Eskander, Neural network controller for apermanent magnet generator applied in a wind energy conversion system, Renewable Energy, Vol. 26, pp. 463–477, 2002. [13] R. Hunter, G. Elliot, Wind-Diesel Systems, New York: Cambridge University Press, 1994. [14] G.S. Stavrakakis, G.N. Kariniotakis, A general simulation algorithm for the accurate assess- ment of isolated diesel-wind turbines systems interaction, IEEE Trans. Energy Convers., Vol. 10, No. 3, pp. 577–590, 1995. [15] M.J. Hoeijmakers, “The (In)Stability of a Synchronous Machine with Diode Rectifier”, Proceedings of the International Electrical Machines Conference, UK, September 1992, pp. 83–87. [16] W. Koczara, J. Leonarski, R. Dziuba, “Variable Speed Three Phase Power Generation Set”, EPE 2001, Graz, Austria, August 2001. III-2.4. STUDY OF CURRENT AND ELECTROMOTIVE FORCE WAVEFORMS IN ORDER TO IMPROVE THE PERFORMANCE OF LARGE PM SYNCHRONOUS WIND GENERATOR D. Vizireanu 1 , S. Brisset 1 , P. Brochet 1 , Y. Milet 2 and D. Laloy 2 1 L2EP, Ecole Centrale de Lille, Cit´e Scientifique, BP 48, 59651 Villeneuve d’Ascq Cedex, France darius.vizireanu@ec-lille.fr, stephane.brisset@ec-lille.fr, pascal.brochet@ec-lille.fr 2 Framatome ANP, 27 rue de l’Industrie, BP 189, 59573 Jeumont Cedex, France daniel.laloy@framatome-anp.com, yves.milet@framatome-anp.com. Abstract. The paper presents a comparison between sinusoidal and trapezoidal waveforms in order to reduce the torque ripple and the power to grid fluctuation for large direct-drive PM wind generator. Trapezoidal waveform brings 28% higher power density but also two major drawbacks: necessity to vary the DC bus voltage and requirement for an additional filter on the DC bus. Introduction During last decades, an important development of permanent magnet machines domain has been observed, due to the improvement of the permanent magnet characteristics and the occurrence of new power electronic components. The magnets have allowed to eliminate the excitation and the slip rings, and consequently to increase the power of the machines. The new power converters using IGBT or IGCT technologies allow supplying the machines with different waveform voltages and different frequencies, depending on the application. In the present, permanent magnet synchronous machines are used in large power ap- plications as high torque low speed systems for wind energy generators. For these kinds of systems, an important parameter is the electromagnetic torque, and the interest is to minimize torque oscillations which cause lower mechanical stability, audible noise, and accelerated aging of the machine due to vibrations. Inthismoment,theeffortsareconcentrated toincreasethe powerof PMsynchronousgen- erators. But aspecial attention should bepaid to the conceptionofthe power conver ters. The power electronic devices have a certain limit, and special architectures are used to increase the voltage and current capability. Multi-level structures are used to obtain higher voltage capability. To obtain higher rated current, a solution is to do parallel connection of several converters, whichcorrespondstoanincreaseofthenumberofthe legs,or toanincrease ofthe phasenumberofthemachine.Aresultingadvantageisthepossibility toobtainacertainmod- ularity, which allows facilities for the fabrication process, transportation, and maintenance. S. Wiak, M. Dems, K. Kom ˛ eza (eds.), Recent Developments of Electrical Drives, 397–413. C  2006 Springer. 398 Vizireanu et al. The goal of this paper is to study the influence of the electromotive force (e.m.f.) and current waveforms over the electromagnetic torque and to search an optimum topology of the PM synchronous machine (the shape of the magnet and the winding) and associated converter in order to obtain minimum torque pulsation and highest efficiency. System description The system that will be studied is a direct-drive wind generator (Fig. 1). The machine topology is an axial-flux machine with two rotor discs and one inner stator with teeth (Fig. 2). Refs. [1,2] suggest that this architecture has higher power density than the radial-flux PM machine. The converter used is a back-to-back converter, which consists in two PWM converters, a rectifier, and an inverter (Fig. 3). The capacitor from the intermediate circuit is an advantage of this topology, allowing a separate control for both converters and the possibility to compensate asymmetries that appears on both sides. The rectifiercontrolstrategy realizes avector control of thegenerator, Grid Power Converter Figure 1. Direct-drive wind turbine system with PM synchronous generator. Figure 2. Generator’s topology. Figure 3. The back-to-back PWM-VSI power converter. III-2.4. Comparison