05 overvoltages and insulation coordination

390 

5. OVERVOLTAGES AND INSULATION CO-ORDINATION 

Different types of overvoltage may occur in industrial networks. Devices must therefore be 

installed to reduce their magnitude and the insulation level of equipment must be chosen so 

that fault risks are reduced to an acceptable level. 

5.1. Overvoltages 

An overvoltage is any voltage between one phase conductor and earth, or between phase 

conductors having a peak value exceeding the corresponding peak of the highest voltage for 

equipment, defined in standard IEC 71-1. 

An overvoltage is said to be of differential mode if it occurs between phase conductors or 

between different circuits. It is said to be of common mode if it occurs between one phase 

conductor and the frame or earth. 

origin of overvoltages 

Overvoltages can be of internal or external origin. 

internal origin 

These overvoltages are caused by a given network element and only depend on the 

characteristics and structure of the network itself. 

For example, the overvoltage that occurs when a transformer's magnetizing current is 

interrupted. 

external origin 

These overvoltages are caused or transmitted by elements outside the network, for example: 

- overvoltage caused by lightning 

- spread of HV overvoltage through a transformer to the internal network of a factory. 

Publication, traduction et reproduction totales ou partielles de ce document sont rigoureusement interdites sauf autorisation écrite de nos services. 

The publication, translation and reproduction, either wholly or partly, of this document are not allowed without our written consent. 

Industrial electrical network design guide T & D 6 883 427/AE

391 

classification of overvoltages 

Standard IEC 71-1 gives the classification of overvoltages according to their duration and form. 

According to the duration, a distinction is made between temporary overvoltages and transient 

overvoltages: 

- temporary overvoltage: power frequency overvoltages of relatively long duration (from 

several periods to several seconds). 

- transient overvoltage: short-duration overvoltage lasting only several milliseconds, which 

may be oscillatory and is generally highly damped. 

Transient overvoltages are divided into: 

. slow-front overvoltage 

. fast-front overvoltage 

. very-fast-front overvoltage. 

standard voltage forms 

Standard IEC 71-1 gives the standardised wave forms used to carry out tests on equipment: 

- short-duration power frequency voltage: this is a sinusoidal voltage with a frequency 

between 48 Hz and 62 Hz and a duration equal to 60 s. 

- switching impulse: this is an impulse voltage having a time to peak of 250 µs and a time to 

half-value of 2500 µs. 

- lightning impulse: this is an impulse voltage having a front time of 1.2 µs and a time to 

half-value of 50 µs. 

consequences of overvoltages 

Overvoltages in electrical networks cause equipment degradation, a drop in service continuity 

and are a hazard to the safety of persons. 

The consequences can be very varied depending on the type of overvoltages, their magnitude 

and their duration. They are summed up as follows: 

- breakdown in the insulating dielectric of equipment in the case where the overvoltage 

exceeds the specified withstand 

- degradation of equipment through ageing, caused by non-destructive but repetitive 

overvoltages 

- loss of power supply caused by the destruction of network elements 




392 

- disturbance of control, monitoring and communication circuits by conduction or 

electromagnetic radiation 

- electrodynamic stress (destruction or deformation of equipment) and thermal stress 

(elements melting, fire, explosion) essentially caused by lightning impulses 

- hazard to man and animals following rises in potential and occurrence of step and touch 

voltages. 

5.1.2. Power frequency overvoltages 

Power frequency overvoltages are generally caused by: 

- an earth fault 

- resonance or ferro-resonance 

- neutral conductor breakdown 

- a generator voltage regulator or transformer on-load tap changer fault 

- overcompensation of reactive energy following a varmeter regulator fault 

- load shedding, notably when the supply source is a generator 

5.1.2.1. Overvoltage caused by an earth fault 

Overvoltages caused by the occurrence of an earth fault greatly depend on the neutral 

earthing system of the given network. 

unearthed (MV or LV) or impedance earthed (MV) neutral 

Figure 5-1 shows that on occurrence of a solid earth fault, the voltage between the neutral 

point and earth becomes equal to the single-phase voltage: 

VNeutral = Vn 

V n : nominal single-phase voltage 

For a fault on phase 1, VNeutral = − V1 . 

The phase-earth voltage of healthy phases thus becomes equal to the phase-to-phase 

voltage: 

V2E = VNeutral 

+ V2 = V2 −V1 

V3E = VNeutral 

+ V3 = V3 −V1 

whence V2E = V3E = 3Vn 




393 

V 3 

3 

V 2 

2 

V 1 

1 

earth 

fault 

V E 1 

V 2E 

V 3E 

V Neutral Z Neutral 

V 2 V 3 

Neutral 

V 2E 

V 3E 

V 1 

V 1E 

0 

V 1 ,V 2 ,V 3 : phase-neutral voltages 

V 1 E ,V 2 E ,V 3 E : phase-earth voltages 

Z Neutral : earthing impedance (Z Neutral 

= ∞ for an unearthed neutral) 

Figure 5-1: overvoltage on an unearthed or impedance earthed network 

on occurrence of a phase-to-earth fault 

Note 1 : for an impedance earthed neutral, the value of Z Neutral is much greater than the value of the 

transformer and cable impedances and the fault resistance, which is why VNeutral = − V1 . 

Note 2 : in overhead public distribution networks, there are highly resistive faults (several kΩ), having a 

value close to or higher than the earthing impedance. In this case, a highly resistive fault will 

cause an overvoltage lower than 3V n . 




394 

solidly earthed neutral (HV or MV) 

On occurrence of an earth fault on one network phase, a high current is generated which 

circulates in the circuit formed by the fault phase, earth and neutral earth electrode 

(see fig. 5-2). 

At the fault point, the three-phase voltage system is disturbed. The fault phase voltage in 

relation to earth is almost zero if we neglect the fault resistance. The voltages of the other two 

phases in relation to earth are higher than the single-phase voltage, while remaining lower 

than the phase-to-phase voltage. 

V 3 

Z T 

Z C 

V 2 

Z T 

Z C 

V 1 

Z T 

Z C 

fault 

V 1E 

V 2E 

V 3E 

R e 

R f 

V 1 ,V 2 ,V 3 : single-phase voltages 

Z T : transformer impedance 

Z C : cable impedance 

R e : neutral earth electrode resistance 

R f : fault resistance 

Figure 5-2: equivalent diagram of a phase-earth fault when the neutral is solidly earthed 

Thus, we can define an earth fault factor k characterising the phase-earth overvoltage 

occurring on the healthy phases: 

V2E = V3E = kVn 


The symmetrical component calculation method (see § 4.2.2. of the Protection guide) can be 

used to determine the value of k in relation to the positive, negative and zero-sequence 

impedances: 

k = 1 − 

2 

Z + a Z + aZ 

(1) ( 2) ( 0) 

(1) ( 2) ( 0) 

R f 

Z + Z + Z + 3 




395 

In most networks, generators are sufficiently far away to take the approximation Z(1) = Z( 2 ) 

; we 

thus have: 

( ( 1) − ( 0) 

) 

a Z Z 

k = 1 + 

2Z( 1) + Z( 0) 

+ 3R f 

Nomographs can be used to determine factor k for a zero fault resistance (R f =0 ) in relation 

to the ratios R ( 0) 

X( 1) 

and 

X ( 0) 

X( 1) 

for R ( 1) 

= 0 and R( 1) = 05 . X( 1) 

(see fig. 5.3. et 5.4.). 

where: 

R ( 1 ) : positive-sequence resistance seen from the fault point 

X ( 1 ) : positive-sequence reactance seen from the fault point 

R ( 0 ) : zero-sequence resistance seen from the fault point 

X ( 0 ) : zero-sequence reactance seen from the fault point 

When the fault resistance is not zero, we can see in the formula expressing k that the 

overvoltage is weaker. The calculation of the overvoltage with a zero fault resistance thus 

provides an excess value. 

If we again use the diagram in figure 5-2, we can determine these impedances for a practical 

case: 

by taking: 

Z = R + jX 

T T 

Z = R + jX 

C C 

T 

C 

⎫⎪ 

⎬ positive - sequence impedances 

⎭⎪ 

Z 

Z 

= R + jX 

( 0) T T ( 0) 

T 

= R + jX 

( 0) C C ( 0) 

C 

⎫⎪ 

⎬ zero- sequence impedances 

⎭⎪ 




396 

we can determine: 

R( 1 ) = RT + RC 

X( 1 ) = XT + XC 

R( 0) 

= 3Re + RT + RC 

X( 0) = X( 0) T + X( 0) 

C 

Note: 

A factor 3 appears before R e . The reason for this is explained in figure 4-11 of the Industrial 

network protection guide. 

R 8 

(0) 

X (1) 

7 

6 

k=1.7 

5 

k=1.6 

4 

3 

2 

1 

k=1.5 

k=1.4 

k=1.3 

k=1.2 

1 2 3 4 5 6 7 

X(0) 

8 

X (1) 

Figure 5-3: earth fault factor in relation to ratios 

for R ( 1) 

= 0 and R f =0 

X ( 0) 

X( 1) 


R ( 0) 

X( 1) 

R 8 

(0) 

X (1) 

7 

k=1.7 

6 

k=1.6 

k=1.5 

5 

4 

3 

k=1.4 

2 

k=1.3 

k=1.5 

1 

k=1.2 

1 2 3 4 5 6 7 

8 

X(0) 

X (1) 

Figure 5-4: earth fault factor in relation to ratios 

X ( 0) 

X( 1) 

for R( 1) = 05 . X( 1) 

and R f =0 



Industrial electrical network design guide T & D 6 883 427/AE 


R ( 0) 

X( 1)

397 

example 

Let us consider a YNyn, 33 kV/11 kV transformer with a power rating of Sn =24 MVA (see 

IEC 909-2 table 3 A) supplying a network with 240 mm² aluminium cables the longest outgoing 

feeder of which is 5 km. The neutral earth electrode resistance is 0.5 Ω. 

- transformer characteristics: 

U sc =242 . % 

R 

X 

T 

T 

=0046 . 

X( 0) 

T 

XT 

=07 . 

2 3 

U 

( 11 × 10 ) 

we can deduce X = U × n = 0242 × 

T sc 

R T =0056 . Ω 

Sn 

. = 122 . Ω 

6 

24 × 10 

X ( 0 ) T = 085 . Ω 

Note: 

the value of U sc is extremely high in relation to the transformers feeding a network with a 

limiting resistor earthed neutral. The transformer here is a United Kingdom transformer adapted 

to the solidly earthed neutral system. 

The short-circuit voltage has been chosen high on purpose so as to minimise the short-circuit 

R( 0) 

current. Indeed, if U sc is high, the value is minimised ( sinceX( 1 ) XT XC 

) 

X 

= + , which 

( 1) 

decreases the overvoltage factor (see fig. 5-3 and 5-4). 

- cable characteristics: 

L 

RC = ρ 

km 

S 

= 0036 . × 1000 

= 015 . Ω/ 

240 

XC =01 . Ω/ 

km 

We assume that X( 0) C = 3XC 

= 03 . Ω / km . 

Note: 

the value of X C ( ) 0 is highly variable (from 0.2 to 4 X ( ) 1 ) depending on what the cable is made 

of and the return via the earth (remote earth, screen or earthing conductor). 




398 

For a solid fault (R f =0 ) at the transformer terminals: 

R ( 1 ) = R T = 0056 . Ω 

R( 0) = 3Re + RT 

= 3 × 05 . + 0056 . = 156 . Ω 

X ( 1 ) = X T = 122 . Ω 

X ( 0 ) = X ( 0 ) T = 085 . Ω 

whence R( 1) = 005 . X( 1) 

≅0 

R( 0) 

X( 1) 

X( 0) 

X( 1) 

=128 . 

=070 . 

Figure 5-3 shows that k is between 1.4 and 1.5. 

For a solid fault (R f =0 ) 5 km away from the transformer: 

R( 1) = RT + RC 

= 0056 . + 015 . × 5 = 081 . Ω 

R( 0) = 3Re + RT + RC 

= 3 × 05 . + 0056 . + 015 . × 5 = 231 . Ω 

X( 1) = XT + XC 

= 122 . + 01 . × 5 = 172 . Ω 

X( 0) = X( 0) T + X( 0) C = 085 . + 03 . × 5 = 235 . Ω 

whence R( 1) =0.47X( 1) 

R( 0) 

X( 1) 

X( 0) 

X( 1) 

=134 . 

=137 . 

Figure 5-4 shows that k is between 1.2 and 1.3. 




399 

TN earthing system 

The current of an earth fault circulates in the protective conductor. The neutral earth electrode 

resistance is thus not used to determine the zero-sequence impedance 

(see fig. 5-5). 

Z T 

Z C 

V 3 

Z T 

Z C 

V 2 

V 1 

Z T 

Z C 

V 3 V M 

V 2 V M 

R e 

Z PE 

V M 

V 1 ,V 2 ,V 3 : single-phase voltages 

Z T : transformer impedance 

Z C : cable impedance 

Z PE : protective conductor impedance 

V M : potential of exposed conductive parts (masses) in relation to earth 

R e : neutral earth electrode resistance 

Figure 5-5: equivalent diagram of an earth fault in a TN earthing system 

We are interested in the overvoltage of the healthy phases in relation to the exposed 

conductive part, which determines whether or not an insulation fault may occur on the other 

V V V V 

load: kM 

= 2 − M = 3 − M 

Vn 

V 

. 

n 




400 

For a transformer or a cable in low voltage, we can take the zero-sequence impedance to be 

approximately equal to the positive-sequence impedance: Z( 0 )T = ZT 

and Z( 0 )C = ZC 

. 

