DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
Part I- Chapter 1: Electrical Breakdown in Gases
1.4 Breakdown in non-uniform fields
Instructor: Dr. Jian Li
Lecture 3-1
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.1 Description of non-uniform fields
z
z
z
z
z
z
In non-uniform fields, e.g. in point-plane, sphere-plane, rod-plane
gaps or coaxial cylinders, the field strength and hence the
effective ionization coefficient vary across the gap.
Non-uniform degree of an electric field is defined as: ke= Emax/Eav ,
where Emax and Eav are the maximum and average of the electric
field strength, respectively.
ke<2: slightly non-uniform fields.
Ke>4: strongly non-uniform fields.
In uniform field and quasi-uniform field gaps, the onset of
measurable ionization usually leads to complete breakdown of
the gap.
In non-uniform fields, various manifestations of luminous and
audible discharges (partial breakdown) are observed long before
the complete breakdown occurs.
Lecture 3-2
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.1 Description of non-uniform fields
z
A strongly divergent field in a positive point-plane gap
Lecture 3-3
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.2 Breakdown in slightly non-uniform fields
z
At low pressures the Townsend criterion for spark takes the form
⎧ ⎡ d
⎤ ⎫
γ ⎨exp ⎢ α ( x)dx ⎥ − 1⎬ = 1
⎦ ⎭
⎩ ⎣0
∫
z
where d is the gap length.
For the general case to take into account the non-uniform
distribution of α , the criterion condition for breakdown (or
inception of discharge) may be represented as
⎡
exp ⎢
⎣
∫
xc < d
0
⎤
α ( x)dx ⎥ ≈ 108
⎦
or
Lecture 3-4
∫
xc < d
0
α ( x)dx ≈ 18 − 20
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.3 Breakdown in strongly non-uniform fields
1. Corona discharges
z
z
Definition: A corona discharge is an electrical discharge brought
on by the ionization of a gas (fluid) surrounding a conductor,
which occurs when the electric field is strongly non-uniform and
field strength at or near the conductor surface or exceeds a certain
value, but conditions are insufficient to cause complete electrical
breakdown.
Characteristics:
„ Self-sustained discharges in strongly non-uniform fields
„ Inception voltages of coronas smaller than breakdown voltages
„ luminous and audible
Lecture 3-5
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.3 Breakdown in strongly non-uniform fields
1. Corona discharges
z
z
The field strength Ec at the surface of the conductor in air
required to produce a visual AC corona in air is given
approximately by the Peek’s expressions.
For two transmission lines in parallel, a Peek’s expression
(Peek’s law) is as:
⎛ 0.298 ⎞
⎟⎟
Ec = 21.4δm1m2 ⎜⎜1 +
rδ ⎠
⎝
kV/cm
where:
„
„
„
r - conductor diameter; δ - relative density of air
m1 - constant describing surface condition of conductors
m2 - constant of climate.
u c = Ec r ln
d
r
kV
Lecture 3-6
„
d - distance between two lines
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.3 Breakdown in strongly non-uniform fields
1. Corona discharges
z Problems for electric power transmission
„
„
„
„
„
„
z
Power loss
Audible noise
Electromagnetic interference
Purple glow
Ozone production
Insulation damage
Industry application
„
„
„
„
Impulse coronas weaken propagation along transmission lines of
lightning and switching overvoltage waves.
High-speed printing devices
Electrostatic precipitators
Paint sprayers
Lecture 3-7
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.3 Breakdown in strongly non-uniform fields
2. Polarity effect
z In strongly non-uniform fields, partial breakdown starts at
a electrode with smaller radius, not influenced by material
of electrodes.
z Polarities of electrodes influence breakdown processes,
electric strength, and breakdown voltages of gas gaps.
z Polarity effect is significant in strongly non-uniform fields.
z Rod-plane gap is used to illustrate the breakdown in
strongly non-uniform fields as following.
Lecture 3-8
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.3 Breakdown in strongly non-uniform fields
2. Polarity effect
z Positive or anode coronas
z
z
z
Lecture 3-9
Ionization by electron collision takes
place in the high field region close to
the point.
