Statical Analisis Diagnostic Short Circuit Cables MV

8/17/2019 Statical Analisis Diagnostic Short Circuit Cables MV

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Statistical analysis of the double line-to-ground

short-circuit current in MV urban network for

the power cable metallic screen ratingRoman Korab and Edward Siwy

Abstract -- The construction of the metallic screen or other

power cable elements designed for the short-circuit current

conducting has significant influence on the cost of medium

voltage cables in PVC (polyvinyl chloride) or XLPE (cross-linked

polyethylene) insulation. Not only the price of the cable, but also

the technical criteria must be taken into consideration while

choosing the types of cables and the cross-section of the metallic

screen or similar elements. These technical criteria can be based

on the double line-to-ground faults statistical analysis in thenetwork. The paper presents the description of the rules of

carrying out such analyses in urban cable MV network as well as

the sample results of computer simulations. The method of the

double line-to-ground fault currents calculation is consistent with

the international standard [1].

Index Terms-- cable metallic screen rating, double line-to-

ground fault, medium voltage (MV) power cable, MV urban

network, short-circuit current, unsymmetrical faults

I. I NTRODUCTION

T

HE metallic screen is the part of the medium voltage cable

in PVC or XLPE insulation [2]. It is usually made up ofcopper tapes or wires helically stranded over the insulation

layer (in single-core cables) or the belt insulation (in three-

core belted cables). Fig. 1 shows the standard construction of

the single-core MV power cable (not all shown in Fig. 1

elements of the single-core MV power cable have to occur in

every type of the cable). In the single-core cables individual

metallic screens are connected to each other on both ends of

the line. Metallic screens of every cable lines are grounded at

least on one end of the line. In some constructions of three-

core cables the individual thin aluminum screen for each

conductor and the common copper centre conductor are used

instead of the copper metallic screen.

In normal operation conditions, the metallic screen is usedas a return path for both capacitive charging currents and

induced currents. In the event of an electrical fault, the

metallic screen can also conduct short-circuit currents. The

flow of the fault current in metallic screens or other elements

designed for short-circuit current conducting can occur in

principle in two circumstances:

• during the single line-to-ground fault,

• during the double line-to-ground fault in a galvanicconnected network, however, both of ground faults can

be situated in the same cable line as well as in two

different lines.

Sheath Bedding

Cable armour

Metallic screen

Insulation Conductor

Conductor screen

Insulation screen(semi-conductor)

Fig. 1. The standard construction of single-core MV power cable

In the galvanic connected network double line-to-ground

faults can occur in three various cases. All possible cases of

double line-to-ground faults are shown in Fig. 2. In A case

both of line-to-ground faults (in phases L2 and L3) occur in

the same cable section. This cable section is the first section of

the whole cable line, hence the short-circuit current flows only

in the metallic screen of this cable section. In B case both of

line-to-ground faults (in phases L1 and L2) occur in the same

cable line, but in different cable section. In this case short-

circuit currents flow in metallic screens of three cable

sections, however, current flow in the metallic screen of the

first section of this line is induced by the short-circuit current

flow in conductors of phases L1 and L2. In A and B casesappropriate overcurrent protective relays are activated. In C

case line-to-ground faults occur in two different cable lines

and therefore the short-circuit current flows in metallic

screens of both lines. In this case the fault current flow path

impedance value is probably higher than in A and B cases.

The fault current can be interrupted by one of two circuit

breakers installed on the beginning of each cable line,

however, not in all situations both of overcurrent protective

relays are activated (as a general rule in MV network two-

phases overcurrent line protection is applied).

R. Korab is with Silesian University of Technology, Faculty of Electrical

Engineering, Institute of Power Systems Engineering and Control,

2 Krzywoustego St, 44 - 100 Gliwice, Poland (e-mail: [email protected]).

E. Siwy is with Silesian University of Technology, Faculty of Electrical

Engineering, Institute of Power Systems Engineering and Control,

2 Krzywoustego St, 44 - 100 Gliwice, Poland (e-mail: [email protected]).

9th International Conference on Probabilistic Methods Applied to Power SystemsKTH, Stockholm, Sweden – June 11-15, 2006