We thus haveZ( 0) 

= ZT + ZC 

+ 3ZPE 

Z( 1 ) = ZT + ZC 

whence 

k 

M 

= 1 − 

3 

a3Z 

PE 

( Z + Z + Z ) 

T C PE 

aZ 

= 1 − 

PE 

for a solid fault (R f =0 ) 

Z + Z + Z 

PE T C 

a = e 

j2π 

3 

: rotation operator of 120° 

The overvoltage will be maximum when Z T is negligible compared with ZPE + ZC 

, which is the 

case for a long length cable. 

Thus 

kM 

aZ 

≤1 

− 

PE 

ZPE + ZC 

k M will be maximum when the protective conductor cross-sectional area is as small as 

possible, i.e. equal to half the phase conductor cross-sectional area; thus RPE 

=2 RC 

. 

For an aluminium cable cross-sectional area smaller than 120 mm², the reactance can be 

neglected compared with the resistance, which thus gives us: 

ZPE 

Z + Z 

PE C 

≅ 

RPE 

R + R 

PE C 

= 2 3 

since RPE 

=2RC 

2 

whence kM ≤1 

− a 

3 

2 ⎛ 1 

kM ≤1 

− ⎜− + 

3 ⎝ 2 

j 

3 ⎞ 

⎟ 

2 ⎠ 

k M ≤1.45 

We can show that for a cable with a large cross-sectional area (> 120 mm²), the overvoltage 

will be lower than in the case of a small cross-sectional area. 




401 

TT earthing system (see fig. 5-6) 

Z T 

Z C 

V 3 

Z T 

Z C 

V 2 

Z T 

Z C 

V 1 

I f 

load1 load2 

I f 

V N R V e 

M1 R M1 RM2 

R e : substation earth electrode resistance 

R M1 : load 1 and fault load earth electrode resistance 

R M2 : load 2 earth electrode resistance 

V M1 : load 1 and fault load phase-to-earth voltage 

Figure 5-6: equivalent diagram of an earth fault in a TT earthing system 

We want to know the overvoltage of the healthy phases in relation to the exposed conductive 

part, which determines whether or not an insulation fault may occur on the other load: 

V V 

k 2 − M V3 

−VM 

M = = 

Vn 

Vn 

In low voltage, the neutral and load earth electrode resistances are very high in relation to the 

transformer and cable impedance (Z T and Z C are roughly several tens of mΩ). 

We can thus write that the fault current is: 

I 

f 

= 

V1 

R + R 

e M1 

Z + Z I ≅0 

and ( ) 

T C f 

The exposed conductive part of load 1 is connected to phase 1 by the fault (zero impedance). 

The voltage of one healthy phase of this load in relation to the frame is V2 − V1 

or V3 −V1 

Z + Z I ≅0 ) , whence k M = 3 = 173 . . 

(since ( ) 

T C f 




402 

The exposed conductive part of load 2 is at the same potential as the remote earth. 

The voltage of one healthy phase of this load in relation to the exposed conductive part is 

therefore V 2 − V Neutral or V 3 − V Neutral : 

V2 − VNeutral 

= V2 − Re If 

= V2 

− 

ReV1 

Re + RM 

Re 

⎛ 

= V2 −aV2 = V2 ⎜1 

− 

Re + RM 

⎝ 

aRe 

⎞ 

⎟ 

Re + RM 

⎠ 

whence 

kM 

= 1 − 

aRe 

Re + RM 

for 

for 

RM = Re , kM 

= 132 . 

RM > Re , kM 

< 132 . 

The earth electrode resistance of a group of loads is in general higher than the substation 

earth electrode resistance. The overvoltage coefficient will thus be lower than 1.32 on load 2. 

The overvoltage factor is maximum in the TT earthing system for a load having an exposed 

conductive part connected to the same earth electrode as the fault load, we thus have 

k M = 3 

recapitulative table of maximum earth fault overvoltages in relation to the neutral 

earthing system 

Medium and high voltage (1) Low voltage (2) 

solidly earthed neutral 

(HV or MV) 

unearthed or 

impedance 

earthed neutral 

(MV) 

TN system TT system IT system 

< 1.73 * 

(generally 1.2 to 1.4) 

1.73 1.45 1.73 1.73 

(1) : phase-earth overvoltage 

(2) : phase-exposed-conductive-part overvoltage 

(*) : a network with a solidly earthed neutral is generally made up so as to limit overvoltages to values close to 1.2 

to 1.4. 

Table 5-1: maximum overvoltage factor in relation to neutral earthing system 




403 

consequences on equipment selection 

The overvoltage factor and fault duration influence the choice of equipment insulation voltage 

level. 

solidly or limiting impedance earthed neutral in MV, or TT and TN earthing system 

in LV 

Rapid clearance of the fault, and thus a short overvoltage time, means that the switchgear 

phase-earth insulation level does not have to be higher than the nominal single-phase voltage. 

unearthed neutral in MV or IT earthing system in LV 

Since the power supply does not have to be interrupted on occurrence of a first fault, the 

overvoltage is likely to occur for a long period of time (several hours). It is therefore advisable 

to choose switchgear with a phase-earth insulation level that is suitable for the nominal phaseto-phase 

voltage. 

Note: 

some manufacturers give a phase-earth insulation withstand equal to the single-phase voltage, 

but stipulate that their switchgear can be implemented in an unearthed neutral network. There 

are also switchgear standards that specify an insulation level compatible with use in an 

unearthed neutral network. 




404 

5.1.2.2. Resonance and ferro-resonance 

resonance 

The presence of inductive L , capacitive C and resistive R elements, connected, either in 

series or in parallel, causes spreading of current and voltage having values which may be 

dangerous for equipment. 

series resonance 

Figure 5-7 shows a series R, L, C circuit at the terminals of which a voltage U is applied. 

I 

R 

L 

C 

U 

Figure 5-7: series R, L, C circuit fed by a voltage U 

The voltage U is the vectorial sum of the voltages at the terminals of each element: 

U = UR + UL + UC 

1 

= RI + jLωI 

+ 

jCω 

The vectorial diagram in figure 5-8 shows that for certain values of L and C , the voltages at 

the terminals of the inductance and capacitance may be higher than the network voltage U : 

jL I 

1 

jC 

I 

RI 

U 

Figure 5-8: vectorial diagram of a series R, L, C circuit fed by a voltage U 




405 

The resonance phenomenon occurs when UL 

= − UC 

: 

jLωI 

= − 1 

jCω 

LCω 2 = 1 

We thus have U = RI ; the series inductance and capacitance behave like a short circuit. 

For given values of L and C , the angular frequency ω r such that 

a resonant angular frequency. 

LCω 2 r = 1 is said to be 

An overvoltage factor 

supply voltage U : 

f is thus defined which is the ratio of the voltage U L (or U C ) to the 

f 

U L I 

= 

L 

= ω r 

U RI 

f 

Lωr 

1 

= = 

R RCω 

r 

parallel resonance 

Figure 5-9 shows a parallel 

applied. 

R, L, C circuit at the terminals of which a current source J is 

I R I L I C 

J 

R 

L 

C 

U 

Figure 5-9: parallel R, L, C circuit fed by a current source J 




406 

The voltage U is common to the three elements. 

We have the following relation: 

⎛1 1 

J = ⎜ + + 

⎝R jLω 

⎞ 

jCω⎟U 

⎠ 

The resonance phenomenon occurs when IL 

= − IC 

: 

U 

= − 

jLω 

jCωU 

LC ω 2 = 1 

We thus have U = RJ ; the inductance and capacitance behave like an open circuit. 

For given values of L and C , the angular frequency ω r such that 

a resonant angular frequency. 

LCω 2 r = 1 is said to be 

An overvoltage factor is thus defined which is the ratio: 

- between the voltage that is produced at the terminals of the parallel R, L, C circuit when 

the resonance occurs 

- and the voltage that would be produced on occurrence of the resonance if the inductance 

(or capacitance) were the only circuit element 

f 

RJ 

= 

L ωr J 

f 

R 

= = RC ω 

Lω 

r 

r 

The most current example of parallel resonance is the case of a network having harmonic 

currents (patterned by current sources) and reactive energy compensation capacitors 

(see § 8.1.5). 




407 

example: resonance in a Petersen coil earthed HV/MV substation 

Figure 5-10 shows the diagram of a Petersen coil earthed HV/MV substation when an HV 

earth fault flows through the common earth electrode. 

HV 

HV/MVtransformer 

Z MV 

R e1 

I f 

Lc , Rc 

C 

V e 

R e 

I f : HV earth fault current 

Lc , Rc 

: Petersen coil inductance and resistance 

Re , R : earth electrode resistances 

e1 C : MV cable phase-earth capacitance 

V e : rise in substation earth potential 

Z MV : sum of MV cable and transformer impedances 

Figure 5-10: HV earth fault in an HV/MV substation with a Petersen coil earthed neutral 

The symmetrical component method gives us the fault current value as (see § 4.2.2 of the 

Network protection guide): 

I 

f 

= 

3Vn 

Z + Z + Z 

( 1) ( 2) ( 0) 

where 

Z( 1 ) = ZT 

+ Z l 

Z( 2 ) = ZT 

+ Z l 

( 0 Z( ) T + Z0) 

l + e Re1 

ZT 

, Z( 0 ) T :HV transformer positive-sequence (or negative-sequence) and zero-sequence impedances 

Zl 

, Z( 0 ) l : HV line positive-sequence (or negative-sequence) and zero-sequence impedances 




408 

In high voltage, the substation earth electrode value (R e 

) is very low compared with the 

transformer and line impedances. The fault current is thus independent of R e 

; it is thus 

considered to be a source of current with a value of I f . 

The equivalent Thevenin’s diagram of the current source I f with an internal impedance of 

R e 

is shown in figure 5-11. 

R e 

equivalent 

I f 

R e 

V R I e f e 

Figure 5-11: equivalent Thevenin’s diagram of the current source I f with an internal impedance of R e 

The equivalent MV network diagram is thus that shown in figure 5-12. 

R e R c L c 

Z MV Z MV Z MV 

V R I e f e 

C C C 

Figure 5-12: equivalent MV network diagram on occurrence of an earth fault on the substation HV side 

The transformer and cable impedances are negligible compared with the cable phase-earth 

capacitance: ZMV

409 

The simplified MV network diagram is thus that shown in figure 5-13. 

R e R c L c 

V L 

V R I e f e 

3C V C 

Figure 5-13: simplified diagram 

LetV L be the voltage at the inductance terminals. 

We have 

V 

L 

= 

L 

( ω 

3 

1 

ω ) 

R + R + j L − 

c 

ω 

e c c C 

V 

e 

In the case of a Petersen coil earthed neutral, (resonance) tuning between the inductance and 

the MV cable capacitance is aimed at as far as possible. We thus have : Lc ω ≈ 1 and 

3Cω 

VC ≈ VL 

whence 

Lc 

ω 

VL 

= 

R R V . 

e 

+ 

e c 

To minimise the rise in substation earth potential (V e ), the resistance earth electrode must be 

as weak as possible (of the order of 0.5 Ω). 

We can thus neglect R e 

compared with R c , which thus gives us: 

Lc 

ω 

VL = VC 

= 

R V e = QV 

c 

VC 

= QRe If 

e 

Q : coil quality factor 

V C : is equal to the MV cable phase-earth overvoltage in this case 

The coil quality factor must not therefore be too high in order to avoid the risk of a very high 

overvoltage. 

This is why, in some cases, a resistor must be connected in parallel with the coil, in order to 

reduce the quality factor. 




410 

Numerical application: 

Let us take a 63/5.5 kV substation where: 

55 . 

Vn = = 3175 . 

3 

kV 

( ) 

If 63kV = 3kA 

R e =05 . Ω 

Q L c ω 

= = 4 

R 

c 

The rise in potential is: Ve = Re × If 

=1500 V . 

The phase-earth voltage in the cables is: VC 

= Q × Ve 

. 

VC = 1500 × 4 = 6000V 

VC 

=189 . 

Vn 

The overvoltage in the cables is roughly twice the nominal phase-earth voltage. 

It can be dangerous if the substation earth electrode is of poor quality. Indeed, for 

we will have VC 

=113 . Vn 

. 

R e =3 Ω 

It is thus essential to limit the value of R e 

. 




411 

ferro-resonance 

parallel ferro-resonance (see fig. 5-14) 

Let us take a circuit made up of a parallel-connected capacitance, a coil with a saturable iron 

core and a resistance. Let R be the resistance, C the capacitance and L the inductance 

which varies with the current flowing through the coil and the voltage at the circuit terminals. 

I R 

I L 

I T 

I C 

R 

L 

C V 

Figure 5-14: parallel ferro-resonance 

The total current I T flowing through the circuit is then given by the relation (1): 

IT 

V 

= + j ( Cω V −IL) 

(1) 

R 

We cannot express I L as a function of V , owing to the saturation. 

The rms values are given by the relation (2): 

2 

2 V 2 

IT 

= + ( Cω V −IL) 

(2) 

2 

R 

We can thus write relation (3) as follows: 

I 

2 

T 

2 

V 

− = C ωV −I 

2 

R 

L 

(3) 




412 

This equation can be graphically resolved by plotting, as a function of V, the curves 

representing functions (see fig. 5-15): 

2 V 

I = IT 

− 

R 

2 

2 

I = Cω 

V −I L 

(a) 

(b) 

For any value of I T , the intersection of curves (a) and (b) gives the V solutions of equation 

(3); figure 5-15 shows the graphic resolution of this equation. 

