9 Transients in Power Systems€¦ · Shital Patel, EE Department Power System - II (3150911) 17 12...

9 Transients in Power Systems

Shital Patel, EE Department Power System - II (3150911) 1

9.1. Types of system transients

Power system transients are an abnormal situation, where the power system is in

dynamic state with large scale fear caused by fault, operations of switches or other

disturbances.

Transient persists for a very short duration i.e. few μs to 1 s but during its occurrence,

system is subjected to great stress from over voltage or over current. In some of the case

severity of transients are such large that it leads to complete shutdown of plant or black

out of entire area.

The main cause of transients in a system are lightning, switching, short circuit and

resonance.

Usually the classifications of transients is carried out based on the speed of its occurrence

such as

(a) Surge phenomena

This type of transients are caused by lightning and switching. It is extremely fast in terms

of its commencement to conclusion speed.

Surges initiates an electromagnetic waves travelling with the speed of light i.e. 3108 m/s

on transmission line. Transient associated with the surges occurs in few millisecond and

dies out after a few reflection.

The reflections of surges builds up an excessive rate of rise of voltage at open end line or

transformer which may damage insulation of equipment.

Selection of insulation level of line equipment and transformer is based on the

overvoltage caused by surge phenomena.

(b) Short circuit

Short circuits results from symmetrical as well as unsymmetrical faults. Occurrence of

symmetrical fault brings the power transfer across the line to zero immediately, whereas

the partially in case of unsymmetrical fault.

It is moderately fast in terms of its commencement to conclusion speed and its speed

depends upon the time constant of the generator winding. The time range of short circuit

transient is from 10 to 100 ms i.e. first few cycles of short circuit current.

Short circuit current attains a very high value that may result in thermal breakdown of

equipment. It does not cause permanent damage as faulty section is quickly isolated form

healthy section by breaker operation.

(c) Transient stability

Due to the short circuit at any part of power system, there is an instantaneous total or

partial drop in bus voltage. This results in reduction of generator power output.

Initially for some instant, turbine tries to keep power output constant, but if this condition

sustained for more time than it causes most sever type of transient i.e. mechanical

oscillation of synchronous machine rotor.

This electromechanical oscillation leads to the loss of synchronism for some or all

machine. Once it happens then it takes hours to resynchronize such black out system.



Transient stability is slow in terms of its commencement to conclusion speed as rotor

swing is quite low and its time ranges from few milliseconds to one minute.

9.2. Three phase sudden short circuit of an alternator

Under steady state short circuit condition, the armature reaction of a synchronous

generator produces a demagnetizing flux and this effect is modelled as a reactance Xa in

series with the induced emf.

The total reactance leakage reactance Xl and armature reactance Xa of the machine is

called synchronous reactance Xd.

When sudden three phase short circuit occurs at the unloaded synchronous generator i.e.

open circuit condition, it undergoes a transient in all three phases by gradually reaching

to steady state condition.

The circuit breaker has to interrupt the short circuit current before steady state

condition.

When fault occurs, immediately a DC off set current appears in all three phase, each with

different magnitude because each voltage wave has different magnitude at the time of

occurrence of fault.

At the instant of short circuit, current is limited by leakage reactance of machine. Since

airgap flux cannot change instantaneously to counter the demagnetization of armature

short circuit current, current appears in the field winding as well as in damper winding

in the direction of main flux.

This current decays depending upon the time constants of winding. Time constant of

damper wing is much less than the field winding, thus during initial short circuit, damper

winding reactance and field winding reactance appears in parallel with armature

reactance.

During middle period of short circuit damper winding current dies out and it becomes

open circuit. At this instant only field winding reactance appears in parallel with

armature reactance.

During finally steady state period of short circuit, field winding current dies out and it

also becomes open circuit. At this instant only armature reactance appears.

o The reactance of synchronous machine appeared in initial short circuit is called sub

transient reactance (Xd’’).

o The reactance of synchronous machine appeared in middle of short circuit is called

transient reactance (Xd’).

o The reactance of synchronous machine appeared in end of short circuit is called

synchronous reactance (Xd).



