Ground Fault Current Distribution Using A Conventional Short-Circuit

Ground Fault Current Distribution Using A Conventional Short-Circuit Software Carlos A. Muñoz Universidad Nacional de Ingeniería, Lima, Perú

Alberto Rojas COVIEM S.A., Lima, Perú

Abstract Purpose- This article presents the numerical experiments carried out with a conventional short-circuit software to compute the ground fault current distribution at substations grounds. The results obtained with the conventional short-circuit software were validated using the ATP/EMTP software. Also, these results are compared to several ground fault current distribution methods. The main goal of this research effort is to reuse the source code of this conventional short-circuit software to develop the calculation engine of an accurate and easy to use ground fault current distribution software. Methodology- A conventional short-circuit software is used to model a zero sequence network where the zero sequence branches correspond to the self impedances of the conductors and the zero sequence mutual impedances are used to model the couplings between conductors. With this shortcircuit software is even possible to model self and mutual capacitances of conductors. This approach allows modeling unbalanced three-phase transmission lines. The ground resistance of substations and tower footings are modeled as shunt equivalents. A single line to ground fault current is computed manually by getting the zero sequence impedance of an open circuit conductor corresponding to a fictitious branch; then the fictitious branch is removed and a harmonic software is used to inject the fault current as a harmonic current of order one. The harmonic software gives the ground fault current distribution. Research implications- Conventional short-circuit software source code can be reused to develop ground fault current distribution software. The conventional short-circuit approach gives accurate results that are free of round off errors. Key words: Ground fault current distribution, grounding systems, short-circuit software, EHV transmission lines

I.

Introduction

The design of high voltage transmission lines and grounding systems requires computing the ground fault current distribution due to single line and double line to ground short circuits. Accurate results are needed in order to avoid under-designing or over-designing components of transmission lines and substations. The methods applied to solve this problem are, among others, the classical double side elimination method (Dawalibi 1980 Method) [1], Zou et al. Iterative Nodal Method [2] and Zizzo et al. Approach [3]. References [1-3] are useful because they present results for a benchmark test system presented in Reference [1]. In this research effort, conventional short-circuit techniques [4], using the bus admittance matrix, are evaluated for their application to computing the current distribution of single-line and double-line to ground faults. The short-circuit software used corresponds to the Peruvian WinFdc software [5] (load-flow, short-circuit and harmonics). Conventional short-circuit techniques mean that balanced three-phase power systems are solved by building the positive, negative and zero sequence networks using the symmetric components theory. Section II presents the application of WinFdc to perform ground fault current distribution analysis. Section III shows the validation of WinFdc results against ATPDraw/ATP simulations. In Section IV comparisons are made against other methods. Section V presents the application of WinFdc to model the capacitance of 500 kV lines for ground fault current distribution analysis. Finally, in Section VI the main conclusions of this research effort are outlined.

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II.

WinFdc’s Short-Circuit Module

The WinFdc software developed by the authors includes the following modules: 1) MS-Access database, 2) Load Flow, 3) Short-Circuit, 4) Harmonics, 5) Interface with the PSS/E of SiemensPTI, and 6) Interface with CADOpia and AutoCAD. The short-circuit module of WinFdc (NewCf) allows modeling three-phase (LLL), double-phase (L-L), single-phase to ground (L-G) and doublephase to ground (LL-G) faults at buses. Also, NewCf allows modeling faults at specified points of lines; these type of faults are LLL, L-L, L-G, LL-G, 1-OC (phase A open) and 2-OC (phases B and C open). For all of these types of faults, the positive, negative and zero sequence Thevenin impedances are reported. The zero sequence network can include mutual impedances and capacitive susceptances between lines. The harmonics module of WinFdc (FdcHarmo) is developed reusing the source code of NewCf; therefore, for the 50 Hz or 60 Hz fundamental frequency, the sequence networks of NewCf and FdcHarmo are identical. The approach for performing ground fault current distribution analysis is explained below by solving first the benchmark test system of section 4.1 of Reference [1]. This benchmark test system is shown in Figure 2.1:

Figure 2.1 Figure 2.1 above is taken form Figure 4.1 of Reference [1] and the shows three terminals; each terminal is connected to a substation with a line of 100 sections. The impedances of the sections are: Zai = 0.1 + j 0.425 Ω Zgi = 3.5 + j 0.650 Ω Zmi = 0.025 + j 0.190 Ω Ri = 0.01ρ + j 0.0 Ω Rt = 0.003ρ + j 0.0 Ω Rg = 0.0025ρ + j 0.0 Ω