Curve (a) is an ellipse having the equation: 

2 

V 

2 

R 

2 2 

+ I = I T 

and having one half axis which is equal to I T and the other to RI T . An ellipse corresponds 

to each total current value I T . 

Curve I ( V ) 

L presents a very steep slope when V increases owing to the saturation of the 

V 

IL V = 

LV ω . 

coil's iron core: ( ) 

( ) 

On saturation, LV ( ) becomes very weak and the current then highly increases (see fig. 5-15). 

Curve IC = Cω V is a linear function of V (see fig. 5-15). 

Curve (b) shows the development of I − I = ( C V −I 

) 

C L 

ω L as a function of the voltage. 

The OSA portion of curve (b) corresponds to a lead current in relation to the voltage owing to 

the preponderance of the capacitive current. On the other hand, the AB part corresponds to a 

lag current, since the inductive current is preponderant. The intersection of ellipse (a) and 

curve (b) can give: 

- an operating point Q if ellipse (a) is inside ellipse (a") passing through pointA 

- three operating points M , N, P if ellipse (a) is between ellipses (a') and (a") 

- two points S, T if ellipse (a) is equal to ellipse (a') 

- a single point X if ellipse (a) is outside ellipse (a'). 

The ferro-resonant mechanism is described below. 




413 

With the circuit being initially unused, the total current I T is zero, as well as the voltage V , and 

ellipse (a) is reduced to point O . If the current increases, the length of the axes of ellipse (a) 

increases and the voltage rises, the operating point M moves along branch OS of curve (b). 

When the total current exceeds the value 

I T 

' 

for which ellipse (a') cuts curve (b) at S , the 

operating point suddenly jumps from point M to point T located on branch AB of curve (b), it 

then moves along this branch. The voltage thus suddenly increases, going from V S to V T , and 

then it continues to increase if the current I T increases. 

If the total current now decreases, the operating point moves along branch 

there, even if the current drops below the value 

I T 

' 

AB and stays 

corresponding to ellipse (a'). When the 

current reaches the value I T , the operating point is P instead of M . It only returns to 

'' 

branch OS if the current drops below the value I T corresponding to ellipse (a") passing 

through point A. When this occurs, the operating point suddenly jumps from A to Q , and 

the voltage from V A to V Q . 

We can thus see that two stable operating conditions, for which the voltage at the circuit 

terminals takes very different values, for example V M and V P , can correspond to the same 

rms current value I T . 

Finally, if the initial operating conditions correspond to a weak voltage (branch OS ), with a 

resulting capacitive current, it is possible that, following a sudden change in operating 

conditions leading to a transient phenomenon (overcurrent or overvoltage), the resulting 

current becomes inductive and the voltage maintains a high value, even once the disturbance 

has disappeared. 

Ferro-resonance can be avoided if the resistance R is sufficiently weak for ellipse (a) to 

remain within zone OSA, even when there is a high overcurrent. 

I 

I L 

inductiveoperatingconditions 

resonance 

I C V C 

(b) 

C V I L 

I T 

''' 

capacitiveoperating 

conditions 

X 

B 

(a''') 

I T 

' 

I T 

'' 

I T 

O 

Q 

M 

V Q V M 

(a'') 

S 

N 

P 

A 

V S V N V A V P V T 

T 

(a) 

(a') 

V 

Figure 5-15: parallel ferro-resonance - graphic resolution 




414 

series ferro-resonance (see fig. 5-16) 

Let us take a series circuit made up of a resistance, a coil with a saturable iron core and a 

capacitance. We have: 

⎛ I ⎞ 

V = RI + j ⎜VL 

− ⎟ 

⎝ Cω 

⎠ 

(1) 

We cannot express V L as a function of I , owing to the saturation. 

If we move to rms values, we can write: 

2 

2 2 2 ⎛ I ⎞ 

V = R I + ⎜VL 

− ⎟ 

⎝ Cω 

⎠ 

(2) 

or: 

2 

2 2 2 ⎛ I ⎞ 

V − R I = ⎜VL 

− ⎟ 

⎝ Cω 

⎠ 

2 2 2 I 

V − R I = LωI 

− 

Cω 

(3) 

(4) 

R 

I 

L 

C 

V R V L V C 

V 

Figure 5-16: series ferro-resonance 

As for the parallel circuit, this equation can be graphically resolved as a function of I , 

by plotting curves (see fig. 5-17): 

2 2 2 

v = V −R I 


I 

v = VL 

− 

C ω 

Curve VL ( I) 

presents a very small slope when 

coil's iron core VL ( I) = L( I) 

ω V . 

I increases owing to the saturation of the 




415 

On saturation, L( I ) becomes very weak and the voltage almost stops increasing when 

rises. 

I 

The network operating point is located at the intersection of curve (b) having the equation: 

I 

v = VL 

− 

C ω 

and ellipse (a) having the equation: 

2 2 2 

v = V −R I 

There are three possible operating points: 

M , N, P . M and P are stable, N is unstable. 

A voltage disturbance can make the circuit move from point M to point P . This results in a 

high current and high overvoltages at the inductance and capacitance terminals. Ferroresonance 

can be avoided if the resistance R is sufficiently high for ellipse (a) to stay within 

zone OSA, even when there is a high overvoltage. 

V 

V L 

resonance 

V C 

V ''' 

(a''') 

X 

(b) 

V ' 

V 

V '' 

O 

S (a') T 

N (a) 

M P 

Q A 

(a'') 

I Q I M I S I N I A I P I T I X 

I 

Figure 5-17: series ferro-resonance - graphic resolution 




416 

example of parallel ferro-resonance - unearthed neutral three-phase network 

(see fig. 5-18) 

Let us consider a three-phase network with unearthed neutral having a capacitance C 

between each phase and the earth. Furthermore, a voltage transformer, with a similar 

magnetizing inductance to a saturable core reactor, is connected between each phase and 

earth. A parallel inductance-capacitance circuit thus appears between each phase and earth. 

Parallel ferro-resonance can then be sparked between the capacitance and voltage 

transformer of the same phase. 

This ferro-resonance may occur following a transient overcurrent or overvoltage caused by a 

switching operation and notably when the network is energized. Owing to the existing phase 

displacements between the voltages of the three network conductors, the overcurrents and 

switching overvoltages do not have the same magnitude in the three phases. Ferro-resonance 

can thus very easily occur on only two phases, phases 2 and 3 for example. The voltages of 

these two phases in relation to earth correspond to points located on portion AB of curve (b) 

(see fig. 5-15). The voltage of phase 1 corresponds to a point located on the OS part of this 

curve. 

For phases 2 and 3, the capacitance-inductance assembly behaves like an inductance, and for 

phase 1, like a capacitance. If we plot the voltage vector diagram, we can see: 

- that the phase 1 voltage in relation to earth is weak 

- that the voltages in relation to earth of the other two phases are very high 

- that there is a very high potential difference between the neutral point and earth 

(see fig. 5-18). 




417 

These overvoltages will cause a breakdown in equipment insulation if provisions to limit them 

are not taken. 

V 3 

N 

V 2 

V 1 

Ph3 

Ph2 

Ph1 

v 1T 

C 

L 

C 

L 

C 

L 

v N 

V 1 

V 2 

v 3T 

v 2T 

N 

V 3 

Ferro-resonance occuringbetweentwophases 

Figure 5-18: parallel ferro-resonance in an unearthed neutral network 

protection against the risks of parallel ferro-resonance 

A voltage transformer ( VT ) charged by a resistor r behaves like a saturable (magnetizing) 

inductor in parallel with this resistor. 

Thus, in an unearthed network, if a charging resistor is connected to the secondary of the 

voltage transformers, the L-C parallel circuits, made up of these transformers and network 

cable capacitances, are transformed into R-L-C parallel circuits, such that if the resistors are 

correctly sized, the risk of ferro-resonance outlined previously can be avoided (ellipse (a) 

remains inside the zone 0SA - see fig. 5-15): 

- the resistors must be sufficiently weak to be efficient 

- they must not be too weak, so that the VT are not overcharged and their accuracy is 

maintained. 




418 

In the case of 

(see fig. 5-19). 

VT with a single secondary, a charging resistor is installed on each phase 

A resistance value equal to 68 Ω is recommended for a secondary voltage of 

100 

3 V . 

VT VT VT 

r 

r 

r 

measurements 

Figure 5-19: protection against risks of ferro-resonance using resistors with single secondary VT 




419 

In the case of VT with two secondaries, a resistor is installed in the open delta of one of the 

two (see fig. 5-20). 

It is recommended that a power above 50 W be dissipated in the resistor on occurrence of a 

phase-earth fault. 

100 

For a secondary voltage of V , on occurrence of a solid earth fault, the voltage at the 

3 

resistor terminals is equal to 100 V; the resistance value is then determined: 

( ) 

R ≤ 100 2 

50 

R ≤200 Ω 

VT VT VT 

measurements 

r 

Figure 5-20: protection against the risks of ferro-resonance via a resistor with two-secondary VT 




420 

example of series ferro-resonance (see fig. 5-21) 

Figure 5-21 shows a solidly earthed network feeding a three-phase transformer having a deltaconnected 

primary. This can also apply to a star-connected transformer with an unearthed 

neutral. If, when the switch is closed, one of the poles remains accidentally open or closes 

late, for example the pole of phase 1, series ferro-resonance may occur in the circuit including: 

- the magnetizing inductance of transformer windings AC or BC 

- the capacitance of phase 1 in relation to earth. 

Very high overvoltages can occur at the transformer terminals and between phase 1 and the 

earth. 

This type of ferro-resonance has frequently been encountered on HV networks with solidly 

earthed neutral. It may also occur when a switch is opened. The means of protecting against 

this type of ferro-resonance consists in inserting a resistor in the supply transformer neutral 

point earthing. This solution does not however provide total protection since ferro-resonance 

can, for example, occur in the circuit including the transformer AC winding and the 

capacitances of phases 1 and 3 in relation to earth. 

V 3 

V 2 

V 1 

switch 

Ph3 

Ph2 

B 

L 

L 

L 

A 

Ph1 

I f 

C 

C 

C 

C 

Figure 5-21: series ferro-resonance 




421 

5.1.2.3. Neutral conductor breakdown 

Let us consider the diagram in figure 5-22 , where 

Z 1 , Z 2 and Z 3 represent the equivalent 

impedances per phase of all the loads downstream of the neutral breakdown point. 

If the phases are perfectly balanced, the voltage system is not disturbed. 

In the event of load unbalance, the neutral point is displaced and the phase-neutral voltages 

move close to the phase-to-phase voltage for the least loaded phases, while for the loaded 

phases (weak impedance), they drop below the single-phase voltage. 

Z 3 

V 3 

Z 2 

V 2 

Z 1 

V 1 

N 

neutralbreakdown 

Figure 5-22: equivalent diagram of an LV network during neutral breakdown 

Using the superposition theorem, we can show that: 

⎛ Z Z 

V 1// 

2 ⎞ ⎛ Z Z 

V 1// 

3 ⎞ ⎛ Z Z 

N = ⎜ 

⎟ + ⎜ 

⎟ V + 

2// 

3 ⎞ 

3 2 ⎜ 

⎟V1 

⎝Z3 + Z1// 

Z2 

⎠ ⎝Z2 + Z1// 

Z3 

⎠ ⎝Z1 + Z2// 

Z3 

⎠ 

(1) 

The voltage applied to the terminals of a single-phase load on phase 3, for example, will be: 

V3N 

= V3 

−VN 

2 ⎛ 1 

If we know that V2 

= a V 1 and V3 = aV1, 

⎜a = − + j 

⎝ 2 

3 

2 

⎞ 

⎟ 

⎠ 

then we can calculate V 3 N , for example, for the following impedances: 

Z1 = R 

Z2 = 2R 

Z3 = 10R 

(We have taken resistive loads to simplify the calculations.) 




422 

By applying formula (1), we find: 

2 

a 

VN = ⎛4 + 9⎞ 

⎜ ⎟V 

⎝ 16 ⎠ 

1 

we then have V3N = V3 − VN = aV1 

−VN 

15 j10 3 

V3N 

= ⎛ − + ⎞ 

⎜ 

⎟V1 

⎝ 16 ⎠ 

whence V3N 

= 1.43Vn 

Similarly, we can determine: V2N 

= 114 . Vn 

and V1N 

= 06 . Vn 


We can see that once the most sensitive single-phase loads have broken down, there are 

successive breakdowns, following the development of the phenomenon which worsens the 

unbalance (Z 3 increases after the breakdowns and consequently V 3 N increases); this is an 

avalanche phenomenon. 

This risk thus underlines that it is preferable to well balance the loads on the three phases. 




423 

5.1.3. Switching overvoltages 

When switching to energize or de-energize loads transient overvoltages occur on the network. 

These overvoltages are all the more dangerous if the current interrupted is inductive or 

capacitive. The magnitude, frequency and damping duration of these transient overvoltages 

depend on the given network characteristics and the mechanical and dielectric characteristics 

of the switching device. 

