ELECTRICAL CORONA

Reading Time: 18 minutes

WHAT WOULD YOU FIND?

INTRODUCTION

PHYSICS

EFFECTS

AC AND DC CORONA

MATHEMATICAL DESCRIPTION

REMEDIES

EVEN DEMONS CAN BE TAMED!

UNANSWERED QUESTIONS

REFERENCES

Note: A better-edited version of this blog is available in original MS Word fromat, link below:

https://drive.google.com/open?id=14-sLYDWD_Io-uCGAdmw8XkM1w3OsPTre

INTRODUCTION

We have got in our head what is electrical breakdown means actually, refer to the previous blog if not!

The puncturing of the porcelain or polymer insulators is quite rare however the air the major insulator in overhead line give up quite easily if care is not taken. The breakdown of air is a phenomenon called corona discharge. In High-Voltage transmission (HVDC and HVAC) this becomes a critical design consideration. Why?

We find description of this phenomenon as early as 1920s in Peek’s foundational work, electric utilities have been extensively researching on it for past 50 years, still we have not uncovered it much clearly and completely. However, modern system does manage to effectively tackle the corona problems and, in this blog, we will see all about it.

A visual introduction would be very helpful to begin the topic:

https://youtu.be/C0Fry6ktu4w

IEEE definition of the phenomenon is as follows:

A luminous discharge due to ionization of air surrounding a conductor due to electric flux density (or voltage gradient) exceeding a certain critical value is called corona discharge.

We had already seen the distribution of the dielectric field, and we also know that the points at which it exceeds the flux density limit (30 kV per cm for air) the air starts conducting.

PHYSICS OF PHENOMENON: WHAT IS GOING DOWN THERE?

In general, any type of corona can be explained in following layman language:

• Ionization and excitation: Though the air is neutral fluid but there are many sources which don’t allow it to be. The UV radiations from Sun, the Cosmic rays from space, the gamma rays from radioactive decay in soil are major sources for air ionization. These natural ionizing events create 20 ion-electron pair/cubic cm per second.
• Electron accelerates: As soon as the potential gradient threshold limit is surpassed at the surface, it becomes capable to impart enough kinetic energy to the electron, generated from the ionization.
• Collision and Avalanche: The energetic electrons collide with neutral gas molecules and knocks out electrons and effect become cumulative, leading -to formation of a conducting air, the plasma.
• Drift out: Soon the electrons move out of range of high potential gradient and become less energetic and avalanche fades.
• Recombine: The electrons slowly find positive ions and recombine to emit light in visible or UV region, they also initiate chemical reactions leading to formation of ozone, etc.

Note: Not all recombination takes place far away from conductor, they also occur in plasma region.

Now, the polarity of charge on the conductor significantly changes the process.

POSITIVE CORONA

When conductor has positive change:

1. The electrons generated in plasma region are immediately drifted inwards, thus electron density in vicinity of conductor is lesser.
2. of electrons are less but majority of them are in region of high potential gradient, hence the average energy of electrons is high.
3. These electrons cannot support (or initiate) low energy chemical reaction.
4. The high energy level of electron gives the phenomenon its characteristics emission of blue light or UV radiation.

NEGATIVE CORONA

When conductor charge is negative:

1. The electron generated in the plasma region is repelled outwards, so as a result, in this case, large no of electrons in vicinity of conductor is observed.
2. However, more electrons are concentrated in region far way from conductor surface, in low potential gradient hence are in low energy state.
3. Due to low average energy of electrons, inelastic collision with neutral molecule don’t contribute significantly in avalanche as do the knocking of electron by photons (photoelectric effect) emitted from the recombination taking place in high potential gradient region of plasma.
4. Ozone production is a relatively low energy process, average energy electrons in negative corona are perfect initiator.
5. The energy state is also responsible for the characteristic red color of discharge. (Note: Red is low energy radiation compared to violet or blue)

+VE CORONA	-VE CORONA
Less no. of electrons	More electrons
Highly energetic electrons	Low average energy state
Avalanche produced by inelastic collision	Avalanche produced by photoelectric effect
Blue-violet uniform glow	Red glow
Less ozone	More ozone

NOTE: Modes of corona have been further classified based on voltage level. Research paper on the same is listed in references.

