## Corona discharge – Corona effect

Corona effect is in a uniform electric field, a gradual increase in the voltage across the gap causes the gap to break in the form of a spark without pre-discharge. On the other hand, if the electric field is not uniform, the increase in voltage causes a partial discharge of gas at the point where the electric field strength is first highest, that is, at the sharp point, or when the electrode bends or penetrates. This form of discharge is call corona discharge, and the bluish brightness can be observed. This phenomenon is always accompanied by hiss, and the air near the corona becomes ozone. Corona causes considerable power loss in the transmission line and also causes radio interference.

## Mechanism of corona formation on two conductor lines

When a gradually increasing voltage is apply between the two conductors, no sound is heard initially. When the voltage rises, the air around the conductor is ionize, and at a certain voltage, the corona is heard and a squealing noise is heard. This voltage is call the critical breakdown voltage (DCV). When the voltage is further increase, purple visible light appears around the conductor. This voltage is the initial voltage of the visual corona.

When the apply voltage is a DC voltage, the glow seen at the positive pole is more uniform, but the glow at the negative pole is more irregular, usually with streamers in rough places. At AC voltage both conductors appear to have a uniform glow, but in stroboscopic observation the effect is similar to that at DC voltage.

Further voltage increases corona and eventually sparks between the two conductors. If the conductors are place very close together, the corona may not form before the spark discharge occurs. This condition will be consider later.

The voltage drop is non-sinusoidal due to the current waveform in the line as the corona forms. This also causes power loss.

Due to cosmic rays, there are always some electrons in the atmosphere. As the line voltage increases, the velocity of the electrons near the line increases and the electrons gain enough velocity to cause ionization.

### Mechanism of formation

The working voltage in clear weather must be at least 10% below the critical breakdown voltage to prevent corona formation.

Increasing the effective radius can reduce corona formation. Therefore, due to its larger diameter, steel-core aluminum is superior to hard-wired copper wire conductors, and other conditions remain unchanged. The effective conductor diameter can also be increase by using a bundle conductor.

Corona causes a short circuit and acts as a safety valve against lightning surges. In this case, the advantage of corona is that it reduces the effective amplitude of the surge by partially dissipating the energy produced by the corona, thereby reducing transients. The impact of corona on radio reception is rather important. Current flowing in corona discharge contain high frequency component in it. These cause interference near the line. As the voltage increases, an interfering field will appear before any apparent corona loss. This field has a maximum below the line and decays rapidly with distance. The interference at 50 m from the spool is less than 1/10.

## 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 formation

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 formation

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 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

## Visual Corona

Generated voltage of the visual corona discharge is higher than the critical breakdown voltage. In order to form a visible corona, some degree of ionization must occur and the electrons must be pulled into the excited state. The light produced by the discharge is excited, not ionized, and emits excess energy in the form of light and other electromagnetic waves. To obtain the visible corona formation critical voltage, the critical breakdown voltage must be multiplied by a factor that depends on the air density and conductor radius. In addition, it turns out that the values of the irregular elements are different.

The empirical formula for visual corona formation is

The value of the irregularity coefficient mv of the visual corona is

For smooth conductors, m v = 1.0,

= 0.72 is the local corona on multiple strands (patches)

= 0.82, used for corona measured on twisted lines (all lines)

## Stable corona formation

Considering two conductors, it is only the limit of corona formation. Given a thin layer of ionized air r around each conductor, the effective radius is (r r). The change in electrical stress due to this layer can be determined by differentiation. Thereby

The above expression is negative if loge> 1. That is, d / r> e (= 2.718)

In this case, the effective increase in diameter reduces electrical stress, no further increase in stress is formed and the corona stabilizes. On the other hand, for d / r <e, effective increase in diameter causes electrical stress, which leads to further ionization, further increase in radius, and eventually arc discharge.

In fact, the effective limit of d / r is about 15, not e (= 2.718). For normal transmission lines, the ratio d / r is far above 15, so a stable corona is always produce before the flashover.

For example, on a 132 kV line with a pitch of 4 m and a conductor radius of 16 mm, the value of this ratio is d / r = 4 / 16×10-3 = 250 >> 15.

## Power loss due to corona

At first Corona formation is associate with power loss. This loss has little effect on line efficiency, but its impact on voltage regulation is less important. The more important effect is radio interference.

The power loss due to corona is proportional to the square of the difference between the neutral voltage of the line and the critical breakdown voltage of the line. Given by empirical formula

Where E0, rms = critical breakdown voltage (kV) f = power frequency (Hz) E = phase voltage (line to neutral) (kV)

Under stormy conditions, under clear weather, the critical breakdown voltage is consider to be 80% of the critical breakdown voltage.

## An example

Also determining the critical destructive voltage of a 100 km three-phase 132 kV line (including conductors of diameter), in clear and storm conditions, visual voltage of corona onset, line power loss by corona 1.04 cm, equilateral triangle configuration, Distance 3 m. Ambient temperature is 400 ° C and pressure is 750 Torr. The operating frequency is 50 Hz. [The irregular coefficient can be regarded as mo = 0.85 and mv = 0.72]

Air density correction factor is

∴ Critical breakdown voltage = 21.2 0 r loge (d / r) kV to neutral point = 21.2 x 0.925 x 0.85 x 0.52 x loge (3 / 0.0052) = 55.1 kV

Similarly, corona visible voltage = 21.2 x 0.925 x 0.72 x 0.52 x loge (3 / 0.0052) x [1 0.3 / (0.895 x 0.52) 1/2] = 67.2 kV

Power loss in sunny conditions

= 365 kW / phase

Similarly, the power loss in stormy weather is given by:

= 847kW / phase