Xf

+

Eg

Xl

Direct axis subtransient reactance

Xdw

Xa

+

Eg

Xl

Direct axis transient reactance

Xf

Xa

Xa

+

Eg

Xl

Xd

Synchronous Reactance

" "

"

' '

'

1

1 1 1

1

1 1

1

1

g

d l

d

a f dw

g

d l

d

a f

g

d l l a

d

a

EX X I

XX X X

EX X I

XX X

EX X X X I

XX

Synchronous machine is offering time varying reactance from Xd” to Xd’ and finally Xd such

that Xd” < Xd’ < Xd.

If the oscillation of short circuit current of a synchronous machine after the DC off set

current is removed, it is observed that current has three time periods – initial

subtransient period when current is large as machine offers subtransient reactance,

middle transient period when machine offers transient reactance and finally steady state

period when machine offers synchronous reactance.

a

b

c

θ

Extrapolation of transient envelope

Extrapolation of steady envelope

Actual envelope

t

Subtransient period

Transient period

Steady state period



If the transient envelop is extrapolated backward in time, the difference between

transient and subtransient envelope decays fast depending on the damper winding time

constant. Similarly difference between steady state and transient envelop decays in

accordance with the time constant of field winding.

Let,

'

"

Steady state current

' Transient current excluding DC component

" Subtransient current excluding DC component

Direct axis synchronous reactance

Direct axis transient reactance

Direct axis su

d

d

d

I

I

I

X

X

X

"

'

btransient reactance

No load voltage

Difference between transient and subtransient current

Difference between steady state and transient current

Damper winding time constant

Field winding

g

dw

f

E

i

i

time constant

The interrupt ob for finding transient reactance is determined by means of logarithmic

plot. Both current differences decrease exponentially as

//" " ' '0 0and fdw

tti i e i i e

At time t >> τdw the current Δi” dies out and hence

" ' " "0 0log( ) log

dwtf f

t ti i i i

The plot of log (Δi” + Δi’) versus time for t >> τdw becomes straight line with slop of (-1/

τf). As straight line portion of the plot is extrapolated taking inverse log of intercept

corresponding to t = 0.

a

b

c

θ

Extrapolation of transient envelope

Steady state current amplitude

Δi

Δi

t

1 ' ' "0 00

0

log ( ) log expt

ft

tab i i i ab

Though the machine reactances are dependent upon magnetic saturation, the value of

machine reactances are used to calculate fault current and stability limits.



9.3. Restriking voltage after removal of short circuit

Restriking voltage is the transient voltage that appears at or in close immediacy to reach

zero current pause during arcing time i.e. voltage that appears across the breaking

contact at the instant of arc extinction.

L

C

CB

Fault

ie

Restriking Voltage

Recovery Voltage

Time

earc

Vmax

2Vmax

When an alternator connected to a busbar and the load is removed after a short circuit

occurs, it is required to determine the voltage across the circuit breaker during the

opening period.

Let, consider the circuit having L inductance per phase up to fault point and C capacitance

to earth of circuit breaker terminal.

When circuit breaker operates under fault condition, before current interruption the

capacitance C is short circuited by fault and this short circuited current is limited by

inductance L of the system.

When breaker contacts are opened and the arc finally extinguishes at current zero, a

voltage v is suddenly applied across capacitor and so across breaker contacts. The current

i that flows through the fault is not injected to capacitor and inductor.

When breaker contacts are open and arc is extinguished, the current i is diverted through

C so that the voltage v, which is so far been effective only across L is suddenly applied to

inductance L and capacitance C in series.

This L-C series combination forms an oscillatory circuit having natural frequency in order

of 10 Hz to 10 kHz depending on the value of L and C.

2

12

21

n nf

LC

LC

Initial charging current surges tends to carry the voltage across the capacitor and hence

across circuit breaker contacts to double voltage i.e. 2Vmax. This restriking voltage

transient re-establishes the arc.

Assume short circuit current i lags behind the system voltage by 90° and zero time at zero

current.



