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Index Terms --Ground potential rise, ground resistance,programming, protections, step voltage, touch voltage.

I. N OMENCLATURE

Ig Ground fault current.tf Fault duration time.h Grounding system depth.R g Ground resistancehs Surface material thickness.H First layer thickness.

Uniform soil resistivity.

1 First layer resistivity.2 Second layer resistivity.s Surface material resistivity.

II. I NTRODUCTION

HE simplified techniques for grounding systems design insubstations and transmission lines allow those persons

with a basic training in these type of systems, to be able tomake this work having no need of the use of more complexcalculation tools. However, in some particular cases theresults obtained by these means do not reproduce accuratelythe reality and, in general lines, the system may be oversizedto accomplish with the applying norms and recommendations.In some cases, the problems founded in the practice can’t beanalyzed using simplified techniques without incurring inimportant errors, so it can be necessary to use more complexcalculation algorithms.

L. M. Coa is with Inelectra S.A.C.A., Lechería, Anzoátegui, Venezuela(email: [email protected]).

III. T HE SOFTWARE

SPATC program was designed in Inelectra S.A.C.A. for thecalculation of the determining parameters in the design of grounding systems. This program was developed under thecalculations tool Matlab from Mathworks, Inc.

One of the most important characteristics of the SPATC isits capacity to collect the data of the grounding system from adxf file generated once made the drawing of the ground grid in

AutoCAD .The program allows the user to select a dxf file that

contains all the data relative to dimensions of the ground grid,offering a graphical interface and avoiding therefore thetedious work of having to introduce this informationmanually.

This characteristic of the program required of aconsiderable time for the establishment of a pattern within thedxf file that allowed locating the information needed for theSPATC to accomplish the calculations. It was a delicate stageof the process, considering that when drawing up a simple line

in AutoCAD , the generated dxf file is an ASCII file conformed by approximately 6 thousand lines of characters.

The SPATC (Fig. 1) offers to the user a graphical interfacethat facilitates the introduction of data for the groundingsystem simulation, allows in addition to review the obtainedresults in a organized way, including graphs and a writtenreport with the data and the results of the simulated project.

Fig. 1. The SPATC .

Comparative Study between IEEE Std. 80-2000and Finite Elements Method application for

Grounding Systems AnalysisL. M. Coa

T

1-4244-0288-3/06/$20.00 ©2006 IEEE

2006 IEEE PES Transmission and Distribution Conference and Exposition Latin America, Venezuela

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As it is appraised in Fig. 2, the SPATC allows to directlyintroduce the data in the initial screen; this screen isconformed by the following parts:

Fig. 2. SPATC main screen.

A. Suelo (Soil)This panel contains the fields corresponding to the soil

model for which is going to make the simulation. It containsthe following fields:

1) Modelo del Suelo (Soil Model) .2) Profundidad del 1er Estrato (First layer thickness) .3) Resistividad del 1er Estrato (First layer resistivity) .4) Resistividad del 2do Estrato (Second layer resistivity) .

5) Capa Adicional Superficial (Surface material) .6) Altura (Height) .7) Resistividad (Resistivity) .

B. Datos del Proyecto (Project Data)In this panel the technical data for the simulations are

introduced, more ahead that data will be also included in thefinal report.

1) Nombre del Proyecto (Project name) .2) Corriente de Falla (Ground fault current) .3) Profundidad del SPAT (Grounding system depth) .4) Conductor .

C. Resultados (Results)It contains the information referred to the results obtained

in the simulation.

IV. T HE METHODOLOGY

The program was based on the method described byMeliopoulos for grounding systems analysis [2].

Basically, it consists on getting the system partitioned inton finite conductor segments and assuming that the current oneach one of the segments is uniformly distributed along the

finite element. The transfer resistances, mutual resistances andself-resistances for the segments are represented as VDFs(Voltage Distribution Factors) and the association between thevoltage and currents in the conductor segment i, is:

n

j jtiji I RV

1

(1)

Where:

Rtij VDF between segments i and j (self is i = j ).V i Potential at conductor segment i.

I j Current flowing into earth from segment j.n Total segments number.Due to the low resistance of the conductor material,

generally it is assumed that the entire ground grid is at thesame potential; thus, the voltage of all the segments will beapproximately equal, so:

V V V V V n...210

And then, the equations for each conductor segment will beas follow:

n

j jtnj

n

j j jt

n

j j jt

I RV

I RV

I RV

1

12

11

With the equations system above, the value for the potential V is assumed to calculate the currents flowing intoearth.

Once obtained the currents, other parameters, as the groundresistance, GPR and the surface potential at any point, can becalculated:

n g I I I I

V R

...321

(2)

g g R I GPR . (3)

n

j jtAj A I RV

1

(4)

Where RtAj is the VDF (or transfer resistance) between theconductor segment j and point A.

Meliopoulos presents VDFs tabulated by transfer resistances, mutual resistances and self-resistance for conductor segments oriented along the three coordinate axesx, y or z [2].

For two-layered soil models the procedure is the same, butthe VDFs equations are relatively more complex, due to themultiples images produced by boundary conditions betweenlayers; however, the equations used for these cases start fromthe same principle described by Meliopoulos [2].

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V. T HE SIMULATION

For effects of validating the results in this document, thecases exposed in the Annex B of the IEEE std 80-2000 wereused as a departure point [1], for which there are, next,comparative tables and the corresponding graphs.

