Corona Effect and Discharge in Power Transmission Lines

Some ionization is always present in air due to cosmic rays, ultra-violet radiations and radioactivity.  Therefore, under normal conditions, the air around the conductors contains some ionized particles (i.e., free electrons and +ve ions) and neutral molecules.

When p.d.is applied between the conductors, potential gradient  is set up in the air which will have maximum value at the conductor surfaces.  Under the influence of potential gradient, the existing free electrons acquire greater velocities. The greater the applied voltage, the greater the potential gradient and more is the velocity of free electrons.

When the potential gradient at the conductor surface reaches about 30 kV per cm (max. value), the velocity acquired by the free electrons is sufficient to strike a neutral molecule with enough force to dislodge one or more electrons from it.

This produces another ion and one or more free electrons, which is turn are accelerated until they collide with other neutral molecules, thus producing other ions.  Thus, the process of ionization is cumulative. The result of this ionization is that either corona is formed or spark takes place between the conductors.

• Related Post: Ferranti Effect – Causes, Advantages & Disadvantages
  

Mathematical Modelling of Corona Effect

Corona effect or corona discharge is a phenomenon that results from a partial discharge in the air (or in any fluid) caused by the ionization of the environment when an electrical current flows in a conductor and when the electric field gradient^[1] is strong enough to ionize the environment, but it is not strong enough to cause dielectric breakdown^[2] or arcing between the conductors.

This phenomenon that is characterized by a glow (mostly with a color in blue/violet spectrum), mainly happens in overhead lines, close to the suspension and strain insulators, when the distance between conductors is much greater than the diameters of the conductors.

Generally for parallel conductors in the air there is corona effect when.

D/r < 5.85

Where:

• r is the radius of the conductors
• D is the distance between the conductors

When studying corona effect, it is important to evaluate the minimum value of the voltage between phases or between one phase and the neutral (or the ground) for which the corona effect takes place.

This voltage is named Critical Disruptive Voltage. If r [cm] is the radius of the conductor, d [cm] is the distance between the conductor and the neutral (or the ground) and U [V] is the gradient of the electric field E (mathematical notation: grad E), the critical disruptive voltage that we will designated as G, is calculated by the equation:

G = (U / (r x ln (d/r)) [V/m]

Where ln represents the natural logarithm.

To corona effect takes place it is necessary that G will be equal or greater than the disruption voltage of the air, that at atmospheric pressure (1.01325×10⁵ Pa = 1 atm = 760 mmHg^[3]) and at a temperature of 25 ºC is equal to 30 kV/cm – considering the maximum value of U – or 21.2 kV/cm – considering the rms^[4] value of U.

Designating by G₀ the value of grad E that obeys to the above condition the critical value of the disruption voltage (U_C) is calculated by the equation:

U_C = G₀ x r x ln (d/r) [kV/phase]

For different conditions of temperature and of atmospheric pressure, the density of the air is also different; it is possible to express that variation by a factor δ that for a given pressure P [Pa] and temperature θ [ºC] is calculated by the equation:

δ = (3.92 x 1.01325×10⁵ x P) / ((273 + θ) x 760)

Being G’₀ the value of grad E corresponding to the new atmospheric conditions, its value is calculated by the equation:

G’₀ = δ x G₀

Hence, the critical value of the disruption voltage (U’_C) is calculated by the equation:

U’_C = G₀ x r x δ x ln (d/r) [kV/phase]

Taking into account the irregularity of the conductor surface and expressing that irregularity as a factor m₀, the value of U’_C is then:

U’_C = m₀ x G₀ x r x δ x ln (d/r) [kV/phase]

Common values of m₀ are:

• Polished conductors: m₀ = 1
• Dirty conductors: m₀ = 0.92-0.98
• Stranded conductors: m₀ = 0.8-0.87

Another value used to characterize the corona effect is the Visual Critical Voltage, represented by U_V, that is the minimum voltage between one phase and the neutral (or the ground) for which the corona effect takes place all along the conductor. That voltage is calculated by the following empirical equation:

U_V = m_v x G₀ x δ x 3 x (1 + (0.3 / √(δ x r)) x ln (d/r) [kV/phase]

Factor m_v is also a “measure” of the irregularity of the conductor, assuming the following values.

