Wind Energy Systems - Wind Energy Systems for Electric Power Generation - page 90

a) b)

Fig. 5.14 Steady-state performance of a doubly-fed induction machine ( a ) current loci; ( b )variable
speed operation (legend see text)

Converter control allows set-value voltage to be fed to the rotor winding, where
magnitude and phase can be chosen arbitrarily as long as, for steady state oper-
ation, the voltage is of slip frequency. Consider Fig. 5.14a, where per-unit stator
current loci appear as circles in the complex plane. The reference circle I 1 , ref ap-
plies to rated stator voltage and rotor short-circuited; it is similar to the circle in
Fig. 5.10a. The three circles I 1a , I 1b and I 1c were calculated for k 2 = 0 , 2 and
ϕ 2 = , respectively, see (5.4). As diameters and center points

vary in the examples, the scaling of parameter slip differ also. Note that the cur-
rent locus I 1a reflects the circle for the machine with the rotor short-circuited, as
in Fig. 5.10a, however with the no-load point at s =

π ;1 , 13 π and 0 , 885 π

−

0 , 2. For the other circuits

0 , 24, respectively. In
the case of I 1c the rated current in generator operation is reached at power factor
unity.
Using a suitable concept, power and power factor of the cascade may be con-
trolled. As an example, consider a performance where, in variable speed operation,
the electric power fed into the grid follows a third power law, representing a wind
turbine operating at optimum power factor c p . This applies up to a specified speed
from where the power is limited to rated value. Consider a second condition that
the stator power factor be unity; this implies that the machine side inverter feeds
the magnetizing reactive power into the rotor winding. Fig. 5.14b shows calculation
results according to this concept, of stator power P 1 , rotor power P 2 and result-
ing generator power P el expressed in per-unit, for variable speed operation within
−

−

0 , 15 and

−

the real current component becomes zero at s =

0 , 4 < s < 0 , 4 . P el follows a third power function up to the reference point chosen
at n / n syn = 1 , 16, with output limitation above.