In this theory, harmonic resonance, its causes and reduction methods of harmonic resonance is given with example.

Harmonic Resonance in Power System

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.

Why harmonics resonance occurs?
The resonance may occur due to following reasons.

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 of harmonic Resonance

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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