Page 220 - Power Electronics Handbook

210 Phasecontrolled rectification and inversion
9.6 Performance factors

The performance of converter circuits can be compared by means of
several factors, the commonest in use being the d.c. voltage ratio, the input
displacement factor, the input power factor and the input current
distortion factor. The d.c. voltage ratio gives the relation between the
converter output at any delay angle 01 and that obtained when the same
converter is operating free of delay angles or overlap. The input
displacement factor is the cosine of the angle between the fundamental
component of a.c. current into the bridge and the supply voltage. It has
been shown, when comparing the various circuits, that this angle Cp
increases (lagging) as the phase-control angle 01 or overlap angle p
increase. For bi-directional converters Cp = a. It is not proposed to consider
this further here.
The input power factor is the ratio of the total mean input power to the
total r.m.s. input volt amperes, and the input current distortion factor is
the ratio of the r.m.s. value of the fundamental to the total input current,
both these factors defining the relationship between the in-phase and
quadrature-phase components of a.c. current. This has been discussed in
previous sections and it was shown then that unidirectional converter
circuits often have the advantage over bi-directional converters in that they
have a lower quadrature, or wattless, current input.
In this section the value of the mean d.c. voltage from a converter will be
found and the harmonic current of this waveform discussed.
The output voltage waveform from a converter with zero delay angle or
phase overlap is composed of a series of cosine curves which are linked
together as in Figure 9.35(a). The duration of each section is equal to h/p,
where p is the pulse number of the converter. The average value V,, of this
waveform is given by equation (9.5) where V is the r.m.s. input voltage.
*
Vav = - + dP
J(2) Vcos 8 de
2~ -r/p
n
= 42) V P sin - (9.5)
P
If a delay angle a is now introduced into the converter, as in Figure
9.35(b), then, since the waveform still follows a cosine wave over its
control range, the average output voltage Vav(a) is given by equation (9.6) and
therefore the d.c. voltage ratio, given by VavcajVa,,, is equal to cos a.
+nlp + a
Vav(a) = P ~(2)vcosede
-nlp + a

= Vavcos(Y (9.6)
To consider the effect of the overlap angle, suppose that the delay angle
is zero, as in Figure 9.35(c), so that the datum for the overlapping