##### Document Text Contents

Page 1

Accurate Calculation And Physical Measurement of Trasmission Line

Parameters to Improve Impedance Relay Performance

Alexander Dierks, Harry Troskie Michael Krüger

Alectrix Eskom Transmission Omicron Electronics, Austria

ABSTRACT

To accurately set an impedance relay it is imperative to

know the impedance of the transmission line as well as

the earth return path accurately. The electrical

impedance parameters of transmission lines are

determined either by using suitable software tools or by

physically measuring the impedance. Both techniques

yield comparable results, if the correct parameters are

entered into the software tool.

I INTRODUCTION

Knowing the accurate overhead transmission line

parameters, which includes an accurate estimate of the

earth return impedance, is a crucial ingredient to being

able to accurately set impedance relays and to ensure

correct operation of such relays for all types of fault in a

power system.

The electrical parameters of an overhead transmission

line are usually calculated using suitable software tools.

Using PowerFactory [1], the effect of entering wrong

parameters on the calculated impedance parameters will

be examined. The impact of ground resistivity, as well

as conductor height above ground and sag, on the zero

sequence impedance will be investigated.

A technique to physically measure the primary

impedance of an overhead line (Z1) as well as the earth

return impedance (Z0) using the OMICRON CPC100

primary test set will then be described.

As a case study an actual line in the ESKOM network

was chosen for which the line parameters were both

calculated as well as physically measured. The results

will be presented.

II CALCULATION OF THEORETICAL

OVERHEAD LINE PARAMETERS

For setting of impedance relays the following primary

line parameters are of importance:

Positive Sequence Impedance: Z1 = R1 + jX1

Zero Sequence Impedance: Z0 = R0 + jX0

All these parameters can be calculated from the

geometrical configuration of the line, the earth

resistivity as well as the physical dimensions and

construction of the actual conductor used.

The geometrical configuration of a line defines the

physical position of the conductors and earth wires in

terms of:

Attachment height of each phase conductor above

ground (Yp).

Attachment height of each earth wire above ground

(Ye).

Horizontal distance of each phase conductor from

the center of the tower (Xp).

Horizontal distance of each earth wire from the

center of the tower (Xe).

A typical geometrical tower configuration illustrating

Yp, Ye, Xp and Xe is shown in Figure 1.

Figure 1: Geometrical Tower Configuration

If multiple lines are strung to the same tower, or if

mutual induction effects of one line to the other need to

be investigated, the physical distance of each conductor

on all lines with respect to one reference point need to

be defined.

The other parameters of importance are:

Average sag of the line and earth wires at midspan.

Earth resistivity of the ground.

For the actual conductors (both phase conductors and

earth wires) the following parameters need to be

entered:

DC resistance of the conductor, which can be

calculated from first principles using the

Yp

Ye

Xp

Xe

455

Inaugural IEEE PES 2005 Conference and Exposition in Africa

Durban, South Africa, 11-15 July 2005

0-7803-9327-9/05/$20.00 ©2005 IEEE

Page 2

conductor resistivity, the length of conductor

and diameter of conductor [2]. The spiralling

of the conductor, operating temperature and

skin effect also has to be allowed for.

Overall diameter of the conductor.

Geometrical Mean Radius [GMR] of the

conductor.

If conductor bundles are used the number of sub-

conductors in a bundle as well as the spacing between

the sub-conductors is of importance.

Calculating the electrical parameters from first

principles is a fairly involved mathematical process

[2,3,4]. Various software tools, such as TMLC from PTI

as well as PowerFactory from Digsilent [1] are available

to achieve the same. In this paper PowerFactory was

used as illustrated in Figure 2.

Figure 2: Overhead Line Parameter Calculation in

PowerFactory

As with any computation the accuracy of the input

parameters determines the accuracy of the calculated

output parameters.

The horizontal distance parameters of both phase and

earth conductors as well as the conductor diameter can

be determined very accurately, usually to less than 1%

error. It is, however, impossible to determine the

attachment height of the phase conductors and earth

wires above ground accurately, due to the varying

height of towers along the length of a line, the ground

profile changing as the line spans across valleys and

sometimes canyons as well as vegetation growing to

various heights under a line. To model the sag of the

conductors is difficult as it depends on the ambient

temperature, conductor tension, etc. A sensitivity study

was thus conducted for a typical line, where the

parameter of sag was varied, while the zero sequence

resistance and reactance was monitored. The effect of a

100% change in sag had negligible effect on the zero

sequence impedance of a line. A similar study on the

average attachment height yielded a similar negligible

effect of average attachment height on the zero

sequence impedance of a line.