Between Sinusoidal and Trapezoidal Waveforms 399 while the inverter controls the energy transfer to the grid. The chopper connected between the converters allows the control of the DC bus voltage and current during breaking regime of the generator. The energy is dissipated over a breaking resistor. The two converters are decoupled at the level of the DC bus. That will permit to reduce the studied system: from the shaft of the generator until the DC bus. To avoid over voltages and protect the transistors, the control of the inverter imposed a constant DC voltage. If the DC voltage is maintained constant, the DC current waveform will give an indication about the powertransfer.Reducingharmonic content of the DC buscurrent will allow reducing the size of the DC bus filter and the har monic filter at the output of the converter. As mentioned before, the goal is to reduce torque oscillations, but also to observe the influence over the quality of the DC bus current. At constant speed, low level of DC bus current harmonics means reduced power fluctuation at the output. Analytical approach In this part, the influences of e.m.f. and current waveforms over the electromagnetic torque are analytically studied, even if the waveforms are not practically feasible. Sinusoidal waveform For a three-phase PM synchronous machine, without damping, the electromagnetic torque has the following expression: T elmg = P elmg  = 1  · 3  i=1 e i ·i i (1) where  is the mechanicalspeed, e i is thee.m.f. corresponding to phase i, andi i is thephase current. Using a FFT for the e.m.f, e 1 = ∞  k=0 E 2k+1 · cos[(2k + 1)θ ] e 2 = ∞  k=0 E 2k+1 · cos  (2k + 1)  θ − 2π 3  e 3 = ∞  k=0 E 2k+1 · cos  (2k + 1)  θ − 4π 3  (2) where θ = ω ·t. Imposing sinusoidal currents in phase with the e.m.f, i 1 = I · cos [ (2k + 1)θ ] i 2 = I · cos  (2k + 1)  θ − 2π 3  i 3 = I · cos  (2k + 1)  θ − 4π 3  (3) 400 Vizireanu et al. The electromagnetic torque could be written as: T elmg = 3E 1 · I 2 · + 3 · I 2 · · 3  i=1 [(E 6k−1 + E 6k+1 ) cos(6kθ)] (4) It is easy to observe that the electromagnetic torque contains only sixth or multiple by six harmonics. The torque harmonics are proportional with the current amplitude. If (6k − 1) and (6k + 1) harmonics have opposite phases, the effect will be to reduce the torque oscillation. Voltage harmonics can be reduced using different winding techniques, but it is impossible to completely eliminate them. But controlling the machine’s phase currents, torque ripple minimization can be realized by injecting current harmonics. When the currents contain odd harmonics, their expressions are: i 1 = ∞  k=0 I 2k+1 · cos[(2k + 1)θ ] i 2 = ∞  k=0 I 2k+1 · cos  (2k + 1)  θ − 2π 3  i 3 = ∞  k=0 I 2k+1 · cos  (2k + 1)  θ − 4π 3  (5) Then, the electromagnetic torque becomes: T elmg = 3 2 · (E 1 I 1 + E 3 I 3 + E 5 I 5 + E 7 I 7 ) + 3 2 · (E 1 I 5 + E 1 I 7 + E 3 I 3 + E 5 I 1 + E 7 I 1 ) ·cos(6kθ ) + 3 2 · (E 5 I 7 + E 7 I 5 ) ·cos(12kθ ) +··· (6) It is possible to reduce the 6k torque harmonics by injecting current harmonics as sug- gested in(6).TheDCcomponentofthetorque can be increased using odd current harmonics in phase with the same order e.m.f. harmonics. Equation (6) showstheinterestoftrapezoidal waveforms to increase the mean value of the torque. Trapezoidal waveforms The interest to study PM machines with trapezoidal waveforms of the e.m.f. emerges from the necessity to increasethepower density. For the samestructure of a machine,itis possible to increase the effective value of the e.m.f. using a full-pitch winding. The result will be also an increase of the harmonic content of the e.m.f. The ideal e.m.f. waveform is an 120 electrical degrees trapezoidal form, while for the current the ideal shape is an 120 electrical degrees rectangular one (Fig. 4) [3,4]. The electromagnetic torque, in this case, can be expressed as: T elmg = 2 · E (tr) · I (tr)  (7) where E (tr) , I (tr) are the peak values of the e.m.f., respectively the current. But in reality, the shape of the e.m.f. is not perfectly trapezoidal, and the current has not a perfect squared waveform. . Dems, K. Kom ˛ eza (eds.), Recent Developments of Electrical Drives, 397–413. C  2006 Springer. 398 Vizireanu et al. The goal of this paper is to study the influence of the electromotive force. control of thegenerator, Grid Power Converter Figure 1. Direct-drive wind turbine system with PM synchronous generator. Figure 2. Generator’s topology. Figure 3. The back-to-back PWM-VSI power. the effective value of the e.m.f. using a full-pitch winding. The result will be also an increase of the harmonic content of the e.m.f. The ideal e.m.f. waveform is an 120 electrical degrees trapezoidal