(phase conductor self impedance) (ground wire self impedance) (mutual impedance between phase conductor and ground wire) (tower footing impedance) (terminals RT1, RT2 and RT3 grounding impedance) (substation RG grounding impedance)

Where ρ is the soil resistivity. The current Ia corresponds to a phase to ground fault at the substation. The following cases are analyzed in Reference [1]: a) 1 energized terminal, 1 line b) 2 energized terminals, 2 lines c) 2 terminals, 2 lines – 1 energized terminal only d) 3 energized terminals, 3 lines e) 3 terminals, 3 lines – 1 energized terminal only Page 2 of 12

In cases (c) and (e) where only 1 terminal is energized, the phase conductors of the other lines are grounded at both ends. Keeping constant the overhead conductor impedances, ρ is varied from 0 to 9000 Ωm. This benchmark test system is modeled with WinFdc as shown below:

Figure 2.2 – Bus data – There are 599 buses

Figure 2.3 – Line data – There are 601 lines

Figure 2.4 – Zero sequence mutual’s – There are 300 mutual’s

Figure 2.5 – Shunt data – There are 301 shunts Page 3 of 12

The data shown from Figure 2.2 to Figure 2.5 has been created using MS-Excel and then it was imported to WinFdc. DeltaLine in Figure 2.3 is a fictitious line with impedance 0.0 + j 1.0 pu at 120 kV and 1000 MVA. Figure 2.6 below shows this fictitious line where a 1-OC fault is simulated with NewCf.

Figure 2.6 – Faults at lines When a 1-OC conductor fault is simulated at DeltaLine, NewCf generates the following short-circuit report:

Figure 2.7 – Short-circuit report The Delta Z0 Thevenin impedance at the substation is 0.3888631814 + j 0.9659102860 pu, after removing the DeltaLine impedance which is 0.0 + j 1.0 pu The calculation of fault current Ia at the substation was made manually using MS-Excel as shown below in Figure 2.8:

Figure 2.8 – Fault current Ia for case (d) and ρ equal to 1000 Ωm Page 4 of 12

All cases of section 4.1 of Reference [1] were simulated with WinFdc/NewCf software. Current Ia is shown below. For ρ equal to zero, Ri, RT1, RT2, RT3 and RG were set equal to 1.0E-06 Ω.

Case ρ (Ωm) 0 100 1000 3000 5000 9000

a 1594.4 1591.4 1562.6 1497.9 1436.7 1328.3

NewCf Results Arc current Ia (amperes) b c 3188.8 3180.0 3099.8 2936.9 2794.1 2557.2

1594.4 1591.4 1563.5 1505.8 1454.5 1367.6

d

e

4783.2 4765.8 4620.7 4351.3 4125.9 3763.2

1594.4 1591.4 1564.7 1512.7 1467.7 1392.0

Table 2.1 – Current Ia for all cases of section 4.1 of reference [1] III

Validation Using ATPDraw

The benchmark test system used in section II of this article was analyzed using ATPDraw/ATP software. The results are given in Table 3.1:

Case ρ (Ωm) 0 100 1000 3000 5000 9000

a 1594.4 1591.4 1562.6 1497.9 1436.7 1328.3

ATPDraw Results Arc current Ia (amperes) b c 3188.8 3180.0 3099.8 2936.9 2794.1 2557.2

1594.4 1591.4 1563.5 1505.8 1454.5 1367.6

d

e

4783.2 4765.8 4620.7 4351.3 4125.9 3763.2

1594.4 1591.4 1564.7 1512.7 1467.7 1392.0

Table 3.1 – Current Ia for all cases of section 4.1 of reference [1] There is an exact agreement between ATPDraw/ATP results and WinFdc results. Current Ia shown in Table 3.1 corresponds to a steady state solution with ATP. Case e with ρ equal to 9000 Ωm gives the greater differences with other methods as is presented in section IV. Therefore, for this case a transient solution was simulated by closing the switch at a time equal to 0.125 cycles (frequency is 60 Hz). The result is shown below in Figure 3.1.

