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WIND ENERGY SYSTEMS - Cd3wd

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Chapter 6—Asynchronous Generators 6–6<br />

Figure 2: DC shunt generator in a battery-charging circuit.<br />

E = k s ω m Φ p V (1)<br />

where Φ p is the magnetic flux per pole, ω m is the mechanical angular velocity of the rotor,<br />

and k s is a constant involving the number of poles and number of turns of conductors. We<br />

see that the voltage increases with speed for a given flux. This means that at low speeds the<br />

generated emf will be less than the battery voltage. This has the advantage that the turbine<br />

will not be loaded at low rotational speeds, and hence will be easier to start.<br />

The generator rotational speed n can be determined from the angular velocity ω m by<br />

n = 60ω m<br />

2π<br />

r/min (2)<br />

The induced voltage E is in series with the resistance R a of the rotor or armature windings.<br />

In this simple model, R a would also include the resistance of the brushes on the commutator<br />

bars.<br />

by<br />

The current flow I f (the excitation current) in the field winding around the poles is given<br />

I f = V g<br />

R f<br />

A (3)<br />

The field winding has inductance, but the reactance ωL is zero because only dc is involved.<br />

Therefore only the resistances are needed to compute currents or voltages.<br />

The flux does not vary linearly with field current because of the saturation of the magnetic<br />

circuit. The flux will increase rapidly with increasing I f for small values of I f , but will increase<br />

more slowly as I f gets large and the iron of the machine gets more saturated. Also, the flux is<br />

not exactly zero when I f is zero, due to the residual magnetism of the poles. The iron tends<br />

to act like a permanent magnet after a flux has once been established. This means that the<br />

Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001

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