2

2

maxmax

max

max

2max

2

2

max 2

max

1

Before opening of circuit breaker

sin sin

cos

, 0,

,

…………(i)

Where,

Peak value of reco

L Ci i i

dvi vdt C

L dt

di v d vC

dt L dt

Vi I t t

L

Vdit

dt L

VdiAt t

dt L

V v d vSo C

L L dt

d vV v LC

dt

V

very voltage (phase- to-neutral)

Restricking voltage (phase- to-neutral)

t = Time (sec)

v

The solution of equation (i)

2max

2max

2 2maxmax max max

2 2 22

2

max

( ) ( )

( ) 1

11

( )1 1

,

…………(ii)

Multiply equation (ii) by and pu

n n

n nn

n

n n n n

Vv s LCs v s

s

Vv s LCs

s

VV V VLCv ss LCs s s j s js s

s sLCOr

V A B C

ss s j s j s j s j

s

2

maxmax

t 0

n

n n

s

VA V

j j



2

max max

2

max max

max max maxmax

Multiply equation (ii) by and put

22

Multiply equation (ii) by and put

22

,

1 1 1( )

2 2 2 2

n n

n

n n

n n

n

n n

n n n

s j s j

V VB

j j

s j s j

V VC

j j

Hence

V V Vv s V

s ss j s j s j s

max max max

( ) 1 1 1 cos2 2 2

n n n n

n

j t j t j t j t

n

j

e e e ev t V V V t

Maximum value of restriking voltage occurs when, dv(t)/dt=0

max

max

1 cos 0

sin 0

sin 0

n

n n

n

n

n

dV t

dt

V t

t

t

t

LC

Note

o Only solid fault is considered i.e. no arcing.

o Magnitude of the positive sequence impedance is constant for the period for which

overvoltage is to be determined.

o Effects of saturation and corona are neglected

o Charging current of the transmission line before the fault and load currents are

neglected.

o Current interruption takes place at current zero when the voltage passes through

maximum value.

o System is lossless.



9.4. Classification of restriking voltage transient

The circuit that suffers from voltage transients can be placed under two category.

(a) Single frequency oscillatory transient

L

C

CB

Fault

ie

Restriking Voltage

Recovery Voltage

Time

earc

Vmax

2Vmax

When breaker contacts are open, an arc is formed which generally extinguished at a

current zero. At that time circuit voltage is at peak and it appears across the breaker

terminal but it delays in doing so because of presence of capacitance C i.e. first capacitance

gets charged and then it establishes the voltage across breaker terminal.

Restriking transient voltage at natural frequency of L-C series circuit superimposed on

system voltage i.e. recover voltage.

The natural frequency of oscillation is in the order of 1000 to 10,000 Hz.

(b) Double frequency oscillatory transient

L1

C1

CB

FaultC2

L2

ie

Restriking Voltage

Recovery Voltage

Time

earc

Vmax

2Vmax

In some the case, circuit breaker has section of line on its both side i.e. L and C on both

side of breaker contacts. Before fault clearing, both circuit breaker contacts are at same

voltage.

Once fault has been cleared and arc is extinguished, both side of the circuit oscillates at

their own natural frequencies. Hence a composite double frequency transient appears

across breaker terminals.

When the circuit breaker operates in such case, the load is completely isolated from the

generator and the two halves of the circuit behave independently. Before the switch

operates, the voltage across the capacitors is

2

1 2

c

LV V

L L

Usually L2 > L1 hence the capacitor voltage is a little less than the source voltage at any



time. When the current passes through zero value, the voltage is at its maximum.

When the circuit breaker interrupts the current at its zero, the capacitor C2 oscillates with

L2 at a natural frequency f2 and C1 oscillates with L1 at a natural frequency f1.

1 2

1 1 2 2

1 1and

2 2f f

L C L C

Hence, opening of the circuit breaker results in double frequency transients in the system.

9.5. Travelling waves on transmission lines

Transmission line parameter R, L and C are uniformly distributed over the length of line

and for steady state analysis it is represented by lumped parameter. But for transient

analysis transmission line needs to be represented by distributed parameter.

To understand the travelling wave phenomenon over transmission line, let L and C are

the inductance and capacitance per unit length of the line.

