Harmonic Resonance

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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