Cap 4_En - Revizuit

7/25/2019 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.


11/14

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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Cap 4_En - Revizuit