The earth resistivity used for line parameter calculation

is a hotly debated subject. The earth resistivity changes

with type of soil, dampness as well as season related

variances. Typical average values used are 100 m for

damp soil and up to 700 m for dry sand. Investigating

the effect of changing this parameter from 100 m to

1000 m (i.e. +1000%) resulted in R0 changing by 14%

and X0 by 6%. Both sensitivities can be regarded as

minimal. If a line has a good quality earth wire, it can

further be deduced that the earth resistivity used in the

simulation has minimal effect on the result for the zero

sequence impedance of the line.

As a last parameter the DC resistance of the earth wire

was varied. Plotting the calculated zero sequence

resistance and reactance against the DC resistance

yields an interesting dependency (as can be seen in

Figure 3). This characteristic can be explained by

considering the parallel impedance phenomena of the

earth wire and the actual earth return impedance through

ground. For low values of DC resistance, the overall

zero sequence impedance of the line tends towards a

constant value (i.e. independent of DC resistance). This

impedance is dominated by the earth wire impedance.

The earth return impedance through ground, which is in

parallel to the earth wire impedance, is too high to have

a significant effect on the overall zero sequence

impedance. For high values of DC resistance, the

overall zero sequence impedance again tends towards a

constant impedance, which is this time dominated by

the earth return impedance. Here the earth wire

impedance is too high to have an effect on the overall

zero sequence impedance. In the range of 0.1 to 10

/km, the zero sequence impedance varies

considerably. Considering, that typical values of DC

resistance for the various kinds of conductor fall into

this range, care must be taken to enter the correct DC

resistance for the conductor used. This value normally is

readily available from the conductor manufacturer or

can be calculated from first principles with relative ease.

0

0.2

0.4

0.6

0.8

1

1.2

0.001 0.01 0.1 1 10 100 1000

DC Resistance [Ohm / km]

R0 [Ohm/km] X0 [Ohm/km]

Figure 3: DC Resistance Sensitivity Analysis

456

Page 3

All the above calculations were done for a 515 Tower

strung with Twin Dinosaur conductors (45cm conductor

spacing) and Greased Horse earth wire. As average

attachment height of both the phase conductors and

earth wires, the tower heights along the length of a line

were averaged out.

III PHYSICAL MEASUREMENT

3.1 Theory

The physical measurement of the impedance of an

overhead line is based on Ohm’s law:

Z = V / I

To accurately measure the impedance a current Itest

needs to be injected into the impedance to be measured,

whilst the voltage drop Vtest across the impedance needs

to be measured accurately in terms of amplitude and

phase angle. The complex impedance Z is calculated by

performing a complex division of Vtest divided by Itest.

The real component of the resulting complex impedance

is the resistive component and the complex component

is the reactive component of the impedance measured.

To measure the impedance of a three phase transmission

system consider the equivalent circuit of a transmission

line as shown in Figure 4:

Figure 4: Equivalent Circuit of Transmission Line

By injecting a current into each of the following

measurement loops A-B, B-C, C-A, A-N, B-N, C-N, A-

B-C-N (see Figure 5 for an illustration of the injection

into the A-B loop), the ‘loop’ impedances ZA-B, ZB-C,

ZC-A, ZA-N, ZB-N, ZC-N and ZA-B-C-N can be determined,

were:

ZA-B = ZA + ZB

ZB-C = ZB + ZC

ZC-A = ZC + ZA

ZA-N = ZA + ZE

ZB-N = ZB + ZE

ZC-N = ZC + ZE

ZA-B-C-N: ( ZA//ZB//ZC ) + ZE

Figure 5: Injection Test for A-B loop

These equations represent a system of seven equations

with four unknown variables, i.e. an over determined

system. The equations can be re-arranged to calculated

ZA, ZB, ZC and ZE as follows:

ZA = (ZA-B + ZC-A – ZB-C) / 2

ZB = (ZB-C + ZA-B – ZC-A) / 2

ZC = (ZC-A + ZB-C – ZA-B) / 2

ZL = (ZA + ZB + ZC) / 3

ZE = ZA-B-C-N – (ZL / 3)

ZL is the positive sequence impedance of the line. ZE is

the earth impedance of the line with the earth wire in

parallel. As an alternative the earth impedance can also

be calculated as follows:

ZE = ((ZA-N –ZA) + (ZB-N –ZB) + (ZC-N –ZC)) / 3

From ZL and ZE the earth impedance compensation

factors can be determined:

kL = ZE / ZL

Z0/Z1 = 3*kL + 1

Z0 = ( 3*kL + 1) * ZL

3.2 Test Set up

The injection of an accurate current into the actual line

as well as the voltage measurement is utilized using an

OMICRON CPC 100 [5] in conjunction with a CP

CU20 coupling unit.

