**A Full Guide about Corona Effect / Corona Discharge in Transmission Lines**

Table of Contents

- 1 What is Corona or Corona Discharge?
- 2 What is the Difference between Corona effect and Skin Effect.
- 3 Theory of Corona Formation
- 4 Mathematical Modelling of Corona Effect
- 5 Important terms related to Corona
- 6 Factors & condition effecting Corona
- 7 Power Loss due to Corona
- 8 Methods of reducing corona effect
- 9 Solved Examples of Corona Calculations
- 10 Advantages and Disadvantages of Corona Effect

**What is Corona or Corona Discharge?**

When an alternating potential difference is applied across two conductors whose spacing is large as compared to their diameters, there is no apparent change in the condition of atmospheric air surrounding the wires if the applied voltage is low.

However, when the applied voltage exceeds a certain value, called **critical disruptive voltage**, the conductors are surrounded by a faint violet glow called **corona**.

The **phenomenon of corona** is accompanied by a **hissing sound, production of ozone, power loss and radio interference**.

The higher the voltage is raised, the larger and higher the luminous envelope becomes, and greater are the sound, the **power loss** and the **radio noise**. If the applied voltage is increased to breakdown value, a **flash-over** will occur between the conductors due to the breakdown of air insulation.

**Corona effect** or * corona discharge in transmission lines and power system* may be defined as:

The phenomenon of violet glow, hissing noise and production of ozone gas in an overhead transmission line is known as corona.

If the conductors are polished and smooth, the corona glow will be uniform throughout the length of the conductors, otherwise the rough points will appear brighter. With d.c. voltage, there is difference in the appearance of the two wires. The **positive wire** has **uniform glow** about it, while the **negative conductor** has **spotty glow**.

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**What is the Difference between Corona effect and Skin Effect.**

Difference between Corona and skin effect as follows.

**Corona Effect / Discharge:**

As described above, corona is an effect of violet glow, hissing noise and production of ozone gas in an overhead transmission line is known as corona which leads to hissing sound, production of ozone, power loss and radio interference in power system.

**Skin Effect:**

Skin effect is a behavior or tendency of alternating current to flow through the surface (outer layer) of a conductor instead of the core of the wire in power system transmission lines.

In this scenario, the current density is lager near the surface of the wire or conductor and decreases with greater depths in the conductor which leads to increase in resistance of the conductor, thus increase the overall power loss in the power system (generally transmission lines).

**Theory of Corona Formation**

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.

**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* (**1.01325×10 ^{5} 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 **G _{0}** the value of

**grad E**that obeys to the above condition the

**critical value of the disruption voltage**(

**U**) is calculated by the equation:

_{c}**U _{c} = G_{0} 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 1.01325×10 ^{5} 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 G**

_{0}Hence, the *critical value of the disruption voltage* (**U’ _{c}**) is calculated by the equation:

**U’ _{c} = G_{0} 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* **m _{0}**, the value of

**U’**is then:

_{c}**U’ _{c} = m_{0} x G_{0} x r x δ x ln (d/r)**

**[kV/phase]**

Common values of **m _{0}** are:

*Polished conductors*:**m**_{0}= 1*Dirty conductors*:**m**_{0}= 0.92-0.98*Stranded conductors*:**m**_{0}= 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 G_{0} 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 **Uc** 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**

_{c}^{2}) x 10^{-5}[kW/km/phase]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 / cmIn 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 / cmwhere **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

**m**= 1 for polished conductors_{o}- = 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.

**Factors & condition 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.

**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**

It has been seen that intense corona effects are observed at a working voltage of 33 kV or above. Therefore, **careful design** should be made to avoid corona on the sub-stations or bus-bars rated for 33kV and higher voltages otherwise highly ionized air may cause flash-over in the insulators or between the phases, causing considerable damage to the equipment.

The corona effects can be reduced by the following methods:

**By increasing conductor size**

By increasing conductor size, the voltage at which corona occurs is raised and hence corona effects are considerably reduced. This is one of the reasons that **ACSR conductors** which have a **larger cross-sectional area** are used in transmission lines.

**By increasing conductor spacing.**

By increasing the spacing between conductors, the voltage at which corona occurs is raised and hence corona effects can be eliminated. However, spacing cannot be increased too much otherwise the cost of supporting structure (e.g., bigger cross arms and supports) may increase to a considerable extent.

**Solved Examples of Corona Calculations**

**Advantages and Disadvantages of Corona Effect**

Corona effects on communication lines. Corona has many advantages and disadvantages. In the correct design of a high voltage overhead line, a balance should be struck between the advantages and disadvantages. Below are the Advantages and disadvantages of Corona.

**Advantages**

- Due to corona formation, the air surrounding the conductor becomes conducting and hence virtual diameter of the conductor is increased. The increased diameter reduces the electrostatic stresses between the conductors.

- Corona reduces the effects of transients produced by surges.

**Disadvantages**

- Corona is accompanied by a loss of energy. This affects the transmission efficiency of the line.
- Ozone is produced by corona and may cause corrosion of the conductor due to chemical action.
- The current drawn by the line due to corona is non-sinusoidal and hence non-sinusoidal Voltage drop occurs in the line. This may cause inductive interference with neighboring Communication lines.

**Good to know:**

^{[1]} **Gradient** is a differential operator that when applied to a scalar field F defines the vector in which direction is achieved the greatest rate of increase of that field.

^{[2]} **Dielectric breakdown** of an insulating material happens when the value of the electric field applied to that material is too high, causing the material to become conductive. In the air this breakdown happens when the value of the **electric field** is ≈ **3×106 V/m**. In this case a **disruption** takes place.

^{[3]} Between brackets are indicated pressure units: **Pa** – Pascal; **atm** – atmosphere; **mmHg** – millimeter of mercury.

^{[4]} **rms**: **root mean square**, a measure of the magnitude of a varying quantity.

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