cap 4_en - revizuit
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Chapter 4
SWITCHING PROCESSES
Switching equipment is an important category of electrical equipment having the
main role of establishing and interrupting the conduction in electrical circuits.
The commutation of circuits can be dynamic or statically, after as the switching
equipment performs this operation by mechanical way, through the closing and opening of
electrical contacts, respectively by controlled adjustment of a electrical parameter of
impedance type (for example resistance), specific for switching equipment withoutcontacts.
If the physical processes that occur in switching equipment, during connecting the
circuits, sometimes present less importance, the dynamic disconnection, accompanied by
the ignition of electric arc between contacts, raises difficult problems related to its
extinguishing.
4.1. Ignition and properties of electrical arc
The dynamic disconnection of circuits crossed by the current is close relation with
the ignition between switching equipment contacts of an electric arc through which the
current continues to flow.
Electric arc of disconnection is an autonomous discharge, through which the space betweencontacts, generally electro-insulating, becomes good conductor of electricity characterized
by current density and conductivity of high values, high temperature, pressure greater than
atmospheric pressure and potential gradient (intensity of electric field) of low value.
Fig.4.1 shows volt-ampere
characteristic of a gas discharge, where it
can be localized the electric arc. Glow
discharge occurs for voltage drops at
cathode of 200 ... 250 V, at currents of
10-5 ... 10-1A. The arc discharge has high
levels of current intensity (10 ... 105 A),
respectively reduced levels for the voltage
drop (10 ... 20 V).
The discharge through electricarc, defined as autonomous discharge in
gases, is obtained when it is not necessary
an external ionizing agent, the degree of
ionization of the gas being high enough. In
this way the process creates an electrons
and ions avalanche.
Fig.4.1Volt-ampere characteristic of the gases
discharge
u [V]
100
200
300
i [A]
10-2 10-1 1 10 102 1050
103
b ca
a-Glow dischargeb-Transition zonec-Electric arc discharge
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The voltage us, at which is obtained the crossing from an autonomous discharge toa non-autonomous one its called breakdown voltage and its given by Paschen's law.
According to this, in hypothesis of an uniform electric field established between two
electrodes placed at distance din a gaseous medium located at pressure p, the breakdown
voltage depends only on the product (pd).
Dependence us(pd) is given by Paschen's curves, useful in switching equipment
operating with gaseous environment. These curves, experimentally determined for different
gases are given in Fig.4.2. In construction of switching equipment, it follows that, for an
imposed distance of insulation, d,should be established the values of gas pressure, p, so
that for the breakdown voltage, us, to result of greatest possible values.
H2
0 0.1 0.2 0.3
pd [Pa.m]
1000
2000
us
V]
H2
2
2
CO2
CO2
SO2SO2
O
O
cathod anodelectric arc
ua
E
0
0 x
x
uCuK
uA
EKEa
EA
Fig.4.2 Fig.4.3Paschens curves Arc voltage and potential gradient
The voltage distribution and potential gradient along an arc column in stationary
state is shown in Fig.4.3, resulting that, in the vicinity of the cathode, there is a sudden
variation of voltage, called the cathode voltage drop, uK, the potential gradientcorresponding,EK, having high values.
Along the arc column the voltage uC varies almost linearly so that the potentialgradient can be considered constant of value Ea. At the anode, there is also a sudden
variation of voltage due to the anode voltage drop, uA.
Cathode voltage drop, with values of 10 ... 20 V, can be considered constant, for
the same environment and the same electrodes material. Anode voltage drop has dependent
values of current intensity through electric arc. According to Fig.4.3, the arc voltage, ua,
can be written as:u u u ua K C A ; (4.1)
neglecting the voltage drops at electrodes and supposing constant the potential gradient,Ea,
the relation (4.1) can be written:
u Ea a , (4.2) being the length of the column.
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The extinction of electric arc, the final stage of the disconnection process, is
obtained by deionization of its column which leads to recovery of dielectric strength of
space between switching equipment contacts.