The OMICRON CPC 100 (as shown in Figure 6) is a

universal primary injection test set capable of injecting

currents up to 800Aac and 400Adc as well as voltages

up to 2000Vac. It also provides means to accurately

measure the amplitude and phase angle of ac voltages

and currents, as well as the amplitude of dc voltage and

currents. Calculation functions are provided to calculate

ratio, resistance, reactance, impedance in amplitude and

phase angle, inductance, capacitance, active power,

reactive power and apparent power in magnitude and

ZSA ZA

ZSB ZB

ZSC ZC

ZSE ZE

ECEBEA

ZA

ZC

ZE

ZB

Vtest

Itest

457

Page 4

phase angle. The prime application of the CPC 100 is to

perform ratio, phase angle and polarity tests on CTs,

VTs and power transformers. For CTs the magnetisation

curve can be recorded with automatic calculation of the

‘knee point’. For power transformers a tap changer

continuity test can be performed. The amplifier outputs

are regulated, i.e. any waveform to be injected is

synthesized by a Digital Signal Processor (DSP). This

has the advantage that the output frequency can be

shifted away from the nominal 50Hz, when small

signals are measured. The 50Hz interference can then be

filtered out using a good quality band-pass filter.

Figure 6: CPC 100 Primary Injection Test Set

The CP CU20 coupling unit provides galvanic isolation

between the CPC 100 and the overhead line by means of

safety transformers for both the injected and measured

signals. At the same time the CU20 transforms the

current signal from the CPC 100 (up to 20A) down to a

more practical 10A. The voltage measurement is

utilized via a 500V:100V voltage transformer. The

current measurement is effected via a 25A:5A current

transformer. For all impedance measurements a four-

wire impedance measurement technique is used, to

eliminate the impedance of the test leads. For accidental

high voltage on any of the circuits, voltage arrestors for

voltages greater 500V are built in to protect the test

equipment and the users, e.g. from inductions of parallel

lines. A schematic diagram of the CU 20 is shown in

Figure 7. The actual unit is shown in Figure 8.

Figure 7: Schematic Diagram of CP CU 20

Figure 8: CP CU 20 unit

The CPC 100 provides a variety of test modules called

‘test cards’. For this specific test the Sequencer test card

is used, as it provides the feature to inject multiple tests

after each other without any delay in between the tests.

One of such test cards with all individual tests needs to

be set up for each fault loop. The test is suggested for

test frequencies of 30Hz, 50 Hz, 70 Hz and 110 Hz. For

each individual test, the injected test current and the test

voltage is automatically measured in terms of amplitude

and phase angle. The resistance and reactance is

calculated on-line.

Tests can be pre-prepared on a PC using the CPC Editor

software to allow for a speedier test set up at site. The

tests defined for the B-C measurement loop are shown

in Figure 9.

CP CU20 Connection in 4-Wire-Technique

CT 25A : 5A

Safety Transformer

250V : 20A

500V : 10A

Overhead

Line or

Cable

Booster Output

CPC 100

High Power Voltage

Arrestors

95mm²

Safe Potential Separation

VT 500V : 100V

458

Page 5

Figure 9: CPC Editor / Sequencer Module

The tests files, which are saved in XML file format, can

then be uploaded to the CPC prior to the test using the

CPC Explorer. After a test is finished, the results can be

downloaded to the PC also using the CPC Explorer. The

results can then be analysed, printed out as well as

backed-up. Figure 10 shows the CPC Explorer.

Figure 10: CPC Explorer

The results of a specific test can then be loaded into

Excel using the ‘Excel File Loader’, which is a specially

prepared Excel template. In Excel the data can be post-

processed as well as illustrative graphs be plotted.

3.3 Important test considerations

The capacitive and inductive coupling to parallel lines,

which are energized, must be considered:

1) Capacitive coupling exists if parallel lines are

energized. The line under test then acts as a

capacitive voltage divider between the energized

line and ground. Depending on the distances

between the energized and de-energized conductor

as well as the de-energized conductor and ground,

voltages up to 50% of nominal voltage are possible.

Such voltages obviously pose a serious danger to

the equipment and personal life.

2) Inductive coupling is due to parallel lines carrying

current, esp. during possible fault conditions. The

current induced in a de-energized line due to the

high current on the parallel line can result in lethal

voltages if one end of the line is earthed and other

end is connected to test equipment.

The following pre-cautions during a test are therefore

suggested to minimize risk:

A) The remote end of the line is to earthed via earth

switches and working earth for the full duration of

the test. The local end of the line is earthed via the

earth switch. Working earth need to be applied, but

not connected to earth, as these will be used to

inject the test current.

