Wind power technology - Wind Power Integration: Connection and System Operational Aspects - page 65

Stator winding

bs axis

as'

br axis

bs

ar'

cs w r

br

ar axis

q

cr

Air gap

as axis

cr'

br'

ar

bs'

cs'

Rotor winding

as

cs axis

cr axis

Figure 3.10 Schematic diagram of a three-phase induction machine (Kundur,

1994)

Rotation

ω

r

Axis of phase ar

i ar

i bs

v bs

v ar

v br

R s : Stator resistance
R r : Rotor resistance
L s : Stator leakage inductance
L r : Rotor leakage inductance
L m : Magnetising inductance

i br

θ v as

R r , L r

Axis of phase as

R s , L s

i as
i cs

v cr

v cs

i cr

L m

Rotor Stator

Figure 3.11 Stator and rotor electrical circuit of an induction machine (Kundur,

1994)

electrical circuits. The stator consists of three-phase windings as , bs and cs dis-
tributed 120 apart in space. The rotor circuits have three distributed windings ar ,
br and cr . The angle q is given as the angle by which the axis of the phase ar rotor
winding leads the axis of phase as stator winding in the direction of rotation, and w r
is the rotor angular velocity in electrical rad/s. The angular velocity of the stator
field in electrical rad/s is represented by w s ¼ 2 p f s .
Voltages are induced in the rotor phases by virtue of their velocity relative to
the stator field, in accordance with Faraday's Law (2.10). The magnitude of the
induced e.m.f. is proportional to the slip. If the rotor is stationary, then the induc-
tion machine may be regarded as a transformer. Suppose the induced rotor voltage