Deionization arc column is achieved by recombination of charged particles and
their diffusion.
Recombination intensity depends on the nature, temperature and pressure of gas in
which burns the electric arc. Low values for temperature, respectively high for pressure and
potential gradient favour the recombination.
Deionization by diffusion consists in spreading of charged particles in zones far
away from the burning space of electrical arc, thus obtaining the decreasing of its column
conductivity.
4.2. Modelling of electric arc characteristics
Considered as a circuit element, the electric arc has properties of nonlinear
resistor, being characterized by a nonlinear dependence between voltage and current
intensity which crossing through it.
Volt-ampere characteristics of electric arc can be static or dynamic, if the variation
velocity of current intensity is very small (in particular zero) or, contrary, it has high
values. The electric arc of direct current (DC) has both static and dynamic characteristics,
while the electric arc of alternating current (AC) has only dynamic characteristics.
4.2.1. Characteristics of DC electric arc
In Fig.4.4a are shown the static volt-ampere characteristics of DC electric arc
obtained for different constant lengths of column.
The curves shape can be explained by the fact that at the increasing of current
intensity, there is a temperature increasing within arc column, causing an important
increase of gas conductivity which leads to decreasing of arc voltage.
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i
1 > >
0
di/dt=0
i0
=const.u'st1
a b
Characteristcs:
dynamic, di/dt>0
static, di/dt=0
dynamic, di/dt
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In Tab.4.1 are given the constant values of Ayrton function for different contact
materials. According to relations (4.3), (4.4), Ayrton approximation function shows a linear
variation of arc voltage ua, related to the length of arc column, for the same current.Also, often in calculations, the approximation function proposed by Nottingham is
used:
u i a c b d ian( ) ( ) , (4.5)
where a, b, c, dare constants, and -column length of electric arc.
The exponent nis computed with the relation
n T
2 62 10
4
, . , (4.6)
Tis vaporization temperature of anode in absolute degrees.
The independence of voltage drops to the electrodes related to the length of the
arc column is considered in Rieder's function, which is expressed:
,i
ln)()i(ua
3
(4.7)
, , , are constants, and - column length of electrical arc.
In Tab.4.2 are given the constant values of Rieder function for different contact
materials.
Tab.4.2
Coefficients of Rieder function
Coefficient
Material [V] [m] [V/m] [A]Copper 0,013
Silver 26 0,011 5,4.105 0,0074
Wolfram 0,016
4.2.2. Characteristics of AC electric arc
As opposed to DC electric arc, the AC electric arc is only a quasi-stationary
process which, at unitary length of the column, is characterized by an equation of powersbalance having the expression:
E i pdQ
dta , (4.8)
where Q is the energy from the arc column, Ea, i-potential gradient, respectively current
intensity andp-power ceded to environment as heat per unit time.
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According to the hypothesis advanced by Mayr, the dependency between the arc
column conductance, G, and the energy Qcan be expressed by the following relation:
G Ke
Q
Q 0 , (4.9)
where Ki Q0are constants.
Because, for the column of unitary length, we can write:
Gi
Ea , (4.10)
after applying the logarithmic function and derivation with respect to time, taking into
account of (4.8), the relation (4.9) leads to the equation:
,p
iu
Tdt
dG
G
a
a
1
11
(4.11)
uais the electric arc column voltage of length .
In the hypothesis of a constant value, P0, for power dissipation per length unit of column
and adopting the notation:
,P
QT
0
0a (4.12)
where Tais the time constant of electrical arc, the differential equation (4.11) becomes:
,TP
Piu
dt
du
u
1
dt
di
i
1
a0
0aa
a
(4.13)
known as the electric arc equation in dynamic conditions.
