Page 776 - Industrial Power Engineering and Applications Handbook

Power capacitors: behaviour, switching and improvement of power factor 23/733
the system. If the capacitors are grounded star, they will This means that the capacitor will offer a low reactance
provide a return path for the third harmonic quantity to the higher harmonics and will tend to magnify the
through their grounded neutral and help the system to harmonic effect due to higher harmonic currents on
generate third harmonic disorders. As the harmonic account of this. In fact, harmonic currents have a greater
components affect a capacitive circuit more than any heating effect too compared to the fundamental component
other equipment connected in the system, our main due to the skin effect (Section 28.7).
emphasis will be a study of the harmonic effect on a
capacitive circuit.
But as the harmonics do exist in the system, they do
affect an inductive load. They may also disturb a where Ich and Xch have been considered as the capacitive
communications network as a result of capacitive coupling, current and the reactance of the capacitor respectively.
whose effects are magnified in the presence of capacitor at a particular harmonic frequency& = n ..f: The effective
units in the power system. It is therefore considered current caused by all the harmonics present in the system
relevant to discuss this subject in more detail to make can be expressed by
the harmonic study more informative.
Here we briefly discuss the sources of generation of I,,, = d(1: + 9 I& + 25 + 49 If,], + . . . ti2 lL'hn)
harmonics of different orders, their likely magnitudes (23.2)
and possible influence on the capacitor and inductive
loads, connected in the system. We also study their where I, = rated current of the capacitor. and
and
lch7
influence on a communications network. Such a network Ich3, lchs, lchn etc = magnitude ol' the
is affected when it is running in parallel, and in close harmonic current components at different harmonic
vicinity of long-distance HT distribution power lines. orders.
Sometimes the communication lines may be running Based on the system studies carried out and Table
through the same structures on which the power lines are 23.1, it has been assessed that in actual operation, effective
running. current through a capacitor circuit may increase up to
1.3 times its rated current, I,, Le. Ich = 1.3 I, to account
A Effects of harmonics on the performance of a for all the harmonic effects (V; ,f,,: equation (23.4)). A
capacitor unit capacitor unit is thus designed for at least 30% continuous
overload capacity (Section 25.6). Its switching and
B\ the harriionic voltage\ protective devices are selected along similar lines.
The effective harmonic voltage can be expresed by Summarizing the above, the harmonic quantities when
present in a system on which are connected a few capacitor
banks affect the capacitors as follows:
where V,, = effective harmonic vultage Overcurrent will mean higher losses ([:h . R).
V, = system voltage and Overcurrent will also mean an overvoltage across the
V,,?, Vh5, Vh7 and Vh, etc. = magnitudes of the capacitor units, which would inflict greater dielectric
harmonic voltage components in terms of stresses on the capacitor elements.
fundamental voltage at different harmonic orders. Since the harmonic disorders occur at higher frequencies
than the fundamental Uh >,f). they cause higher dielectric
Referring to the data available from experiments, as losses due to a higher skin effect.
shown in Table 23. I, it has been estimated that a Vh of
1. I VI should be sufficient to account for the harmonic Harmonic output of a capacitor unit
effects. For this dielectric strength is designed a capacitor The rating of a shunt capacitor unit
unit and selected a switching or protective device.

B: the knrrmtiic currents kVAr = fi 1 . (v in volts and 1, in amperes)
1000
A harmonic component affects the performance of a
V
capacitor unit significantly due to diminishing reactance and I, = -
at higher frequencies, which adds to its loading xc
sub\tantially and can be analyscd as follows: a.
I"
:. kVAr = ~ 1000 . x, (23.3)
217 ' v2 ' 2nf.c.
If n IS the harmonic order, such as 3, 5, 7 and 9 etc.. then or kVAr = 1000 (23.4)
the harmonic frequency
Generalizing, kVAr,, oi V; .fl,
01
and harmonic reactance kVAr, a p,2 + 3 . Vi3 + 5 . Vh5 + 7 + . . . II . V,; )
(23.5)