Figure 3.1 – Transient simulation of current Ia with ATPDraw/ATP Page 5 of 12

Using the plot tool of ATPDraw, the peak value of current Ia, after the transient has died out, is 1968.3 amperes. The rms value of current Ia is 1391.8 amperes (Ia = 1968.3/√2); that is very close to the steady state solution of 1392.0 amperes. Therefore, these simulations with ATPDraw/ATP validate WinFdc/NewCf results. When using a steady state solution with ATPDraw/ATP, the differences with WinFdc/NewCf are about 1 mA. IV

Comparisons with Other Methods

In this section, we compare the results for the benchmark test system analyzed in References [1-3]. 1) Dawalibi 1980 Method Section 4.1 of Reference [1] presents the values of current Ia. Table 4.1A shows these currents and Table 4.1B shows the errors taking WinFdc/NewCf as the exact values of current Ia.

Case ρ (Ωm) 0 100 1000 3000 5000 9000

Dawalabi 1980 Method Arc current Ia (amperes) b c

a 1594.5 1591.6 1562.8 1498.2 1437.0 1328.6

3161.6 3158.8 3106.0 3009.1 2932.2 2807.4

1580.7 1577.5 1536.8 1448.4 1374.6 1260.1

d

e

4723.0 4722.9 4637.0 4485.9 4370.2 4184.6

1573.9 1569.6 1507.1 1371.8 1269.2 1129.6

Table 4.1A

Case ρ (Ωm) 0 100 1000 3000 5000 9000

Dawalabi 1980 Results Errors in % The reference values are the NewCf results a b c d 0.01 0.01 0.01 0.02 0.02 0.02

-0.85 -0.67 0.20 2.46 4.94 9.79

-0.86 -0.87 -1.71 -3.81 -5.49 -7.86

-1.26 -0.90 0.35 3.09 5.92 11.20

e -1.29 -1.37 -3.68 -9.32 -13.52 -18.85

Table 4.1B Dawalibi 1980 method errors increase with the value of ρ. This can be due perhaps to round of errors, if the calculations were performed using simple precision, or it can be due to a limitation of the double side elimination method. As shown below, the Zou et al. IterNodal method also gives the greatest errors for high values of ρ in cases (c) and (d). 2) Zou et al. IterNodal Method Section III-B of Reference [2] presents the values of current Ia. Table 4.2A shows these currents and Table 4.2B shows the errors taking WinFdc/NewCf results as the exact values of current Ia. Page 6 of 12

Case ρ (Ωm) 0 100 1000 3000 5000 9000

Zou IterNodal Results Arc current Ia (amperes) b c

a 1594.4 1591.4 1562.6 1497.9 1436.7 1328.3

3188.8 3180.0 3099.8 2936.9 2794.1 2557.2

1594.4 1590.0 1549.9 1468.5 1397.0 1278.6

d

e

4783.3 4765.8 4620.6 4351.3 4125.8 3763.2

1594.4 1588.6 1540.2 1450.4 1375.3 1254.4

Table 4.2A Zou IterNodal Results Errors in % The reference values are the NewCf results a b c

Case ρ (Ωm) 0 100 1000 3000 5000 9000

0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00

0.00 -0.09 -0.87 -2.48 -3.95 -6.51

d

e

0.00 0.00 0.00 0.00 0.00 0.00

0.00 -0.17 -1.57 -4.12 -6.29 -9.88

Table 4.2B The IterNodal method shows an exact agreement for cases (a), (b) and (d). For cases (c) and (e), where there are lines out of service, perhaps the phase conductor of these lines is not grounded at both ends in the analysis made by Zou et al. 3) Zizzo et al. Approach Section 8 of Reference [3] presents the values of current Ia. Table 4.3A shows these currents and Table 4.3B shows the errors taking WinFdc/NewCf results as the exact values of current Ia.

Case ρ (Ωm) 0 100 1000 3000 5000 9000

a --1696.0 1571.0 1525.0 1502.0 1427.0

Zizzo Approach Results Arc current Ia (amperes) b c --3394.0 3152.0 3049.0 3004.0 2954.0

--1696.0 1576.0 1525.0 1443.0 1359.0

Table 4.3A

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d

e

--5091.0 4729.0 4575.0 4506.0 4401.0

--1686.0 1576.0 1482.0 1364.0 1211.0

Case ρ (Ωm) 0 100 1000 3000 5000 9000

Zizzo Approach Results Errors in % The reference values are the NewCf results a b c d --6.57 0.54 1.81 4.55 7.43

--6.73 1.68 3.82 7.51 15.52

--6.58 0.80 1.28 -0.79 -0.63

--6.82 2.34 5.14 9.21 16.95

e --5.95 0.72 -2.03 -7.06 -13.00

Table 4.3B The Zizzo et al. approach shows errors greater than 10% for high values of ρ (ρ equal to 9000 Ωm). V