Considering that the current intensity through electric arc is sinusoidal:
i t I t ( ) sin , 2 (4.14)
for the solution of differential equation (4.13) it is obtained the expression:
,
)T(
)tsin(I
tsinP)t(u
a
a
221
21
2 0
(4.15)
where:
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.T
arctga
2
1 (4.16)
In Fig.4.5 are presented the curves ua(t) given by equation (4.15), for different
values assigned to multiplication (Ta).For (Ta)0are obtained characteristics close to
those of DC arc while for (Ta),the arc voltage is close to a sinusoid.
T =0a
T =0,25a
T =0,5a
t
u , ia
In Fig.4.6 are shown the dynamic volt-ampere characteristics of AC arc.
Another conductance model is based on the Cassie hypothesesavailable for high values of arc current intensity.
Using the conductance models (Mayr, Cassie, etc.), it allows a correct analysis, in
terms of quality, of the applications where the electric arc occurs as circuit element.
Advanced conductance models with several independent parameters are used to
develop the modern techniques in power switching.
4.3. Electric arc extinction
In the dynamic switching, the disconnection process of circuits includes, as
essential phase, the electric arc extinction triggered to the contacts separation of switching
equipment. The extinction is produced in different manner, depending on the nature of
current (alternating or direct current).
4.3.1. Electric arc extinction of direct current
It is considered the DC circuit R, L (Fig.4.7) where during disconnection, between
contacts A, K, it is ignited an electric arc, on his column having the voltage ua(i). The
equation of transient state for this circuit is:
0 2
ua
i
0
1 2
Fig.4.5
The arc current and voltage
Fig.4.6
Volt-ampere characteristics
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Ldi
dtRi u i U i ia ( ) , ( ) , (4.17)(4.17)0 0
U is DC voltage of supply. Using the Ayrton approximation, for equation (4.17) it is
determined the expression:
Ldi
dtRi
iU i i
, ( )0 0 , (4.18)
, , , are constants, and -column length of electrical arc.
During the steady state electric arc (the constant current through the arc), the
equation (4.18) becomes:
i
R L
U u (i)a
A
K i
u
N ua(i)U-Ri
S
0Ldi/dt
U
i2i1 U/R
Fig.4.8 Fig.4.9 Fig.4.7 Fig.4.8Inductive circuit The stability analysis
Ri . (4.19)U i2 0 ( )
Analyzing this equation, it conducts to some conclusions regarding the electric arc
stability in a DC inductive circuit.
Equation (4.19) may admit two real solutions, positive and distinct i1i2,in thiscase the circuit of Fig.4.7 having two points of operation, N and S (Fig.4.8). These are
determined by the intersection of the load straight line (U-Ri) with volt-ampere
characteristic, ua(i)of electrical arc.
The operation point N corresponds
to unstable burning because at small
variations of current intensity around i1
value, resulting the trends of divergent
variation in relation to i1 (for i>i1 to get
di/dt>0, so an increasing trend of current
intensity, while for i
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In steady state, so at variations with low speeds di/dtof the current intensity, whenthe self-induced voltage on the coil can be neglected, the necessary condition for electric
arc extinction, Fig.4.8, it can be written as:
u i U Ri ia ( ) , . (4.20)If in some industrial applications (welding, arc furnaces, etc.) the aim is to perform
a stable burning of electric arc, in technique of switching equipment is necessary to make
an unstable burning, favourable to arc extinction.
According to the above considerations, there are two principle possibilities,
applicable for DC electric arc extinction: movement of volt-ampere characteristic to
increased values of arc voltage, respectively the rotation of load straight line,
corresponding to increased values of circuit resistance.The usage, separated or combined, of the methods mentioned leads, at limit, at
superposition of the operating points N and S (Fig.4.9), the necessary condition for electric
arc extinction is thus satisfied.
According to the relation (4.2), it is mentioned the following usual possibilities for
extinguishing: the increase of arc voltage by columns elongation and its deionization, the
increase of disconnected circuit resistance and the modulation of arc current.