B) Before lifting the working earths at the local end,

the total amount of capacitive current flowing

through the earths should be measured. The

induced capacitive voltage, which is the voltage

applied to the test set when the local earths are

lifted, can be approximated by multiplying the

measured capacitive current with the line

impedance. The CU20 is protected for voltages up

to 500V only. If greater voltages are determined, a

test is not possible.

C) For all test lead manipulations, i.e. when changing

the measurement loop, the local earth switch must

be switched in. All operations of the earth switch

have to be conducted only by a qualified HV plant

operator.

D) During tests and while the Earth switches are open

nobody is allowed near any of the test leads or the

CU20 coupling unit.

Measurement interference when injecting current at

50Hz must be considered, e.g. injecting 10A into a line

with ZL = ZE = 1�Ÿ will result in voltages in the range of

20V being measured. The induced voltages in a de-

energized line often exceeds such values, which makes

accurate measurements impossible. The currents are

therefore injected at frequencies of 30Hz and 70Hz. The

voltage measurement is filtered with a good quality

band-pass filter, which is tuned to the injected

frequency. To determine the result at 50Hz, the result

for 30Hz and 70Hz need to be averaged.

IV CASE STUDY

As a case study the 400kV line from Athene substation

to Invubu substation near Richards Bay was selected.

This line is of critical importance, as Athene substation

supplies the Hillside Aluminium smelter and Invubu

supplies other big industry plants near Richards Bay.

Hillside Aluminium smelter is the biggest single

electricity consumer in the Eskom network.

The line is 21.85km long consisting of two sections

each with different tower design. For the first 7.062km

tower type 515 and for the remaining 14.787km tower

type 510 is used, which is part of the original line from

Invubu to Umfolozi substation. The whole line is strung

with twin dinosaur conductors (450mm conductor

spacing) for the phase conductors. Greased Horse earth

459

Page 6

wire is used on the 515 towers and Greased Tiger on the

510 towers. A picture of tower 1 near Athene substation

is shown in Figure 12.

Figure 12: Tower 1 near Athene substation

The geometrical parameters as well as conductor

parameters for this line were entered into the line

impedance function of PowerFactory. For the earth

resistivity a value of 500 m was assumed as during

winter the soil can be assumed to be fairly dry. Average

sag was assumed to be 30% of the average attachment

height. The impedances calculated are as follows:

Z1 = 0.540 +j 6.770 = 6.79 @85º

Z0 = 4.192 +j 15.837 = 16.38 @75º

In June 2004 the primary line impedance of this line

was measured during an outage. During the test,

injections were done at 30Hz, 50Hz (rejected), 70Hz,

90Hz and 110Hz to confirm the linearity of the

resistance and reactance measurements. Figure 11

graphically illustrates the resistance and reactance

measured at each frequency. The calculated resistance

and reactance at 50Hz is also illustrated. Note, that the

measurement at 50Hz is clearly ‘out of step’, i.e. not

trust worthy. The linear dependency of reactance with

respect to frequency is clearly visible. The resistance is

independent of frequency. A summary of the full test

results can be viewed in Appendix A, which shows all

the impedances and earth fault compensation factors

calculated.

0

5

10

15

20

25

30

35

20 40 60 80 100 120

Frequency [Hz]

Im

p

e

d

a

n

c

e

[

O

h

m

]

R(f) X(f) Rcalc (50Hz) Xcalc (50Hz)

Figure 11: Frequency Response Characteristic of Z1

The impedances measured were as follows:

Z1 = 0.587 +j 7.128 = 7.15 @85º

Z0 = 4.623 +j 16.067 = 16.718 @74º

The measured impedance values show a good

correlation with the calculated impedance values. The

deviation between calculated and measured values is

5% for Z1 and 2% for Z0.

The test was finished within one hour.

IV CONCLUSION

The electrical parameters of overhead transmission lines

can be simulated very effectively using common

software tools available. To ensure accurate impedance

estimates, care should be taken to enter accurate and

correct parameters.

The primary line impedance can be physically measured

with a relatively simple test set up. The results yielded a

good correlation to the values simulated using a

software tool.

REFERENCES

[1] DIgSILENT: PowerFactory Software V13.1;

DIgSILENT GmbH, 2004.

[2] Glover, J. Duncan / Sarma, Mulukutla: Power

System Analysis and Design; PWS Publishers,

Boston 1987

[3] Carsons, John R: Wave Propagation in Overhead

Wires with Ground Return; Bell System Tech. J.

1926.

[4] Anderson, Paul: Analysis of Faulted Power

Systems, The Iowa State University Press, 1973

[5] OMICRON: CPC 100 Users Manual V1.30;

Omicron Electronics GmbH, 2004.