5.1.3.1. Interrupting principle 

Interrupting an electric current using an ideal device involves the resistance of the device going 

from zero before interruption to an infinite value just after interruption. The interruption occurs 

the instant the current crosses zero. 

It is impossible to make such an ideal device, but with the interrupting techniques being based 

on the behaviour of the electric arc in different dielectric media we can come close to it. 

circuit-breaker interruption 

The instant the current is interrupted, an electric arc is created between the terminals of the 

switching device. The conductive electric arc tends to be held by the ionizing phenomenon of 

the dielectric caused by the energy dissipated. 

Around current zero crossing, the dissipated energy decreases dropping below the thermal 

energy supplied to the medium, the arc cools down and its resistance increases. 

When the current crosses zero, the arc resistance becomes infinite and the arc is interrupted. 

Between the start and end of interruption, the voltage between the poles of the switching 

device goes from zero to the network voltage. This change gives rise to a high frequency 

transient phenomenon called the transient recovery voltage (see fig. 5-23). 




424 

R 

L 

I 

V 

C 

V A 

I V 

V A 

t 

L, R : inductance and resistance equivalent to the network upstream of the circuit-breaker 

C : upstream network capacitance 

Figure 5-23: transient recovery voltage during circuit-breaker interruption 

fuse interruption 

On occurrence of a short circuit, the value of the current flowing through the fuse is higher than 

its nominal fusing value. 

Interruption can thus occur at any instant and not necessarily the moment the current crosses 

zero. 

Figure 5-24 gives an example of a transient overvoltage which occurs on the network after a 

wire fuse has fused. 

Volts 

1000 

225 

~1ms 

t 

Figure 5-24: transient overvoltage on fusion of a wire fuse 




425 

5.1.3.2. Load switching 

de-energizing loads 

inductive load 

single-phase circuit 

Let us consider the equivalent single-phase diagram in figure 5-25 with an ideal circuit-breaker 

CB which has a zero arc resistance the instant the contacts separate and which carries out 

interruption when the current crosses zero. Before operation of the circuit-breaker, between 

pointsA and B, there is a voltage drop due to the load current flowing through L s . 

At the instant of interruption, the voltage at B suddenly reaches the voltage at A and the 

capacitance C s is charged through L s . The energy exchanges between C s and L s make 

voltage oscillations at frequencies of 5 to 10 kHz occur. 

The voltage at 

C suddenly decreases to zero and the capacitance C p is then discharged 

through L . The energy exchanges between C p and L create voltage oscillations at 

frequencies going from 1 to 100 KHz. 

A 

I s 

B 

I D 

I 0 

CB 

C 

I L 

L s 

V A 

C s 

C p 

L 

L p 

L s : network inductance upstream of the circuit-breaker 

C s : network capacitance upstream of the circuit-breaker 

L : load inductance 

L p : stray inductance 

C p : network capacitance downstream of the circuit-breaker 

CB : circuit-breaker 

Figure 5-25: interruption in an inductive load network 




426 

The phenomena observed are illustrated by curves in figure 5-26. 

V A 

V B 

V C 

I s 

I D 

I L 

VD = VB −VC 

t 

t 

t 

t 

t 

t 

t 

t 0 t 1 

t 0 : separation of contacts 

t 1 : zero current 

Figure 5-26: interruption cycle of an ideal device 




427 

three-phase circuit 

When the three-phase circuit in figure 5-27 is interrupted, the first phase which sees the 

current crossing zero interrupts this current. There follows a transient current circulating in the 

two uninterrupted phases. Thus, if phase 1 interrupts the current first a transient voltage is 

obtained between points C 1 , C 2 and earth which is capable of reaching a value of 2 V $ n for 

an ideal circuit-breaker. For an actual circuit-breaker, the overvoltage coefficient is higher than 

or equal to 2. 

$ V n : peak value of the phase-neutral nominal voltage 

Note: 

the current crosses zero on the following phase after 1/3 of a period (7 ms at 50 Hz), while the 

period of oscillations is roughly 1 ms. 

L s B 1 C 1 

L 1 

A 1 V 1 

C s 

L p 

C p 

L s B 2 C 2 

L 2 

A 2 V 2 

N 

C s 

L p 

C p 

L s B 3 C 3 

L 3 

A 3 V 3 

C s 

L p 

C p 

Figure 5-27: equivalent diagram of a three-phase circuit during interruption 

restrike phenomenon 

The instant a circuit is interrupted, the voltage at the terminals of the circuit-breaker quickly 

increases (roughly from 0.1 to 0.5 kV/µs). If the circuit-breaker poles separate shortly before 

the current reaches zero (for an inductive circuit, this corresponds to the maximum voltage), 

regeneration of the dielectric medium may not be sufficient to withstand the stress-voltage. 

Indeed, in this case, the voltage is maximum and the poles are closer together. 

Renewed breakdown then occurs accompanied by overvoltages with a peak to peak 

magnitude of 2 V $ n . This phenomenon is called restrike. 




428 

multiple restrike 

If we consider the single-phase diagram in figure 5-25, we can see that in the case of restrike, 

the voltage at point C almost instantaneously reaches the voltage at point B . 

The capacitance C p is charged by a high frequency current (roughly 1 MHz) circulating in the 

Lp, Cs, CB and C p circuit. 

This high frequency current very quickly crosses zero (1 µs). 

If the circuit-breaker manages to interrupt the current at that moment, the restrike phenomenon 

is repeated as the distance between the circuit-breaker contacts is still very small. 

Furthermore, the peak-to-peak magnitude of the oscillation is then equal to 4 $ V n . 

The overvoltage increase makes the occurrence of a second breakdown highly probable. 

Indeed, the increase in dielectric withstand through the increase in the distance between the 

circuit-breaker contacts may be lower than the increase in overvoltage. 

This is why a multiple restrike phenomenon occurs with overvoltages of increasing magnitude 

(see fig. 5-28). 

In theory, such a phenomenon may generate overvoltages having a peak value equal to the 

dielectric withstand limit of the open device, without a definite interruption of the current being 

obtained. In practice, this case remains exceptional as it is enough for one of the restrikes to 

allow the power frequency current to be restored; a new current half wave then flows through 

the circuit-breaker. The circuit-breaker interrupts this half-wave the moment it crosses zero 

when the distance between the contacts is sufficient. Thus the types of circuit-breakers 

undergoing multiple restrike usually manage to interrupt the current without causing 

overvoltages of very high magnitude. 

V C 

t 

Figure 5-28: voltage V C in case of interruption with multiple restrike 




429 

chopping current (weak inductive currents) 

When weak currents, notably lower than the nominal current of the circuit-breaker, are 

interrupted, the arc which occurs occupies a small volume. It consequently undergoes 

considerable cooling linked to the circuit-breaker's capacity to interrupt much higher currents. 

Owing to this fact, the arc becomes unstable and its voltage may present relatively large 

variations, while its absolute value remains lower than the network voltage (case of SF6 or 

vacuum). These voltage variations may generate high frequency oscillating currents, with a 

magnitude that may reach 10% of the current at 50 Hz, in the nearby capacitances (Cs, Lp, 

Cp 

circuit in figure 5-25). Superposing these high frequency currents on the current at 50 Hz 

results in multiple crossings of the current through zero around zero of the fundamental wave 

(see fig. 5-29). 

The circuit-breaker interrupts the current the first time it crosses zero while the load current 

(only the current at 50Hz) is not zero. The value of this current represents what we call the 

chopping current ( I chop ) . 

currentinthe 

circuit-breaker 

I chop 

"chopping" 

current 

extinction 

possible 

50Hzwave 

Figure 5-29: superposition of a high frequency oscillating current 

on a power frequency current 




430 

The current is then interrupted as in the case in figure 5-25 except for the peak-to-peak 

⎛1 

2⎞ 

magnitude of the oscillations, due to the presence of energy stored in L ⎜ LI 

⎝ a ⎟ which is 

2 ⎠ 

⎛1 

2 

added to that in the capacitance C p CpV 

$ ⎞ 

⎜ n ⎟ . 

⎝2 

⎠ 

If V$ c max is half the peak-to-peak maximum value of the oscillation at point C, we can write: 

1 

2 

2 1 2 1 2 

C V$ C V$ 

p cmax = p n LIa 

2 

+ 2 

$ $ L 

Vcmax 

= Vn 

+ 

C I 

2 2 

a 

p 

$ V n : phase-neutral nominal voltage peak value 

in single-phase. 

For a three-phase circuit $ V n must be added in order to take into account the transient 

operating conditions linked to the non-simultaneous interruption of the phases, whence: 

$ $ $ L 

Vcmax 

= Vn + Vn 

+ 

C I 

2 2 

a 

p 

This phenomenon is notably problematic in the case of an arc furnace transformer power 

supply. 

Indeed, the transformer is generally connected not very far away from the busbar. Thus the 

value of C p is very weak and therefore the value of V $ c max high. 

We can determine 

V $ c max by taking: 

L : transformer leakage inductance 

C p : capacitance of the cable linking the circuit-breaker to the transformer 

I a : transformer magnetizing current 

Schneider carried out an analysis for a single-phase arc furnace transformer where: 

V 

Vn = 15000 3 

; L =826 . H ; Cp =1475 . nF ; Ia =436 . A 

we find V$ =85 . V$ 

cmax 

n 

Installing an R, C circuit in parallel with the circuit-breaker allowed the overvoltage to be 

reduced to 2 $ V n . 




431 

virtual chopping current - simultaneous interruption of the three phases 

The transients generated by the first phase that creates overvoltages may cause, owing to the 

capacitive coupling between the phases, oscillating currents inside circuits Lp, Cp, Cs 

of the 

other phases. 

It is thus possible to obtain zero current in these phases, immediately (several hundreds of a 

microsecond) after interruption of the first phase. 

If the circuit-breaker interrupts such currents, a chopping current phenomenon is then created 

with very high chopping current and overvoltage values. 

chopping current and multiple restrike 

Current chopping and multiple restrike are frequently linked. 

Overvoltages caused by current chopping can themselves lead to restrike. They are almost 

systematic in the case of the virtual chopping current. 

capacitive loads (see fig. 5-30) 

Interruption of capacitive circuits, such as a capacitor bank or off-load cable, raises less 

difficulties than the interruption of inductive circuits. 

Indeed, the capacitances remain charged at the peak value of the 50 Hz wave after extinction 

of the arc when the current reaches zero and the recurrence of voltage at the switchgear 

terminals is accompanied by a 50 Hz wave. 

Nevertheless, one half period after interruption, the device is subjected to a voltage equal to 

twice the 50 Hz peak voltage ( 2 V $ n ) . 

If the speed and dielectric withstand of the device are not sufficient to withstand this stress, 

restrike may occur. It is followed by a voltage reversal at the terminals of the capacitances, 

raising them to a phase-neutral voltage equal to 3 $ V n maximum (if damping is neglected). 




432 

When the supply voltage reverses back, a half period later, the potential difference at the 

device terminals then reaches 4 $ V n . Such an overvoltage can obviously cause renewed 

restrike between the device contacts, and the previously described oscillation mechanism is 

renewed with increased magnitude, leading to a new rise in the phase-neutral voltage of the 

capacitances ( 5 V $ n ) . 

The cumulative effect of multiple restrike is obviously highly dangerous for the network 

components as for the device itself. 

This rise in overvoltages can be avoided by choosing the appropriate equipment, i.e. which 

does not allow restrike. 

V 

VC 

5 V $ n 

20ms 

VC V $ n 

$V n 2 Vn $ 

4 V $ n 

interruption 

VC 

3 V $ n 

t 

Figure 5-30: voltage rise on separation of a capacitor bank from 

the network by a slow operating device 




433 

energizing a load 

inductive circuit 

When a device closes, on an inductive circuit (no-load transformer, motor on starting), there is 

a moment when the dielectric withstand between its contacts drops below the applied voltage. 

A breakdown occurs causing sudden zero voltage at the device terminals. 

This is accompanied by oscillations with stray capacitances which cause high frequency 

currents to circulate in the circuit-breaker. 

Depending on the speed of the device, prestrikes may or may not occur up to complete closing 

of the poles. 

Multiple prestrike is accompanied by successive overvoltages which decrease until the device 

is completely closed. 

The phenomenon is highly complex and involves several parameters: 

- the characteristics of the switching device 

- the characteristic impedance of the connections 

- the natural frequencies of the load circuit 

which means that a mathematical simulation model is required to pre-determine the 

overvoltage values. 

capacitive circuit (capacitor bank) 

When a capacitor bank is energized via a slow operating device, prestrike occurs between the 

contacts close to the wave peak of 50 Hz. 

A damped oscillation in the LC system in figure 5-31 then occurs at a frequency above 

50 Hz concentrated around the peak. In this case the maximum overvoltage is 2 V $ n . It 

corresponds to the maximum overvoltage admissible by the capacitors (see IEC 831-1 for LV 

and 871-1 for MV or HV). 

With a faster device, prestrike does not necessarily occur around the 50 Hz peak and 

consequently the overvoltage is smaller. 

When put out of service, the bank remains charged at a voltage going from 0 to the peak 

voltage of the network. 




434 

If the bank is energized shortly afterwards, a breakdown due to the application of a voltage of 

opposite polarity may give rise to an overvoltage of 3 V $ n . 

L 

CB 

U 

C 

Figure 5-31: closing operation of a capacitive circuit 

To ensure the safety of persons, the capacitor banks are fitted with a discharging resistor 

having a time constant allowing 75 V to be reached after 3 minutes in LV and 10 minutes in 

HV. 