4.3.2. Electric arc extinction of alternating current
AC arc extinction is facilitated by periodical crossing through zero of current
intensity, moments when the deionization of column is maximum. Processes are different,
depending on the voltage level: long electric arc (high voltage) or short (low voltage).In the process of long arc extinction, some parameters of the disconnected circuit
are involved (transient recovery voltage that produces the dielectric stress in circuit breaker
and the current intensity, which stressed thermal the circuit breaker) as well as some
specific parameters of circuit breaker (breakdown voltage of extinction chamber that
depends on the cooling degree and medium of extinction).
In short time intervals that contain the moments of crossing through zero of
current intensity, the arc columns temperature and its conductance decrease rapidly, and
thus it is performed an increasing of dielectric strength of space between contacts.
In the moments of AC arc extinction, on the space between contacts of switching
equipment the transient recovery voltage is applied. It consists from a steady state supply
voltage with the pulsation , on which it overlaps a component of transient state of the
disconnected circuit, of pulsation e>>.
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R LIi
k
k
CZsu (t)r
u(t)
t
u, i
1
3
2
0
a bFig.4.10
Disconnecting a short circuit at the terminals of circuit breaker: a-electrical equivalent
circuit; b-transient state at disconnection, 1-supply voltage; 2 transient recovery
voltage, 3-short circuit current.
In general, it is assumed that the permanent extinction of AC arc is obtained in that
moment of passing through zero of the current when the transient recovery voltage has a
small drift velocity, which can not determine the re-ignition of electrical arc.
Fig.4.10a shows the electrical equivalent circuit of a short-circuit current
interruption, produced at the circuit breaker terminals.
In the most cases, the short-circuit currents are inductive because the parameters
of electrical lines comply the inequalityL>>R.In Fig.4.10b, as the time origin (t=0) is considered the moment of zero crossing of
the short-circuit current ik(t), at which corresponds the peak value of the supply voltage
(curve 1). Curve 2 represents the transient recovery voltage, which containing the supply
voltage, at which is added a transient state component of the oscillating circuit (Fig.4.10a).
The final extinction of long electric arc, between the contacts of high voltage
switching equipment is dictated by the time evolution of conductance G(t)of its, after zero
crossing of current.
In the moment of current zero crossing, the electric power received from the
source is cancelled, but it is continuing the heat transfer from the arc column to the
environment.
If the heat evacuation is taking place with great intensity, the deionization
processes perform quick decreasing of conductance G(t), according to the curve 3 from
Fig.4.11b, and the final electric arc extinction, so the interruption of the circuit.
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24-Feb-96 09.04.40
19.54 19.56 19.58 19.60 19.62-10
-5
This is only possible if the electrons density from residual plasma does not exceed the limit
specified of 109/cm3. Otherwise, after an initial decrease, the conductance increases, after
the curve 3 of Fig.4.11a, and the electric arc is reignited.
Thus, the long arc extinction is obtained through a powerful deionization of thecolumn due to evacuation into the environment, in the vicinity of the moments of current
zero crossing, of a big heat quantity.
The short electric arc is ignited between the contacts of low voltage switching
equipment. Due to its small length of the order 1 ... 3 mm, the extinction is obtained
because of the processes from the contacts vicinity, which are neglected when the electric
arc is long.
Thus, it consists that a requirement for the re-ignition of the short electric arc
between contacts is that, after current zero crossing, voltages with values of 150 ... 250 V
shall be applied on contacts in order to ensure the appropriate potential gradient for the
electronic emission from new cathode.
If the applied voltages have lower values, the short electric arc is finally
extinguished at the first current zero crossing.
4.4. Modelling of recovery voltage between contacts of switching equipment
The measured voltage between the terminals of switching equipment with closed
contacts and crossed by current reaches values of tens of millivolts, which are distributed
mainly on the contact resistance. Between the open contacts of the same equipment can be
measured, in the steady state, values which depend on the supply voltage and the electrical
installation structure. These two states determine the initial values, respectively the final
values corresponding to the transient state of dynamic disconnection.