© Copyright KTH 2006


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The main reasons for the double line-to-ground faults

occurrence are disadvantageous voltage and current transients

during the single line-to-ground fault. The frequency and the

probability of the double line-to-ground faults occurrence

among other things depend on the duration of the single line-

to-ground fault and the length of galvanic connected lines in

the network. The network neutral point treatment has an

essential influence on the frequency and the probability of the

double line-to-ground faults occurrence. These faultsfrequently occur in networks operated with compensated or

isolated neutral, less frequently in networks with resistive

grounded neutral. Various quantitative estimation of number

of double line-to-ground faults in the total number of faults

can be found in the literature. It is usually assessed that no

more than 25 % of single line-to-ground faults transform into

double line-to-ground faults. The research into several MV

cable urban networks performed in the 80’s of the twentieth

century [3] showed, that the share of double line-to-ground

faults in the total number of faults is not larger than 15 % (5 %

on average). The mentioned research also showed, that the

biggest possible annual frequency of the double line-to-

ground faults occurrence in the network made of cables in

PVC or XLPE insulation is not larger than 10 per 100 km of

lines.

II. THE METHOD OF THE DOUBLE LINE-TO-GROUND FAULT

CURRENTS CALCULATION

For the double line-to-ground currents calculation the MV

network model shown in Fig. 2 is used. The network is

supplied with a bulk power transformer. The power source is

characterized by the short-circuit power and by the transfer

resistance and reactance ratio. In the network model single- or

three-core cables in various insulation (PVC, XLPE, oil-

impregnated paper) can be modeled. Modeled cables can havedifferent rated voltages and various cross-sections of metallic

screens or the common copper centre conductors. Various

network configurations are permissible. It is assumed that

metallic screens or common centre conductors of every cable

lines are grounded on both ends of the line.

The mutual location of fault points in MV network has a

significant impact on the double line-to-ground fault current

flow path impedance. The mentioned factor also influences

the fault currents flow. The resultant fault current flow path

impedance is equal to the sum of positive and negative

sequence power source impedance, and impedances of the

power cables situated on the fault current flow path. The valueof the double line-to-ground short-circuit current, in kA, can

be calculated on the basis of a symmetrical-components

method [4], using the following formula

Z Z

U , I

s

n z

∆Σ+=

12

2

11 (1)

where:

U n - network nominal voltage, in kV,

Z 1 s - positive sequence impedance (equal to the negative

sequence impedance) of the power source, in Ω,

Σ∆ Z - additional impedance, equal to the sum of

impedances of all power cables situated on thedouble line-to-ground fault current flow path, in Ω.

After the substitution to (1) the value of additional impedance

Σ∆ Z = 0, the maximum possible value of double line-to-ground short-circuit current is obtained. In this case, the short-

circuit current value is equal to a phase-to-phase short-circuit

current value during the fault on MV busbar. It can be

calculated by using the formula as follows

" k

" k

s

n" k z I , I

Z

U , I I 33

122 8660

2

3

2

11==== (2)

where is a value of initial symmetrical (three-phase)

short-circuit current, in kA, during the fault on MV busbar.

"

k

I 3

Formulas for calculating the single-core cable additional

impedance and the short-circuit current flow in metallic

screens during double line-to-ground faults are shown in

Fig. 3. Similar formulas for the traditional three-core cables

and the three-core cables with the common copper centre

conductor are shown in Fig. 4. These formulas were derived

on the basis of a ground-return circuit method [5].Fig. 2. The three possible points (A, B and C) of double line-to-ground faults

in the medium voltage distribution cable network




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1 x

L

12 x x ≤

2 z I

2 z I

2 I

4 I

1 I

3 I

5 I

( ) ( ) L

x xaa Z

L

xa x xa Z 21101

21

1210 22 −−+++=∆ ( )

m p

mrpmr

Z Z

Z Z Z Z Z

−

−−−=

2

1 prpr R Z Z a +−=0

m p

m p

p

Z Z

Z Z

Ra

+−

−=

2

2

12

( )

−+=

L

xbb

L

xb I I z

210

1121 122 I I I z −= ( )

−+=

L

xbb

L

xb I I z

110

2123 324 I I I z −= ( )

L

x xbb I I z

211025

−−=

m p

p

Z Z

Rb

−=0

m p

m p

p

Z Z

Z Z

R

+−

=21

2b

Fig. 3. The equivalent circuit scheme and formulas for calculating the single-core cables additional impedance and the short-circuit current flow in the metallic

screens during double line-to-ground faults

12 x x ≤

1 x

L

2 z I

2 z I

1 I 2 I 1 I

12 x x ≤

1 x

L

2 z I

2 z I

1 I 1 I 2 I

( )( ) 201

2

21110 2 xa Z

L

x xa xa Z −+

−+=∆ mr Z Z Z −=1 prpr R Z Z a +−=0

p

p

Z

Ra

2

1

−=

L

x xb I I z

21121

−= 122 I I I z −=

p

p

Z

Rb =1

Fig. 4. The equivalent circuit scheme and formulas for calculating the additional impedance of the traditional three-core cables or the three-core cables with the

common copper centre conductor and the short-circuit current flow in the metallic screens or the common centre conductor during double line-to-ground faults