Means of protecting loads 

The phenomena created by de-energizing (or energizing) loads, which we have studied, lead 

to transient overvoltages which may be dangerous for both loads and other network elements. 

Table 5-2 gives the level of overvoltages and their characteristics for each phenomenon 

studied. 

Chopping 

current 

Multiple 

restrike 

Occurrence of 

phenomenon 

at every 

interruption 

interruption with 

separation 

close to zero 

current 

Number of 

overvoltage 

peaks 

Overvoltage 

value 

dU/dt order of 

magnitude 

Remark 

1 2 to 4 $ V n 0.1 kV/µs favours restrike 

0 to 20 2 to 7 $ V n 

Prestrike at every closing 1 to 50 2.5 $ V n 

$ V n : phase-neutral voltage peak value 

10 kV/µs 

10 kV/µs 

Table 5-2: different types of overvoltage 




435 

The loads affected by these phenomena are off-load transformers, neutral point coils (neutral 

reactance earthing) and motors during the starting period for inductive circuits as well as 

capacitor banks for capacitive circuits. 

Transformers undergo impulse wave dielectric tests; because of this, they are better built than 

motors to be able to withstand the transients caused by restrike (see IEC 76-3). 

The case of motors is different. At each start, they must withstand the transients caused by 

prestrike. Moreover, even if interruption during the starting period does not occur very often, it 

is nevertheless a possibility and they are then subjected to multiple restrike. 

Motors are thus especially sensitive to multiple prestrike, because of its high rate of 

occurrence, as well as to multiple restrike, due to the magnitude of the overvoltages produced. 

These overvoltages cause deterioration of the insulation of the first turns. 

In order to limit overvoltages, Zn0 type surge arresters can be connected in parallel with the 

load. 

But the best method consists in using switching devices suitable for the type of application. 

Table 5-3 gives the behaviour of medium voltage switchgear with respect to the phenomena 

relating to the switching overvoltages studied. 

Switchgear 

Puffer-type SF 6 circuitbreaker 

Rotating arc SF 6 circuitbreaker 

and contactor 

Multiple 

prestrike on 

closing 

Current 

chopping 

Multiple 

restrike 

Overall behaviour 

no weak no No problem. Below 300 

kW, use a rotating arc 

SF 6 circuit-breaker. 

no no no No problem. 

Vacuum circuit-breaker yes yes yes Use surge arresters 

Vacuum contactor yes weak yes Use surge arresters 

Magnetic blast circuitbreaker 

and contactor 

no no no No problem. 

Minimum oil circuit-breaker no yes yes Use surge arresters 

Table 5-3: behaviour of medium voltage switchgear 




436 

5.1.3.3. Circuit-breaker clearance of phase-earth faults 

Let us consider the three-phase network shown in figure 5-32 in which phase 1 is affected by 

an earth fault. 

In this case, the network is equivalent to the diagram in figure 5-33 which corresponds to the 

case examined in paragraph 5.1.2.1. 

At the start of contact separation, the arc voltage is weak and remains constant. 

On the other hand, just before interruption, this voltage, called the extinction voltage, increases 

to a more or less high value which may exceed $ V n . This voltage depends on the type of 

circuit-breaker (air, oil, SF 6 , vacuum) as well as the arc extinction technique (cooling, 

lengthening, rotating arc). 

When the current crosses zero, the arc is extinguished and the recovery voltage magnitude 

will depend on the extinction voltage as follows: 

- for the case of neutral earthing via resistance (the fault current is in phase in relation to the 

voltage), the extinction voltage limits the magnitude of recovery voltage oscillations 

- for the case of neutral earthing via reactance (the fault current is phase shifted by 

relation to the voltage), the extinction voltage increases the magnitude of oscillations. 

π 

2 in 

After interruption, restrike may take place if re-generation of the dielectric medium is not fast 

enough in relation to the rise in recovery voltage. In this case, the magnitude of oscillations 

may reach double the size of the first recovery voltage. 

If we neglect the transformer and line impedances, the voltage at the terminals of the neutral 

V N is equal to the difference between the supply voltage and the 

earthing impedance ( ) 

voltage at the circuit-breaker terminals. The voltage 

V N is vectorially added to the voltage of 

the healthy phases and may lead to the latter reaching higher overvoltages than the 

overvoltages observed on the fault phase. 

The curves in figure 5-34 give the overvoltage levels recorded on occurrence of an earth fault 

in relation to the network characteristics and the earthing impedance. 




437 

We can see that reactance earthing of the neutral (case with restrike) clearly increases the 

magnitude of the overvoltages. Resistance earthing is thus preferable. In the latter case, we 

see that the overvoltages do not exceed 240 % when the ratio of the current in the earthing 

resistor to the network capacitive current is equal to 2 (see fig. 5-34). In networks with 

resistance earthing, the following relation should therefore always be respected if possible: 

IrN 

>2IC 

I rN : current in the neutral earthing resistor during the fault 

I C : currents in the network phase-earth capacitances (see § 4.3 of Protection guide) 

V 3 CB 

V 2 

V 1 

Ph3 

Ph2 

Ph1 

or 

Z N 

r N 

C C C 

I f 

Z N : neutral earthing impedance (or r N ) 

C 

I f 

: phase-earth capacitance 

: fault current 

CB : circuit-breaker 

V1, V2, V3 

: single-phase voltages 

Figure 5-32: phase-earth fault clearance 

X net 

CB 

~ 

or 

Z N 

r N 

C 

I f 

I C 

I rN 

X net : network reactance 

C : fault phase earth capacitance 

Z N or r N : neutral earthing impedance (or resistance r N ) 

I f : fault current 

Figure 5-33: fault circuit on occurrence of a phase-earth fault 




438 

High resistance earthing with restrike in the 

fault or circuit-breaker, case of industrial 

networks for which IrN

439 

Reactance earthing: (network reactance) 

Voltage at circuit-breaker terminals 

Voltage at the terminals of the reactance 

Resistance earthing: 

(network reactance) 

Voltage at circuit-breaker terminals 

Voltage at the terminals of the resistor 

: arc extinction voltage 

Figure 5-35: transient voltage on circuit-breaker opening during a permanent phase-earth fault 


The publication, translation and reproduction, either wholly orpartly, of this document are not allowed without our written consent. 


440 

5.1.4. Atmospheric overvoltages 

general 

The earth and the electrosphere, the conductive area in the atmosphere (about 50 to 100 km 

thick), constitute a natural spherical capacitor which is charged by ionization, thus producing 

an electric field directed towards the ground of roughly several hundred volts/metre 

Since air is not very conductive, there is thus an associated permanent conduction current, of 

roughly 1 500 A for the entire earth's globe. Electrical balance is ensured during discharges by 

rain and strokes of lightning. 

The formation of storm clouds, masses of water in the form of aerosols, is accompanied by 

charge separation electrostatic phenomena: the positively charged light particles are driven by 

the rising air currents, and the negatively charged heavy particles fall because of their weight. 

At the base of the cloud, there may also be islets of positive charges where heavy rains are 

located. 

On an overall macroscopic scale, a dipole is created. 

When the breakdown withstand limit gradient is reached, a discharge is produced inside the 

cloud or between clouds or between the cloud and the ground. In the latter case, it is referred 

to as lightning. 

The cloud-ground electric field can reach 15 to 20 kV/metre on flat ground. But the presence of 

obstacles deforms and locally increases this field by a factor of 10 to 100 or even 1 000 

depending on the form of the obstacles (also called the "peak effect"). The atmospheric air 

ionizing threshold is thus reached, i.e. roughly 30 kV/cm, and corona effect discharges are 

produced. When these discharges are located on fairly high objects (tower, chimney, pylon) 

they may divert lightning to this objects. 

classification and characteristics of strokes of lightning 

Strokes of lightning are classed according to the origin of the discharge (or leader) and their 

polarity. 

Depending on the leader origin, the stroke of lightning may be: 

- either descending from the clouds to the ground in the case of fairly flat land 

- or ascending from the ground to the clouds in the case of mountainous land. 

Depending on the polarity the following distinctions between lightning strokes are made: 

- negative when the negative part of the cloud is discharged, which represents 80 % of cases 

in temperate countries 

- positive when the positive part of the cloud is discharged. 




441 

form and magnitude of the lightning wave 

The physical phenomenon of lightning corresponds to a source of impulse current the actual 

form of which is highly variable: it consists of a front rising up to the maximum magnitude of 

several miscroseconds to 20 µs followed by a decreasing tail of several tens of µs (see 

figure 5-36). 

Figure 5-36: oscillogram of a lightning current 

The magnitude of strokes of lightning varies according to a log-normal distribution law. We can 

thus determine the probability of a given magnitude being exceeded (see figure 5-37). We can 

see, for example, that for the average curve (IEEE), the probability of exceeding a magnitude 

of 100 kA is 5 %. This means that 95 % of lightning strokes have a magnitude less than 

100 kA. 

Figure 5-37: probability of exceeding positive and negative lightning stroke magnitudes, 

according to IEEE (experimental statistic) 




442 

Similarly, the steepness of the wave front varies according to a log-normal distribution law. Let us 

determine the probability of exceeding a given front steepness (see fig. 5-38). We can see that the 

probability of exceeding a front steepness of 50 kA/µs of a negative stroke of lightning is 20 %. 

Figure 5-38: probability of exceeding the front steepnesses of positive and negative 

lightning currents according to IEEE (experimental statistic) 

standard wave form 

The lightning impulse wave form given by IEC 71-1 is a 1.2/50 µs wave (see fig. 5-39): 

- rise time to the maximum value of 1.2 µs 

- time to half-value of 50 µs. 

Figure 5-39: standard lightning impulse voltage wave form (IEC 71-1) 




443 

lightning density 

On a world-wide scale, 63 billion discharges are recorded on average each year which 

corresponds to 100 discharges per second. In France, this figure varies from 1.5 to 2 million 

lightning strokes per year. 

We then define the lightning density as being the number of days per year on which 

thunder has been heard in a place. 

In France, the average value of is 20 with a variation range going from 10 in channel 

coastal regions up to over 30 in mountainous regions. 

The value of may be much higher and reach 180 in tropical Africa or Indonesia. 

lightning strike density 

The lightning strike density represents the number of lightning strikes per km 2 per year, 

whatever their current value levels. 

In France, varies between 2 and 6 lightning strikes/km 2 /year depending on the region. 

lightning impact mechanism 

The lightning impact mechanism begins with a leader from a cloud which approaches the 

ground at a low speed. When the electric field is sufficient, sudden conduction is established 

giving rise to the lightning discharge. 

An experimental practical approach has enabled the relation linking the current of the 

lightning strike to the distance between the starting point (leader position) and discharge point 

(point of impact connected to the earth) to be found: 

or 

according to the authors. 

: striking distance, in m 

: lightning current, in kA 




444 

By applying an electro-geometrical model to a vertical rod with a height (see fig. 5-40-a), 

we can show that there are two distinct zones: 

- zone 1 : this is located between the ground and the parabola which is the locus of the 

equidistant points of and the ground; the instant the flash occurs, any leader 

located in this zone will touch the ground since it is nearer to this than to 

- zone 2 : this is located above the parabola; the instant the flash occurs, any leader located 

in this zone will be picked up by point on the vertical rod as soon as the 

distance between and the leader is less than the striking distance . 

Figure 5-40-a: diagram of different protection zones offered by a vertical rod 

For a lightning current with a value of , and thus a given striking distance, the distance x between 

the point of impact on the ground and the point where the rod is fixed to the ground (called the rod 

pick-up radius) is: 

if 

if 

The rod pick-up radius is thus all the greater the more intensive the lightning stroke. 

For very weak currents, the pick-up radius becomes less than the height of the rod which is then 

able to pick up the current along its length. This has been experimentally proved. 




445 

application to equipment protection using a lightning conductor 

The lightning conductor diverts lightning to itself in order to protect equipment. Its principle is 

based on the striking distance; tapered rods are placed at the top of equipment to be 

protected, they are connected to the earth by the most direct path (the lightning conductors 

surrounding the structure to be protected and interconnected with the earthing network). 

The electrogeometric model allows the zone to be protected to be determined using the fictive 

sphere method. 

The point of impact of the lightning is determined by the object on the ground the closest to the 

leader starting distance d. Everything happens as if the leader was surrounded by a fictive 

sphere with a radius d moving with it. For good protection, the fictive sphere rolling on the 

ground reaches the lightning conductor without touching the objects to be protected 

(see fig. 5-40-b). 

Protection against direct lightning strikes is approximately good in a cone the top of which is 

the top of the lightning conductor and the half-angle at the top is 45 °. 

leader 

d=criticalstrikingdistance 

protected 

zone 

(cone) 

fictive 

sphere 

lightning 

conductor 

45° 

Figure 5-40-b: determining the zone protected by a lightning conductor 

using the "fictive" sphere method 


The publication, translation and reproduction , either partly of this document are not allowed without our written consent. 


446 

direct lightning strike (on phase conductors) 

When lightning strikes the phase conductor of a line, the current i( t ) is shared out in equal 

quantities on either side of the point of impact and is spread along the conductors. These have 

a wave impedance Z the value of which is between 300 and 500 Ω. This impedance is that 

seen by the wave front, is independent of the length of the line and of a different type from the 

impedance at 50 Hz. 

This results in a voltage wave of: 

( ) 

U ( t) 

= Z. 

i t 

2 

which spreads along the line (see fig. 5-41). 