For the considered cases, the design data are the followingones:

Ig = 1908 A.tf = 0.5 s.

= 400 .m.s = 2500 .m.

hs = 0.102 m.h = 0.5 m

A. Square grid without ground rods

Fig. 6. Square grid without ground rods.

These are the obtained results using both techniques.

TABLE ICOMPARATIVE TABLE FOR CASE 1

IEEE std 80-2000 SPATC Ground resistance 2.78 2.62GPR 5304 V 4996.22 V

IEEE Standard 80 method gives in addition results for maximum allowable touch and step voltages, as well as themaximum real voltages in the system for which thecalculations are being made. For this example the followingresults were obtained:

Maximum allowable touch voltage = 838.2 VMaximum real touch voltage. = 1002.1 V

For which the SPATC offers the following graph (Fig. 7)that comprises of the set of 7 graphs included in the folder with the project results.

In Fig. 7 it is possible to observe how on the corners of the

grounding system, the maximum limit for touch voltages isviolated. Among other graphs offered by the program (Fig. 8),are those of touch voltages contours and the two-dimensionsgraphs for touch and step voltages in trajectories previouslyindicated.

Fig. 7. Maximum and real touch voltages for case 1.

Fig. 8. Graphs contained in the results folder.

Finally, another of the most important advantages of theSPATC is the possibility of obtaining a written report thatcontains the data and results of the project, specifying thetouch and step voltages with its coordinates andcorresponding status.

Fig. 9. Written report segment for the case 1.

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B. Rectangular grid with ground rodsThe following example extracted from the IEEE Standard

80 annexes consists of a mesh that, in this case, includesvertical ground rods (Fig. 10) [1].

Fig. 10. Rectangular grid with 10 m ground rods.

For which the following results were obtained:

TABLE IICOMPARATIVE TABLE FOR CASE 2

IEEE std 80-2000 SPATC Ground resistance 2.62 2.25GPR 4998.96 V 4298.1 V

The results for maximum and real touch voltages calculatedfor the system, for IEEE Standard 80 are as follows [1].

Maximum allowable touch voltage = 838.2 VMaximum real touch voltage = 595.8 V

Whereas the results obtained by the SPATC for this secondcase, are in the following graph (Fig. 11).


C. Equally spaced grid with ground rods in two-layer soil In order to illustrate the simulation of grounding systems

for two-layered soil model cases (Which apply to most of thecases in the practice), the B.5 example of the IEEE Standard80 annexes was used; this arrangement is shown in Fig. 12[1].

Fig. 12. C. Equally spaced grid with ground rods in two-layer soil.

And the results obtained from the calculation of this caseare as follows:

TABLE IIICOMPARATIVE TABLE FOR CASE 3

IEEE std 80-2000 SPATC Ground resistance 1.353 1.359GPR 2581.52 V 2592.97

It can be observed that, for this case, when the groundresistance value obtained is low, the difference on the resultsis almost insignificant. This small difference for the groundresistances brings as a consequence a proportional difference

between the GPR results for each one of the methods.

Additional, the computer program of EPRI TR-10622,applied for this case in the IEEE Standard 80 [1], gives thefollowing results for the critical voltages.

Em = 49.66 % of GPR Es = 18.33 % of GPR

While the SPATC offers Fig. 13 as a result to evaluatetouch voltages (These are, in fact, the most critical potentialdifferences in a grounding system design) in the simulatedsystem, in addition to the two-dimension graphs for touch andstep voltages in trajectories previously specified.

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VI. A CKNOWLEDGMENT

The author gratefully acknowledges the contributions of S.Meliopoulos for his previously research on this topic.

VII. C ONCLUSIONS

One of the differences between both previously studiedmethods is the form in which the critical voltages for thecalculated system are given. During the development of theSPATC a great importance was paid on knowing not only thevalue for the maximum real touch voltage in the system, butalso these voltages behavior in all the area occupied by thesimulated ground grid, since this allows to locate points of special interest on the corresponding planes of the facilities, insuch a way that is possible to take the necessary preventiveactions at the time of execute a grounding system design.

It can be observed in addition, that exists a differences pattern between the results of ground resistance and thereforeof GPR; the values given by the method proposed by IEEEStandard 80 are generally more pessimists, even when thisfactor is not necessarily unfavorable it can take the design toan oversizing.

Also it was stated, by means of the simulations, the factthat the most critical touch voltages can be found in thecorners for rectangular meshes cases, as observed for case 1 inFig. 7.

Finally it is possible to affirm that the finite elementsmethods represent without a doubt a very effective instrumentfor the grounding systems study, since they offer the

possibility of making a closest to the reality detailed analysis.In spite of involving more complex algorithms of calculationsthat requires the use of computational tools, is necessary toconsider that, nowadays, needing a computer is not really alimitation.

VIII. R EFERENCES

[1] IEEE Guide for Safety in AC Substation Grounding , IEEE Std 80-2000(Revision of IEEE Std 80-1986). New York, USA. 2000.

[2] S. Meliopoulos, Power System Grounding and Transients , MarcelDekker, Inc. New York, USA. 1998.

IX. B IOGRAPHY

Luis Coa was born in Barcelona,Anzoátegui - Venezuela, on May 24, 1983.He graduated from the Universidad deOriente.

His employment experience includes

Inelectra, S.A.C.A. His special field of interest includes programming, groundingsystems, digital systems.

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