Civil Engineering Reference
In-Depth Information
machine rotor is, therefore, highly slip-dependent, as is discussed later in
this chapter.
We take a note here that the performance of the induction machine is
completely determined by the equivalent circuit parameters. The circuit
parameters are supplied by the machine manufacturer, but can be deter-
mined by two basic tests on the machine. The full-speed test under no load
and the zero-speed test with blocked rotor determine the complete equiva-
lent circuit of the machine.
2-3
The equivalent circuit parameters are generally expressed in perunit of
their respective rated values per phase. The rated impedance per phase is
defined as the following:
Rated voltage per phase
Rated current per phase
ohms.
Z
rated
=
(6-10)
For example, the perunit (pu) stator resistance is expressed as the following:
R
in ohms
R
=
1
(6-11)
1
perunit
Z
in ohms
rated
and similar expressions for all other circuit parameters. When expressed as
such, X
and X
are equal, each a few to several percent. The R
and R
are
1
2
1
2
approximately equal, each a few percent of the rated impedance.
The mag-
netizing parameters X
and R
are usually large, in several hundred percent
m
m
of Z
, hence, drawing negligible current compared to the rated current.
For this reason, the magnetizing branch of the circuit is often ignored in
making approximations of the machine performance calculations.
All of the above performance equations hold true for both the induction
motor and the induction generator by taking the proper sign of the slip. In
the generator mode, the value of the slip is negative in the performance
equations
rated
wherever it appears. We must also remember that the real power
output is negative, that is the shaft receives power instead of delivering it.
The reactive power drawn from the stator terminals remains lagging with
respect to the line voltage, hence, we say that the induction generator delivers
leading reactive power. Both of these mean that the magnetizing
volt-amperes are supplied by an external source.
6.2.5
Efficiency and Cooling
The values of R
in the equivalent circuit represent electrical losses
in the stator and the rotor, respectively. As will be seen later, for a well-
designed machine, the magnetic core loss must equal the conductor
and R
1
2
loss.
Therefore, with R
expressed in perunit of the base impedance, the
induction machine efficiency is approximately equal to the following:
and R
1
2
