A
ccurate Calculation And Physical Measurement of Trasmission Line
P
arameters 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:
x Attachment height of each phase conductor above ground (Yp).
x Attachment height of each earth wire above ground (Ye).
x Horizontal distance of each phase conductor from the center of the tower (Xp).
x Horizontal distance of each earth wire from the center of the tower (Xe).
A typical geometrical tower configuration illustrating Yp, Ye, Xpand 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:
x Average sag of the line and earth wires at midspan. x Earth resistivity ȡ of the ground.
For the actual conductors (both phase conductors and earth wires) the following parameters need to be entered:
x DC resistance of the conductor, which can be calculated from first principles using the Yp
Ye
Xp
Xe
Inaugural IEEE PES 2005 Conference and Exposition in Africa Durban, South Africa, 11-15 July 2005
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.
x Overall diameter of the conductor.
x 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 1000m (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
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 B, B-C, C-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 EC EB EA ZA ZC ZE ZB Vtest Itest
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
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 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
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 500m 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] Impedance [Ohm] 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;
Appendix A: Results Comparison Measurements: R [ȍ] X [ȍ] Z [ȍ] Phi (°) A-B: ZA + ZB 1.269 15.328 15.380 85.27° B-C: ZB + ZC 1.128 13.808 13.853 85.33° C-A: ZC + ZA 1.127 13.631 13.677 85.28° A-E: ZA + ZE 1.952 9.960 10.149 78.91° B-E: ZB + ZE 1.937 10.187 10.370 79.24° C-E: ZC + ZE 1.913 10.235 10.412 79.41° A-B-C-E: ZA//ZB//ZC + ZE 1.541 5.356 5.573 73.95° Calculation of impedances: ZA 0.634 7.576 7.602 85.22° ZB 0.635 7.752 7.778 85.32° ZC 0.493 6.055 6.075 85.35° ZE from Measurement A-E 1.318 2.384 2.724 61.07° ZE from Measurement B-E 1.302 2.435 2.761 61.87° ZE from Measurement C-E 1.420 4.180 4.414 71.23°
Impedance results:
Line impedance ZL 0.587 7.128 7.152 85.29° Ground impedance ZE 1.345 2.980 3.269 65.70° Zero sequence impedance Z0 4.623 16.067 16.718 73.95°
Grounding Factor:
kL = ZE / ZL 0.457 -19.591 RE / RL and XE / XL 2.291 0.418 Z0 / Z1 2.338 -11.344
PowerFactory / Digsilent: Simulated Line Data:
Z1: Section 1: T1 - T20 0.181 2.286 Z1: Section 2: T21 - T61 0.373 4.481 0.554 6.767 6.790 85.32° abs Error - Z1 -0.033 -0.361 -0.362 % Error - Z1 -5.65% -5.06% -5.06% Z0: Section 1: T1 - T20 1.713 5.383 Z0: Section 2: T21 - T61 2.493 10.452 4.206 15.835 16.384 75.12° abs Error - Z0 -0.417 -0.232 -0.334 % Error - Z0 -9.03% -1.44% -2.00%