Application to EHV Power Lines

The Peruvian interconnected power grid has several 500 kV transmission lines [6]; some of them have a length greater than 300 km. The authors of this article had been thinking of the impact of modeling the capacitance when performing ground fault current distribution analysis. Two 500 kV lines have been analyzed with and without modeling the capacitance; these lines are: 1) L-5006 of 384.28 km that connects Carabayllo to Chimbote 500 kV substations, and 2) L-5001 of 89.19 km that connects Chilca to Carabayllo 500 kV substations. 1) Line L-5006 Line L-5006 has the following characteristics:  Phase conductors: 4 x ACAR 800 MCM  Ground wire: 1 x OPGW 96.3 mm2 (assumed data)  Number of spans: 739 (there are 738 towers)  Span length: 0.520 km (average length)  Transpositions: ABC to BCA at tower #126, and BCA to CAB at tower #361  Total length: 384.28 km  Tower resistance: 25 Ω (maximum footing impedance)  Soil resistivity: 300 Ωm (uniform soil, assumed data)

Figure 5.1 – Line L-5006 ATPDraw Data

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Line L-5006 was analyzed with and without modeling the capacitances of conductors. The PI model for lines was used [7]; a punch file was first created including the capacitances, then a second punch file was created as a copy of the first punch file and the capacitive susceptance was set to zero. The ground resistance of Carabayllo and Chimbote are assumed to be 0.5 Ω. Line L-5006 includes three line reactors with the following characteristics:  Reactors: 3 x 120 MVAr at 500 kV, each with a neutral reactor of 456 Ω  S.E. Carabayllo: 1 reactor  S.E. Chimbote: 2 reactors Line L-5006 is analyzed as energized at Carabayllo and ground faults are simulated at Chimbote. For the case including the line capacitances, the voltage at Carabayllo is set to 489.8 kV in order to get about 500 kV at Chimbote; when the line capacitances are neglected, the voltage at Carabayllo is set to 500.0 kV. The power grid is modeled at Carabayllo with a threephase short-circuit power of about 7000 MVA (actual short circuit power); this short-circuit power corresponds to about 8 kA of LLL fault, a sensitivity analysis is made when the shortcircuit power is 14000 MVA and 28000 MVA. Figure 5.2 below shows the ATPDraw model of this network equivalent:

Figure 5.2 – Carabayllo 500 kV network equivalent Table 5.1 below shows the results using ATPDraw/ATP and WinFdc: L-5006 - Line to ground fault at Chimbote 500 kV – Phase A to ground Chimbote total fault current If and grounding grid current Ig in amperes Short-circuit power

14000 MVA 28000 MVA If Ig If Ig Using ATPDraw/ATP With capacitance 1176.5 618.1 1270.3 675.2 1320.8 706.1 Without capacitance 1100.4 752.4 1179.5 806.4 1223.4 836.5 Difference in % -6.47 % 21.73 % -7.15 % 19.43 % -7.37 % 18.47 % Using WinFdc (NewCf and FdcHarmo) With capacitance 1176.5 618.1 1270.3 675.2 1320.8 706.1 Without capacitance 1100.4 752.4 1179.5 806.4 1223.4 836.5 1) The difference in % takes the values with capacitance as the exact values 2) Without capacitance the line reactors are not modeled If

7000 MVA

Ig

Table 5.1

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2) Line L-5001 Line L-5001 has the following characteristics:  Phase conductors: 4 x ACAR 550 MCM  Ground wires: 2 x ACSR Dotterel for the first 23 spans and for the last 23 spans 2 x ACSR Minorca for the intermediate 128 spans  Number of spans: 174 (there are 173 towers)  Span length: 0.453 km (average length with ACSR Dotterel – 2x23 spans) 0.534 km (average length with ACSR Minorca – 128 spans)  Transpositions: There are no transpositions  Total length: 89.19 km  Tower resistance: 25 Ω (maximum footing impedance)  Soil resistivity: 300 Ωm (uniform soil, assumed data)

Figure 5.3 – Line L-5001 ATPDraw Data Line L-5001 was analyzed with and without modeling the capacitances of conductors. The PI model for lines was used [7]; a punch file was first created including the capacitances, then a second punch file was created as a copy of the first punch file and the capacitive susceptance was set to zero. The ground resistance of Chilca and Carabayllo are assumed to be 0.5 Ω. Line L-5001 does not have line reactors. Line L-5001 is analyzed as energized at Chilca and ground faults are simulated at Carabayllo. For the case including line capacitances, the voltage at Chilca is set to 488.7 kV in order to get about 500 kV at Carabayllo; when the line capacitances are neglected, the voltage at Chilca is set to 500.0 kV. The power grid is modeled at Chilca with a three-phase short-circuit power of about 7000 MVA (about 8 kA of LLL fault) and latter the short-circuit power is increased to 14000 MVA and 28000 MVA.

