TRANSMISSION AND DISTRIBUTION
How capacitors affect
harmonics, and what is resonance?
Information from Elspec
The use of power factor correction capacitors can result in resonance in circuits where harmonics are present. In order to understand the PFC
capacitor affect on harmonic current,we need to understand the harmonic sources and their nature.
Most utlities worldwide produce electricity
with a high quality sinusoidal waveform
having ver y low distortion. However, as
we move closer to the load, the distortion
increases. The source of power for the
average power consumer is the voltage
source. The most popular implementation
being the power distribution transformer. As
the voltage source, the power distribution
transformer's job is to maintain a stable
voltage across its secondary windings. The
load impedance for the voltage source
should be much higher than the internal
winding impedance. Ideally the internal
winding impedance should be zero, but
practically it is as much as 5 – 7% of the full
load impedance, because of reactance
and parasitic resistance (Fig. 1).
The quality of the voltage sine wave on an
unloaded distribution transformer depends
on quality of power generation and the
interference from the other distribution
branches.
Lets consider the theoretical case where
power is generated exclusively for one
distribution transformer, and the voltage is
a pure sine wave. In that case, any load
connected to the transformer secondary
will “see” the pure sine wave voltage
and will draw current based on the load
impedance. When the load impedance
is linear the current waveform will follow
the voltage wave shape. If the load
impedance is changing periodically, as
in chopped or other non-linear operated
loads, the current waveform may be very
different from the voltage sine wave. The
non-sinusoidal current can be represented
as sum of a series of sine waves starting
with the fundamental frequency and
including multiples of the fundamental,
called harmonics.
Harmonics are created by nonlinear
loads, and initially they are current waves.
The frequencies (harmonic order) and
the magnitudes of those current waves
depends exclusively on the nature of the
load. For example most DC drives have
6-pulse rectifiers, which generate mostly
5th and 7th order harmonics. The 5th
harmonic has a frequency five times the
fundamental and the 7th is seven times the
fundamental. The harmonic is actually the
power source at the high frequency. Since
the harmonics exist in the current drawn,
the source is treated as a current source.
Unlike the voltage source, the ideal current
Fig. 1: The distribution transformer behaves like a voltage source.
source has infinity internal impedance and
prefers zero load impedance to maintain
the current (Fig. 2).
The nonlinear load can be represented as
linear load part and the high frequency
current sources. For simplicity consider
the situation where the only one of the
connected loads is nonlinear and is
produces only 5th order harmonic current
(Fig. 3).
The 5th harmonic current is produced by
the current source which is part of the
load operation, and is fed to the network
through the junction A. From the junction
A the current will choose the lowest
impedance path to flow. The left side
impedance is the internal impedance of
the distribution transformer in additional to
the line impedance. The total impedance
of the left side is very much lower than
the fully loaded right side. Most of the
harmonic current will flow towards the
power transformer (Fig. 4).
Following the line and internal transformer
impedances the harmonic current creates
the high frequency voltage drop. This
is how voltage harmonics are created.
In addition, the current, which passes
through transformer secondary will create
Fig. 2: Ideal current source.
the harmonics on the primary transformer
side as well.
Now assume that power factor correction
is required due to a low power factor at
the fundamental frequency. Power factor
correction capacitors are added to
correct the power factor. (Fig. 5)
The harmonic current coming to the
junction B will encounter the capacitor
and connected in parallel to it resistance
and reactance. The resistance part is
negligible in most cases, so basically the
above can be represented as parallel
resonance circuit in the path of the 5th
harmonic current. In the case where Xl
will be equal to Xc parallel resonance will
take place (Fig. 6).
Parallel resonance raises the circuit
Fig. 3: Harmonic source acts as a current source connected across the load.
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TRANSMISSION AND DISTRIBUTION
Fig. 4: Most of the harmonic current flows in the low impedance path.
Fig. 5: PFC capacitors can create a resonant circuit at harmonic frequencies.
Fig. 6: Resonant circuit at 5th harmonic.
Fig. 7: Detuned capacitor
configuration prevents
resonance.
impedance. Current circulates between
the capacitor and the inductance without
being passed to the grounded terminal.
In the case of parallel resonance or even
close to resonance condition, the path,
which includes distributing transformer and
PF capacitors have a very high impedance
at the harmonic current frequency. At
parallel resonance condition the harmonic
current is forced to go to the load. Since
the path impedance is increased the
voltage harmonic is increased as well
too. This situation may cause a significant
damage to the electrical infrastructure.
Normally, the weakest part which fails first
in such a condition is the PF capacitor.
The PF capacitor most likely cannot
withstand the high harmonic current which
is circulating between the capacitors and
the distribution transformer.
Parallel resonance between the PFC
capacitors and the distribution transformer
windings is an extremely dangerous
situation for the entire electrical system. The
resonance condition depends only on the
connected capacitance and the network
impedance. A small harmonic source
may create noticeable voltage distortion
and damage to the electrical network.
PFC equipment manufacturers strongly
recommend the use of a “detuned ”
configuration as a standard for any PFC
application.
The parallel resonance frequency always
exists in cases where the capacitors are
used for PF correction. The way to prevent
parallel resonance occurring is to insure
that the frequency of resonance is located
outside the harmonic range. This is the
main idea behind the “detuned” system
configuration. The 7% or 5,67% inductors
move the resonance point below the 4th
harmonic which insures safe operation for
the three phase delta capacitors in cases
where the third harmonic is balanced
(Fig. 7).
The PFC capacitor itself has linear
impedance. Once connected it does not
create any harmonics current by itself. But,
because of parallel resonance possibility
the PFC capacitors can dramatically
affect the harmonic situation on the
network.
The electromechanical connected
capacitors are affected by heavy
transients on the connection/disconnection
point. The transients have a nonlinear
waveform, which, of course, injects a
lot of harmonics for a short time. Elspec
equipment has completely transient free
operated capacitors and no harmonics
are generated on the connection and
disconnection events.
Contact Graham Whittle,
Impact Energy, Tel 031 201-7191,
graham@impactenergy.co.za 
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