U 

i 

U Z i = 

2 

i 

t 

Figure 5-41: lightning strike on a phase conductor 




447 

Depending on the magnitude of the lightning current, two cases may occur: 

full impulse propagation 

⎛ 

If the maximum voltage ⎜U Z I 

max = 

⎝ 2 

max 

string, the entire (full) wave spreads along the line. 

⎞ 

⎟ 

⎠ 

is below the sparkover voltage U a of the insulator 

chopped impulse propagation 

In the case where U max ≥ U a , as a first approximation, insulator sparkover occurs at the value 

of U a , and a phase-earth fault occurs at 50 Hz due to the arc being maintained. The lightning 

that is propagated is thus broken at the maximum value corresponding to U a . 

The lightning current causing this flashover, for a given line, is called the critical current 

such that: 

I C 

U 

IC 

=2 a 

Z 

For lines, the order of magnitude of I C is: 

- 5.5 kA at 225 kV, which corresponds to a probability of exceeding the magnitude according 

to the IEEE method of 95 % (see figure 5-37) 

- 8.5 kA at 400 kV, which corresponds to a probability of exceeding the magnitude according 

to the IEEE method of 92 % (see figure 5-37). 

In medium voltage, flashover is systematic in the case of a stroke of lightning occurring due to 

the small distances in the air of the insulator string. This flashover of the insulator gives rise to 

a phase-earth fault current, called a follow current, which is held at the power frequency of 50 

Hz until it is cleared by the protections. 




448 

indirect lightning strikes (lightning protection rope or pylons) 

When lightning strikes the line protection rope, part of the current flows through the pylon since 

the protection rope is connected to it (see fig. 5-42). 

This results in a potential rise at the top of the pylon the value of which depends on the self 

inductance L of the pylon and the resistance R of the earth electrode: 

( ) 

⎡ 

U ( t) = k Ri( t) 

+ L di t ⎤ 

⎢ 

⎥ 

⎣ dt ⎦ 

k : ratio of the current shunted into the pylon by the incident current 

k .i 

lightningstrike 

i 

U protectionrope 

L 

k.i 

R 

U = k ⎡ R × I + L di ⎤ 

⎢ 

⎣ dt ⎥ 

⎦ 

Figure 5-42: lightning strike on a protection rope 

The voltage U may reach the impulse sparkover voltage of the insulators and cause a 

breakdown. This is "back-flashover". Part of the current is then propagated along the affected 

phase(s) towards the users. This current is in general greater than that of a direct lightning 

strike. 




449 

In extra high voltage (> 220 kV), back-flashover is unlikely (the flashover level of the insulators 

is high), which is why it is useful to install protection ropes thus limiting the number of service 

interruptions. But below 90 kV back-flashover occurs even if the value of the earth electrode 

resistance is low (< 15 Ω); the usefulness of protection ropes is thus limited (more frequent 

service interruptions). 

induced impulse 

A stroke of lightning that falls anywhere on the ground behaves like an electromagnetic field 

radiation source. 

The steeper the rising front of the lightning current the greater the radiation. 

For front steepnesses of 50 to 100 kA/µs, the effects of this field will be felt several hundreds 

of metres, if not kilometres, away. 

The magnetic field H at a point located at a distance of r from a circuit through which a 

currentI flows, is given in the relation: 

H 

I 

= 2 πr 

This field creates induced voltages in the neighbouring circuits which are able to reach 

dangerous values both for equipment and persons. 

case of a loop 

Let us consider the loop formed by the supply cable and the telecommunication link in figure 

5-43, with a surface S and located 100 m from the lightning impact which has a current rising 

front steepness of 80 kA/µs. 




450 

The induced voltage is given in the relation: 

dφ 

e = − = − S dB = − µ 

dt dt 0 

S dH 

dt 

µ = 4 π × 10 

0 

−7 

: magnetic permeability of the vacuum 

now 

dH 

dt 

3 

1 dI 1 10 6 

= = × 80 × = 127 × 10 

2πr 

dt 2π 

× 100 −6 

10 

A/ m/ 

s 

−7 6 

whence e = 4 π10 × 120 × 127 × 10 = 19kV 

A phase-earth overvoltage of 19 kV thus occurs on the loop. This has a very short duration 

( ≈ 1µ 

s ) but can cause insulation breakdown. 

To avoid this risk, the surfaces of the loops must be reduced. 

lightningimpulse 

frontsteepness=80kA/µs 

telecommunicationlink 

computer 

magneticfield 

100m 

circuit 

loop 

surface=120m² 

printer 

supplycable 

phase-earthinsulation 

subjectedto19kV( 1µs) 

earth 

Figure 5-43: circuit loop 




451 

impulse wave transference in a transformer (see IEC 71-2 - appendix A) 

In lightning impulse conditions, the transformer behaves like a capacitive divider with a ratio of 

s ≤0.4 . It is equivalent to a capacitance C t (see figure 5-44-a). 

lightningwave 

equivalent 

C t 

U 1 

U sU 0 1 

U sU 0 1 

U 1 : impulse voltage on the high voltage terminal 

U 0 : no-load voltage transferred 

Figure 5-44-a: impulse wave transference in a transformer 

U 0 represents the no-load overvoltage, i.e. when the secondary outgoing terminals are not 

connected to any cables or lines. This overvoltage is generally not acceptable by the 

transformer. 

In reality, the transformer is connected to a network with a capacitiance 

role of a voltage divider with the transformer capacitance C t (see fig. 5-44-b). 

C s . This plays the 

U0 = sU1 

C t 

C s U 2 

U 2 : voltage transferred to the secondary with a network 

Figure 5-44-b: transformer with its equivalent network 

The voltage transferred to the secondary is thus: 

U 

C 

= 

t 

C + C sU 

2 t s 

1 




452 

The values of C t are generally between 1 and 10 nF. The capacitance of a cable is close to 

0.4 nF/m. Thus, several tens of metres of cable will greatly reduce the overvoltage transferred 

to the secondary. 

In general, the network is sufficiently widespread for the overvoltage transferred not to raise 

any difficulties. 

However, in the case of a short cable, e.g. between a specific transformer and a load (arc 

furnace, etc.), the overvoltage transferred may be unacceptable for the equipment on the low 

voltage side. 

To reduce the magnitude of the impulse transferred, it is possible to: 

- use a surge arrester with a lower sparkover voltage on the high voltage side 

- install a surge arrester on the low voltage side between each phase and earth 

- increase the capacitance between each phase and earth on the low voltage side. 

5.1.5. Propagation of overvoltages 

Overhead lines and cables constitute a propagation media for any overvoltage wave likely to 

occur on a network. 

For high frequencies (case of switching and lightning overvoltages), the line is characterised by 

its so-called "characteristic" or "wave" impedance: 

Z 

c ≈ 

L 

C 

L : line inductance 

C : line capacitance 

We can see that this impedance is independent of the length of the line. 

The speed of the wave propagation on an overhead line is close to the speed of light: 

for cables, it is equal to v 

c = 3 × 10 8 m/s (300 m/µs) 

c 

= 

εr 

ε r : relative permittivity of the cable insulating material 




453 

The value of v is close to 150 m/µs. 

This gives us an idea of the way a lightning wave spreads along a conductor. Figure 5-45 

shows how a lightning wave spreads along an overhead line in relation to time and space. 

development 

intime 

V 

front:200kV/µs 

400kV 

2µs 

t(toxconstant) 

spreadin 

space 

V 

400kV 

front:0.66kV/m 

600m=300 x2µs 

x(totconstant) 

Figure 5-45: diagram showing how a lightning wave spreads along an overhead line 

in relation to time and space 

Let us closely examine the phenomenon that is produced at a point M , where a change of 

impedance exists, separating two circuits with characterstic impedances of Z 1 and Z 2 

(see fig. 5-46). 

v 1 v 2 

i 1 i 2 

Z 1 

v' 

1 

M Z 2 

' 

i 1 

Z1, Z2 

: upstream and downstream characteristic impedances 

v1, i1 

: incident wave upstream of M 

v2, i2 

: wave transferred downstream of M 

' ' 

1 1 

v , i : wave reflected upstream of M 

Figure 5-46: propagation of a wave at a change of impedance point 

M 




454 

Upstream of 

M , we have: 

' 

v1 = Z1i1 

and v1 = − Z1i1 

(1) 

immediately downstream of M : 

at point M : 

We can thus deduce: 

v2 = Z2i2 

(2) 

v2 = v1 + v1 

' and i2 = i1 + i1 

' (3) 

' 

( ) 

' ' 

2 1 1 1 1 1 1 1 2 1 

v = v + v = v − Z i = v −Z i −i 

whence 

v 

2 

Z 

= 

2 

Z + Z 

2 1 

× 2v 

1 

In particular: 

' 

1 1 

- for a line short-circuited to earth, Z 2 = 0; we can deduce from this that v 2 = 0 and v = −v 

- for a conductor without a change of impedance, Z2 = Z1 

; we can deduce from this that 

v2 = v1 

and v 1 = 0 

' 

- for an open line, Z 2 = ∞ ; we can deduce from this that v2 = 2v1 

and v1 = v1 

. 

' 

To conclude, at the point of change of impedance, the maximum voltage value may reach 

double the incident wave. This is the case of a line feeding a transformer as its impedance in 

relation to the lightning wave is very high in relation to the characteristic impedance of the line. 




455 

5.2. Overvoltage protection devices 

5.2.1. Principle of protection 

The protection of installations and persons against overvoltages is greatly improved when 

disturbances flow to earth, and this is done as close as possible to the sources of disturbance. 

This requires low impedance earth electrodes to be implemented. 

Thus, three overvoltage protection levels can be distinguished: 

1 st protection level 

The objective is to avoid a direct impact on structures by catching the lightning and directing it 

towards designated flow points, via: 

- lightning conductors, whose principle is based on the striking distance; a rod placed at the 

top of a structure to be protected captures the lightning and evacuates it through the 

earthing network (see fig. 5-40-b) 

- meshed or Faraday cages 

- lightning protection ropes (see fig. 5-42). 

2 nd protection level 

Its aim is to ensure that the basic impulse level (BIL) of the substation components has not 

been exceeded. 

In HV, this type of protection is established using elements ensuring that the lightning wave 

flows to earth, such as: 

- spark-gaps 

- HV surge arresters. 

3 rd protection level 

Used in LV as an extra protection for sensitive equipment (computers, telecommunication 

devices, etc.). 

It uses: 

- series filters 

- overvoltage limiters 

- LV surge arresters. 




456 

5.2.2. Spark-gaps 

operation 

The spark-gap is a simple device made up of two electrodes, the first connected to the 

conductor to be protected and the second connected to earth. 

At the place where it is installed in the network, the spark-gap constitutes a weak point where 

overvoltages can flow to earth and thus protects the equipment. 

The sparkover voltage of the spark-gap is set by adjusting the distance in the air between the 

electrodes so as to obtain a margin between the impulse withstand of the equipment to be 

protected and the impulse sparkover voltage of the spark-gap (see fig. 5-47). For example, 

B = 40 mm on French public EDF 20 kV networks. 

birdproofrod 

earthelectrode 

phaseelectrode 

45° 

45° 

electrode 

holder 

B 

rigid 

anchoringchain 

deviceforadjustingB 

andlockingtheelectrode 

Figure 5-47: MV spark-gap with birdproof rod 




457 

advantages 

The main advantages of spark-gaps: 

- their low price 

- their simplicity 

- the possibility of setting the sparkover voltage. 

drawbacks 

- The sparkover characteristics of the spark-gap are highly variable (up to 40 %) depending 

on the atmospheric conditions (temperature, humidity, pressure) which modify the ionization 

of the dielectric medium (air) between the electrodes. 

- the sparkover level depends on the overvoltage. 

- spark-gap sparkover causes a power frequency phase-to-earth short circuit owing to the arc 

being maintained. The short circuit lasts until it is cleared by the switching devices (this 

short circuit is called a follow current). This means that it is necessary to install shunt circuitbreakers 

or rapid reclosing system on the circuit-breaker located upstream. Because of this, 

the spark-gaps are unsuitable for the protection of an installation against switching 

overvoltages. 

- the sparkover caused by a steep front overvoltage is not instantaneous. Due to this delay, 

the voltage actually reached in the network is higher than the chosen protection level. To 

take this phenomenon into account, it is necessary to study the voltage-time curves of the 

spark-gap. 

- sparkover causes the appearance of a steep front broken wave which could damage the 

windings of the transformers or motors located nearby. 

Although still used in certain public networks, spark-gaps are currently being replaced by surge 

arresters. 




458 

5.2.3. Surge arresters 

To overcome the drawbacks of spark-gaps, different models of surge arresters have been 

designed with the aim of ensuring better protection of installations and good continuity of 

service. 

Non-linear resistor type gapped surge arresters are especially found in HV and MV 

installations which have been in operation for several years. The current tendency is to use 

zinc oxide surge arresters which provide better performance. 

definitions 

Surge arrester discharge current 

The surge or impulse current which flows through the arrester after a sparkover of the series 

gaps. 

Surge arrester follow current 

The current from the connected power source which flows through an arrester following the 

passage of discharge current. 

Surge arrester residual voltage 

The voltage that appears between the terminals of an arrester during the passage of discharge 

current. 

5.2.3.1. Non-linear resistor type gapped surge arresters (see IEC 99-1) 

operating principle 

In this type of surge arrester, a variable resistor (varistor), which limits the current after the 

passage of the impulse wave, is associated with a spark gap. 

