surface potential calculation for grounding grids

First International Power and Energy Coference PECon 2006 501November 28-29, 2006, Putrajaya, Malaysia

Surface Potential Calculation for GroundingGrids

Sherif Ghoneim', Holger Hirsch2, Ahdab Elmorshedy3, Rabah Amer4

'Email:,

l 2Institute of Power Transmission and Storage (ETS), University of Duisburg-Essen, Germany3'4Faculty of Engineering, Cairo University, Egypte;2 .3

o .; 4rabah amer

Abstract: One of tasks of the grounding systems isto maintain the voltage rise due to dischargingfault current into grounding grids at the minimumvalue to insure the safety of public and personnel.The objective of the paper is to make a comparisonbetween the addition of horizontal rods andvertical rods to the grounding grids to improve theperformance of it. A Boundary Element Approachuses to get the numerical computation ofgrounding system analysis such as the equivalentresistance and the distribution of potential on theearth surface due to fault currents. This studydescribes the importance of vertical ground rodsnot only decrease the grounding grid resistance butalso reduce the step and touch voltages.

Index terms: Grounding grids, Boundary Elementmethod, Computer methods for groundinganalysis, System protection.

I. INTRODUCTIONA safe grounding design has two main objectives:

* To carry the electric currents into earth undernormal and fault conditions withoutexceeding operating and equipment limits oradversely affecting continuity of service.

* To ensure that the person in the vicinity ofgrounded facilities is not exposed to thedanger of electric shock.

The problem under consideration is that the safetyvalues of the step and touch voltages for the humanthat in the vicinity of the grounded facilities [1].

Ground grids are considered an effective solutionfor grounding systems for all sites which must beprotected from lightning strokes such as,telecommunication towers, petroleum fields,substations and plants. Ground grids produce an equi-potential surfaces and should provide a very smallimpedance but the ground grids are consideredcomplex arrangement and many research efforts havebeen made to explain the performance of groundingimpedance of its under lightning and faultconditions[2,3]. Vertical ground rods is connected tothe grid to have low values of ground resistance whenthe upper layer of soil in which the grid is buried, is ofmuch higher resistivity than that of the soil beneath.

The dissipation of the electrical current into thesoil is a well-known phenomenon which equations canbe stated from Maxwell's Electromagnetic Theory [4].Nevertheless, their application and resolution for thecomputing of grounding grids of large installations inpractical cases present some difficulties.

First, no analytical solutions can be obtained formost of real problems. On the other hand, thegeometry of the grounding grids in main earthingsystems (a mesh of interconnected bare conductorswith a relatively small ratio diameter-length) makes itvery difficult to use standard numerical methods: Theuse of techniques commonly applied for solvingboundary value problems in engineering, such as finiteelements or finite differences, is indeed extremelycostly since the discretization of the domain (theground excluding the electrode) is required. Therefore,obtaining sufficiently accurate results should implyunacceptable computing efforts in memory storageand CPU time.

In the last decades, some intuitive techniques forgrounding grid analysis such as the Average PotentialMethod (APM) have been developed. A newBoundary Element Approach has been recentlypresented [4-6] that includes the above mentionedintuitive techniques as particular cases. In this kind offormulation the unknown quantity is the leakagecurrent density, while the potential at an arbitrarypoint and the equivalent resistance for grounding gridsmust be computed subsequently.

Studying the effect of vertical grounding rods thatadd to the grounding grid on earth surface potential(ESP) is investigated in this paper. This studydescribes the importance of vertical grounding rodsnot only decrease the grounding grid resistance butalso reduce the step and touch voltages.

II. METHOD OF CALCULATIONThe results in this paper are produced by the

techniques that have been implemented in a computeraided design (CAD) system for grounding grids ofelectrical substations called TOTBEM [4]. Theproblem focused in this paper is which the best, theaddition of vertical rods to the grounding grids orhorizontal rods to get the best performance ofgrounding grids.

The characteristics of the grid are 1OxI0 m2, theradius of the grid conductor ( r ) is 5 mm, the length ofvertical rods ( Lvr ) is (land 2m), its radius of ( r, ) is(5 and 8 mm) , the grid depth (h) is 0.5 m, the

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resistivity of the soil (p) is 100 Q.m, and the totalground potential rise (GPR) is defined as 1. Thegrounding resistance has two components: thedissipation resistance which is the resistance of theground between the ground electrode and referenceground and the resistance of the metal parts of theground electrode and the grounding conductor. Thelast resistance is usually much smaller than thedissipation resistance, then the ground resistance isequal to the dissipation resistance only.