460

Accurate Calculation And Physical Measurement of Trasmission Line

Parameters to Improve Impedance Relay Performance

Alexander Dierks, Harry Troskie Michael Krüger

Alectrix Eskom Transmission Omicron Electronics, Austria

ABSTRACT

To accurately set an impedance relay it is imperative to

know the impedance of the transmission line as well as

the earth return path accurately. The electrical

impedance parameters of transmission lines are

determined either by using suitable software tools or by

physically measuring the impedance. Both techniques

yield comparable results, if the correct parameters are

entered into the software tool.

I INTRODUCTION

Knowing the accurate overhead transmission line

parameters, which includes an accurate estimate of the

earth return impedance, is a crucial ingredient to being

able to accurately set impedance relays and to ensure

correct operation of such relays for all types of fault in a

power system.

The electrical parameters of an overhead transmission

line are usually calculated using suitable software tools.

Using PowerFactory [1], the effect of entering wrong

parameters on the calculated impedance parameters will

be examined. The impact of ground resistivity, as well

as conductor height above ground and sag, on the zero

sequence impedance will be investigated.

A technique to physically measure the primary

impedance of an overhead line (Z1) as well as the earth

return impedance (Z0) using the OMICRON CPC100

primary test set will then be described.

As a case study an actual line in the ESKOM network

was chosen for which the line parameters were both

calculated as well as physically measured. The results

will be presented.

II CALCULATION OF THEORETICAL

OVERHEAD LINE PARAMETERS

For setting of impedance relays the following primary

line parameters are of importance:

Positive Sequence Impedance: Z1 = R1 + jX1

Zero Sequence Impedance: Z0 = R0 + jX0

All these parameters can be calculated from the

geometrical configuration of the line, the earth

resistivity as well as the physical dimensions and

construction of the actual conductor used.

The geometrical configuration of a line defines the

physical position of the conductors and earth wires in

terms of:

Attachment height of each phase conductor above

ground (Yp).

Attachment height of each earth wire above ground

(Ye).

Horizontal distance of each phase conductor from

the center of the tower (Xp).

Horizontal distance of each earth wire from the

center of the tower (Xe).

A typical geometrical tower configuration illustrating

Yp, Ye, Xp and Xe is shown in Figure 1.

Figure 1: Geometrical Tower Configuration

If multiple lines are strung to the same tower, or if

mutual induction effects of one line to the other need to

be investigated, the physical distance of each conductor

on all lines with respect to one reference point need to

be defined.

The other parameters of importance are:

Average sag of the line and earth wires at midspan.

Earth resistivity of the ground.

For the actual conductors (both phase conductors and

earth wires) the following parameters need to be

entered:

DC resistance of the conductor, which can be

calculated from first principles using the

Yp

Ye

Xp

Xe

455

Inaugural IEEE PES 2005 Conference and Exposition in Africa

Durban, South Africa, 11-15 July 2005

0-7803-9327-9/05/$20.00 ©2005 IEEE

Page 2

conductor resistivity, the length of conductor

and diameter of conductor [2]. The spiralling

of the conductor, operating temperature and

skin effect also has to be allowed for.

Overall diameter of the conductor.

Geometrical Mean Radius [GMR] of the

conductor.

If conductor bundles are used the number of sub-

conductors in a bundle as well as the spacing between

the sub-conductors is of importance.

Calculating the electrical parameters from first

principles is a fairly involved mathematical process

[2,3,4]. Various software tools, such as TMLC from PTI

as well as PowerFactory from Digsilent [1] are available

to achieve the same. In this paper PowerFactory was

used as illustrated in Figure 2.

Figure 2: Overhead Line Parameter Calculation in

PowerFactory

As with any computation the accuracy of the input

parameters determines the accuracy of the calculated

output parameters.

The horizontal distance parameters of both phase and

earth conductors as well as the conductor diameter can

be determined very accurately, usually to less than 1%

error. It is, however, impossible to determine the

attachment height of the phase conductors and earth

wires above ground accurately, due to the varying

height of towers along the length of a line, the ground

profile changing as the line spans across valleys and

sometimes canyons as well as vegetation growing to

various heights under a line. To model the sag of the

conductors is difficult as it depends on the ambient

temperature, conductor tension, etc. A sensitivity study

was thus conducted for a typical line, where the

parameter of sag was varied, while the zero sequence

resistance and reactance was monitored. The effect of a

100% change in sag had negligible effect on the zero

sequence impedance of a line. A similar study on the

average attachment height yielded a similar negligible

effect of average attachment height on the zero

sequence impedance of a line.