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Individual symbols used in Fig. 3 and Fig.4 represent: The condition (3) was checked for all cable sections in

analyzed MV network. An exceeding of the rated short time

(one-second) thermal current was recorded when the condition

(3) was not satisfied. Such situations are extremely rare due to

quite unusual and unlikely location of the fault points. A

repetition cycle (in years) of the exceeding of the rated short

time thermal current has to be sufficiently long, longer than

the average service life of the cable line.

Z 1 - cable line positive sequence impedance, in Ω,

Z r - conductor impedance, in Ω,

Z p - metallic screen impedance, in Ω,

R p - metallic screen resistance, inΩ,

Z m - mutual conductors impedance, in Ω,

Z rp - mutual conductor and metallic screen impedance, in Ω,a1, a2 - cable line per unit impedance for calculating the

additional impedance Σ∆ Z , in Ω/km, Computer simulations were performed for a few real 6 kVand 20 kV networks [6]. These were pure cable networks

(6 kV networks) or cable networks with some overhead line

sections (20 kV networks). Analyzed networks operate with

isolated, compensated or resistive grounded neutral. The

duration time of double line-to-ground faults was equal to a

time delay of a delayed overcurrent protection plus 0,2 s. All

calculations of the short-circuit current flow were performed

for the actual value of the short-circuit power as well as for

the increased one (after the replacement of the present bulk

power transformer with the bigger one).

b0, b1 - short-circuit current flow coefficients, dimensionless

value,

I 1, I 2, I 3, I 4, I 5 - currents flowing in individual sections of

metallic screens, in kA.

One of the following currents I 1, I 2, I 3, I 4 and I 5 has the biggest

value. The biggest current value in next sections of this paper

is marked with the I max symbol.

Formulas shown in Fig. 3 and Fig. 4 have a general nature,

i.e. they can be applied when one of fault points is located in

the given cable section and the second fault point is located in

a different one. When the second fault point is located in the

cable section situated closer to the power source, in certainformulas x2 = 0. In other situations, when second fault point is

located in the cable section situated farther to the power

source, in certain formulas x1 = L. When both fault points are

located outside the considered cable section, then x1 = x2 = L.

In such cases the additional impedance is equal to 2 Z 1. This

result is consistent with the symmetrical-components method.

Fig. 5 to Fig. 10 show the frequency histograms of double

line-to-ground fault currents flowing in conductors or in

metallic screens of power cables for two chosen urban MV (6

and 20 kV) networks. In all mentioned figures an average

value of appropriate current is represented by a thick line.

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

f r e q u e n c y

''

22 k z I I

kA49102 , I ' '

k =

III. THE SAMPLE R ESULTS OF COMPUTER SIMULATIONS

The statistical modeling method is used for calculations of

the short-circuit current flow in the metallic screens during

double line-to-ground faults. It was assumed that a probability

of the fault points location is equal in the whole cablenetwork. For each combination of the fault point location the

following quantities are calculated:

• the impedance of individual power cable sectionssituated on the fault current flow path,

• the whole impedance of the fault current flow path,Fig. 5. The frequency histogram of double line-to-ground fault current in 6 kV

cable conductor for the actual (126 MVA) value of the short-circuit power• the value of the double line-to-ground short-circuit

current I z 2,

• the value of currents flowing in metallic screens of allcable sections situated on the fault current flow path.

During computer simulations of double line-to-ground

faults the following condition was checked each time

thr k k th I T nm I T I ≤+= )(max (3) n

0 0.2 0.4 0.6 0.8 1

0

0.1

0.2

0.3

0.4

''

22 k z I I

f r e q u e

c y

kA3452 , I ' ' k =

where:

I th - thermal equivalent short-circuit current, in kA,

T k - duration of double line-to-ground short-circuit

current, in s,

I max - the biggest current flowing in individual sections of

metallic screens, in kA

m, n - factors for the calculation of the thermal equivalent

short-circuit current, dimensionless values, Fig. 6. The frequency histogram of double line-to-ground fault current in 20 kV

cable conductor for the actual (214 MVA) value of the short-circuit power I thr - rated short time (one-second) thermal current, in k Α.




