TVN en Electrical Strength 1 0 RP

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High Voltage Engineering

Electrical Strength

Ionization

Ionization is the process by which an electron is removed from an atom, leaving the atom with a nett positive charge (positive ion)

First ionization potential is energy required for removing of electron from its normal state in atom to a distance well beyond the nucleus

5/22/2011 High Voltage Engineering 2

Ionization Processes

Ionization by simple collision

2𝑚𝑒𝑣

2 > 𝐸𝑖

• 𝑀 + 𝑒− ⟶𝑀+ + 2𝑒−

Excitation (excited molecule)

• 𝑀 + 𝑒− ⟶𝑀∗ + 𝑒−

• Excited molecule M*can give out a photon of emitted energy h

• 𝑀∗ ⟶𝑀+ ℎ𝜐

Double electron impact

• 𝑀∗ + 𝑒− ⟶𝑀+ + 2𝑒−

Photo-ionization

• Ionization by photon of frequency v with energy hv greater then ionization energy of the molecule

• 𝑀 + ℎ𝜐 → 𝑀+

+ 𝑒−

Electron Attachment/detachment

• If a gas molecule has unoccupied energy levels/when a negative ion gives up its extra electron

• 𝑀 + 𝑒− → 𝑀−

• 𝑀− → 𝑀 + 𝑒−

Breakdown in Gases

Electron Avalanche Mechanism (Townsend Breakdown Process)

• One free electron between electrodes is supposed and electrical strength is sufficiently high

• Simple collision of free electron produce 2 free electrons and one positive ion

• Electrons and positive ions create electron avalanche

Townsend’s first ionization process

Towsend’s first ionization coefficient α • Number of electrons produced by an electron per unit

length of path in the direction of the field

nx is number of electrons at a distance x from the cathode

Increase in electrons dnx in additional distance dx :

• 𝑑𝑛𝑥 = 𝛼𝑛𝑥𝑑𝑥

• 𝑑𝑛

𝑛𝑥

= 𝛼 𝑑𝑥𝑥

𝑛𝑥

• ln𝑛𝑥

𝑛0= 𝛼𝑥

• 𝑛𝑥 = 𝑛0𝑒𝛼𝑥

Townsend’s first ionization process

If the anode is at distance x=d from cathode, the number of electrons nd striking the anode per second is:

• 𝑛𝑑 = 𝑛0𝑒𝛼𝑑

On the average each electron leaving the

cathode produces (𝑛𝑑−𝑛0)

𝑛0 new electrons.

In terms of current

• 𝐼 = 𝐼0𝑒𝛼𝑑

Townsend’s second ionization process

Make the log on both sides of previous equation

• ln 𝐼 = ln 𝐼0 + 𝛼𝑥

From observations the real current increased more rapidly

The additional current is given by presence of positive ions and photons

The positive ions release the electrons by collisions with gas molecules and bombardment of the cathode

The photons also release electrons after collisions with gas molecules or after impact on cathode

Let n0 be the number of electrons released from the cathode by UV radiation and n+ the number of electrons released from cathode by positive ion collisions

Townsend second ionization coefficient 𝜈 is number of electrons released from cathode per incident positive ion, then

• 𝑛 = (𝑛0 + 𝑛+)𝑒𝛼𝑑

n is number of electrons reaching the anode

Then the number of electrons released from gas is

• 𝑛 − 𝑛0 + 𝑛+

Each electron has one positive ion and is assumed that each positive ion releases 𝜈 electrons from the cathode

• 𝑛+ = 𝜐 𝑛 − 𝑛0 + 𝑛+

• 𝑛+ =𝜐(𝑛−𝑛0)

1+𝜐

Substituting n+ in previous expression for n :

• 𝑛 = 𝑛0 +𝜐 𝑛−𝑛0

1+𝜐𝑒𝛼𝑑 =

𝑛0+𝜐𝑛

1+𝜐𝑒𝛼𝑑

• ⟹ 𝑛 =𝑛0𝑒

𝛼𝑑

1−𝜐 𝑒𝛼𝑑−1

In terms of current

• 𝐼 =𝐼0𝑒

𝛼𝑑

1−𝜐(𝑒𝛼𝑑−1)

Townsend Breakdown Mechanism

If the voltage between electrodes increasing the current at the anode is

• 𝐼 =𝐼0𝑒

𝛼𝑑

1−𝜐(𝑒𝛼𝑑−1)

