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9.7.6 Normal flow of harmonic currents
Harmonic currents tend to flow from the nonlinear loads (harmonic sources) toward the point of
lowest impedance, usually the utility source, figure 97. The impedance of the utility source is
usually much lower than parallel paths offered by loads. However, the harmonic current will split
depending on the impedance ratios of available paths. Higher harmonic currents will, therefore,
flow to capacitors that offer low impedance to high frequencies.
Figure 97 Normal flow of harmonic currents
9.7.7 Parallel resonance
Parallel resonance (figure 98) occurs when the system inductive reactance and capacitive
reactances are equal at some frequency. It can also occur where is connected to the same bus

bar
as a harmonic source.
Parallel
resonance
will then
occur between the
system
impedance and the
capacitor.
If the combination of capacitor banks and system inductance result in a parallel
resonance near one of the characteristic harmonics generated by a nonlinear load, that harmonic
current will excite the “tank” circuit, causing an amplified current to oscillate between the energy
storage in the inductance and the energy storage in the capacitance. This high oscillating current
can cause excessive voltage distortion.
Figure 98 Parallel resonance conditions
Frequency at which parallel resonance occurs can be estimated by the following simple equation:
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View Full Document where
H
is the harmonic order.
X
C
and
X
L
are reactances at the fundamental frequency.
9.7.8 Series resonance
Series resonance occurs when an inductive reactance and capacitive reactance that are in series
are equal at some frequency. This condition occurs as a result of the series combination of
capacitor banks and line or transformer inductances. Series resonance presents a low impedance
path to harmonic currents and tends to draw in, or “trap,” any harmonic current to which it is
tuned. Series resonance can result in high voltage distortion levels between the inductive and the
capacitive elements in the series circuit. Another concern
with
series resonance is that high
capacitor currents can flow for relatively small harmonic voltages. The actual current that will
actually
flow will depend on the quality factor, Q, of the circuit.
One example of a possible series resonance
circuit is a load center transformer that has capacitors connected to its secondary bus (figure 99).
This circuit appears as a series circuit when viewed from the primary side of the transformer.
In general,
t
o determine which resonance condition exists, it is necessary to measure the
harmonic currents in
the
load and supply, together with harmonic voltage at the bus
s
.
If
the
current flowing into the power system from the bus is small, while the harmonic voltage is high,
resonance within the power system is indicated.
9.7.9 Effect of system loading
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This note was uploaded on 02/04/2011 for the course EE 587 taught by Professor Dr.mohammedsafiuddin during the Spring '11 term at SUNY Buffalo.
 Spring '11
 Dr.MohammedSafiuddin
 Impedance

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