EFFECTS

Now corona have observeed to produce the following effects:

Light emission:

The recombination of electrons with positive species emit characteristics electromagnetic-waves. More on that later.

Radio Noise:

Experimental data have shown that the corona current is pulsating in nature. We haven’t found out yet! The frequency of this current lies in wide range of order of MHz, large part of which lies in our defined radio frequency band.

This current produces two unwanted effects:

1. This high-frequency corona current, called harmonics adds to load current of transmission line and cause distorted current and voltage sine waveforms, highly undesirable. In layman terms, it is called power pollution.
2. Bound by laws of physics they produce electromagnetic waves in rf band, which interfere with the telecommunication signals. Depending on the distance, orientation, and several other factors the effect ranges from negligible noise to complete distortion of the communication signal.

Note: The radio waves and light emission are occurring on the same physics rules. 

Audible Noise:

Energy discharge is occurring in form of fast-moving particles in air. And audible noise is nothing but pressure disturbance in air created by motion of air particles. Corona discharge sounds like a hissing, low amplitude and occurs over wide frequency spectral range.

4. Chemical effects:

The ionized electrons start a cumulative process of forming electrically charged species. Oxygen atoms are major neutral atoms to form radicals O, which then combine with O or O2 to form O2 or O3 respectively. The reactive nascent oxygen also combines with metals and organic matter. The reactive ozone under extreme electrical stress might also react with stable nitrogen to form oxides. The ozone also reacts with insulation material, corroding them slowly, leading to damage without a sign of warnings.

Moreover, over a certain concentration ozone has proved to be toxic to life.

All of these are confirmed by many shreds of evidence like the smell of ozone, deposition of white powder, and worn out insulators.

The insulation degradation is additive effect of corona and other environmental factors

Power loss:

All of these effects which include light, radio waves, audible waves generation and also, heat produced, lead to a waste of energy. To calculate the corona power loss, we have some methods and empirical formula, none of them with error less than 30%. Which marks the complexity of corona discharge!

Conductor vibration:

The effects mentioned above are monitored to determine the corona performance of any transmission lines. However, a weird, not much considered effect is also there, mechanical vibration of conductors.

The wires under tests for corona noticed to vibrate in fundamental and other harmonics.

AC and DC CORONA

**Contribute

HVAC	HVDC
Poor foul weather performance	Better performance in foul weather
More radio interference and audible noise	Reduced RI and AI in wet weather

MATHEMATICAL DESCRIPTION

We have already calculated the potential gradient distribution in space for parallel conductor case and we also know that it is maximum at the surface of conductor.

And is given by,

For a given conductor spacing, and given voltage level, the potential gradient obtained at the surface will be constant, independent of any other external factors.

Now, the maximum dielectric stress that could be handled by air is g₀, 30 kV/cm.

How come?

We know the distribution of potential gradient:

Maximum voltage that could be applied is:Let us see that if it is true that the corona always begins as soon as the potential gradient, g_0, i.e. 30 kV/cm is reached at surface? Or the air can withstand more or less?

The question is reasonable because it has been observed for same voltage level and conductor arrangement, system have shown different corona characteristics. Negligible corona in dry summer but effect multiplies 100X in foul weather/rainy season. 

Effect of conductor spacing:

Question is same like: does the elastic limit of a rod depends on its physical dimension like its length. Clearly the rod always breaks at the same unit stress, no matter how long or short it is, so does the air’s dielectric strength is independent of conductor spacing. (Assuming air as a rod) 

Effect of conductor diameter:

It’s a well-established experimental fact that the air is apparently stronger at surface of small conductor, for same conductor spacing the potential gradient at surface of small conductor for onset of corona is greater than 30 kV/cm.