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In Fig. 5 through 10 the fault currents are related to the

phase-to-phase short-circuit current value during the fault on

MV busbar. The value of the phase-to-phase short-circuit

current is shown in each figure. Usually in 6 kV networks the

value of the bulk power transformer impedance (calculated at

the lower voltage side of this transformer) is very small.

Hence, as a general rule, the value of the phase-to-phase

short-circuit current is large, larger than in 20 kV networks,

but it quickly decreases as the distance between the fault pointlocation and the MV busbar increase. In 20 kV networks the

phase-to-phase short-circuit current decrease is slower. The

main reason for the quick 6 kV phase-to-phase short-circuit

decrease is a power cable reactance. The value of 6 kV power

cable reactance is not much smaller than the reactance of

20 kV power cable, whereas a voltage in 6 kV network is

more than 3 times smaller than in 20 kV network.

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

''

2max k I I

f r e q u e n c y

kA49102 , I ' '

k =

Fig. 7. The frequency histogram of the biggest value of current flowing in 6 kV

cable metallic screens for the actual (126 MVA) value of the short-circuit power

0 0.2 0.4 0.6 0.8 1

0

0.1

0.2

0.3

0.4

''2max k I I

f r e q u e n c y

kA3452 , I ' '

k =

Fig. 8. The frequency histogram of the biggest value of current flowing in 20 kV

cable metallic screens for the actual (214 MVA) value of the short-circuit power

The value of double line-to-ground currents in the given

network mainly depends on the bulk power transformer rated

power. The level of the short-circuit power on 110 kV busbar

as well as the neutral point treatment in MV network have

much smaller influence on the value of these currents. The

value of double line-to-ground currents quickly decreases as

the distance between fault points increases. The longer

individual power cable sections and the smaller the cross-

section of the metallic screens are, the bigger decrease in fault

current is. The influence of these factors is growing when the

bulk power transformer rated power is increasing. As a result

double line-to-ground fault currents in 6 kV networks are

much smaller than in 20 kV networks.

For the actual value of the short-circuit power, the average

value of fault currents flowing in cable metallic screens in

analyzed real 20 kV networks ranges from 3.0 to 3.7 kA. Forthe maximum possible value of the 20 kV short-circuit power,

the average value of these fault currents increases and ranges

from 4.0 to 4.9 kA (which gives about 45 ÷ 60 % of the


20 kV busbar). In analyzed 6 kV networks, for the actual

value of the short-circuit power, the average value of fault

currents flowing in cable metallic screens ranges from 1.8 to

2.4 kA. For the maximum possible value of the 6 kV short-

circuit power the average value of these fault currents ranges

from 2.0 to 2.7 kA (which gives about 12 ÷ 15 % of the


MV busbar).

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

f r e q u e n c y

''

2max k I I

kA65162 , I ' '

k =

Fig. 9. The frequency histogram of the biggest value of current flowing in 6

kV cable metallic screens for the increased (200 MVA) value of the short-

circuit power

0 0.2 0.4 0.6 0.8 1

0

0.1

0.2

0.3

0.4

''

2max k I I

f r e q u e n c y

kA2482 , I ' ' k =

Fig. 10. The frequency histogram of the biggest value of current flowing in

20 kV cable metallic screens for the increased (330 MVA) value of the short-

circuit power




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V. CONCLUSIONS IV. THE POWER CABLE METALLIC SCREEN R ATING

The rated metallic screen cross-section should be

determined on the basis of computer simulations in a way

which makes the repetition cycle (in years) of the exceeding

of the rated short time thermal current sufficiently long. It

means that the probability of the exceeding of the rated short

time thermal current should be sufficiently small. The

repetition cycle of several score years guarantees that the

exceeding of the rated short time thermal current of cable

metallic screens will not occur in all service life of the

considered cable network. Table 1 presents detailed results of

the repetition cycle for analyzed 6 kV and 20 kV networks for

different power cables types and different values of the short-

circuit power on MV busbar. It was assumed in simulations

that the annual frequency of the double line-to-ground faults

occurrence is equal to 2 per 100 km of lines.

Rational criterions for the power cable metallic screen

rating was formulated on the basis of computer simulations

results. These criterions depend on the network rated voltage,

the neutral point treatment and the double line-to-ground

duration time. Very often power cables with the minimal (6,

10 or 16 mm2) cross-section of metallic screen can be installed

in networks, especially with the resistive grounded neutral.