If

-Vg= GP

Fig. 1. Illustration of the grounding system (Vg is theground potential rise (GPR), If is the fault current, Vtis the touch voltage, Vs is the step voltage and h is theburial depth of the grid).

if

(c) ~~~~~~~(d)

voltage is defined as the maximum touch voltage to befound within a mesh of a ground grid. The maximumtouch voltage is the difference between the GPR andthe lowest potential in the grid boundary [7]. Themaximum percentage value of Vto011h is given by

Vtuh00:::::Vgrid Vmin"oVtoucho gri m x 100 (1)Vgrid

Where, Vgrid is the ground potential rise (GPR), whichequal the equivalent resistance of grid multiplies in thefault current and Vmin is the minimum surfacepotential in the grid boundary.

The step voltage is the difference in surfacepotential experienced by a person bridging a distanceof 1 m with his feet without contacting any othergrounded object [7]. Furthermore, the maximum stepvoltage of a grid will be the highest value of stepvoltages of the grounding grid. The maximum stepvoltage can be calculated by using the slope of thesecant line.

Figures 3. a, b and c. illustrate the fact that thenumber of meshes has a significant effect in reducingthe touch and step voltage. The surface potential incase of 36 meshes grid is much flatter than that gridwith 4 and 16 meshes and hence the values of step andtouch voltages are lowest. Also it is shown in figure 4that an increase in the number of meshes makes thecurve of earth surface potential much flatter and then areduction in the grid resistance, touch and stepvoltages, also it is seen that the max touch voltagemoves towards the corner mesh in the grid.

I).1 4

Fig. 2. Different configurations of grids. (a) 4 meshes.(b) 16 meshes. (c) 36 meshes. (d) 4 meshes withvertical rods.

III. COMPUTATION RESULTSIn this section, the 3D graphs explain the earth

surface potential along diagonal profile for the squaregrid with different number of meshes.

It is clear that the ground potential rise (GPR) aswell as distribution of the earth surface potential(ESP) during the current flow in the grounding systemare important parameters for the protection againstelectric shock. The distribution of the earth surfacepotential helps to determine the step and touchvoltages, which are very important for human safe.

By definition, the touch voltage is the differencebetween the ground potential rise (GPR) and thesurface potential at the point where a person isstanding while at the same time having his hands incontact with a grounded structure, and the mesh

Fig 3.a. 4 meshes.

.-

-1.

(t .\ 1

/,q00 ,,

Fig. 3.b. 16 meshes.

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addition of vertical rods plays an important part to getthe same results and decreases the cost of design.

No of meshes 36 4No. of vertical rods 0 9

Vertical rods length (m) 0 2Total grid length (m) 140 78

Resistance (Q) 4.26 4.29GPR (V) at 100 A 426 429

Max touch voltage 0/, GPR 25.0 31.1Max touch voltage (V) 106.5 133.419Max step voltage 00 GPR 16 16

Table 1Fig. 3.c. 36 meshes.

P-.ct5

c)PsHv:

1 Mesh4 Mesh16 Mesh36 Mesh

-20 -10 0 10Distance from the center of grid (m)

"Diagonal Profile".

20

C.3.;zuC)P-.u0Iz!.-o;zV.

7s

44

450

400

y350

300

-wthout rods-wth rods

250-

200-

150 -

100

50

-20 -10 0 10Distance from the center of grid (m) "

Diagonal Profile".

Fig. 4. Effect of the number of meshes on the earthsurface potential.

IV. EFFECT OF GROUND RODSGround rods are one of the most important

solutions when the upper layer of the soil in which thegrid is buried, is higher resistivity than that of thedown layer.

This section discusses the effect of ground rodcharacteristics (length and radius of the rod) on earthsurface potential. It is clear from figures 5, 6 and 7that the ground rods cause a reduction in the earthsurface potential, moreover the reduction of the gridresistance, but no significant change in the earthsurface potential when the ground rod radiusincreases.

The following table 1 explains that an addition ofground rods with 2m lengths to the 4 meshesgrounding grid for the case of study gives nearestresults when add the horizontal conductors to the same

grid. The difference in the max touch voltage betweenthe two cases is 26.919 V but the difference in thetotal length of conductors is 62 m as shown from thetable and hence, an increase in the cost of designoccurs when add horizontal rods. Therefore the

Fig. 5. Effect of the vertical rods on the earth surfacepotential at the same fault current. (16 meshes)

450

400

ct ~~~300-4-y

_ / 'tt250

ci ~~~200

150

100

50-Lvr =2 m

-Lvr =1 m

-20 -10 0 10Distance from the center of grid (m) "

Diagonal Profile".

20

Fig. 6. Effect of the vertical rod length on the earthsurface potential at the same fault current. (16 meshes)

I-F.1

V,

20

, ,

1

ct

504

0

0ta)

450

350

300

250

200

150

100

50As

-rvr= 0.008 m-rvr= 0.005 m

-20 -10 0 10 20

Distance from the center of grid (m) "DiagonalProfile".

Fig.7. Effect of the vertical rod radius on the earthsurface potential at the same fault current. (16 meshes)

V. EFFECT OF GRID DEPTHThe results explained that the grid depth plays an

important role in decreasing the grid resistance and theearth surface potential, this fact appears in figure 8.

