Performance and Operation Management - Wind Energy Systems for Electric Power Generation - page 120

Fig. 6.4 Rotor model of induction machine ( a ) Space-vector diagram; ( b ) block diagram

Choosing the rotor flux space vector as reference, it is positioned in the d-axis
which is also the real axis. Hence (6.20) expressed by components becomes:

τ 0 r d

ψ r
dt

L s i sd = ψ r + where ψ r = ψ rd = ψ r

(6.21)

L s i sq = τ 0 r ω r ψ r where ω r = ω re f − ω rot

The electromagnetic torque is expressed by:

T el = 3

2 z p i sq ψ r

(6.22)

It is seen that the torque is defined by the product of q-axis current and d-axis
flux; consequently i q is called the torque building component and i d the flux-building
component. The equation of motion for the one-mass inertia model is:

J d

ω rot
dt

= T el + T L (6.23)

Figure 6.4 shows space vector diagram and a block diagram representation of
the rotor model based on (6.20-6.22). In the figure the rotational speed is calculated
according to (6.23) which of course may be replaced when a measured speed value
is available.
In Fig. 6.4b i sd , i sq and T L are the input values; calculated results are

r and
T el . To apply the rotor model, the current components may be obtained from mea-
sured currents in stator frame by a transformation, when the rotor angular frequency
is known from measurement or estimation. For flux oriented control, rotor flux and
torque signals serve as the actual values.

ψ r , ω

6.2.2.4 Transient Model

In order to calculate the behavior of a cage induction machine subjected to varia-
tions of the load torque a transient model can be used. Consider a machine operating