# What is Ferroresonance?

Ferroresonance is a resonance phenomenon caused by the nonlinear inductance and system capacitance. For better understanding of ferroresonance, it is worth to remind the linear resonance in LRC circuit.

**Linear Resonance**

Let us consider a linear LRC circuit as shown in figure below.

Total Impedance of Network Z = (jωL – j/ωC) where w = 2πf

If frequency f is varied such that Z = 0 then the current through the circuit will shoot as only resistance R will limit the current. ** This frequency (ω = 1/√LC) is called Resonance frequency.** Generally, the resistance of a practical system is quite low as compared to inductance and capacitance of circuit. Therefore, under resonance condition, the current through the circuit will be theoretically infinite but practically it will be quite high. Such resonance phenomenon is called Linear Resonance as the value of Inductance (L) and Capacitance (C) of circuit is fixed. It shall be noted that, linear resonance do not take place at power frequency as clear from above discussion.

**Ferroresonance**

Let us consider a power system consisting of a source and a transformer. The Transformer is connected to the source by mean of high capacitance Cable. For the sake of understanding and practical calculation, let us ignore the transformer phase to phase and phase to ground capacitance. But it shall be noted that at voltage higher than 15 kV, these capacitance become significant enough to be considered. Single phase equivalent circuit of the system is shown in figure below.

In the above figure, shunt capacitance is cable capacitance to ground. It is obvious from the above figure that, even in case of Switch S2 is open, magnetizing current I is flowing through the transformer through shunt capacitance of cable. Thus it makes a series circuit of cable capacitance and transformer reactance.

** Transformer reactance is not fixed rather it varies. How?** In fact transformer reactance does not only depends upon the frequency but it also depends on the magnetic flux in the transformer core. Therefore, the reactance will follow the saturation or magnetization curve of core as shown below.

Thus for a particular value of flux in the core, it may happen so that inductive reactance becomes equal to capacitive reactance. Mathematically,

ωL = 1/ωC

L = 1/ω^{2}C as L is variable here.

Thus for the above value of transformer inductance L, resonance will take place. This resonance is called Ferroresonance. Due to Ferroresonance, the current through the circuit will be very high. This high current will cause overvoltage due to equipment impedance as V = I_{R}xZ_{equipment } where I_{R} = Current under Ferroresonance and Z_{equipment} is impedance of equipment.

**Difference between Ferroresonance and Linear Resonance**

Ferroresonance is different from linear resonance. Following are some important differences between them:

- Linear Resonance take place at a frequency determined by the value of inductance and capacitance (w = 1 / √LC). Ferroresonance take place at power frequency.

- Value of inductive reactance at power frequency is constant in linear resonance. The value of inductive reactance is nonlinear as determined by magnetization / saturation curve of core material.