Electrons are readily drawn into the
anode, leaving the positive space
charge behind.
The space charge causes a reduction
in the field strength close to the
anode and at the same time increases
the field further away from it.
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.3 Breakdown in strongly non-uniform fields
2. Polarity effect
z Positive or anode coronas
z
z
Lecture 3-10
The high field region moves further
into the gap extending the region for
ionization.
The field strength at the tip of the
space charge may be high enough for
the initiation of a cathode directed
streamer which subsequently may
lead to complete breakdown.
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.3 Breakdown in strongly non-uniform fields
2. Polarity effect
z Negative or cathode coronas
z
z
z
Lecture 3-11
The electrons are repelled into the
low field region and become attached
to the gas molecules.
The negative ions tend to hold back
the positive space charge, which
remains in the space between the
negative charge and the point.
In the vicinity of the point, the field
is grossly enhanced, but the
ionization region is reduced. The
effect is to terminate ionization.
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.3 Breakdown in strongly non-uniform fields
2. Polarity effect
z Negative or cathode coronas
z
z
Lecture 3-12
Once ionization ceases, the applied
field sweeps away the negative and
positive ion space charge from the
vicinity of the point, and the cycle
starts again after the clearing time
for the space charge.
To overcome this retarding action of
the ions, a higher voltage is required,
and hence negative breakdown
voltage is higher than the positive
breakdown voltage.
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.3 Breakdown in strongly non-uniform fields
2. Polarity effect
z Inception of coronas
„
„
„
For positive coronas, positive space charge causes a reduction in
the field strength close to the anode. This enhances the inception
voltages of positive coronas.
In contrast for negative coronas, positive space charge enhances
the field strength close to the cathode. This reduces the inception
voltages of negative coronas.
Therefore, coronas occur first during negative half cycles under
AC voltages when applied voltages increase.
Lecture 3-13
leader
1.4.4 Breakdown in long air gap
air avalanche streamer
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
(a) Leader and its front streamer m-k; (b) avalanche occurring at the head of streamer;
(c) streamer m-k transforming into leader and the new streamer n-m;
(d) new avalanche occurrences; (e) field distribution in long air gap
Lecture 3-14
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.4 Breakdown in long air gap
z
Leader discharges
„
„
„
„
z
A leader is a hot, highly conductive channel of plasma.
Leader enhances its front field and a new streamer is hence
generated in the space.
New streamers improve the progress of leader discharge.
The leader effectively projects the electrical field from the nearby
electrode further into the gap.
Final jump (末跃/主放电)
„
„
„
If the power source has sufficient voltage and current, it makes the
streamer zone longer and transfers the spark discharge in the stage
of final jump.
The final jump often does not identify with leader, due to its huge
current and velocity.
Breakdown occurs at the stage of final jump.
Lecture 3-15
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.4.4 Breakdown in long air gap
z
Brief conclusions / 小结
„
„
„
„
„
„
„
流注通道电子被阳极吸引
→电子浓度↑
→电流↑ →热损耗↑ →温度↑
→流注中热电离↑
→电导↑，电流↑
→流注变成高电导的等离子体（先导）
→电场↑→新流注→先导不断推进。
Lecture 3-16
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5 Breakdown under impulse voltages
Lecture 3-17
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5.1 Definition of impulse voltages in standards
z
Full lightning impulse voltages (1.2/50 impulses)
National and IEC standards define:
T1=1.2 μs ± 30%
T2=50 μs ± 20%
T1 = 1.67T
T ′ = 0.3 T1 = 0.5T
„
„
„
O1: virtual origin, defined where the line AB cuts the time axis.
T1: front time, a virtual parameter, defined as 1.67 times the interval T.
T2: time to half-value , a virtual parameter.