The earth resistivity used for line parameter calculation

is a hotly debated subject. The earth resistivity changes

with type of soil, dampness as well as season related

variances. Typical average values used are 100 m for

damp soil and up to 700 m for dry sand. Investigating

the effect of changing this parameter from 100 m to

1000 m (i.e. +1000%) resulted in R0 changing by 14%

and X0 by 6%. Both sensitivities can be regarded as

minimal. If a line has a good quality earth wire, it can

further be deduced that the earth resistivity used in the

simulation has minimal effect on the result for the zero

sequence impedance of the line.

As a last parameter the DC resistance of the earth wire

was varied. Plotting the calculated zero sequence

resistance and reactance against the DC resistance

yields an interesting dependency (as can be seen in

Figure 3). This characteristic can be explained by

considering the parallel impedance phenomena of the

earth wire and the actual earth return impedance through

ground. For low values of DC resistance, the overall

zero sequence impedance of the line tends towards a

constant value (i.e. independent of DC resistance). This

impedance is dominated by the earth wire impedance.

The earth return impedance through ground, which is in

parallel to the earth wire impedance, is too high to have

a significant effect on the overall zero sequence

impedance. For high values of DC resistance, the

overall zero sequence impedance again tends towards a

constant impedance, which is this time dominated by

the earth return impedance. Here the earth wire

impedance is too high to have an effect on the overall

zero sequence impedance. In the range of 0.1 to 10

/km, the zero sequence impedance varies

considerably. Considering, that typical values of DC

resistance for the various kinds of conductor fall into

this range, care must be taken to enter the correct DC

resistance for the conductor used. This value normally is

readily available from the conductor manufacturer or

can be calculated from first principles with relative ease.

0

0.2

0.4

0.6

0.8

1

1.2

0.001 0.01 0.1 1 10 100 1000

DC Resistance [Ohm / km]

R0 [Ohm/km] X0 [Ohm/km]

Figure 3: DC Resistance Sensitivity Analysis

456

Page 3

All the above calculations were done for a 515 Tower

strung with Twin Dinosaur conductors (45cm conductor

spacing) and Greased Horse earth wire. As average

attachment height of both the phase conductors and

earth wires, the tower heights along the length of a line

were averaged out.

III PHYSICAL MEASUREMENT

3.1 Theory

The physical measurement of the impedance of an

overhead line is based on Ohm’s law:

Z = V / I

To accurately measure the impedance a current Itest

needs to be injected into the impedance to be measured,

whilst the voltage drop Vtest across the impedance needs

to be measured accurately in terms of amplitude and

phase angle. The complex impedance Z is calculated by

performing a complex division of Vtest divided by Itest.

The real component of the resulting complex impedance

is the resistive component and the complex component

is the reactive component of the impedance measured.

To measure the impedance of a three phase transmission

system consider the equivalent circuit of a transmission

line as shown in Figure 4:

Figure 4: Equivalent Circuit of Transmission Line

By injecting a current into each of the following

measurement loops A-B, B-C, C-A, A-N, B-N, C-N, A-

B-C-N (see Figure 5 for an illustration of the injection

into the A-B loop), the ‘loop’ impedances ZA-B, ZB-C,

ZC-A, ZA-N, ZB-N, ZC-N and ZA-B-C-N can be determined,

were:

ZA-B = ZA + ZB

ZB-C = ZB + ZC

ZC-A = ZC + ZA

ZA-N = ZA + ZE

ZB-N = ZB + ZE

ZC-N = ZC + ZE

ZA-B-C-N: ( ZA//ZB//ZC ) + ZE

Figure 5: Injection Test for A-B loop

These equations represent a system of seven equations

with four unknown variables, i.e. an over determined

system. The equations can be re-arranged to calculated

ZA, ZB, ZC and ZE as follows:

ZA = (ZA-B + ZC-A – ZB-C) / 2

ZB = (ZB-C + ZA-B – ZC-A) / 2

ZC = (ZC-A + ZB-C – ZA-B) / 2

ZL = (ZA + ZB + ZC) / 3

ZE = ZA-B-C-N – (ZL / 3)

ZL is the positive sequence impedance of the line. ZE is

the earth impedance of the line with the earth wire in

parallel. As an alternative the earth impedance can also

be calculated as follows:

ZE = ((ZA-N –ZA) + (ZB-N –ZB) + (ZC-N –ZC)) / 3

From ZL and ZE the earth impedance compensation

factors can be determined:

kL = ZE / ZL

Z0/Z1 = 3*kL + 1

Z0 = ( 3*kL + 1) * ZL

3.2 Test Set up

The injection of an accurate current into the actual line

as well as the voltage measurement is utilized using an

OMICRON CPC 100 [5] in conjunction with a CP

CU20 coupling unit.