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Table 5.2 below shows the results using ATPDraw/ATP and WinFdc: L-5001 - Line to ground fault at Carabayllo 500 kV – Phase A to ground Carabayllo total fault current If and grounding grid current Ig in amperes Short-circuit power

14000 MVA 28000 MVA If Ig If Ig Using ATPDraw/ATP With capacitance 3479.2 1585.6 4421.5 2015.2 5115.1 2331.3 Without capacitance 3534.3 1611.4 4502.8 2053.0 5217.1 2378.8 Difference in % 1.58 % 1.63 % 1.84 % 1.88 % 1.99 % 2.04 % Using WinFdc (NewCf and FdcHarmo) With capacitance 3479.2 1585.6 4421.5 2015.2 5115.1 2331.3 Without capacitance 3534.3 1611.4 4502.8 2053.0 5217.1 2378.8 1) The difference in % takes the values with capacitance as the exact values If

7000 MVA

Ig

Table 5.2 The ground fault current distribution analysis for L-5006 shows an error of +21.7% for the current dissipated to ground (Ig) at Chimbote 500 kV grounding grid, when the line capacitance is neglected. Nevertheless, the current Ig is low due to the great length of line L-5006. In the case of line L-5001 the error of current Ig is about +2.0%; for this line, the impact of neglecting the capacitance is small. There is an exact agreement between the fault currents If and Ig computed using WinFdc and the same currents using ATPDraw/ATP. The numerical experiments, carried out with WinFdc to perform ground fault current distribution analysis, were successful. A research effort will be carried out to add models of transformers and autotransformers for grounding analysis. VI

Conclusions

Ground fault current distribution analysis were performed using a conventional short-circuit software. The results were validated using ATPDraw/ATP software. The comparisons show an exact agreement for computing the total fault current and the current dissipated by the grounding system of the substation. The classical double side elimination method can give errors of up to 19% for the total fault current when the ground resistance of the electrodes is high. The IterNodal method gives accurate results when there are no deenergized lines. Zizzo et al. approach can give errors of up to 17% for high values of ground resistance. The numerical experiments using WinFdc to perform ground fault current distribution analysis were successful. The short-circuit calculation engine of WinFdc (NewCf) is well tested to be reused to develop a ground fault current distribution software. A research effort will be carried out to add models of transformers and autotransformers for grounding analysis. References: [1] [2]

F. P. Dawalibi, “Ground fault current distribution between soil and neutral conductors”, IEEE Transaction on Power Apparatus and Systems, Vol. PAS-99, No. 2, March/April 1980.. J. Zou, J. Lee, J. Li, S. Chang, “Evaluating ground fault current distribution on overhead transmission lines using an iterative nodal analysis”, The International Journal for Computations and Mathematics in Electrical and Electronic Engineering, Vol. 30, No. 2 2011, pp. 622-640. Downloaded from Research Gate web site.

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[3] [4] [5] [6] [7]

G. Zizzo, M. L. Di Silvestri, D. La Cascia, E. R. Sanseverino, "A method for the evaluation of fault current distribution in complex high voltage networks", Electric Power Systems Research, Accept May 7 2015, pp. 100-110. Paul M. Anderson, "Analysis of Faulted Power Systems”, The Iowa State University Press, USA, Third printing 1978. A. Rojas, C. A. Muñoz, “WinFdc 2.04 User Manual”, in Spanish, COVIEM S.A., Lima, Peru. COES SINAC web site: www.coes.org.pe. Dr. W. Scott Meyer, Dr. Tsu – hui Liu, ATP Rule Book, Canadian / American EMTP User Group, 1987-1996.

About the authors: Carlos A. Muñoz is associate professor at Universidad Nacional de Ingeniería in Lima, Peru. He is also the general manager of COVIEM S.A. COVIEM designs, builds and carries out the commissioning of electrification projects. His research interests are load-flow, short-circuit, electrical protections and grounding systems. He can be contacted at [email protected]. Alberto Rojas is a consultant engineer. He works at COVIEM S.A. in Lima, Peru, His research interests are load-flow, short-circuit, harmonics and grounding analysis; and also software development for power systems studies. He can be contacted at [email protected]. Manuscript finished on May 22, 2017.

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