So, air breakdown potential gradient at surface is gv not g0, so the equation becomes:

Let us call gv as apparent dielectric strength of air.

The experimentally calculated formula for the minimum potential gradient at surface to start corona is:

Now, let us suppose that  occur at  from the centre, so:

It comes out that g0 should always be occurring at distance of  0.301sqrt(r) from surface of conductor not at the surface of conductor. At surface there should be some higher value, gv.

These terms however become insignificant for larger diameter conductors.

People have tried to explain the phenomenon using different theories, among them best suited is the electron theory.

“The 30 kV/cm is limit just sufficient to accelerate the electron over its mean free path to acquire as much as energy to form ions by collisions. The electrons would require some finite distance to get sufficiently energetic, on the other hand, the potential gradient from the surface goes on decreasing hyperbolically. Thus, greater potential at the surface of conductor is required than the dielectric strength of air, so that electrons get enough time (distance) to get enough kinetic energy.

Here rises a very intriguing question, and it is, would corona will not take place if we keep the conductors spacing less than 0.301sqrt(r).

Its is quite amazing to know the answer as big “YES”.

The experiments have shown that the same fragile air, in experimental setups of small air spacing has been made to withstand gradients as high as 200 kV/cm.🤐🤐

Then why we don’t hang our wires as close as possible? 🙃

Note 1: It should be noted here that the 0.301sqrt(r) distance is several times greater than the mean free path, so the electron undergoes many collisions before actual ionizing collision. It is only after accelerating for this distance the electron gain required K.E. To get real clear, a dive into the depths of Kinetic theory of gas is required.

Note 2: When we are talking of ionization of air in actual it is the oxygen which is being ionized to form highly chemically active O, (30 kV figure is respect to that only). The radical than combines with different ions to form ozone, oxides, etc. depending on its energy level.  

Air density: Effect of temperature and pressure

Does the temperature and the pressure also have influence on the g0 and gv?  

Yes!

Different high voltage transmission systems (HVDC/HVAC) have shown an increase in corona loss from 3 to 100 times in foul weather than in clear sunny day. This indicates that meteorological conditions affect the g0 that’s why corona intensifies for same system and same voltage level.

We know that the for decreasing air density the intermolecular spacing will widen, which also implies that mean free path of electrons will increase, thus potential gradient (g0) required decreases, with decreasing air density.

δ is the relative density.

Using, the ideal gas equations, the ratio of density is calculated at two different temperatures and pressure, reference taken as 25° C and 75cm pressure ( δ is taken as 1). (PM=dRT)

But this proportionality relation seems not applicable for the gv, thus the equation was taken of form:

Repeated experiments, and fitting the results led to revealing f(δ) as:

So,

and the new accelerating distance becomes:

Accelerating distance increases with decreasing density. WHY?

We at CEV also cannot figure out, share with us if you can.

Conclusion: For decreasing air density the dielectric strength of air decreases proportionally, whereas the apparent strength also shows a non-proportional decrease.

 

Effect of Conductor surface:

To consider the effect of surfaces on corona discharge becomes of crucial importance when designing any product like connectors, spacer dampers, markers, end lockers, etc for high voltage applications.

To get an intuition of how the surface would impact the corona discharge, consider a uniform sphere being excited by high-voltage, for any voltage level the electric lines of force in air (or dielectric lines) around the surface on conductor is uniformly distributed. Now if we excite a metal sample which has non-uniform sharp corners then would the field distribution remain uniform?

The answer is no.

Various techniques are employed to find the rough distribution of electric field around the products, most viable is the FEM technique. This Finite Element Method (FEM) is used more popularly in civil and mechanical engineering, in visualizing the stress, compression and tension and identify the weak and vulnerable points in their structures.

Those same FEM techniques are used to get computer models simulations of the product to identify high potential gradient points.

