What actually is Harmonics Resonance??

Before going to the point of Resonances let me discuss something about Harmonics.

Harmonics are multiple of fundamental frequency rather than it is not a fundamental frequency. Here the simple demonstration is

H = n * F

where,

H = harmonics , n = integers and F = fundamental frequency

Let i give an Example

H = 5 * 50 = 250 Hz ( so this is 5th Harmonic )

H = 7 * 50 = 350 Hz ( 7th Harmonic )

It is simple Harmonics are the integer multiple of Fundamental Frequency and this multiple frequency combine with fundamental frequency to give Distorted waveform.

Main thing is Harmonics are Reactive in Nature.

Harmonic currents produced by non-linear electronic loads are injected in to the power system Network. Depending on the response of the grid, the injected current could simply flow in to the grid harmlessly or create electrical power system resonance resulting in damaging overvoltage or overcurrent conditions.

*Impedance of the system to each harmonic frequency

*Presence of any capacitor banks

*Amount of resistive loads

Some Key Point need to know before going into this.

1.Non-linear loads produce harmonic current which are then injected in to the power grid.

2.The current flowing in to the source (grid) produces voltage drop proportional to the impedance offered to that particular harmonic frequency component.

3.If the source inductance and capacitance form a series or parallel resonant circuit, then the injected current can cause very high current and voltage distortion.

Power System Network usually more inductive rather than Resistive. Let the X/R ration determine system reactance and Resistance.

Resonance

Two main point that causes resonance in Electrical Network.

1. Inductive reactance
2. capacitive reactance

Inductive Reactance

Power system impedance is primarily inductive at the nominal frequency. The impedance varies depending on the harmonic frequency.

For an inductance ‘L’

X = 2* Phi *F * L

Capacitive reactance

Power system capacitors could be power factor correction capacitors, cable capacitance, breaker capacitance etc. The impedance varies inversely depending on the harmonic frequency.

For a capacitor ‘C’

X = 1 / 2* Phi * F * L

Resonances is the point where the Inductive reactance equal to the capacitive reactance.

So this point is called Resonances point.

There are two types of Resonance in System

1. Parallel Resonance

2. Series Resonance

Parallel Resonance

In Parallel resonance the sources reactance is parallel to the capacitive reactance.At particular frequency both Sources reactance is equal to Capacitive reactance.

Xs = Xc

Equivalent circuit

This cause the System Impedance to become very high.

Z ( parallel impedance ) = ( R+jXs ) || -jXc

Here R+jXs is Sources impedance and -jXc is capacitive reactance.

Z = R + jXs * - j Xc / ( (R +jXs) + ( - jXc ))

Z = ((R + jXs * -jXc )/ R+jXs) * (R +jXs * - jXc) / -jXc))

For the length of Calculation Resultant is

Z = 1 / R

Hence at Parallel Resonance the value of Impedance at resonance is Maximum and Current is Minimum.

In Parallel Resonance the circuit draws a very small current and power from the sources.

Real time Analysis data:

Due to High Impedance the Circuit draws current from sources is minimum. In above data you can see the current reduce and often power reduce when capacitor switch ON and form resonance condition.

Voltage & Current in capacitor at Parallel resonance:

Due to parallel resonance very high voltage in capacitor.(for simple understanding in open circuit the impedance is maximum and voltage is maximum.)

Vcap = Xs * Ip

so , Vcap is voltage at capacitor , Ip is primary current.since the impedance is very large this cause large voltage drop across capacitor.

Current at capacitor.

During parallel resonance condition current flowing in capacitor and in transformer is magnified upon the level of harmonic current injected.

Icap = Vp / Xc

we know Vp = Ip * Xs

I cap = ( Ip * Xs ) / Xc

So the Xs and Xc are equal and cancel each other.Let the resultant is

I cap = Ip

so current at capacitor is greatly amplified and it is greater or lesser then Primary current (Ip) depends on Q factor of system.

Series Resonance

Series resonance can occur when the series combination of the facility transformer inductance and the shunt capacitor bank in the facility resonates at a harmonic frequency that in injected from the distribution system.

Equivalent circuit

Since Xs = Xc, the impedance is Minimum and equal to resistance.where as current is Maximum.

Z = R+j(Xs - Xc)

So the Resultant is

Z = R

Due to series Resonance current taken from the sources is increases and Power also increases.

Voltage across Capacitor

Due to current increases in circuit the voltage across the capacitor also increases.

Vcap = I * Xc

Practically speaking a series resonant condition will also have a parallel resonance condition due to circuit topology. So both parallel and Series resonance occurs in system.

Conclusion:

The difference between series and parallel resonance in power system is that series resonance creates a low impedance (draw maximum current in to the system) whereas parallel resonance creates a large impedance which even in the presence of small current can create large harmonic voltage drop and hence cause voltage stress related damages of capacitors.