The dynamic disconnection consists of two phases: the first one, between the
separation time of contacts and that of final arc extinction which is followed by the second
one, characterized by the transient recovery voltage between the contacts of switching
equipment.
The power supply voltage, highlighted between the open contacts of switching
equipment, after final arc extinction on transient duration is called the transient recovery
voltage.
On transient duration of recovering voltage, its values recorded between the
contacts of switching equipment, usually exceed the nominal values, the installation
insulation is thus, stressed by the switching overvoltages.
0
5
10
15
t [ms]
i [A], u , Ga
2
13
23-Feb-96 15.35.34
19.50 19.55 19.60 19.65 19.70 19.75-10
-5
0
5
10
15
t [ms]
i [A], u , Ga
2
3 1
a b
Fig.4.11
The phenomena at current zero crossing: a) thermal re-ignition: 1- arc voltage;
2 - current intensity, 3 - arc conductance; b - definitive extinguishing:
1 -transient recovery voltage.
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The analysis of this process provides useful information regarding the design,
construction, testing and operation of switching equipment.
4.4.1 The dynamic disconnection in AC installations
In order to highlight some aspects regarding the recovery voltage in the AC
installations, it considers the electrical equivalent diagram of a short-circuit disconnection,
Fig.4.10a, short-circuit produced at the circuit breaker terminals.
The circuit parameters are considered concentrated, unlike the real case from the
power installation, where they are distributed. From this point of view, the circuit study of
Fig.4.10a is interesting especially for testing of the switching equipment because, in thetesting laboratories the circuits are typically consisted of elements with concentrated
parameters.Considering the origin when the electric arc is extinguished, which occurs at the
zero crossing of short-circuit current intensity, the equation that describes the circuits
operation from Fig.4.10a can be written as:
000220
202
220
t
rrr
rr
dt
du,)(u,u
dt
du
dt
ud)tsin(U (4.21)
and it admits the oscillatory solution:
,tcossintsincossin
CZUe2)tsin(
CZU2)t(u
eueu
e
u
e
t
ur
(4.22)
where:
.,,
LC
1,
L2
R
,R
C
1L
arctg,2
,C
1LRZ
022
0e0
u
2
2
(4.23)
In real conditions of short-circuit, the equivalent circuit is highly inductive (L
>>R), so it can be considered:
2. (4.24)
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Taking into account the relations (4.23), the parameters andZcan be written as:
.
C
4Z,
2arctg
20
220
22220
2
(4.25)
Because in real installations the following relations are checked:
0 0 e e, , (4.26)
for parameters from (4.25) it is obtained the expressions:
2
1, Z
C. (4.27)
Taking into account the relations (4.23) ... (4.26), the solution (4.22) leads to the
following simplified expression of transient recovery voltage:
,tcosetcosU2)t(u etr (4.28)um
which is plotted in Fig.4.12.
During the very short transient state it is
considered cost1, thus the expression (4.28) can be
still simplified and it is obtained: ,tcose1U2)t(u etr (4.29)
Based on the relation (4.29), it can define the specific
parameters of transient recovery voltage, with a single
frequency, such as:
the peak value, umfor et=, is given by:
;e1U2u em
(4.30)
the oscillation factor, ,defined by the relation:
u
Uem e
21 1, 2; (4.31)
the natural frequency of oscillation, fe:
t0
Um
u(t)
u, u r
ur(t)
Fig.4.12
Transient recovery voltage
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fee
2. (4.32)
As it can see, the parameters of transient recovery voltage have dependent values
of parameters of electrical installations.
Thus, the natural frequency of medium voltage networks (6 ... 35 kV) is 3 ... 4
kHz, while for networks of high and very high voltage, where the distance between the
conductors of overhead power lines leading to high levels of inductance, it is 0.5 ... 1 kHz.
The oscillation factor usually has the values 1.3 ... 1.6.
Through the parameters feand , the transient recovery voltage has an important
influence on the extinction process of AC electric arc, as it is described in 4.3.2.
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