Comparative Study between IEEE Std. 80-2000

and Finite Elements Method application for

Grounding Systems AnalysisL. M. Coa

Abstract- This paper presents a brief compilation of typicaland particular cases of grounding systems calculation usingprocedures proposed by IEEE std 80-200 [1], simulated bymeans of a software developed under the mathematical toolMatlab, based on the Finite Elements Method [2]. This studyconsists, basically, of tables and graphics that shows a series ofinteresting results and offer a reliable and practical instrumentfor the grounding systems design.

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

I. NOMENCLATURE

1g Ground fault current.tf Fault duration time.h Grounding system depth.Rg Ground resistancehs Surface material thickness.H First layer thickness.p Uniform soil resistivity.Pi First layer resistivity.P2 Second layer resistivity.Ps Surface material resistivity.

II. INTRODUCTIONT HE simplified techniques for grounding systems design in

substations and transmission lines allow those personswith 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., Lecheria, Anzoategui, Venezuela(email: luis.coaginelectra.com).

III. THE SOFTWARE

SPATC program was designed in Inelectra S.A.C.A. for thecalculation of the determining parameters in the design ofgrounding 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 inAutoCAD.

The program allows the user to select a dxf file thatcontains 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 linein AutoCAD, the generated dxf file is an ASCII file conformedby 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.

1-4244-0288-3/06/$20.00 ©2006 IEEE

2

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:

rig. z. 3IAI C 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)2)3)4)5)6)7)

Modelo del Suelo (Soil Model).Profundidad del ler Estrato (First layer thickness).Resistividad del ler Estrato (First layer resistivity).Resistividad del 2do Estrato (Second layer resistivity).Capa Adicional Superficial (Surface material).Altura (Height).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 (Groundfault 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. THE 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

Vi==RtjIjj=l

(1)

Where:Rtu VDF between segments i andj (self is i =j).Vi Potential at conductor segment i.I1 Current flowing into earth from segmentj.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:

VO = V1 = V2 Vn V

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

n

V = RtljIjj=1n

V = YRt2jIjj=1

n

V = E, RtnjIjj=1

With the equations system above, the value for thepotential 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:

R = V9 II +I2 +I3 + ...+In

GPR = Ig9Rgn

VA = jRtAJIjj=l

(2)

(3)

(4)

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

Meliopoulos presents VDFs tabulated by transferresistances, mutual resistances and self-resistance forconductor 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].

3

V. THE 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.p 400 Q.m.Ps 2500 Q.m.

sh = 0.102m.h =0.5m

A. Square grid without ground rods. M ... ..... 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.

vdltaj-s tie Tolue an el Perirretro de la lalla

1cO

bOcz

0,c

?ni

100

Fig. 7. Maximum and real touch voltages for case 1.H.... ......i. .........I....l...

...~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...~.... ..

I.-..........-- U.......... SE

I | I|ii l.. ..._lugg

I ! 1Fig. 6. Square grid without ground rods.

These are the obtained results using both techniques.

TABLE ICOMPARATIVE TABLE FOR CASE 1

IEEE std 80-2000 SPATCGround resistance 2.78 Q 2.62 QGPR 5304 V 4996.22 V

IEEE Standard 80 method gives in addition results formaximum 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 voltageMaximum real touch voltage.

838.2 V1002.1 V

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

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

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.

Proyecto ej1(1) Fecha: 25/3/2006 Hora: 17:53:33If: 1908[Amps]t: 0.5[seg]Resistividad 1: 400 [Ohm-m]Altura de Capa Adicional en Superficie: 0.102[m]PLesistividad de Capa Adicional en Superficie: 2500[Ohm-m]Diametro de Conductor: 0.01 [m]Resistencia de Malla: 2.6186[Ohms]GPR: 4 996. 222 [Volts]Longitud aproximada del conductor: 1540 [m]

Reporte de Voltajes de Toque y Voltajes de Paso

X [mr] Y [mrr] St [v] Status

0.00 0.00 941.39 EXCEDE1.75 0.00 745.45 OK3.50 0.00 658.59 OK5.25 0.00 547.41 OK

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

0.00 36.801 .75 31.153.50 108.755.25 20 7 28

OKOKOKOK

duo

700

ao

Y [mY] v s [ V] Statu s

4

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

80 annexes consists of a mesh that,vertical ground rods (Fig. 10) [1].

84fm

in this case, includes

- -- n-TI

I

C. Equally spaced grid with ground rods in two-layer soilIn 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].

44 i SO.gm

Ew

Rectangular grid with 10 m ground rods.

For which the following results were obtained:

TABLE IICOMPARATIVE TABLE FOR CASE 2

IEEE std 80-2000 SPATCGround resistance 2.62 Q 2.25 QGPR 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].

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

And the results obtained from the calculation of this case

are as follows:

TABLE IIICOMPARATIVE TABLE FOR CASE 3

Maximum allowable touch voltageMaximum real touch voltage

838.2 V595.8 V

IEEE std 80-2000 SPATCGround resistance 1.353 Q 1.359 QGPR 2581.52 V 2592.97

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

V ltFje5 de ToqLe en el Pe-imc -ro do la Mhalla

*300

1cL 5

:: 400-

z00

1c

c

Soo

200

100

Fig. 11. Maximum and real touch voltages for case 2.

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 differencebetween 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

Es49.66 % of GPR18.33 % 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.

I

Fig. 10.

.r~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-- loooow -M

j

0 .1 -"IrI --I

5

V;oltaju- d- Toqje en PI PPerimi*ot du la M1ala

IX. BIOGRAPHY

Luis Coa was born in Barcelona,1Lw*- Anzoategui Venezuela, on May 24, 1983.

He graduated from the Universidad deOriente.

His employment experience includesInelectra, S.A.C.A. His special field ofinterest includes programming, groundingSystems, digital systems.

ar)40~ 60

4020

Fig. 13. Maximum and real touch voltages for case 3.

VI. ACKNOWLEDGMENT

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

VII. CONCLUSIONSOne of the differences between both previously studied

methods 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 ofspecial 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 differencespattern 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 thepossibility 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. REFERENCES[1] IEEE Guide for Safety in AC Substation Grounding, IEEE Std 80-2000

(Revision of IEEE Std 80-1986). New York, USA. 2000.[2] 5. Meliopoulos, Power System Grounding and Transients, Marcel

Dekker, Inc. New York, USA. 1998.