LOAD

VSC1

L1 L2 L3 Ln

C2 C3 Cn

S

When switch S is closed, the inductance L1 acts as an open circuit and C1 as short circuit

instantaneously.

At the same instant the next section cannot be charged because the voltage across the

capacitor C1 is zero and hence charging of the capacitor C2 through L2 is not possible. It

takes take some finite time to charge all successive section of line.

Voltage at the consecutive sections builds up gradually and this gradual building up of

voltage over the transmission line is viewed as a voltage wave travelling from one end to

the other end.

Let, wave after time t has travelled through a distance x and a distance dx is travelled by

the waves in time dt.

Current in the transmission line is the rate at which the charge flows into and out of the

line and the velocity of the travelling wave over the transmission line is dx/dt.

(VCx) VC (i)dq d dx

I VCvdt dt dt

Voltage is the rate at which the flux linkages link around the transmission line due to the

current flowing in up to distance x

(ii)

d d LIx dxV LI LIv

dt dt dt



Taking the ratio of equation (ii) and (i)

2

2

C

V LIv

I VCv

V I L

I V C

V L

CI

V LZ

I C

The ratio of voltage to current has the dimensions of impedance i.e. surge

(characteristics) impedance of the line. It is also known as the natural impedance because

it has nothing to do with the load impedance i.e. purely a characteristic of the

transmission line.

The value of this impedance is about 400 ohms for overhead transmission lines and 40

ohms for cables.

The vast difference in the surge impedance of overhead transmission line and cable is

because of the fact that in a cable conductors are much closer to each other compared to

overhead transmission line so it possesses much smaller L and much larger C.

Now, multiplying equation (ii) and (i)

2

7 0

7

0

12 7

8

1

1

1

22 10 ln

ln

1

4 10

1

4 8.852 10 1 10

3 10 m/s

=Velocity of light

rm

ms

s

r

VI LIv VCv

vLC

vLC

D

DD

D

Above equation suggest that, velocity of propagation of the travelling waves over the

overhead transmission lines is equals to the velocity of light.



In actual practice because of the resistance and reactance of the lines the velocity of the

travelling wave is slightly less than the velocity of light i.e. approximately 250 m/μs.

Equation also concludes that the velocity of propagation of the travelling waves over the

cables is smaller than the velocity of propagation of the travelling wave over the overhead

lines because of the permittivity i.e. for overhead lines εr = 1 and for cable εr > 1.

9.6. Reflection and refraction of travelling wave

Vi , ii Vt , it

Vr , ir

ZC1 ZC2

Discontinuity (Junction)

When travelling wave arrives at a discontinuity in a line, where Zc of the line changes

abruptly.

Some adjustments must take place, if proportionality between voltage and current wave

is to be maintained. This adjustment takes the form of initiation of two new wave pairs.

The reflected voltage wave and its companion current wave travelled back down the line

and are superimposed on the incident wave.

The refracted voltage wave and its companion current wave penetrates and travels

beyond the discontinuity.

Let,

1 2

, Incident wave pair

, Reflected wave pair

, Refracted(transmitted) wave pair

, Characteristic impedances

Reflection coefficient (for voltage)

Refraction(transmission) coefficient (fo

i i

r r

t t

C C

v i

v i

v i

Z Z

r voltage)

Applying Kirchhoff’s voltage and current law at junction.

1 1 2

(i)

(ii)

ti ri r t

C C C

i r t

vv vi i i

Z Z Z

v v v

Solving equation (i) and (ii)

2 1 2

1 2 1 2

2andC C C

r i i t i i

C C C C

r i

Z Z Zv v v v v v

Z Z Z Z

i i



Note

o Open circuited line : ZC2 = ∞ gives α = 1, β = 2

o Short circuited line : ZC2 = 0 gives α = -1, β = 0

o Matched termination : ZC2 = ZC1 gives α = 0, β = 1

It is observed that for matched termination, there is no reflection and line acts as

infinitely long. This thought is important in communication lines but not in power line.