But in some cases the recommended in standard [2] metallic

screen cross-section can be insufficient.

Until now in Polish MV cables networks three-core and

single-core cables with 50 mm2 metallic screens cross-section

were commonly used. The application of proposed rules in

practice makes the use of power cable with the smaller

metallic screens cross-section possible. The installation of

power cables with the smaller metallic screens cross-section

cause significant savings of network investment costs.TABLE I

THE R EPETITION CYCLE (IN YEARS) OF THE EXCEEDING OF THE R ATED

SHORT TIME THERMAL CURRENT FOR POWER CABLE METALLIC SCREENS VI. R EFERENCES

Short-circuit

power

Power cables installed in analyzed network:Type / Conductor cross-section [mm2] /

Metallic screen cross-section [mm2]

Analyzed

network

MVA Real *) 5C/120/16 5C/240/25 5F/120/35

155 171 32 48 82

175 141 30 41 73U n = 6 kV

lenght = 42,5 km200 111 29 36 66

222 577 16 125 90

260 215 9 59 46U n = 20 kV

lenght = 25 km330 74 6 21 22

[1] “Short-circuit currents in three-phase a.c. systems – Part 3: Currents

during two separate simultaneous line-to-earth short-circuits and partialshort-circuit currents flowing through earth,” International Standard IEC

60909-3, 2nd ed., 2003.

[2] “Distribution cables with extruded insulation for rated voltages from

3,6/6 (7,2) kV to 20,8/36 (42) kV,” Polish Standard PN–HD 620 S1:

2002(U).

[3] G. Bartodziej, J. Popczyk, K. Żmuda, “Verification of the short–circuit

withstand of wires of 6–20 kV cables in industrial networks,” IV

International Symposium on Short–Circuit Currents in Power Systems,

Universite de Liege, Technical University of Lodz, Liege, 6–8.10.1990.

[4] J.D. Glover, M.S. Sarma, "Power system analysis and design," 3rd ed.

Pacific Grove: Brooks/Cole, 2002.*) – different types of power cables with the different conductor cross-section;

mostly the metallic screen cross-section is equal to 50 mm2 [5] M. Krakowski, ”The ground-return circuit”, Warsaw: WNT 1979 (in

Polish).

Until now in Polish MV cable network three-core and

single-core cables with 50 mm2 metallic screens cross-section

were commonly used. For such metallic screen cross-sectionthe exceeding of the rated short time thermal current in

analyzed networks is extremely rare. The results presented in

Table 1 show that in most cases the metallic screen cross-

section can be much smaller than 50 mm2. But it should be

emphasized that the recommended in standard [2] metallic

screen cross-section equal to 16 mm2 can be insufficient,

especially in 20 kV networks.

[6] K. Żmuda, R. Korab, E. Siwy, ” The analysis of possibility of the cross-

section of the metallic screen reduction in the MV power cables in the

urban networks,” Silesian University of Technology, Gliwice, Tech.

Rep. MZE 04-073JK, February 2004, (in Polish).

VII. BIOGRAPHIES

Roman Korab was born in Zawiercie, Poland, on

October 6, 1973. He obtained his M.Sc. and Ph.D.

degree from the Silesian University of Technology

in 1998 and 2003, respectively.

He is presently working at Faculty of Electrical

Engineering, Institute of Power Systems

Engineering and Control. His research interests

mainly include power system operation and

development economics, optimization and control.

The presented method of calculation of double line-to-

ground short-circuit currents include some safety factors.

These factors result from following assumptions:

• the permissible short-circuit temperature is valuated with

some margin of safety,• the infinite value of 110 kV busbar short-circuit power is

assumed,

Edward Siwy was born in Piekary Sl., Poland, on

January 17, 1963. He obtained his M.Sc. and Ph.D.

degree from the Silesian University of Technology

in 87 and 1997, respectively.• non-resistive double line-to-ground faults, power cableconnections and groundelectrodes are assumed, He is presently working at Faculty of Electrical

Engineering, Institute of Power Systems

Engineering and Control. His research interests

mainly include transmission and distribution

networks optimization.

• the possibility of faster short-circuit interruption by cut-off or ground-fault protections is omitted.

Mentioned assumptions make the possibility of the exceeding

of the rated short time thermal current smaller.



Statical Analisis Diagnostic Short Circuit Cables MV

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