- Sometimes harmonic resonance occurs between power capacitor and transformer which may cause high magnification of harmonics.
- The resonance can happen at one particular frequency is called as resonance frequency ( f_{r} ) in a system in which inductive reactance ( X_{L} ) and capacitive reactance ( X_{C} ).
- The net impedance becomes low when the inductive reactance X_{L} is equal to capacitive reactance X_{C}.
- The magnitude of the current becomes high particularly at resonance frequency.
- The resistance of the network will limit the current.
- Series resonance due to external harmonics in the supply system and resonance between capacitor in the electrical system
- Parallel resonance within a given electrical system and resonance between internal capacitors and inductive loads
- Typically, the inductive reactance of the system remains constant but the capacitive reactance varies in order to main higher power factor.
- The resonance frequency falls, if the capacitor increases as the resonance frequency is inversely proportional the capacitance.
- Lower the resonance frequency is dangerous because it may match with any harmonics and causes more damage.
f_{r}
= 1 / 2π √ LC
Causes of Harmonic Resonance
- Over heating of bus bar
- Higher rate of failure of equipment
- Frequency failure of capacitors
- Frequent blow of fuses
- False tripping of MCCBs
Reduction of Harmonic Resonance
- The harmonic resonance is reduced by DETUNE FILTER which consists of reactor is in series with each capacitor.
- The detune filter creates one resonance frequency which offers higher impedance for high frequency harmonics.
- The resonance at higher frequency harmonics ( 5^{th} harmonics and above ) can be avoided.
Example
A 500 kVA industrial transformer with
percentage impedance % Z = 4.5 with 500 kVA automatic power factor correction
panel. Calculate the resonance frequency. |
Solution
Short
circuit power kVA_{sc} = kVA / ( % Z / 100 )
=
500 / ( 4.5/100 )
=
500 / 0.045
= 11,111 kVA
Resonance
frequency f_{r} = f × √ kVA_{sc} / kVAr
Where
f
= Supply frequency
f_{r}
= Resonance frequency
kVA_{sc}
= Short circuit power
kVAr
= Rating of capacitor for power factor improvement
Case
1 : 150 kVA capacitor is connected for power factor improvement
Resonance
frequency = 50 × √ 11,111 / 150
= 50 × 8.60
= 430 Hz
This frequency closely matches with the
ninth harmonic frequency ( 450 Hz ). There is no resonance occurs in this case
Case
2 : 500 kVA capacitor is connected for power factor improvement
Resonance
frequency = 50 × √ 11,111 / 500
= 50 × 4.71
= 235.5 Hz
This frequency closely matches with the
fifth harmonic frequency. The fifth harmonics is least order harmonic with
higher magnitude. The resonance at this harmonic may damage the equipment.
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