safety parameters of grounding devices at an electric power plant

7/29/2019 Safety Parameters of Grounding Devices At An Electric Power Plant

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Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 2, No 1, February 2013

1

SAFETYPARAMETERS OF GROUNDING DEVICES AT

AN ELECTRIC POWERPLANT

Yury Chikarov1 Tek Tjing Lie1 and Nirmal Nair2

1Department of Electrical and Electronic Engineering, Auckland University of

Technology, Auckland, New [email protected], [email protected]

2Department of Electrical and Computer Engineering, University of Auckland,

Auckland, New [email protected]

ABSTRACT

Grounding provides safety and in some cases a return circuit for load currents and also an uniformdistribution of the voltage on the surface of the earth at power plants. If grounding conductors are

damaged, it may cause unintended protective relay operation causing feeders to be tripped. It can also

result in failure of the grounding device itself, secondary circuits cables and structural elements. The

circuits may attain unacceptable voltages when short-circuit fault currents occur in these devices. This

paper proposes analysis of possible values of safety in terms of Touch and Step Voltage under malfunctions

of electric power plants and damaged horizontal elements of the grounding devices. The information

described in the article can be referred to an electric power plant with the grounding device made as a grid

with a number of meshes in it.

KEYWORDS

Grounding, Safety, Touch and Step Voltage, Distribution, Short Circuit.

1.INTRODUCTION

The grounding grid elements are hidden in depth of the soil structure and because of influencingfactors like soil structure, dampness, presence of salts and acids, electric corrosion, freezing

process etc., some elements may become damaged. This can lead to failures in operation ofsecondary commutation circuits in case of short circuits under abnormal operating conditions and

also to high voltage hazards on electrical equipments frames, damages of insulation, thermal

destructions that can potentially cause hazardous situation in and around the electric power plant.

The main parameters of safety for electric power plants are the mesh (touch) and step voltages[1]. Value of the second criterion is almost always lower than the first one [2]. But it is necessary

to take into account Step Voltage in situations when a person does not touch any enclosure of

equipment but is standing on the conductive earth. More over in case of horizontal elementsdamages the uniform distribution of the potential on the surface of the earth is may not bemaintained which can lead to hazardous situation for people.

During abnormal situations such as insulation failures of equipment, lightning strokes and etc.,

high currents flow to the earth through the grounding grid. The highest value of voltage will be on

the edge elements of the grounding device. In practice, these high values are not experienced by a


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person standing on the top stratum of soil. Since the earth is a conductor, some of the energy willstill be perceived on the surface of earth by people standing on it (see Figure 1). Thus, the touch

and step voltages will have other values as explained below.

Fig. 1. Touch and Step Voltage Exposure

It is shown in the Figure 1 that if the horizontal elements of the grid do not have any failures, thepotential distribution curve within a territory of the electric power plant will have an ideal

distribution. Thus, the magnitudes ofVtouchand Vstep will not be dangerous for staff or equipment(shown as Vtouch1 and Vstep1 in Figure 1). Ideally the best option is to have a straight line as thepotential distribution curve but it will take a lot of labour and capital investment. On the other

hand if damaged elements occurred, the Vtouch and Vstep values will be very high and not safeanymore (shown as Vtouch2and Vstep2 in Figure 1). From Figure 1, the dashed lines are for the casewith damaged horizontal element which affects the overall integrity of the grounding system.

The mathematical models of the current and potential distribution in the grounding grids are

developed based on the graphs theory and matrix algebra [3, 4]. These are - a versatilecombination of tools for electric networks calculations and can be used for the grounding grids as

well.

The main contribution of this paper is to analyze and present the most hazardous potentials that

can arise in the grounding grids and on the surface of earth due to failures of its horizontalelements. The information presented in this paper describes the worst case scenario of thepotential distribution on the surface of earth in most hazardous regions of the grounding grid.

2.NETWORK MODEL AND ITS ANALYSIS

There are a number of mathematical [5-8] and computer [9, 10] models of the processes withrespect to the grounding grids potential exposure to touch and step potentials. More often they are

based on the circuit theory or electromagnetic field theory of the processes. The commonapproach of these models is to firstly calculate currents following which an evaluation of the

potentials above the grounding grids conductors can be made. It is possible to evaluate groundingperformance parameters such as current distribution, potentials and touch and step voltages at

various parts of a power plant. However there are no specifics about possible changes of the earthsurface potentials in case of breaks or damages to the bonding of the horizontal elements.

All horizontal and vertical elements shown in Fig. 2 represent not only self resistance ofconductors itself (steel, copper, copper clad etc.) but also lumped resistances to earth of the buried

in soil conductors. It consists of three parts: (i) a self resistance of the conductor material, (ii)


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contact resistance between material of the element and soil and (iii) soil resistivity itself. Thus,the full resistance to the current which leaks from the element to earth can be presented as

soilcontmeverhor RRRR ++=.).( . (1)

Please note the first two elements (Rme and Rcont) have very small values and often can be

neglected.