Let see the result of a study for a HV hardware manufacturing company which exactly proved these theories using the FEM techniques. (refer 123)

 

It comes out that the points with sharp edges (high radius of curvature) has high degree of concentration of field lines thus greater potential gradients and are points where dielectric strengths are first crossed.

When tested for corona performance of the connector the results were as expected.

Visuals confirm that the points predicted by simulation came out to point sources of corona.

To take the effect of surface roughness there is an irregularity factor, m. So, the apparent dielectric strength becomes:

m is 1 for smooth surfaces 

Conclusion: If the conductors get weathered over time and develop rough surfaces, the corona will start at lower voltage levels, at the sharp edges.

Finally, the expression for voltage level at which corona will begin for parallel wire is:

REMEDIES

Corona discharge is highly undesirable in transmission lines because of the effects it produces. An average yearly loss for ±500 kV HVDC line is estimated to be around 25W/m, which is considerably large if summed over a year for larger distances. Included with radio interferences in telecom signals, noise pollution, emission of ozone which degrade the insulation and have toxic environmental effects, the corona discharge becomes a costly affair!

The current majorly employed techniques to check corona are:

Bundled conductors:

Bundling of conductors is the most effective and widely used techniques, to decrease the potential gradient on conductor surface for a given voltage level or in other way to increases the corona inception voltage and thus improving the corona performance of a transmission line.

For increasing voltage levels two, four, six and sometimes eight stranded conductors per phase are bundled using spacer damper at regular intervals are employed. These dampers keep in check that the conductors maintain required distance during high-winds.

Now the actual question to be answered is how the potential gradient at the conductor surface decreases for a system of bundle conductors. The computation of electric field for a bundled arrangement can be done using numerous available mathematical tools.

Various research papers have used techniques of conformal mappings, simulated charge methods, FEM, integral equations, and other methods to calculate the field distribution much accurately.

Here let us use basic superposition method to conclude that the gradient decreases for bundle conductors.

Consider a single conductor of radius r, at voltage V from a plane at relatively large distance D.

Equations of electric field in space, conductor voltage and charge are as follows:

Now if we take two conductors at same voltage separated by a spacing S, then charge redistribution takes place.

Let Q1 and Q2 be charge on conductor 1 and 2 respectively:

Potential at surface of conductor 2 is (by integrating electric fields along x-axis):

Similarly, by geometry potential at the conductor 1 surface is:

Now as we know-

Which leads to-

So, the potential becomes:

Assuming S≈r,

Since we are computing for same voltage level, clearly-

If not accurately, we can surely say that:

Now calculating the electric field at the surface of conductor 2:

Solidly we can conclude from the above expressions that the potential gradient decreases with adding more conductors in for one phase.

More accurate methods of calculation are given in references xx and yy.

Here are graphic simulations of electric field calculated for single, two, three and four conductors.

         

Notice how the gradient decreases for increasing the no of conductors in a bundle.

For three and four conductors bundle field even decreases more:

             

Another important point to be noted is that the dependence of potential gradient is not linear for a given no of conductors in bundle. The potential gradient is a function of bundle geometry and achieves minimum value only for a particular value of bundle radius (conductor spacing).

Note:

1. All the corona performance parameters like loss, radio interference, audible noise, etc. seemed to improve considerably for bundled conductors.
2. Further study would reveal other advantages, like:
   1. Better thermal properties, better cooling due to increased surface area
   2. Reduced line inductance
   3. Increased transmission capacity
3. However, wind and ice loads are greater for this arrangement, and also complication in designing and placing spacers is there.

Corona Rings:

Another effective remedy has same underlining principle of redistribution of electric field lines such that the potential gradient limit is exceeded only at few points!

Use of curved smooth metal rings (shown above) called as corona ring connected to the high voltage hardware reduces the gradient on conductor surface by redistributing field in more uniformly.