The OMICRON CPC 100 (as shown in Figure 6) is a

universal primary injection test set capable of injecting

currents up to 800Aac and 400Adc as well as voltages

up to 2000Vac. It also provides means to accurately

measure the amplitude and phase angle of ac voltages

and currents, as well as the amplitude of dc voltage and

currents. Calculation functions are provided to calculate

ratio, resistance, reactance, impedance in amplitude and

phase angle, inductance, capacitance, active power,

reactive power and apparent power in magnitude and

ZSA ZA

ZSB ZB

ZSC ZC

ZSE ZE

ECEBEA

ZA

ZC

ZE

ZB

Vtest

Itest

457

Page 4

phase angle. The prime application of the CPC 100 is to

perform ratio, phase angle and polarity tests on CTs,

VTs and power transformers. For CTs the magnetisation

curve can be recorded with automatic calculation of the

‘knee point’. For power transformers a tap changer

continuity test can be performed. The amplifier outputs

are regulated, i.e. any waveform to be injected is

synthesized by a Digital Signal Processor (DSP). This

has the advantage that the output frequency can be

shifted away from the nominal 50Hz, when small

signals are measured. The 50Hz interference can then be

filtered out using a good quality band-pass filter.

Figure 6: CPC 100 Primary Injection Test Set

The CP CU20 coupling unit provides galvanic isolation

between the CPC 100 and the overhead line by means of

safety transformers for both the injected and measured

signals. At the same time the CU20 transforms the

current signal from the CPC 100 (up to 20A) down to a

more practical 10A. The voltage measurement is

utilized via a 500V:100V voltage transformer. The

current measurement is effected via a 25A:5A current

transformer. For all impedance measurements a four-

wire impedance measurement technique is used, to

eliminate the impedance of the test leads. For accidental

high voltage on any of the circuits, voltage arrestors for

voltages greater 500V are built in to protect the test

equipment and the users, e.g. from inductions of parallel

lines. A schematic diagram of the CU 20 is shown in

Figure 7. The actual unit is shown in Figure 8.

Figure 7: Schematic Diagram of CP CU 20

Figure 8: CP CU 20 unit

The CPC 100 provides a variety of test modules called

‘test cards’. For this specific test the Sequencer test card

is used, as it provides the feature to inject multiple tests

after each other without any delay in between the tests.

One of such test cards with all individual tests needs to

be set up for each fault loop. The test is suggested for

test frequencies of 30Hz, 50 Hz, 70 Hz and 110 Hz. For

each individual test, the injected test current and the test

voltage is automatically measured in terms of amplitude

and phase angle. The resistance and reactance is

calculated on-line.

Tests can be pre-prepared on a PC using the CPC Editor

software to allow for a speedier test set up at site. The

tests defined for the B-C measurement loop are shown

in Figure 9.

CP CU20 Connection in 4-Wire-Technique

CT 25A : 5A

Safety Transformer

250V : 20A

500V : 10A

Overhead

Line or

Cable

Booster Output

CPC 100

High Power Voltage

Arrestors

95mm²

Safe Potential Separation

VT 500V : 100V

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Page 5

Figure 9: CPC Editor / Sequencer Module

The tests files, which are saved in XML file format, can

then be uploaded to the CPC prior to the test using the

CPC Explorer. After a test is finished, the results can be

downloaded to the PC also using the CPC Explorer. The

results can then be analysed, printed out as well as

backed-up. Figure 10 shows the CPC Explorer.

Figure 10: CPC Explorer

The results of a specific test can then be loaded into

Excel using the ‘Excel File Loader’, which is a specially

prepared Excel template. In Excel the data can be post-

processed as well as illustrative graphs be plotted.

3.3 Important test considerations

The capacitive and inductive coupling to parallel lines,

which are energized, must be considered:

1) Capacitive coupling exists if parallel lines are

energized. The line under test then acts as a

capacitive voltage divider between the energized

line and ground. Depending on the distances

between the energized and de-energized conductor

as well as the de-energized conductor and ground,

voltages up to 50% of nominal voltage are possible.

Such voltages obviously pose a serious danger to

the equipment and personal life.

2) Inductive coupling is due to parallel lines carrying

current, esp. during possible fault conditions. The

current induced in a de-energized line due to the

high current on the parallel line can result in lethal

voltages if one end of the line is earthed and other

end is connected to test equipment.

The following pre-cautions during a test are therefore

suggested to minimize risk:

A) The remote end of the line is to earthed via earth

switches and working earth for the full duration of

the test. The local end of the line is earthed via the

earth switch. Working earth need to be applied, but

not connected to earth, as these will be used to

inject the test current.

