Recent Developments of Electrical Drives - Part 40 pot

For efficient capture of wind power, turbine torque or turbine speed should be controlled to follow the optimal tip-speed-ratio TSR.. Assuming that the permanent magnet generator torque

The internal resistance, Rbat, is assumed to be constant and the internal voltage, Ebat, varies with state of charge The internal terminal voltage, Vs, in discharge and charge operations,

is given respectively by [14]:

Ibat 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:

Idischarge= Ebat

2Rbat −1

2



E2bat

R2bat −4Pout

Icharge= − Ebat

2Rbat+1

2



E2 bat

R2 bat

+4Pout

Poutis the power delivered or received by the battery

The state of charge of the battery may be calculated by:

CSOC discharge= ηdisch

Ccap∗3600

 t

t =0

CSOC charge= ηch

Ccap∗3600

 t

t =0

Ccapis the capacity of the battery in Ampere-hours and (ηdisch,ηch) are efficiency factors of discharge and charge operations respectively

The Csoccan have a value between 0% and 100% The 0% corresponds to a fully dis-charged state and 100% correspond to a fully dis-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 current, 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

Jdω

0 10 20 30 40 50 60 0

50 100 150 200 250 300

Shaft speed (rd/s)

v1< v2 < v3< v4

v1

v2

v3

v4

A C D

B

ORC

Figure 4 Wind turbine torque characteristics.

J is the inertia in kgm2

K is a constant, it depends on generator characteristics

I=Tt

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 vi

Consequently, the wind maximum power transfer is ensured by the operations points following the curve controlled with MPPT unit (Fig 5) In our approach, 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 Ebatminand 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 Ebatmax 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]

0 10 20 30 40 50 60 0

3000 4000 5000 6000

Shaft speed (rd/s)

v 1

v2

v 3

v4

A

C

B

2000 1000

Figure 5 Wind turbine power characteristics.

Desired speed

ωmax

ωmin

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 the system has been implemented 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 output current of the wind generator We can conclude that the current follows well the reference generated according to the MPPT law

6000

5000

4000

3000

2000

1000

0

Shaft speed (rd/s)

Figure 7 Simulation of the maximum regime characteristics (MPPT) for a given wind turbine.

150

100

50

0

Shaft speed (rd/s)

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

wind generator rectified current references current

5 10 15 20 25

Time (s)

Figure 9 Wind generator rectified current of the wind generator and its reference.

Estimated reference speed Actual speed

Time (s)

0 20 40 60 80 100 120

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 diesel generator power contribution is a function 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

We have point out that this control strategy, based on 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 `a la r´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 a permanent 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

PERFORMANCE OF LARGE PM

SYNCHRONOUS WIND GENERATOR

1L2EP, 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

2Framatome 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

In this moment, the efforts are concentrated to increase the power of PM synchronous gen-erators But a special attention should be paid to the conception of the power converters 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, which corresponds to an increase of the number of the legs, or to an increase of the phase number of the machine A resulting advantage is the possibility to obtain a certain mod-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.

2006 Springer.

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 rectifier control strategy realizes a vector control of the generator,

G r i d 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.

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 power transfer Reducing harmonic content of the DC bus current will allow reducing the size of the DC bus filter and the harmonic 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

where is the mechanical speed, e i is the e.m.f corresponding to phase i , andi iis the phase current

Using a FFT for the e.m.f,

e1=∞

k=0E 2k+1· cos[(2k + 1)θ]

e2=∞

k=0E 2k+1· cos



(2k+ 1)



θ −2π

3



e3=∞

k=0E 2k+1· cos



(2k+ 1)



θ −4π

3



(2)

whereθ = ω · t Imposing sinusoidal currents in phase with the e.m.f,

i1= I · cos [(2k + 1)θ]

i2= I · cos



(2k+ 1)



θ −2π

3



i3= I · cos



(2k+ 1)



θ −4π

3

The electromagnetic torque could be written as:

T elmg= 3E1· I

2·  +

3· I

2· ·

3



i=1

[(E6k−1+ E6k+1) cos(6k θ)] (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:

i1= ∞

k=0

I 2k+1· cos[(2k + 1)θ]

i2= ∞

k=0

I 2k+1· cos



(2k+ 1)



θ −2π

3



i3= ∞

k=0

I 2k+1· cos



(2k+ 1)



θ −4π

3



(5)

Then, the electromagnetic torque becomes:

T elmg= 3

2·  (E1 I1+ E3 I3+ E5 I5+ E7 I7)

2·  (E1 I5+ E1 I7+ E3 I3+ E5 I1+ E7 I1)· cos(6kθ)

2·  (E5 I7+ E7 I5)· cos(12kθ) + · · · (6)

It is possible to reduce the 6k torque harmonics by injecting current harmonics as

sug-gested in (6) The DC component of the torque can be increased using odd current harmonics

in phase with the same order e.m.f harmonics Equation (6) shows the interest of trapezoidal 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 increase the power density For the same structure of a machine, it is 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)

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