9.7. Variation in voltage and current with the receiving end open circuited

VS

Sdx

When switch S is closed, a voltage and current wave of magnitudes vi and ii travels

towards the receiving open circuited end.

If Zc is the characteristic impedance of the line, than wave is going to see a change in

impedance from Zc to infinite at last element dx of the line.

As the current at the open circuited end is zero, the electromagnetic energy vanishes and

it is transformed into electrostatic energy. As a result, let the change in voltage and

current is

2 21 1

2 2i r

r i c i i

Li Cv

Lv i Z i v

C

vi

ii

1

vi

ii

2

t = t2

t = t1

vr

vi

t = t3

vr

t = t4

vr

vr

ir

t = t5

vr

ir

Also,

1 1

1

r i

r i

C C

r i

r i

r i

v v

v v

Z Z

i i

i i

i i



For a transmission line with an open circuited end, voltage and current wave pair reflects

back fully i.e. voltage positively and current negatively with reflection coefficient α = 1.

9.8. Variation in voltage and current with the receiving end short circuited

VS

Sdx

When switch S is closed, a voltage and current wave of magnitudes vi and ii travels

towards the receiving short circuited end.

If Zc is the characteristic impedance of the line, than wave is going to see a change in

impedance from Zc to zero at last element dx of the line.

As the voltage at the short circuited end is zero, the electrostatic energy vanishes and it

is transformed into electromagnetic energy. As a result, let the change in voltage and

current is

2 21 1

2 2i r

ir i i

c

Cv Li

vCi v i

L Z

vi

ii

1

vi

ii

2

t = t2

t = t1

ir

ii

t = t3ir

t = t4

iiir

vr

t = t5

ir

vr

Also,

1 1

r i

r i

C C

r i

i i

v v

Z Z

v v

For a transmission line with a short circuited end, voltage and current wave pair reflects

back fully i.e. voltage negatively and current positively with reflection coefficient α = 1.

9.9. Variation in voltage and current with the receiving end connected to

cable



LineCable

(vi,ii) (vt,it) When switch S is closed, a voltage and current wave of magnitudes vi and ii travels

towards the receiving end connected to the cable.

If Zc1 is the characteristic impedance of the line, than wave is going to see a change in

impedance from Zc1 to ZC2 at last element dx of the line.

When wave travels over the line and enters the cable looks into a different impedance,

hence it suffers reflection and refraction at the junction. As a result, let the change in

voltage and current is

2

1 2

2 Ct i

C C

Zv v

Z Z

The impedance of the overhead line and cable are approximately 400 Ω and 40 Ω. With

these values, voltage entering the cable becomes vt = 0.181vi. It means voltage wave

travelling along the line reduces its strength when enters into the cable.

For this reason, an overhead line terminated near a station is connected to the station

equipment through a short length of underground cable.

9.10. Variation in voltage and current with the receiving end terminated

through capacitor

V C

Z

Let, DC surge of infinite length travels over the line of surge impedance ZC1 = Z and is

incident on the capacitor then the voltage across the capacitor i.e. refracted voltage can

be

2

1 2

1 12

2 ( ) ( ) ( )2( ) 2 ( )

1 11

Or,

1

…………(i)1 1

Multiply equation (i) by and put 0

1

C i i it i

C C

Z v s v s v sCs ZCv s v sZ Z s s ZCs sZ s s

Cs ZC

A BZCs

s s sZC ZC

s s

A



1 1Multiply equation (i) by and put

1

Hence,

1 1( ) 2 ( ) 2 ( )

1 1

( ) 2 ( ) 1t

ZC

t i i

t i

s sZC ZC

B

A Bv s v s v s

s ss sZC ZC

v t v t e

It is to be noted that, terminating impedance is not a transmission line, therefore, v t(t) is

not a travelling wave but it is the voltage across the capacitor C.

