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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
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Ionization Processes
Ionization by simple collision
•1
2𝑚𝑒𝑣
2 > 𝐸𝑖
• 𝑀 + 𝑒− ⟶𝑀+ + 2𝑒−
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Ionization Processes
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−
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Ionization Processes
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−
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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
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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
𝑥
𝑛𝑥
= 𝛼 𝑑𝑥𝑥
0
𝑛𝑥
𝑛0
• ln𝑛𝑥
𝑛0= 𝛼𝑥
• 𝑛𝑥 = 𝑛0𝑒𝛼𝑥
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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
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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
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Townsend’s second ionization process
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
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Townsend’s second ionization process
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
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Townsend’s second ionization process
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
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Townsend’s second ionization process
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)
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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
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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
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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
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Streamer or Kanal mechanism
Photons generate secondary electrons by the photoionization process
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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
𝛼
𝑝 as a function of field strength
E and gas pressure p
•𝛼
𝑝= 𝑓
𝐸
𝑝
Substituting this into Townsend’s criterion, we have
• 𝑒𝑓
𝐸
𝑝𝑝𝑑
=1
𝜐+1
After modification and substituting 𝐸 =𝑉𝑏
𝑑 for uniform field we get
• 𝑓𝑉𝑏
𝑝𝑑=
𝐾
𝑝𝑑
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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
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Paschen’s Law
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Polarity Effect
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Polarity Effect
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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)
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Influence of Water Content on Vb
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Measured quantities of liquid insulators
Analytical • Acid value
• Sediments
• Water content
Physiochemical • Electrical strength
• Resistivity
• Loss factor
• Relative permitivity
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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 %
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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
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Variation of Vb with time application
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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!
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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%
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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
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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
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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
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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
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