Wind Power - Understanding Renewable Energy Systems - page 214

The rotor of a synchronous machine has the same speed as the stator field.
The north pole of the rotor always follows the south pole of the stator. If a
synchronous machine operates as a motor, the north pole of the rotor and the
south pole of the stator are not directly on top of each other; the load of the
motor causes a shift between the rotor and stator poles. The load angle ϑ that

rises with the load describes this shift.
If a synchronous machine operates as a generator, for example in a wind
turbine, the synchronous speed of the rotating field in the stator also defines
the rotor speed. However, there is also a shift between the poles of the rotor
and stator. Now, the rotor pole moves ahead of the stator pole. The load angle
changes its sign from negative to positive. The load angle increases with the

force that drives the rotor. The rotational speed always remains constant, i.e.
the rotor runs synchronously with the stator frequency. The rotational speed
n s of the rotor only changes with the frequency f of the rotating field or the
pole pair number p .

ϑ

Electrical description of a synchronous machine
All three phases of the stator windings produce a main field that is connected
to the rotor. The useful inductance L h and the useful reactance X h · f 1 · L h

reflect this. Besides the useful field there are leakage fields that are not
connected to the rotor. The leakage reactance X
σ

=2· π

describes these leakages. The
rotor field of a rotating rotor induces a voltage leak in the stator. This voltage
is also called the synchronous internal voltage V p . The rms value of the induced
voltage is proportional to the excitation current I E in the rotor:

(5.80)

in other words, the induced voltage can be adjusted by changing the excitation
current.
Besides the voltage drop over the reactances there is an ohmic voltage drop
at the stator resistance R 1 . Hence, the equation for the equivalent circuit that
describes the connection between the stator current I 1 and stator voltage V 1
for one phase becomes:

(5.81)

The influence of the stator resistance R 1 is low for large machines so that it
can be neglected. The useful reactance X h and the leakage reactance X can be

σ

united as the synchronous reactance:

(5.82)

This simplifies the equation of the one-phase equivalent circuit (Figure 5.24):

(5.83)