Generators - Wind Energy Systems for Electric Power Generation - page 29

3.2.2 Performance Equations and Equivalent Circuits

3.2.2.1 Model Assumptions

Conventional models describe a three-phase machine of symmetrical construction,
for operation with the stator winding terminals connected to a symmetrical, si-
nusoidal supply of constant voltage and frequency. In wound-rotor machines slip
power may be recovered in terms of voltages and currents of slip frequency. Ana-
lytical equations and respective equivalent circuits serve to determine electric and
magnetic quantities for steady-state operation by complex calculus. The use of these
models with constant parameters implies:

• constant magnetizing inductance, i.e. neglecting main field saturation effects,

• neglecting eddy-current losses in conducting parts except windings,

• neglecting the influence of current displacement in windings,

• neglecting the influence of temperature variation on resistances.

The conventional T-model in Fig. 3.2 is a two-mesh, per-phase representation of
a wound rotor machine, where the rotor winding terminals are accessible via slip-
rings and brushes. It shows a specialized form of a transformer model, where the
primary (stator) circuit is magnetically coupled with the secondary (rotor) circuit.
The primary winding is supplied by voltage U 1 of frequency ω 1 . All secondary side

quantities are referred to the primary side by using both a real transformer ratio k
representing the windings ratio, and the frequency ratio

ω 2 are
stator and rotor frequency, respectively. For cage rotor machines the secondary side
mesh is short-circuited, U 2 = 0.
Figure 3.3 is equivalent to Fig. 3.2 when the machine is supplied by a fixed fre-
quency

ω 1 / ω 2 , where ω 1 ,

ω 1 , as in grid operation. Inductive parameters are represented by reactances

( X = L ). Secondary side quantities referred to the primary side are indicated by

aprime( ) added to the symbol.
In the equivalent circuit representations the parameters are denoted as follows:
R 1 ; R 2 = k 2 R 2 are primary and secondary side resistances,
L m is the main field (magnetizing) inductance,
L 1 = L m + L σ1 ;

ω 1 ·

L ' 2 = L m + L ' σ2 are primary and secondary side total

inductances, the respective leakage inductances being L σ1 ; L ' σ2 = k 2

L σ2 ,

k is the conventional primary/secondary fundamental winding ratio,
s is the slip as defined in (3.1).

Fig. 3.2 Asynchronous machine T-model circuit