Depth = 0.5m450 Depth = 0.8m

Depth = 1 m

50-

300o ~~~~250-

o200150-

100

50

-20 -10 0 10 20Distancefrom the center of grid (m)

"diagonal profile".

Fig. 8. Effect of grid depth on the earth surfacepotential at the same fault current. (16 meshes)

VI. CONCLUSIONSThis paper aims to explain the role of the vertical

ground rods that add to the grounding grid in reducingthe value of grid resistance, step and touch voltages toa value that is safe for public and human. Additionalvertical ground rods gives nearest results to thatresults when add the horizontal rods to the same grid,then the addition of vertical rods to the grounding gridgives a good performance and decrease the cost ofdesign. The grid resistance and ground potential risedecrease with the increase of the burial depth andnumber of meshes of the grounding grids.

VII.ACKNOWLEDGEMENTThe authors gratefully acknowledge the help in

the grounding analysis of Prof. Ignasi Colominas fromthe Civil Engineering School of the University of LaCoruna (Spain).

VIII. REFERENCES

[1] S. Benda, "Earthing and Bonding in LargeInstallations", ABB Review, No. 5, pp. 22-29,1994.

[2] R. Verma and D. Mukhedkar, "FundamentalConsiderations and Impulse Impedance ofGround Grids", IEEE Transaction on PowerApparatus and Systems, Vol. Pas-100, pp. 2053-2059, March 1981.

[3] F. Menter and L. Gercev, "EMTP-Based Model ofGrounding System Analysis" IEEE Transactionson Power Delivery, Vol. 9, pp. 1838-1849, Oct.1994.

[4] I. Colominas, F. Navarrina, M. Casteleiro, "ABoundary Element Numerical Approach forEarthing Grid Computation", ComputerMethods in Applied Mechanics &Engineering, vol. 174, pp 73-90, 1990.

[5] I. Colominas, F. Navarrina, M. Casteleiro, "ANumerical Formulation for Grounding Analysisin Stratified Soils", IEEE Transactions on PowerDelivery, vol. 17, pp 587-595, April 2002.

[6] F. Navarrina, I. Colominas, " Why Do ComputerMethods for Grounding Analysis ProduceAnomalous Results?," IEEE Transaction onpower delivery, vol. 18, No. 4, pp 1192-1201,October 2003.

[7] IEEE Std.80, "IEEE Guide for safety in ACsubstation grounding", New York, 2000.

IX. BIOGRAPHIESSherif Ghoneim (PhD student): Received B.Sc. andM.Sc. degrees from the Faculty of Engineering atShoubra, Zagazig University, Egypt, in 1994 and2000, respectively. Starting from 1996 he was ateaching staff at the Faculty of Industrial Education,Suez Canal University, Egypt. Since end of 2005 he isa guest researcher at the Institute of Energietransport-und Speicherung (ETS) of the University of Duisburg-Essen, under the supervision of Prof. Dr.-Ing. HolgerHirsch. His research focuses in the areas of earthsurface potential calculation and improving designs ofgrounding grids.

Holger Hirsch (Prof. Dr.-Ing.): After his PhD fromthe University of Dortmund, Germany, he had workedas head of EMC Test NRW GmbH, Dortmund,Germany. He became full Professor at the sameuniversity in 1998 where he taught theoretical andpractical EMC subjects until 2003. Since beginning2003 he is the head of the Institute ofEnergietransport- und Speicherung (ETS) of theUniversity of Duisburg-Essen, Germany, where he is

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engaged in the teaching, testing and measurementtechniques of EMC and HV systems and equipment.He is a member of different workgroups of CISPR,IEC, ETSI and DKE.

Ahdab Elmorshedy (Member IEEE): received theB.Sc., M.Sc. and Ph.D. in 1971, 1974, and 1978respectively, in Electrical Engineering, from CairoUniversity, Egypt. Since 1971, she joined the facultyof Electrical Engineering at Cairo University, Egypt asa Teaching staff. During the academic years of 1979to 1981, she was a research scientist in the Departmentof Electrical Engineering, College of Engineering atOhio State University, Columbus, Ohio, U.S.A. Since1988 she was a Professor at the Department ofElectrical Engineering, Cairo University. Her researchactivities include grounding, protection and safety ofpower systems, over-voltage transients, and pollutionof insulators.

Rabah Amer: received the B.Sc., M.Sc. and Ph.D. in1975, 1979, and 1983 respectively, in ElectricalEngineering, from Cairo University, Egypt. Since1975, he joined the faculty of Electrical Engineering atCairo University, Egypt as a Teaching staff. Since1994 he was a Professor at the Department ofElectrical Engineering, Cairo University. His researchactivities include grounding, gas discharge, electricand magnetic field calculations, prediction ofpolluted insulators flashover using laser methods,lightning protection of petroleum companies, andoverhead transmission line design and commissioning.Also, he is a consultant for petroleum, industrial andelectrical companies.