Civil Engineering Reference
In-Depth Information
Most of the flux links both the stator and the rotor. The flux which does
not link both is called the leakage flux. The leakage flux is represented by
the leakage reactance. One-half of the total leakage reactance is attributed to
each side, namely the stator leakage reactance X
and the rotor leakage
1
reactance X
in
Figure 6-6(b)
.
The stator and the rotor conductor resistance
are represented by R
2
and R
, respectively. The magnetizing parameters X
1
2
m
represent the permeability and losses (hysteresis and eddy current)
in the magnetic circuit of the machine.
The slip dependent rotor resistance R
and R
m
· (1-s)/s represents the electrome-
chanical power conversion. The power conversion per phase of the three-
phase machine is given by I
2
2
R
· (1 -s)/s. The three-phase power conversion
2
2
is then as follows:
(
)
2
P
=⋅ ⋅−
3
I
R
1
s
s watts
.
(6-6)
em
2
⋅
2
The machine capacity rating is the power developed under rated condi-
tions, that is as follows:
P
P
em rated
em rated
Machine Rating
=
kW
or
horsepower
.
(6-7)
1000
746
The electromechanical power conversion given by Equation 6-6 is physi-
cally appreciated as follows. If the machine is not loaded and has zero
friction, it runs at the synchronous speed, the slip is zero and the value of
R
, as
it should be. When the rotor is standing still, the slip is unity and the value
of R
(1-s)/s becomes infinite. The rotor current is then zero, and so is P
2
em
· (1-s)/s is zero. The rotor current is not zero, but the P
is zero, as the
2
em
mechanical power delivered by the standstill rotor is zero.
At any slip other than zero or unity, neither the rotor current nor the speed
is zero, resulting in a non-zero value of P
.
The mechanical torque is given by the power divided by the angular speed,
that is as follows:
em
TP
em
=ω
(6-8)
em
where T
= electromechanical torque developed in the rotor in new-
ton-meters
em
ω
= angular speed of the rotor = 2
π
.N
· (1-s)/60 in mechanical radi-
s
ans/sec.
Combining the above equations, we obtain the torque at any slip s, as follows:
(
)
2
T
=
180 2
π
N
.
I
R
s Newton-meters
(6-9)
em
s
2
2
in equation (6-9) is determined by the equivalent circuit
parameters, and is slip dependent. The torque developed by the induction
The value of 1
2
