design and implementation of thyristor switched shunt capacitors a ...

harmonic that the load generated. If the main purpose is filtration of one specific
harmonic, then the tuned filter would be a good choice. However, practical
considerations to use a passive filter should be taken into account. A malfunction
in one of the capacitors, temperature and aging cause the tuning frequency
shifted upwards. Therefore, the harmonic filters are tuned as a detuned filter
in practical applications which means that the tuning frequency is chosen below
the harmonic frequency (approximately 10%).
The tuning frequency can be determined by the following formula:
f t =
1
2π √ L f C f
, (2.2)
where L f and C f are the filter inductance and capacitance respectively. When a
filter is tuned to a distinct frequency, in frequency domain, the resonance values
of the filter need to be taken into consideration. There are two types of resonance
that can occur during an operation. The first one is the series resonance which
is the main design purpose of harmonic filters. The series connected capacitor
and inductor impedances in one phase become the same due to waveforms at
different frequencies. In this case, the resulting impedance turns out to be only
resistive and a significant current flow is expected though the filter. The next
type is the parallel resonance which appears at the frequency just below the series
resonance frequency and becomes crucial in a filter design as every filter can face
with this problem. This time, the reactance of the capacitor becomes equal to
the system total shunt inductive reactance (when the transformer, source and
line impedances are included). As a result, a significant current flows through
the transmission lines and the critical equipment may be damaged, such as
connection points and semiconductor switches.
A typical frequency diagram of a detuned filter (tuned to 225 Hz) is shown
in Figure 2.6.
The frequencies that create parallel and series resonances are
clearly shown on this figure. If the system has some critical harmonics below the
tuning frequency, the parallel resonance of the filter can excite these harmonics.
Therefore, harmonic spectra of the system should be carefully examined in order
not to cause a resonance that increases the current passing through the circuit
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