Effects of Harmonics on Capacitors | Interaction of Harmonics with Capacitors - Electrical Volt

Effects of Harmonics on Capacitors | Interaction of Harmonics with Capacitors

Capacitors are widely used in the electrical network for power factor correction. The electrical loads like induction motor, electric furnace draw reactive power for their functioning. The reactive current does not contribute for useful work, it increase the line losses in the electrical network. The capacitor banks are installed to compensate the reactive power. The net current, thus, gets reduced as the capacitive kVAr of the capacitor banks nullify the reactive kVAr,

Effects of Harmonics  on Capacitors

 The varibale frequency drives,slip power recovery  systems, soft starters, DC drives draws non linear current from the supply source and harmonics is generated in the system. The working of the capacitor banks under harmonic rich environment may get adversely affected. 

The resonance between the inductance of the transformer and the capacitance of the capacitor banks may happen at certain harmonic frequencies.The capacitor does not generate harmonics, however the capacitor can magnify the harmonic current under resonance condition.
 
The capacitors along with  the power system elements which are inductive in nature affect system impedance in two ways.
 
A. Series Resonance
 Series resonant circuit is formed by combination of reactive and capacitive reactance.
series resonant circuit
The reactance of the inductor is proportional to the frequency and reactance increase with an  increase in the frequency.
The reactance of the capacitor is inversely proportional to the frequency and reactance decrease with an  increase in the frequency.
frequency vs Xc graph
When inductor and capacitor is connected in the series, the total impedance of the circuit with frequency is as per below given graph.
resonant frequency graph of LC circuir
From above graph, it is clear that at resonant frequency the impedance of the circuit reduces to a minimum value. The current abnormally increase because of low impedance at resonant frequency.The reactance of the  primary winding of the transformer and the capacitor connected at the secondary winding acts as a series resonating circuit and provide a low impedance path for harmonic current whose frequency is close to the resonating frequency.
 
Thus the circuit offers very low impedance at resonating frequency which results into multiple fold increase in the current.
 
B. Parallel Resonance
 

Parallel resonant circuit is formed by combination of reactive and capacitive reactance connected in parallel.

parallel resonance circuit
The LV side of the transformer along with the power factor correction capacitor behaves as a parallel resonating circuit at resonating frequency the impedance offered is very high consequently the harmonic current causes an increased harmonic drop which may be accompanied with distortion of the fundamental. Transformers and capacitors are additionally loaded.
resonant frequency graph- parallel resonant circuit
Under resonant condition, the capacitor draws excessive current and magnify the harmonic current. The blowing of fuses and or failure of capacitor banks is the symptom of the harmonic resonant phenomenon. The capacitor draws excessive current and raise the system voltage under resonance. The de-tuned filters is the solution  for avoiding resonance in the electrical network.
 
The harmonic current gets amplified under resonance phenomenon.  Illustrative example is as given below.
 
effect of a capacitor on harmonic current
How to Calculate Resonance point in a electrical network?
 
Point of resonance :
 
In order to establish the frequency of resonance of the system along with the capacitor bank generally computer modeling techniques are used. However for rough calculation the following formula can be used.
  FR = 50  ( KVASC / KVARC  )
where,
 fR –  Resonating frequency
KVAsc= System short circuit level at point of correction
KVARC= KVAR rating of capacitor bank
 
solved example on resonance
Short circuit MVA = 15/0.1 = 150 MVA
Resonating frequency  
 
FR  = 50  ( KVASC / KVAR )
FR  50  ( 150000 /1000 )
FR = 612 Hz
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