For case of infinite current

• 1 − 𝜐 𝑒𝛼𝑑 − 1 = 0

• 𝜐 𝑒𝛼𝑑 − 1 = 1

• 𝜐𝑒𝛼𝑑 ≈ 1

Townsend Breakdown Mechanism

The condition 𝜐𝑒𝛼𝑑 = 1 is known as Townsend criterion or Townsend breakdown criterion

Townsend criterion defines the threshold sparking condition, if 𝜐𝑒𝛼𝑑 < 1 the current I is not self-sustained

Streamer or Kanal mechanism

When avalanche reaches critical size the combination of space charge field and applied field lead to intensive ionization and excitation of the gas particles in front of avalanche

Then the recombination of electrons and positive ions producing photons

Streamer or Kanal mechanism

Photons generate secondary electrons by the photoionization process

Paschen’s Law

From the experimental results for the breakdown voltage and uniform field gaps as a function of gap length and gas pressure can be derived expression of coefficient

𝑝 as a function of field strength

E and gas pressure p

•𝛼

𝑝= 𝑓

Substituting this into Townsend’s criterion, we have

• 𝑒𝑓

𝑝𝑝𝑑

𝜐+1

After modification and substituting 𝐸 =𝑉𝑏

𝑑 for uniform field we get

• 𝑓𝑉𝑏

𝑝𝑑=

𝑝𝑑

Paschen’s Law

This shows that the breakdown voltage is a function of the product of gas pressure and gap length

• 𝑉𝑏 = 𝐹 𝑝𝑑

This relation is known as Paschen’s law

Paschen’s Law

Polarity Effect

Liquid Dielectrics

Sizable electrical strength (5 – 30 kV/mm)

Ability to dissipate heat

Protect solid insulators from humidity and air

Ability to arc extinction

Electrical strength is mostly influenced by the sort and quantity of solid or liquid particles (fibers or water drops)

Influence of Water Content on Vb

Measured quantities of liquid insulators

Analytical • Acid value

• Sediments

• Water content

Physiochemical • Electrical strength

• Resistivity

• Loss factor

• Relative permitivity

Electrical Strength of Mineral Oils

Sparking voltage of the distance 2.5 mm is measured, the mineral oil is continuously blended

Following values are recorded in a protocol • 6 measured values of Vb (kV) • Mean value 𝑉𝑏 • Standard deviation s

• Variation coefficient 𝑣 =𝑠

𝑉𝑏

Measurement is satisfactory if the variation coefficient 𝑣 < 20 %

Breakdowns in Solid Materials

The dielectric strength of solid materials is affected by many factors (temperature, humidity, duration of test, impurities or structural defects, type of voltages, etc.)

There are various mechanism: • Intrinsic breakdown

• Electromechanical breakdown

• Breakdown Due to Treeing and Tracking

• Thermal Breakdown

• Electrochemical breakdown

Variation of Vb with time application

Intrinsic Breakdown

In case of pure and homogenous dielectric materials, the temperature, environmental conditions suitably controlled and if the voltage is applied for very short time (10-8s) the dielectric strength increases rapidly to an upper limit – intrinsic dielectric strength

The required voltage stress is in order of 1MV/cm

In practice no insulating material is pure!

Electromechanical Breakdown

Due to the presence of electric induction the dielectric materials are subjected to electrostatic compressive forces

When these forces exceed the mechanical withstand strength the material collapse – reduction of thickness

For any real value of voltage the thickness reduction shouldn’t be more then 40%

Treeing and Tracking

In solid materials some gas or liquid pockets are often present

The dielectric strength of material is always equal to dielectric strength of weakest impurities

The charge concentration at voids within the dielectric lead to breakdown step by step

The breakdown is not by single discharge channel but by a tree like structure

Treeing can be observed in all dielectric materials where the non-uniform field is applied

Treeing and Tracking

Tracking is process when the conductive paths (usually carbon) on insulation surfaces are formed

The presence of organic substances is needed to tracking phenomena will occur

Thermal Breakdown

When the insulating material is subjected to electrical field, the material is heated up due to dielectric losses and conduction currents

The conductivity of material is increasing with temperature – positive feedback

The point of instability is reached when the generated heat exceeds the heat dissipated by material - breakdown

Thermal Breakdown

Under alternating currents the total heat generation is:

• 𝜎𝐸2 + 𝑉2𝜔𝐶 tan 𝛿

Whereas the heat is generated primarily from dipole relaxation – dielectric losses

TVN en Electrical Strength 1 0 RP

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