Capacitor connection at T-junction

V C

Z1 Z2

V C

Z1

Z2

Let, DC surge of infinite length travels over the line of surge impedance ZC1 = Z1 and is

incident on the capacitor then the voltage across the capacitor i.e. refracted voltage can

be

2 2

22 1 2 1

2 1 21 21

2 1 2

1 2

1 2

1

2 12

12 ( ) ( ) ( )( ) 2 ( )

1

1 '

, '

Or,

1

…………(i)1 1

' '

Multiply equ

C i i it i

C C

Z Z

sCZZ v s v s Z Z C v s Z Cv s v s

Z Z ZZ Z s s sZ s s ssCZ Z Z C Z C

Z ZWhere Z

Z Z

Z C A B

ss s s

Z C Z C

1

1

ation (i) by and put 0

'

1 1Multiply equation (i) by and put

' '

'

s s

ZA

Z

s sZ C Z C

ZB

Z



'

2

1 1 2

2

1 2

Hence,

2' 1 1( ) 2 ( ) 2 ( ) 1 ( ) 1

1 1 1

' ' '

2( ) ( ) 1

tZ C

t i i i

t i

ZA B Zv s v s v s v s

s Z Z Zs s sZ C Z C Z C

Zv t v t e

Z Z

It is to be noted that, terminating impedance is not a transmission line, therefore, v t(t) is

not a travelling wave but it is the voltage across the capacitor C.

9.11. Variation in voltage and current with the receiving end terminated

through inductor

V

Z1 Z2

L

v1 v2i1

V

Z1

Z2

L

v1 v2i1

Let, DC surge of infinite length travels over the line of surge impedance ZC1 = Z1 and is

incident on the inductor then the voltage across the inductor i.e. refracted voltage can be

221

1 2 1 2

211

2 2 1 2 1 2

2

22 2 1

1 21 2

2

1 2

22 ( ) ( )( )

2( ) ( ) 2 ( )1( )

2 ( ) 2 ( )( ) ( )

Or,

C i it

C C

t i it

i it t

Z sLZ v s v sv s

Z Z s Z Z sL s

Z sLv s v s v si s

Z sL Z sL Z Z sL s s Z Z sL

ZZ v s v sLv s Z i s

Z Zs Z Z sL ss

L

ZAL

Z Z ss s

L

1 2

2

1 1

…………(i)

Multiply equation (i) by and put 0

B

Z Zs

L

s s

ZA

Z Z



1 2

1 2 1 2

2

1 1

22

1 2 1 21 1

22

1 2

Multiply equation (i) by and put

Hence,

1( ) 2 ( ) 2 ( ) 1

2( ) ( ) 1

t i i

Z Zt

Lt i

Z Z Z Zs s

L L

ZB

Z Z

ZA Bv s v s v s

Z Z Z Zs Z Zs sL L

Zv t v t e

Z Z

It is to be noted that, when rate of rise of incoming traveling wave is infinite, the outgoing

wave beyond L rises much more gradually.

9.12. Attenuation and distortion of travelling waves

Behaviour of traveling wave on multiconductor transmission line is more complex than

lossless simple twin conductor transmission line.

For multiconductor transmission lien, travelling wave’s attenuation and distortion is

required to address.

Distortion is caused by losses and multiconductor arrangement and attenuation is

accompanied by distortion.

Attenuation is caused by series resistance and leakage resistance and determination of

attenuation is generally empirical.

X = 0

X

Δx

v0,i0 v,iRΔx LΔx

CΔxGΔx

Δxv,i

Let,

Magnitude of surge at distance x from point of origination

Resistance per unit length

Inductance per unit length

Capacitance per unit length

Conductance per unit length

Power loss in the diff

xv

R

L

C

G

dp

erential element



The power loss,

2 2

2 2 2

2 2

22

2

2

0 0

2

0

0

0

2

2

2

2

ln2

At 0, ln

ln2

ln

Where,2

C

C

C C

C

C

C

C

C

C

x

C

dp i Rdx v Gdx

d i Z i Rdx v Gdx

iZ di i R v G dx

iZ di i R iZ G dx

R Z Gdidx

i Z

R Z Gi x A

Z

x i i A i

R Z Gix

i Z

ix i i e

i

R Z G

Z

C

2 2

22 2

2 2

2

2

2

2

0 0

2

0

0

0

2

2

2

ln2

At 0, ln

ln2

ln

C

C

C C

C

C

C

C

C

C

dp i Rdx v Gdx

vd i Rdx v Gdx

Z

vdv i R v G dx

Z

v vdv R v G dx

Z Z

R Z Gdvdx

v Z

R Z Gv x A

Z

x v v A v

R Z Gvx

v Z

vx v v

v

2

Where,2

x

C

C

e

R Z G

Z

Above equation concludes that current and voltage waves get attenuated exponentially