B) Before lifting the working earths at the local end,

the total amount of capacitive current flowing

through the earths should be measured. The

induced capacitive voltage, which is the voltage

applied to the test set when the local earths are

lifted, can be approximated by multiplying the

measured capacitive current with the line

impedance. The CU20 is protected for voltages up

to 500V only. If greater voltages are determined, a

test is not possible.

C) For all test lead manipulations, i.e. when changing

the measurement loop, the local earth switch must

be switched in. All operations of the earth switch

have to be conducted only by a qualified HV plant

operator.

D) During tests and while the Earth switches are open

nobody is allowed near any of the test leads or the

CU20 coupling unit.

Measurement interference when injecting current at

50Hz must be considered, e.g. injecting 10A into a line

with ZL = ZE = 1�Ÿ will result in voltages in the range of

20V being measured. The induced voltages in a de-

energized line often exceeds such values, which makes

accurate measurements impossible. The currents are

therefore injected at frequencies of 30Hz and 70Hz. The

voltage measurement is filtered with a good quality

band-pass filter, which is tuned to the injected

frequency. To determine the result at 50Hz, the result

for 30Hz and 70Hz need to be averaged.

IV CASE STUDY

As a case study the 400kV line from Athene substation

to Invubu substation near Richards Bay was selected.

This line is of critical importance, as Athene substation

supplies the Hillside Aluminium smelter and Invubu

supplies other big industry plants near Richards Bay.

Hillside Aluminium smelter is the biggest single

electricity consumer in the Eskom network.

The line is 21.85km long consisting of two sections

each with different tower design. For the first 7.062km

tower type 515 and for the remaining 14.787km tower

type 510 is used, which is part of the original line from

Invubu to Umfolozi substation. The whole line is strung

with twin dinosaur conductors (450mm conductor

spacing) for the phase conductors. Greased Horse earth

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Page 6

wire is used on the 515 towers and Greased Tiger on the

510 towers. A picture of tower 1 near Athene substation

is shown in Figure 12.

Figure 12: Tower 1 near Athene substation

The geometrical parameters as well as conductor

parameters for this line were entered into the line

impedance function of PowerFactory. For the earth

resistivity a value of 500 m was assumed as during

winter the soil can be assumed to be fairly dry. Average

sag was assumed to be 30% of the average attachment

height. The impedances calculated are as follows:

Z1 = 0.540 +j 6.770 = 6.79 @85º

Z0 = 4.192 +j 15.837 = 16.38 @75º

In June 2004 the primary line impedance of this line

was measured during an outage. During the test,

injections were done at 30Hz, 50Hz (rejected), 70Hz,

90Hz and 110Hz to confirm the linearity of the

resistance and reactance measurements. Figure 11

graphically illustrates the resistance and reactance

measured at each frequency. The calculated resistance

and reactance at 50Hz is also illustrated. Note, that the

measurement at 50Hz is clearly ‘out of step’, i.e. not

trust worthy. The linear dependency of reactance with

respect to frequency is clearly visible. The resistance is

independent of frequency. A summary of the full test

results can be viewed in Appendix A, which shows all

the impedances and earth fault compensation factors

calculated.

0

5

10

15

20

25

30

35

20 40 60 80 100 120

Frequency [Hz]

Im

p

e

d

a

n

c

e

[

O

h

m

]

R(f) X(f) Rcalc (50Hz) Xcalc (50Hz)

Figure 11: Frequency Response Characteristic of Z1

The impedances measured were as follows:

Z1 = 0.587 +j 7.128 = 7.15 @85º

Z0 = 4.623 +j 16.067 = 16.718 @74º

The measured impedance values show a good

correlation with the calculated impedance values. The

deviation between calculated and measured values is

5% for Z1 and 2% for Z0.

The test was finished within one hour.

IV CONCLUSION

The electrical parameters of overhead transmission lines

can be simulated very effectively using common

software tools available. To ensure accurate impedance

estimates, care should be taken to enter accurate and

correct parameters.

The primary line impedance can be physically measured

with a relatively simple test set up. The results yielded a

good correlation to the values simulated using a

software tool.

REFERENCES

[1] DIgSILENT: PowerFactory Software V13.1;

DIgSILENT GmbH, 2004.

[2] Glover, J. Duncan / Sarma, Mulukutla: Power

System Analysis and Design; PWS Publishers,

Boston 1987

[3] Carsons, John R: Wave Propagation in Overhead

Wires with Ground Return; Bell System Tech. J.

1926.

[4] Anderson, Paul: Analysis of Faulted Power

Systems, The Iowa State University Press, 1973

[5] OMICRON: CPC 100 Users Manual V1.30;

Omicron Electronics GmbH, 2004.

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