Page 167 - Power Electronics Handbook

Phase control 159
To derive the rating of the devices let Vbe the r.m.s. input voltage to the
a.c. lines, R the load resistance, and a the firing angle delay. Then the
r.m.s. current rating of each thyristor and diode in Figures 8.l(a) and
8.l(b) is given by equation (8.1).

= - [1--+- sin 2a I”
a
V
JWR n2Jt
For Figure 8.l(c) the diodes conduct only in each half cycle, so that their
rating is given by equation (8.1), but the thyristor conducts during both
half cycles so equation (8.1) must be multiplied by a factor V2. If a triac is
used in Figure 8.l(a) in place of the two thyristors then it also carries
current in both half cycles, and the same multiplying factor must be used
when obtaining its rating.
It was mentioned in Chapter 1 that thyristor ratings can conveniently be
obtained on an r.m.s. basis, except at very low conduction angles. At these
control settings the ratio of peak to r.m.s. current is large and care must be
taken not to exceed the repetitive peak current. All devices must be rated
to withstand a peak repetitive voltage of Vq2.
The r.m.s. load voltage and currents are similarly given by equation (8.2)
and it is seen from these equations that for a = 0 the values of current and
voltage are those of the sine wave input.
”

V, = [ 1 [ V42) sin’ 0 de]
Jr
a
1”

L J
The load voltage and current waveforms shown in Figure 8.l(d) are rich
in harmonics, and Figure 8.2 gives the Fourier analysis of the spectrum up
to the seventh. Where load harmonics must be minimised a.c. chopper
regulators are preferred, as described in Section 8.3.
It was mentioned in Chapter 6 that for inductive loads the control
thyristors do not cease conduction when the input voltage reverses, but are
kept on by energy stored in the load, which is fed back to the supply.
Figure 8.3 shows the modified waveforms for a series resistance-induct-
ance load of power factor angle +. Thyristor TH1 in Figure 8.l(a) is fired at
time tl, which causes the load current to flow, the rising edge of the current
being slower than for a purely resistive load. Thyristor THI is kept
conducting until time tZl, energy flowing from the load to the supply from