# Critical Disruptive Voltage

**What is Critical Disruptive Voltage?**

Critical Disruptive Voltage is defined as the minimum phase to neutral voltage required for the Corona discharge to start.

Basically corona discharge is the current discharge in the air. Therefore it is quite obvious that surrounding air shall breakdown for corona to start. From the basic of Electrostatics, we can say that a dielectric can only breakdown if the strength of electric field is strong enough. But electric field is given as

E = -dV/dx = -Potential Gradient

Thus for corona to start, the potential gradient at the surface of conductor must be greater than the dielectric strength of air.

**Calculation of Critical Disruptive Voltage**

Suppose two conductors each of radius ‘r’ is separated by a distance ‘d’. If phase to neutral voltage is V then potential gradient ‘g’ at the surface of conductor is given as

g = V / [rlog(d/r)]

For corona to start,

g ≥ Dielectric Strength of Air

But Dielectric Strength of Air at a temperature of 25°C and atmospheric pressure = 21 kV /cm (rms)

Therefore at standard temp. and pressure (25°C and atmospheric pressure),

g ≥ 21

V / [rlog(d/r)] ≥ 21

V ≥ 21[rlog(d/r)]

Minimum conductor phase voltage to start corona is Critical Disruptive Voltage (Vc). Therefore,

Vc = 21[rlog(d/r)]

The above expression gives the value of critical disruptive voltage at standard temp. and pressure. But the dielectric strength of air density. Air density in turn is dependent on atmospheric temp. and pressure and hence air density correction factor shall be taken into account while calculating Vc. If atmospheric temp is t °C, pressure is ‘b’ mm of Hg then air density correction factor is given as

ß = [3.92b / (273+t)]

Vc = ß x[rlog(d/r)]

At standard temp. and pressure, ß = 1.

Again, corona discharge depends on the conductor surface condition. Therefore conductor surface irregularity factor shall be taken care by multiplying Vc by surface irregularity factor µ. Hence critical disruptive voltage

*Vc = µxß x[rlog(d/r)]*

Value of surface irregularity factor µ for different surface condition is given below.

Surface Condition |
Value of Surface Irregularity Factor µ |

Polished Surface | 1 |

Conductor with dust deposit | 0.92 to 0.98 |

Stranded Conductor | 0.8 to 0.87 |