Environmental Engineering Reference
In-Depth Information
Fig. 3.3 T-model for asynchronous machine connected to the grid
Note the definitions
L m 2
L 1 L 2 ;
· ξ
k = N 1
I 2 = I 2
1
N 2 · ξ 2 ;
U 2 = U 2 ·
σ
= 1
k ;
k
where
N 1 , N 2 are the winding turns and
ξ 2 the fundamental winding factors of the
primary and secondary windings, respectively;
ξ 1 ,
σ
is the total leakage coefficient.
Rotational angular speed
Ω
and slip s are related by the following equation:
s = ω 2
Ω
Ω syn
syn = 2
π
f 1
= ω 1
z p
Ω
=(
ω
ω
2 ) / z p ;
ω 1 = 1
at
Ω
(3.1)
1
z p
where z p is the number of machine pole pairs, and
Ω syn is the synchronous angu-
lar speed.
When fed from a source with phase voltage r.m.s. value U 1 of frequency f 1 ,the
voltage equation may be written:
U 1
U 2 / s
= ( R 1 + jX 1 )
I 1
I 2
jX m
(3.2)
( R 2 / s + jX 2 )
jX m
Provisions may be added in the equivalent circuit model to take load-independent
(constant) losses approximately into account. To model the iron loss, a resistance
R Fe is connected in parallel to the magnetizing reactance, Fig. 3.4a. This is a physi-
cally plausible way to model the eddy-current loss due to the main flux oscillations;
however the hysteresis loss which follows a different dependency can only roughly
be covered by this method. A different but simple method is to model the constant
losses (friction, windage and iron losses) by inserting a resistance R p parallel to the
machine terminals, Fig. 3.4b.
Asynchronous machines are capable of self-excitation when, in order to supply
the magnetizing current, capacitors are connected parallel to the machine terminals.
To model this effect it is necessary to adapt the model by taking the non-linearity
due to saturation of the main field inductance into account.
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