16.1 POWER SEMICONDUCTOR-CONTROLLED DRIVES 775(^0) π/2 πω 2 π t
2 π/3
3 π/2
Phase voltage
Phase current
−Id
Id
Figure 16.1.22Rotor voltage and current waveforms.
- V 1
I 1
−
E 1
R 1 jXl 1 jX′l 2
jXm R′a
R′b
S
I′ 2 Figure 16.1.23mental equivalent circuit of thePer-phase funda-
drive with static rotor resistance
control.
1
T
[
Id^2 R(T−ton)
]
or Id^2 R( 1 −δ)
The effective value of resistance is then given by
R∗=( 1 −δ)R (16.1.50)
The total resistance across the diode bridge is
Rt=R∗+Rd=Rd+( 1 −δ)R (16.1.51)
The per-phase power absorbed byRtis^1 / 3 Id^2 Rt, whereIdis related to the rms value of the rotor
phase current,
√
3 / 2 Irms. Thus, the effective per-phase resistanceReffis given by
Reff= 0. 5 Rt (16.1.52)
From the Fourier analysis of the rotor phase current with quarter-wave symmetry, the fundamental
rotor current is(
√
6 /π )Id,or( 3 /π )Irms. It can be shown (as in Problem 16.1.14) that the per-phase
fundamental equivalent circuit of the drive referred to the stator is given by Figure 16.1.23, where
Ra=R 2 +Reff (16.1.53)
and
Rb=
(
π^2
9
− 1
)
Ra (16.1.54)
As in Chapter 13, the primed notation denotes referral to the stator, andR 2 is the per-phase
resistance of the rotor. The resistanceR′a/Saccounts for the mechanical power developed and
the fundamental rotor copper loss, whereas the resistanceR′brepresents the effect of the rotor
harmonic copper loss.