• Polished conductors: m_v = 1
• Rough conductors: m_v = 0.72-0.82

Another value that must be calculated when studying the corona effect is the losses caused by this effect; considering the rms value of U_C and being U the rms rated voltage of the network, both in kV, and f [Hz] the rated network frequency, losses by corona effect (P_CO) are calculated by the equation:

P_CO = 242.2 x ((f + 25) / δ) x √(r/d) x (U(exp)2 – U_c²) x 10^-5 [kW/km/phase]

• Related Post: Typical AC Power Supply system (Generation, Transmission and Distribution)
  

Important Terms Related to Corona

The phenomenon of corona plays an important role in the design of an overhead transmission line. Therefore, it is profitable to consider the following terms much used in the analysis of corona effects:

Critical Disruptive Voltage

It is the minimum phase-neutral voltage at which corona occurs. Consider two conductors of radius r (cm) and spaced d (cm) apart.  If V is the phase-neutral potential, then potential gradient at the conductor surface is given by:

g =[V/ r log_e (d/r)] volts / cm

In order that corona is formed, the value of g must be made equal to the breakdown strength of air.  The breakdown strength of air at 76 cm pressure and temperature of 25ºC is 30 kV/cm (max) or 21·2 kV/cm (r.m.s.) and is denoted by g_o.

If V_C is the phase-neutral potential required under these conditions, then,

g_o =[V_c/ r log_e (d/r)] volts / cm

where g_o = breakdown strength of air at 76 cm of mercury and 25ºC = 30 kV/cm (max) or 21·2 kV/cm (r.m.s.)

• ∴ Critical disruptive voltage, V_c = g_o r log_e d/r

The above expression for disruptive voltage is under standard conditions i.e., at 76 cm of H_g and 25ºC.  However, if these conditions vary, the air density also changes, thus altering the value of g_o.

The value of g_o is directly proportional to air density.  Thus the breakdown strength of air at a barometric pressure of b (cm) of mercury and temperature of tºC becomes δ go where

δ = air density factor = 3.92b / 273 +  t

Under standard conditions, the value of δ = 1.

• ∴ Critical disruptive voltage ,V c = g_o δ r log_e d/r

Correction must also be made for the surface condition of the conductor.  This is accounted for by multiplying the above expression by irregularity factor m_o.

• ∴ Critical disruptive voltage, V_c = m_o g_o δ r log_e d/r …. kV/phase

where,

• m_o = 1 for polished conductors
• = 0·98 to 0·92 for dirty conductors
• = 0·87 to 0·8 for stranded conductors

Visual Critical Voltage

It is the minimum phase-neutral voltage at which corona glow appears all along the line conductors.

It has been seen that in case of parallel conductors, the corona glow does not begin at the disruptive voltage V_c but at a higher voltage V_v , called visual critical voltage.

The phase-neutral effective value of visual critical voltage is given by the following empirical formula :

where m_v is another irregularity factor having a value of 1·0 for polished conductors and 0·72 to 0·82 for rough conductors.

• Related Post:  Power Distribution in Industries
  

Factors & Conditions Effecting Corona

The phenomenon of corona is affected by the physical state of the atmosphere as well as by the conditions of the line.  The following are the factors upon which corona depends :

Atmosphere

As corona is formed due to ionization of air surrounding the conductors, there-fore, it is affected by the physical state of atmosphere.  In the stormy weather, the number of ions is more than normal and as such corona occurs at much less voltage as compared with fair weather.

Conductor size

The corona effect depends upon the shape and conditions of the conductors.  The rough and irregular surface will give rise to more corona because unevenness of the surface decreases the value of breakdown voltage.  Thus a stranded conductor has irregular surface and hence gives rise to more corona that a solid conductor.

• Related Post: Introduction to Harmonics – Effect of Harmonics on Power System

Spacing Between Conductors

If the spacing between the conductors is made very large as compared to their diameters, there may not be any corona effect.  It is because larger distance between conductors reduces the electrostatic stresses at the conductor surface, thus avoiding corona formation.

Line Voltage

The line voltage greatly affects corona.  If it is low, there is no change in the condition of air surrounding the conductors and hence no corona is formed. However, if the line voltage has such a value that electrostatic stresses developed at the conductor surface make the air around the conductor conducting, then corona is formed.

Power Loss Due to Corona

Formation of corona is always accompanied by energy loss which is dissipated in the form of light, heat, sound and chemical action.  When disruptive voltage is exceeded, the power loss due to corona is given by:

Methods of Reducing Corona Effect