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TitleAccurate Calculation and Physical Measurement of Trasmission Line Parameters to Improve Impedance Relay Performance
TagsElectrical Impedance Electrical Resistivity And Conductivity Electrical Resistance And Conductance Transformer Ac Power
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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


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.


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.


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

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

DC resistance of the conductor, which can be
calculated from first principles using the






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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

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

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.








0.001 0.01 0.1 1 10 100 1000

DC Resistance [Ohm / km]

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

Figure 3: DC Resistance Sensitivity Analysis


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.


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,

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













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

Line or

Booster Output

CPC 100

High Power Voltage

Safe Potential Separation

VT 500V : 100V


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

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.


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


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









20 40 60 80 100 120

Frequency [Hz]







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.


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.


[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.


[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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