## The Corona current waveform

The Corona discharge under normal circumstances, the parallel current in the line is almost purely capacitive, the applied voltage is 900 volts, and there is no line power loss under no load condition. When the applied voltage increases and corona is formed, the air conducts and power loss occurs. The shunt current does not advance the voltage 900. Therefore, the current waveform consists of two components. The loss component is non-sinusoidal and appears only when the destructive critical voltage is exceeded in either polarity. The resulting waveform is show in Figure. Analysis of the corona current reveals that there is a strong third harmonic component.

## Mechanism of corona formation – Corona discharge

The stress around the conductor is maximum at the conductor surface itself and decreases rapidly with increasing distance from the conductor. Therefore, when the stress rises to a critical value next to the conductor, ionization will only start in this region and the air in this region becomes conductive. The effect is to increase the effective conductor diameter while keeping the voltage constant. This has two implications. First, increasing the effective sharpness of the conductors reduces the stress outside the region, and second, it reduces the effective spacing between the conductors and increases the stress. Depending on which effect is stronger, stress increases or decreases with increasing distance. When stress increases, further ionization occurs, and arcing inevitably occurs.

Under normal conditions, the breakdown strength of air can be set to 30 kV / cm. Coronas are of course affect by the physical state of the atmosphere. In stormy weather, the number of ions normally present is much higher than normal, and the voltage form by the corona is much lower than in clear weather. This reduced voltage is typically about 80% of the sunny day voltage.

The conditions for stabilizing the corona can be analyze as follows.

The electrical stress at the distance x from the conductor of radius x and the distance d from the return conductor is

Where q is the charge on each conductor of length l.

### Mechanism of corona formation – Corona discharge ctd

Therefore, the potential V can be determine from V = ∫dx.

The two charges (+ q and -q) produce equal potential differences, so the total potential difference between the two conductors is twice this value. Therefore, the voltage from the conductor to the neutral point (half the difference) is equal to this value. Therefore, the conductor to neutral voltage is

Therefore, the electrical stress at distance x is

[Note: x and V can both be peak or rms values]

For equally spaced three-phase lines, V is the voltage to the neutral and even if d is equally spaced, the stress is give by the same equation.

For air, the maximum value = 30 kV / cm, so rms = 30 / √2 = 21.2 kV / cm.

The conductor has no electrical stress, so maximum stress occurs when x is minimal, that is, when x = r.

Therefore, for E0, rms is the rms value of the critical breakdown voltage to the neutral point.

### Mechanism of corona formation ctd

Corona is likely to occur if the conductor surface has irregularities. Therefore, a random coefficient m0 is introduced to solve this reduction. Typical value of this coefficient

For smoothly polished conductors, m 0 = 1.0,

= 0.98 to 0.93 (for rough conductors),

For cables with more than 7 strands, ≈ 0.90, and

= 0.87 to 0.83 for 7-strand cable.

A correction factor is introduce because the formation of corona is influence by the mean free path and thus the air density. The air density correction factor is give by the general formula. Where p is the pressure expressed in torr and t is the temperature express in 0 ° C.

Then the critical breakdown voltage can be programmed according to the following formula:

E 0, rms = 21.2 m0 r loge (d / r) kV to neutral