as they travel over the line and the magnitude of attenuation depends upon the

parameters of the line. Since the value of resistance depends not only on the size of the

conductors but also on the shape and length of the waves. An empirical relation for

calculating the voltage and current at any point on the line after it has travelled through

a distance x units and is

0

01

vv

kxv

When x is in km, v and V0 are in kV than the value of attenuation constant k is

k = 0.00037 for chopped waves

= 0.00019 for short waves

= 0.0001 for long waves

In the estimation of transmission line transients, the effect of attenuation and distortion

are normally ignored for simplicity in analysis. The results so obtained are pessimistic i.e.

voltage computed are higher than that obtained actually.

9.13. Capacitance switching of transmission line

Switching of a capacitance i.e. disconnecting a line or a cable or capacitor bank creates

serious problems in power systems in terms of abnormally high voltages across the



circuit breaker contacts.

L

C1

CB

C2V Vg Vc

Vc=Vg=V

Vc

t1

ir

t2 t3

5Vg

3Vg

Consider the equivalent circuit of an unloaded transmission line carrying only capacitive

current i. Line is opened by a circuit breaker at the instant t1 when capacitive current is

passing through zero.

Under this situation the current leads the voltage by about 90°. If current interruption

takes place when it passes through zero then the capacitor is charged to negative

maximum voltage.

After instant t1, the breaker contacts is subjected to potential difference of Vg and Vc. At

instant t2, the voltage across breaker contacts becomes twice the maximum value of Vg.

Within such interval of half cycle, beaker contacts are subjected to severe voltage change

with the result that breaker may restrike.

If such condition occurs, the voltage across breaker contacts falls almost instantaneously

from twice the maximum value of Vg to zero.

In doing so, high frequency oscillations are setup that builds up the voltage three times

the maximum value of Vg. The line is charged to three times the maximum value of Vg to

earth after interruption of restriking current.

At this instant, voltage across breaker contacts is twice the maximum value of Vg and

generated voltage is itself Vg. The voltage across breaker is continuously increases and

reaches the value four times the maximum value of Vg.

If breaker restrikes again, than whole cycle repeats and voltage reaches to eight times the

maximum value of Vg.

The extreme condition of capacitance switching is very rare, but if that occurs it causes

serious damage to the system.

9.14. Overvoltage due to arcing ground

Under balanced conditions and complete transposed transmission lines, the potential of

the neutral is near the ground potential and the currents in various phases through the

shunt capacitors are leading their corresponding voltages by 90° and displaced from each

other by 120° i.e. net sum of the three currents is zero.



When a line to ground fault occurs in any of one phase, voltage across the shunt capacitor

of that phase reduces to zero whereas those of the healthy phases become line to line

voltages displaced by 60° rather than 120°.

Net charging current is three times the phase current under balanced condition. These

currents flow through the fault and the windings of the alternator. The magnitude of this

current is sufficient to sustain an arc.

Therefore an arcing ground occurs. This is due to a flashover of a support insulator i.e.

flashover acts as a switch.

If the arc extinguishes when the current is passing through zero value, the capacitors in

healthy phases are charged to line voltages. The voltage across the line and the grounded

points of the post insulator superposition the capacitor voltage and the generator voltage.

This voltage is good enough to cause flashover that is equivalent to restrike in a circuit

breaker.

Because of the presence of the inductance of the generator winding, the capacitances

forms an oscillatory circuit and builds up to still higher voltages. Arc may reignite causing

further transient disturbances that may finally lead to complete rupture of the post

insulators.

9 Transients in Power Systems€¦ · Shital Patel, EE Department Power System - II (3150911) 17 12...

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