After evacuation of the impulse wave to earth, the surge arrester is only subjected to the 

network voltage and the follow current is limited by the varistor. 

The arc is systematically extinguished after the 50 Hz wave of the single-phase-to-earth fault 

current has reached zero. 

Owing to the variation of the resistance, the residual voltage is maintained close to the 

sparkover level. Indeed, this resistance decreases with the increase in current. 

Various techniques have been used to make non-linear resistor type gapped arresters. The 

most conventional method uses a silicon carbide (SiC) resistor. 

Some surge arresters also have voltage grading systems (resistive or capacitive dividers) and 

arc blowing systems (magnets or blow-out coils). 




459 

characteristics 

Variable resistor type surge arresters are characterised by: 

- the rated voltage, which is the maximum specified value of the power frequency rms voltage 

permitted between its terminals for which the surge arrester is designed to function 

correctly. This voltage can be continuously applied to the surge arrester without this 

modifying its operating characteristics. 

- the sparkover voltages for the different wave forms (power frequency, switching impulse, 

lightning impulse, etc.). 

- the impulse current evacuation capacity. 

5.2.3.2. Zinc oxide (ZnO ) surge arresters 

operating principle 

Figure 5-48 shows that, unlike the non-linear resistor type gapped surge arrester, the zinc 

oxide surge arrester is only made up of a highly non-linear variable resistor. 

The resistance goes from 1.5 MΩ at the duty voltage (which corresponds to a leakage current 

below 10 mA) to 15 Ω during discharge. 

Following the passage of the discharge current, the voltage at the terminals of the surge 

arrester become equal to the network voltage. The current which flows through the surge 

arrester is very weak and is stabilised around the value of the earth leakage current. 

Because of the high non-linearity of the ZnO surge arrester a high current variation causes a 

low voltage variation (see fig. 5-49). 

For example, when the current is multiplied by 10 7 , the voltage is only multiplied by 1.8. 




460 

connectingspindle 

flange 

(aluminiumalloy) 

elasticstirrup 

exhaustpipeand 

overpressuredevice 

intheupperand 

lowerflanges 

rivet 

ZnO blocks 

washer 

faultindication 

plate 

spacer 

exhaustpipe 

thermalshield 

porcelainenclosure 

compressionspring 

flange 

rubberseal 

prestressedtightness 

device 

ringclamping 

device 

overpressuredevice 

Figure 5-48: example of the structure of a ZnO surge arrester in a porcelain enclosure 

for 20 kV networks 

peakkV 

U 

600 

500 

400 

300 

Z O n 

200 

100 

SiC 

linear 

.001 .01 .1 1 10 100 1000 10000 

I 

SiC : non-linear resistor type gapped surge arrester made up of a silicon carbide resistor 

ZnO : zinc oxide surge arrester 

linear :U curve proportional to 

I 

Figure 5-49: characteristics of two surge arresters having the same 550 kV/10 kA protection level 




461 

characteristics 

ZnO surge arresters are characterised by: 

- the steady-state voltage which is the permitted specified value of the power frequency rms 

voltage that can be continuously applied between the terminals of the surge arrester 

- the rated voltage which is the maximum power frequency rms voltage permitted between its 

terminals for which the surge arrester is designed to operate correctly in the temporary 

overvoltage conditions defined in the operating tests (a power frequency overvoltage of 10 

seconds is applied to the surge arrester - see IEC 99-4) 

- the protection level defined at random as being the residual voltage of the surge arrester 

when it is subjected to a given current impulse (5,10 or 20 kA according to the class), with a 

wave form of 8/20 µs 

- steep front current impulse (1 µs), lightning impulse (8/20 µs), long duration impulse, and 

switching impulse withstand 

- nominal discharge current. 

Table 5-4 gives an example of the characteristics of a phase-to-earth ZnO surge arrester for 

a 20 kV public distribution network (with tripping on occurrence of the first fault). 

Maximum steady-state voltage (phase-earth) 

Rated voltage 

Residual voltage for nominal discharge current 

Nominal discharge current (8/20 µs wave) 

Impulse current withstand (4/10 µs wave) 

12.7 kV 

24 kV 

< 75 kV 

5 kA 

65 kA 

Table 5-4: example of the characteristics of a ZnO surge arrester for a 20 kV network 




462 

choice of zinc oxide surge arresters in HV 

The general method for choosing a zinc oxide surge arrester in HV consists in determining its 

characteristic parameters using the network data, at the place where it will be installed. 

The parameters characterising the surge arrester are: 

- U C , steady-state voltage 

- U r , rated voltage 

- I nd , nominal discharge current 

- discharge class and energy capacity 

- mechanical characteristics. 

The data relative to the network are: 

- U m , highest phase-to-phase voltage applied to equipment 

- TOV temporary overvoltages (appearing on occurrence of an earth fault or load shedding 

on the public distribution network). 

The choice of the surge arrester involves making a compromise between the equipment 

protection levels and the energy capacity of the surge arrester. 

The protection level must be as low as possible for the equipment withstand. This involves the 

lowest voltage rating possible and thus greater difficulty withstanding temporary overvoltages. 

determining U C and U r 

simplified method using equipment characteristics 

The voltages U C and U r may be directly determined using the highest voltage for the 

equipment U m : 

U 

C 

U 

≥ 

m 

3 

Ur 

= 125 . × 

UC 




463 

more accurate method using temporary overvoltages 

The simplified method has a drawback as it does not take into account the real requirements 

of the network which are generally lower than U m 

3 . 

The temporary overvoltages likely to occur in a network are of two types: 

- overvoltages due to a phase-earth fault the clearance time of which depends on the 

protection system (see table 5.1 - the earth overvoltage factor is equal to 1.73 for unearthed 

or impedance earthed networks) 

- overvoltage due to load-shedding on the public distribution network, of the order of 15 % 

but able to reach 35 % in some networks. 

The temporary overvoltage value to be taken into account is the product of the earth fault 

overvoltage and load shedding factors. 

- specific case 

If one of the temporary overvoltages lasts over 2 hours, it is considered to be a steady-state 

condition for the surge arrester and thus U C is chosen to be equal to this overvoltage and 

Ur 

- general case 

= 125 . × 

UC 

A surge arrester's capacity to withstand temporary overvoltages is given in relation to an 

equivalent voltage lasting 10 seconds ( U 10 s ) expressed in the following equation: 

U TOV T η 

⎛ ⎞ 

10s = ⎜ ⎟ where η ≅002 . 

⎝10⎠ 

T : overvoltage duration 

TOV : overvoltage value 

This formula allows the 10 second overvoltage which would cause the same stress on the 

surge arrester to be calculated for each temporary overvoltage. 

The duration of the temporary overvoltage must be between several seconds and two to three 

hours (U10s 

= 097 . × TOV for T =2 s and U10s 

= 114 . × TOV for T =2 hours ). 

The rated voltage of the surge arrester will be chosen to be above or equal to the maximum 

value of the equivalent 10 second voltages: Ur 

≥max ( U10 s ) . 

We will take 

U 

C 

U 

≥ 

m 

3 




464 

nominal discharge current I nd 

In practice, for the voltage range 1kV ≤Um 

≤ 52kV 

, two values of I nd are available: 5 kA and 

10 kA. 

The value Ind =10 kA is chosen for areas with a high lightning density. 

discharge class and energy capacity 

These are determined by testing or comparison with identical projects. 

mechanical characteristics 

The IEC 99-4 and 99-5 standards fix the allowable pressure limit (expressed in "kA") which 

must be met for the three-phase short circuit at the surge arrester terminals. 

The surge arrester characteristics will also be checked in relation to: 

- the ambient temperature 

- the altitude 

- the level of pollution 

- the mechanical resistance to the wind, seismic stress, frost. 

surge arrester protection level 

The protection level of the surge arrester at the installation point corresponds to the residual 

voltage ( U rsd ) at its terminals when its nominal discharge current flows through it. 




465 

5.2.3.3. Installation of HV and MV surge arresters 

In HV and MV electrical networks, surge arresters are installed at the entrance to the 

substation to ensure protection of the substation transformer and equipment. This protection 

only works if the protection distance and the installation rules are respected. 

protection distance 

The wave propagation phenomenon studied in § 5.1.5. shows that at the point of reflection 

(e.g. MV/LV transformer), the overvoltage reaches double the value of the incident wave. 

The surge arrester peaks at a sparkover voltage U rsd (equal to the residual voltage for 

surge arresters). 

ZnO 

If it is located a considerable distance away, the maximum voltage at the location of the 

equipment to be protected will thus be 2U rsd . Now, the equipment impulse withstand is 

generally lower than 2U rsd . 

To overcome this drawback, the surge arrester is installed at a shorter distance away than the 

"protection" distance D . The surge arrester then undergoes the sum of the incident wave and 

the reflected wave. It is thus sparked for an incident wave below U rsd . 

Assuming that at the equipment termination point, the wave is totally reflected, we can show 

that the overvoltage in relation to the equipment is limited to U = U r D rsd +2 

v 

r 

v 

dV 

= : rise front steepness of the voltage wave, kV/µs 

dt 

: wave propagation speed, m/µs 

For a lightning impulse withstand voltage U l , the surge arrester must therefore be located at 

a distance D such that: 

Ursd 

+ 2r D ≤Ul 

v 

whence 

D U l − U rsd 

≤ 

2r 

⋅v 




466 

Numerical application: 

Let us consider the example illustrated in figure 5-50: 

Ul =125 kV , case of an MV/LV transformer complying with IEC 76.3 

Ursd =75 kV 

, residual voltage of the surge arrester 

r 

v 

=300 kV/ µ s , voltage wave rise front steepness 

=300 m/ µ s , for an overhead line (speed of light) 

125 −75 

we then have D ≤ × 300 

2 × 300 

D ≤25m 

The surge arrester must therefore be installed less than 25 m away from the transformer for 

the overvoltage not to exceed the lightning impulse withstand value. 

lightningimpulse 

A 

D 

B 

transformer 

overheadline 

Z C 

Z C 

surgearrester 

Figure 5-50: protection distance of a surge arrester protecting a transformer fed 

by an overhead line 




467 

5.2.4. protection of LV installations 

general 

LV installations are protected against overvoltages by installing devices in parallel; 3 types of 

devices are used: 

- overvoltage limiters located on the secondary of MV/LV transformers (only in an IT 

earthing system); they only provide protection against power frequency overvoltages 

- low voltage surge arresters installed in LV switchboards or incorporated in loads 

- surge diverters designed to protect telephone networks, LV terminal boxes and loads. 

The main technologies used are: 

- zener diodes 

- gas discharge tubes 

- zinc oxide varistors. 

Zener diodes have the drawback of only ensuring the protection of a precise point in the 

network. The gas discharge tube requires the addition of a varistor to prevent follow current. 

Variable resistor-type surge arresters are currently the most cost-effective solution owing to 

their simplicity and reliability 




468 

LV surge arrester installation rules 

The equipment is only protected properly if certain installation rules are followed: 

- rule 1 

The length of the connection between the surge arrester and its disconnecting circuit-breaker 

must be below 0.5 m. 

disconnecting 


L

469 

connection layout according to the earthing system 

In figures 5-52-a and 5-52-b the connection layouts of the LV surge arrester are shown for 

different earthing systems. 

electricalswitchboard 

RCD 

disconnecting 


equipment 

tobeprotected 

surgearrester 

PE 

PE 

Ph1 

Ph2 

Ph3 

N 

LVneutral 


mainearth 

terminal 

(entrenched 

loop) 

loadearth 

electrode 

TT earthing system 


disconnecting 


equipment 

tobeprotected 

PE 

PE 

surge 

arrester 

Ph1 

Ph2 

Ph3 

N 

PIM 

overvoltage 

limiter 

LVneutral 


mainearth 

terminal 

(entrenched 

loop) 

load 

earth 

electrode 

IT earthing system 

Figure 5-52-a: connection layout of an LV surge arrester for 

TT and IT earthing systems 




470 


disconnecting 


equipmentto 

beprotected 

surge arrester 

Ph1 

Ph2 

Ph3 

PEN 

PEN 

LVneutral 


mainearth 

terminal 

(entrenched 

loop) 

loadearth 

electrode 

TNC earthing system 


disconnecting 


equipmentto 

beprotected 

PE 

PE 

surgearrester 

Ph1 

Ph2 

Ph3 

N 

PE 

LVneutral 


mainearth 

terminal 

(entrenched 

loop) 

loadearth 

electrode 

TNS earthing system 

Figure 5-52-b: connection layout of an LV surge arrester 

for TNC and TNS earthing systems 




471 

5.3. Insulation co-ordination in an industrial electrical network 

5.3.1. General 

Co-ordinating the insulation of an installation consists in determining the insulation 

characteristics necessary for the various network elements, in view to obtaining a withstand 

level that matches the normal voltages, as well as the different overvoltages. 

Its ultimate purpose is to provide dependable and optimised energy distribution. 

Optimal insulation co-ordination gives the best cost-effective ratio between the different 

parameters depending on it: 

- cost of equipment insulation 

- cost of overvoltage protections 

- cost of failures (loss of operation and destruction of equipment), taking into account their 

probability of occurrence. 

With the cost of overinsulating equipment being very high, the insulation cannot be rated to 

withstand the stress of all the overvoltages studied in paragraph 5.1. 