FEM simulation confirms the same:

The red regions (relatively sharper) have high potential gradient as act at point source for corona discharge, when electrically connected with the corona ring the field lines become uniform in space, hence improving the corona performance. In this particular case, they also improve the voltage drop distribution in the insulator strings, when used also for this purpose they are technically called grading rings for insulators.

When used specially for conductors (HV apparatus) they are called corona rings.

Nearly all the hardware of high voltage transmission system uses corona rings:

1. Corona rings safeguarding the sharp junction points of conductors and insulator and also improving the string efficiency:

2. Circular corona rings on the switch gears at the HV substation:

Smoothening:

We have already seen in the that the electric field exceeds the threshold limit first at the sharpest points due to greater concentration of lines. So, transmission line components are designed to be free of sharp edges and rough surfaces.

 

DEMONS CAN ALWAYS BE TAMED!  JUST USE SCIENCE

Somewhere in the early 1900s, an experimental scientist Birkeland’s high voltage electric gun demonstration model failed due to short-circuited followed by an arc. But soon he realized that the arc generated could be utilized for some useful purpose. Backed by businessman S Eyde he went on discovering a process you all would have heard of- the Birkeland-Eyde’s process for manufacturing of fertilizers. Since then these gas discharges have been used for industrial processes.

Even though the mysteries of electrical coronas remain largely undiscovered yet this phenomenon have found its applications into many crucial fields. These days corona is used for industrial chemical synthesis, photocopy machines, surface treatment, air pollution control, bactericidal applications, in fact they have even proved to improve the insulation, and many others.

Let us divide this section into two parts, application already being used and applications in which research is going on.

PHOTOCOPIER: It is pretty weird to know that we, electrical engineering student’s whole semester visualized corona as devil and in the end comes out to be principle behind our lifeline. 😅😅😅

AIRCRAFTS

OZONE PRODUCTION

Under-research applications:

AIR POLLUTION CONTROL

ELECTRICAL INSULATION

CONCLUSION

The scientific community along the industrial partners have been exploring Corona discharge for a long time, however due to complexity of phenomenon it has largely remained undiscovered and untapped.

Extensive research for HVDCs:

It has now become an absolute necessity to tap the renewable energy from coastal, offshore, and other remote location to keep up with ever-growing energy demand. HVDC system not just provides a gateway to transfer that large power to large distances by integration of renewables on the grid but also comes with great operational benefits of better efficiency, increased stability (no need of synchronism), reduced right of way and what not.

And in these times when HVDC projects are popping up across the globe, not many high-voltage industry companies share high-expertise in HVDC technology as they have in HVAC. Corona remains a critical consideration in any product design and thus extensive research is required.

Usefulness:

Corona discharge have found application in a wide range of field and still continue to unfold in quite unintuitive ways. Air pollution control and improving the electrical insulation are few examples of that class.

So, corona discharge is not just important from HVDC point of view rather it could be an underlying principle of new innovation to come in future!    

UNANSWERED QUESTION

You can contribute to the blog by sharing your wisdom on the following questions:

1. How to calculate the dielectric strength of air, which atoms will you consider for the equation of ionization?
2. Differentiating AC and DC corona in detail, and thus understanding of HVAC and HVDC lines corona performance.
3. Why accelerating distance increases with decreasing air density?

REFERENCES

1. Corona rings: https://www.slideshare.net/sampengalavenkatesh/52introduction-effects-of-corona-ring-design-by-electric-field-intensity-using-3dcoulomb
2. Drive Link includes:
   1. Dielectric Phenomenon: WF Peek
   2. EPRI 365 kV and above Transmission line reference book
   3. HVDC and HVAC lines corona performance
   4. FEM techniques for HV hardware
   5. FEM analysis of Bundled conductors
   6. Biological Effects of transmission lines

https://drive.google.com/open?id=16BCGlCe3XNldjjMVoQ8FgYfbE0Ai6HfJ 

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