Lecture 3-18
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5.1 Definition of impulse voltages in standards
z
Lightning impulse voltages chopped on tails
„
„
„
Lecture 3-19
T1: front time (1.2 μs ± 30%)
Tc: time to chopping time
( 2-5 μs)
Tj : duration after chopping
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5.1 Definition of impulse voltages in standards
z
Switching impulse voltages ( 250/2500 impulses )
„
„
„
Tp: time to peak (250 μs ± 20%)
T2: time to half-value (2500 μs ± 60%)
Td : time at 90 per cent of crest value
Lecture 3-20
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5.2 Breakdown under impulse voltages
1. Time lag of breakdown
z
z
z
For the initiation of breakdown, an electron must be
available to start the avalanche.
Under an impulse voltage of short duration, a gas gap may
not break down as the peak voltage reaches the lowest
breakdown value.
The time which elapses between the application of voltage
to a gap sufficient to cause breakdown and the breakdown
is called the time lag.
Lecture 3-21
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5.2 Breakdown under impulse voltages
z
Time lag components under an impulse voltage.
t = ts + tf
Vs minimum static
breakdown voltage;
Vp peak voltage;
z
Time lag t consists of two components:
„ the statistical time ts which elapses during the voltage application
until a primary electron appears to initiate the discharge.
„ the formative time tf required for the breakdown to develop once
initiated.
Lecture 3-22
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5.2 Breakdown under impulse voltages
z
z
z
In uniform fields, tf << ts .
In non-uniform fields, tf is more significant than ts .
Factors influencing ts : amount of preionization in gaps
„ sizes of gaps
„ radiation producing primary electrons
„
How to reduce the statistical time lag
UV light, radioactive materials and illumination by auxiliary
sparks
‹ application of an overvoltage (Vp-Vs) to gaps
Factors influencing tf :
„ When the secondary electrons arise entirely from electron emission
at the cathode by positive ions, the transit time from anode to
cathode is the dominant factor determining the formative time.
„ Increasing with the gap length and the field nonuniformity.
„ Decreasing with the applied overvoltage.
‹
z
Lecture 3-23
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5.2 Breakdown under impulse voltages
2. Volt–time characteristics
„
„
Lecture 3-24
Impulse generators are used
to generate impulses of
gradually increasing
amplitude and to determine
the time of breakdown.
At each value, the test must
be repeated a number of
times so as to obtain
consistent values.
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5.2 Breakdown under impulse voltages
2. Volt–time characteristics
„
„
50% breakdown voltage U50％
2-μs breakdown voltage U2μs
Lecture 3-25
In uniform and quasi-uniform
field gaps, the characteristic is
usually sharply defined and it
rises steeply with increasing the
rate of rise of the applied
voltage.
In non-uniform field gaps, due
to larger scatter in the results,
the data fall into a dispersion
band.
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5.2 Breakdown under impulse voltages
2. Volt–time characteristics
z
Relationship between flashover voltage per meter and time
to flashover (3-m gap).
1. Rod-rod gap.
2. Conductor-plane gap.
3. Power frequency
Lecture 3-26
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5.2 Breakdown under impulse voltages
2. Volt–time characteristics
z
z
Left half part of the “U-curve”
Time to crest↓→Time lag↓→U50% ↑
Right half part of the “U-curve”
„ Time to crest↑
→Range of space charge↑
→field strength surrounding electrode↓
→ U50% ↑
Breakdown voltages via time to crest
Tcr under switching impulse voltages
in strongly non-uniform fields
Lecture 3-27
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5.2 Breakdown under impulse voltages
z
Volt–time characteristics in insulation cooperation
Two gaps with volt-time characteristics
in good cooperation
Two gaps with crossed volt-time
characteristics
Volt-time characteristics of two gaps in quasi-uniform field (S1) and
non-uniform field (S2)
Lecture 3-28
DEPT OF HIGH VOLTAGE AND INSULATION ENG， CHONGQING UNIVERSITY
FUNDAMENTALS OF HIGH VOLTAGE ENGINEERING
1.5.2 Breakdown under impulse voltages
z
Experimental results of time lags (example)
Í
Time lag as a function of overvoltage
for four gap lengths in air.
„ The curves represent the average
data for all pressures between
atmospheric and 200 mm Hg
„ The overvoltage represents Vp-Vs
Lecture 3-29