Overcoming the damaging effects of overvoltages supposes an initial approach which consists 

in dealing with the phenomena that generate them, which is not always very easy. Indeed, if 

using the appropriate arc interruption techniques the switchgear switching overvoltages can be 

limited, it is impossible to prevent lightning strikes. 

clearance (see fig. 5-53) 

This term covers two notions: 

- gas clearance (air, SF6, etc.), which is the shortest path between two conductive parts. 

- creepage distance: this is also the shortest path between two conductors, but following the 

outer surface of a solid insulating material (e.g. insulator). 




472 

The clearance is directly related to the withstand of the equipment to different overvoltages. 

distance 

inair 

creepage 

distance 

distance 

inair 

Figure 5-53: air clearance and creepage distance 

overvoltage withstand 

The overvoltage withstand depends on the type of overvoltage applied (magnitude, wave form, 

frequency and duration, etc.). 

It is also influenced by external factors such as: 

- ageing 

- environmental conditions (humidity, pollution) 

- variation in air or insulating gas pressure. 

withstand voltage 

Electrical equipment is characterised by its withstand voltage to different types of overvoltages. 

We can thus distinguish: 

- the power frequency withstand voltage 

- the switching impulse withstand voltage 

- the lightning impulse withstand voltage. 




473 

power frequency withstand voltage 

This corresponds to the equipment withstand to power frequency overvoltages likely to occur 

on the network and the duration of which depends on the network operating and protection 

mode. 

The equipment withstand is tested by applying a sinusoidal voltage with a frequency of 

between 48 Hz and 62 Hz for one minute. The test is valid for nominal network frequencies of 

50 Hz and 60 Hz (see IEC 71-1). 

switching impulse withstand voltage 

This characterises the equipment withstand to switching impulses (only for equipment with a 

standard voltage above or equal to 300 kV). 

The equipment test (see IEC 60-1) is performed by applying a wave with a front time of 250 µs 

and a time to half-value of 2500 µs. 

lightning impulse withstand voltage 

This characterises the equipment withstand to the 1.2 µs / 50 µs lightning voltage wave. 

This withstand voltage concerns all voltage ranges, including low voltage. 

examples of equipment withstand (see table 5-5) 

Highest voltage for the 

equipment 

U m (kV) (1) 

(r.m.s. value) 

Standard short-duration 

power frequency withstand 

voltage (kV) 

(r.m.s.) 

Standard lightning impulse 

withstand voltage (kV) 

(peak value) 

3.6 10 20 

40 

7.2 20 40 

60 

12 28 60 

75 

95 

17.5 38 75 

95 

24 50 95 

125 

145 

36 70 145 

170 

52 95 250 

72.5 140 325 

(1) U m is the highest rms value of the phase-to-phase voltage for which the equipment is specified. 




474 

Table 5-5: standard withstand voltages for 3.6 kV 




475 

5.3.2. Reduction in risks and overvoltage levels 

The risks of overvoltages, and consequently the danger they represent for persons and 

equipment, can be greatly reduced if certain measures of protection are taken: 

- limiting substation earth electrode resistances in order to reduce power frequency 

overvoltages 

- reducing switching overvoltages by choosing suitable switchgear (interruption in SF6) 

- making lightning impulses flow to earth by a first clipping operation (surge arrester or sparkgap 

at the entrance to the substation) with limitation of the earth electrode resistances and 

pylon impedances 

- limiting the residual voltage from the first clipping operation by HV surge arrester which is 

transferred to the downstream network by providing a second protection level on the 

transformer secondary 

- protection of sensitive equipment in LV (computers, telecommunications, automatic 

systems, etc.) by connecting series filters and/or overvoltage limiters to it. 

5.3.2.1. Rise in potential of LV exposed conductive parts following an MV fault in the 

transformer substation 

In this paragraph, we propose to study overvoltages in LV caused by an earth fault on the MV 

side in an MV/LV substation, and the measures to be taken in order to protect equipment and 

persons, in compliance with IEC 364-4-442. 

The values of rises in potential of the substation or LV installation exposed conductive parts 

depend on the values of the earth electrode resistances, the fault current values and the 

earthing system. 

earthing in transformer substations 

A single earth electrode must be installed in a transformer substation, to which must be 

connected: 

- the transformer tank 

- the metallic coverings of high voltage cables 

- the earth conductors of high voltage installations 

- the exposed conductive parts of high voltage and low voltage equipment 

- the extraneous conductive parts. 




476 

symbols 

In the following paragraphs, the symbols used have the following signification: 

I m : part of the earth fault current in the high voltage installation which flows through the earth electrode of the 

transformer substation exposed conductive parts 

R e : transformer substation earth electrode resistance 

V : low voltage installation phase-to-neutral voltage 

U : low voltage installation phase-to-phase voltage 

U f : fault voltage in the low voltage installation, between the exposed conductive parts and earth 

U 1 : stress-voltage in the transformer substation low voltage equipment 

U 2 : stress-voltage in the installation low voltage equipment 

TN − a and IT −a 

earthing systems (see fig. 5-54) 

In these two systems, the substation, neutral and installation earth electrodes are the same. 

Inside the equipotential area, the ground and exposed conductive part potentials increase 

simultaneously. The touch voltage U f is then zero. 

On the other hand, outside this area, the ground potential remains equal to that of the remote 

earth, while the potential of the exposed conductive parts increases to Uf = Re Im 

. 

Thus, when there are exposed conductive parts outside of the equipotential area and the 

touch voltage Uf = Re Im 

cannot be cleared in the time defined in tables 2-3-a and 2-3-b, the 

TN − a and IT − a earthing systems are not acceptable in relation to the protection of 

persons. 

To overcome this drawback, the following provisions must be taken: 

- TN − a earthing system: the neutral of the LV installation must be connected to a separate 

earth electrode, which is the case in the TN − b earthing system (see fig. 5-55) 

- IT − a earthing system: the exposed conductive parts of the LV installation must be 

connected to a separate earth electrode from that of the substation, which is the case in the 

IT − b earthing system (see fig. 5-56). 

TN − b and IT − b earthing systems allow dangerous touch voltages to be cleared but make 

overvoltages occur: 

- in the installation LV equipment for the IT −b 

earthing system 

- in the substation LV equipment for the TN −b 

earthing system. 




477 

substation 

LVinstallation 

U 1 U 2 

MV 

ph1 

ph2 

ph3 

PEN 

LV 

U f 0 

equipotentialzone 

U V 

I 1 

m R e 

outside 

zone 

U U V 2 1 

Uf 

Re Im 

TN −a 

U 1 U 2 

MV 

LV 

Z 

U f 0 

equipotentialzone 

I m R e 

U1 V 3 * 

U2 U1 V 3 * 

(*)afirstLVfaultispresent 

IT −a 

outsitezone 

U R I f e m 

Figure 5-54: rise in potential of TN-a and IT-a earthing systems 




478 

TN − b , TT − b and IT − c earthing systems (see fig. 5-55) 

In these three systems, we can see a rise in potential of the exposed conductive parts of the 

substationU 1 such that: 

U1 = Re Im 

+ V for TN − b and TT − b earthing systems 

U1 = Re Im 

+ V. 3 for IT − c earthing systems with the presence 

of a first fault on the LV side 

Depending on the maximum current value I m , the values of R e must be limited so that U 1 

remains below the power frequency withstand voltage U tp of the substation equipment. 

U 1 ≤U tp 

Table 5-6 gives the maximum values of R e for different values of I m and U tp . 

Values at R e not to be exceeded 

Fault current I m 

U tp = 2 000 V 

U tp = 4 000 V 

U tp = 10 000 V 

(A) 

Class I 

Class II 

Special class 

TN − b ; TT −b 

IT −c 

TN − b ; TT − b ; IT −c 

TN − b ; TT − b ; IT −c 

300 A 5.9 Ω 5.3 Ω 12 Ω 30 Ω 

1 000 A 1.8 Ω 1.6 Ω 3.6 Ω 10 Ω 

5 000 A 0.35 Ω 0.32 Ω 0.72 Ω 2 Ω 

Table 5-6: maximum values of R e in TN − b 

, TT − b and IT − c earthing systems 




479 

U 1 U 2 

MV 

ph1 

ph2 

ph3 

PEN 

LV 

U1 

Re 

Im 

V 

I m RB U2 

V 

R e 

Uf 

0 

U f 

TN −b 

U 1 U 2 

MV 

ph1 

ph2 

ph3 

N 

LV 

U1 

Re Im 

V 

U 

I m R RB R f 

e 

U V 

A 

2 

Uf 

TT −b 

0 

U 1 U 2 

MV 

LV 

* 

U1 

ReIm 

V 3 

U2 

V 3 

I m R e Z 

Uf RAIf UL 

I f RA U f 


IT −c 

Figure 5-55: rise in potential in TN − b, TT − b and IT −c 

earthing systems 




480 

TT − a and IT − b earthing systems 

In these two cases the substation earth electrode and that of the neutral are common. 

The LV installation earth electrode is separate. 

The earth fault current flows through the common earth electrode (neutral/substation). 

As shown in figure 5-56, we can see that there is a risk of breakdown for the LV equipment 

whose earth electrode is separate from that of the substation. 

The following conditions must be met: 

UtM > Re Im 

+ V for the TT − a earthing system 


UtM > Re Im 

+ V 3 for the IT − b earthing system 

whence 

⎧ U V 

R 

tM − 

e < 

⎪ Im 

⎨ 

U V 

R tM − 

⎪ e < 

⎩⎪ 

Im 

3 

for the TT − a earthing system 

for the IT − b earthing system 

where: 

U tM : power frequency withstand voltage of the installation LV equipment equal to 2V + 1000 for V = 220 to 

250 V, i.e. 1500 V 

Table 5-7 gives the values of R e for different values of I m . 

TT −a 

IT −b 

I m = 300 A 4 Ω 3.5 Ω 

I m = 1000 A 1.2 Ω 1 Ω 

I m = 5000 A 0.24 Ω 0.2 Ω 

Table 5-7: maximum values of R e in TT − a and IT − b earthing systems 




481 

U 1 U 2 

MV 

L1 

L2 

L3 

N 

LV 

U1 V U2 

ReIm 

V 

Uf 

0 

U f 

substation 

I m R e 

LVinstallationR A 

TT −a 

U 1 U 2 

MV 

LV 

Z 

I m 

R e 

* 

U1 

V 3 

* 

U2 

ReIm 

V 3 

Uf RA If UL 

I f 

R A 

U f 


IT −b 

Figure 5-56: Rise in potential in TT − a and IT − b earthing systems 




482 

recapitulative table of touch voltages and overvoltages which occur for each earthing 

system 

TN −a 

IT −a 

TT −a 

IT −b 

TN −b 

TT −b 

IT −c 

Touch voltage Y Y N N N N N 

Overvoltage of LV 

installation exposed 

conductive parts 

Overvoltage of 

substation exposed 

conductive parts 

N N Y Y N N N 

N N N N Y Y Y 

Y 

N 

: yes 

: no 

Table 5-8: touch voltages and overvoltages which occur for 

each earthing system 

5.3.2.2. Rise in potential of the LV exposed conductive parts on occurrence of a 

lightning impulse 

When a lightning overvoltage from the distribution network flows to earth in an MV/LV 

substation through a protection device (surge arrester or MV spark-gap), there follows a rise in 

potential of the substation LV exposed conductive parts and/or those of the installation which 

depends on the earthing system. 

The level of overvoltages transferred in LV depends on the clipped value U rsd and the earth 

electrode values. 

To ensure protection of the LV switchgear against these overvoltages, LV surge arresters must 

be installed and the resistance of the substation earth electrode limited so that the equipment 

lightning impulse withstand voltage is not exceeded. 

limiting earth electrode impedances 

As for the case of the MV earth fault, the limit values of the earth electrode impedances are 

calculated for each earthing system. 




483 

The overvoltage at a point on the network where the impedance changes is given in the 

relation: 

v 

2 

Z 

= 

2 

Z + Z 

1 2 

2v 

1 

(see § 5.1.4) 

v 1 = U rsd : corresponds in this case to the clipped overvoltage 

v 2 : overvoltage of the substation exposed conductive parts 

Z 1 = Z c : characteristic impedance of the medium voltage line 

Z 2 = Z e : substation earth electrode impedance 

We thus have: 

v 

Ze 

= 

Z + Z 

2 . 2 

c e 

U 

rsd 

The equipment lightning impulse voltage U tc must be above the overvoltage v 2 , whence: 

Ze 

Utc 

≥ .2Ursd 

Z + Z 

Ze 

≤ 

c e 

Zc 

2U 

( U ) 

rsd −1 

tc 

For Ursd =120 kV and Z c =330 Ω , the impulse impedance Z e 

Z 

resistance R e measured in low frequency: 

e 

Re 

= . 15 . 

is equal to 1.5 times the 

The condition on the value of the substation earth electrode impedance is thus: 

Z 

R c 

e ≤ 

15 . × −1 

U 

( U ) 

rsd 

tc 

The maximum values of R e for the different earthing systems are given in table 5-9. 

Earthing system 

TN − b , TT − b , IT −c 

TT − a , IT −b 

U tc (kV) 4 8 20 3 

R e 3.8 7.7 20.2 2.7 

Table 5-9: maximum values of the MV/LV substation earth electrode resistances 

recommended for limiting MV atmospheric overvoltages transferred in LV

05 overvoltages and insulation coordination

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