Fig. 2. Equivalent scheme of the horizontal and vertical elements in the soil

In accordance with standards [1], [12-13] and [14] the resistance of the vertical and horizontal

elements in the soil can be calculated as

+

++

=

tl

tl

d

l

l

R

ver

ver

ver

ver

ver

vever

7

74ln5,0

2ln

2 .

.

.

.

.

...

, (2)

where ..ve equivalent resistance of earth for the vertical elements, m; t depth of thegrounding grid; lver. length of the vertical element; dver. diameter of the vertical element.

.

2

.

.

... ln

2 hor

hor

hor

hehor

dt

l

l

R

=

, (3)

where ..he equivalent resistance of the earth for the horizontal elements, m; lhor. length of the

horizontal element, dhor diameter of the horizontal element.

The resistance of earth Rsoil depends on the resistivity of different soil stratums (1, 2, 3 etc.).

The number of layers (stratums) can differ from one area to another depending on the soil

structure. With an acceptable level of accuracy often multilayer structure of the earth issubstituted with its two-layer soil equivalent (1, 2). Eventually, the resistivity of the both layers

(1, 2) in the mathematical model is usually replaced with the resistivity of so calledequivalent earth or its analogue (depending on techniques).

For the purpose of modeling it is assumed that the structure of non-homogeneous earth is a two-

layer soil. A real structure of soil is a multilayer structure. Each layer (stratum) has its owncharacteristic. To have the most accurate calculations one can operate with all layers of the soil. It

will demand not only a lot of time but also it is very laborious. On top of that, it will not give a


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dramatic improvement in terms of accuracy. It is a common practice [1] to substitute thismultilayer structure by a two-layer soil. The length of the vertical elements is 3 meters with a

diameter 16 mm. The length of the horizontal elements is 5 meters. Horizontal elements arelocated in the upper layer of earth 1, while vertical elements cross both layers 1 and 2.

Resistivity of the soil stratums are 1=250 m and 2=30 m respectively. The thickness of the

upper layer (h1) is 2 m. The thickness of the lower layer (h2) is

. The values of the elementsdimensions and soil characteristics were chosen as one of the common used examples.

After substitution all values in above-described equations one can obtain

Rhor. = 45.048 ,Rver.= 25.741 .

As one can see values of the resistance mainly depend on the resistivity of soil so they may vary

in a wide range of magnitudes depending on local characteristic of the soil structure.

Computer simulation studies were conducted using a well established MULTISIM software

package. Figure 3 depicts the circuit used in the simulation studies. Figure 4 depicts theequivalent circuit and the values ofRhor and Rver are calculated using equation (2) and (3)

respectively.Voltages at nodes of the circuit were measured by means of voltmeters as shown inFigure 4.

k

l

c

a

b e

f

g

h

i

j

I

q r s

n o p

m

t

Fig. 3. Circuit for Multisim Software Simulation

Fig. 4. Equivalent Circuit for Multisim Software Simulation


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Node Potential, V Potential, % Node Potential, V Potential, %

a 2362 100 k 29.1 1.2

b 561 24 l 37.4 1.6

c 561 24 m 29.1 1.2

e 218 9 n 180 7.6

f 507 22 o 93 4

g 218 9 p 43.8 1.8

h 71.4 3 q 180 7.6

i 120 5 r 93 4

j 71.4 3 s 43.8 1.8

TABLE1.VOLTAGE DISTRIBUTION IN THE NODES OF THE GROUNDING DEVICE

As one can see the maximum voltage is at node a and then decreases with the distance from thisnode.

The simulation results show that the magnitudes of current and voltage at points on the gridfarther than those taken into account were less than 0.5% of the initial value (3 kA) so they can be

neglected

The major part of the current dissipates in the vicinity of 6 meshes from the point of injection.

The potential level at the node t for instance equals 9V which is just 0.38% of the maximumpotential.

As indicated in [1] and [11] the corner mesh voltage is higher than in the centre mesh and it is

considered to be the worst-case scenario. This is because the grounding grid has less elementsjoined together at this point which results in increase of resistance and voltage. Thus for futurecalculation of the worst safety scenario the point of current injection was chosen at node a as

shown in Figure 5.

The example of six meshes grounding device for analysis is presented in Figure 5. The graph foranalysis is shown in Figure 6. This number of meshes has been chosen as an optimal number forcalculation due to the above-described features of the current and potential distribution.


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Fig. 5. Scheme of the Grid for Analysis (I= 3000 A)

After determining the reference node which is node d (remote earth), matrix analysis of the

scheme is conducted. Matrix analysis is used in order to simplify the calculation process becauseof the large number of the branches and nodes of the scheme.

Fig. 6. Graph of the Grid for Analysis

By using graph theory, Kirchoffs and Ohms Laws, matrices M and N are formed whereM is the matrix of branches joints at the nodes and N is the matrix of branches joints in the

independent loops.

The number of rows in matrix M equals to the number of nodes in the scheme except the

reference node. The number of columns in the matrix determines by the number of branches in

the circuit.


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The number of rows in matrix N is the same as the number of loops in the scheme. The number

of columns in the matrix determines by the number of branches in the circuit.

The next step is to develop impedances Zn or admittances Yn matrices of the horizontal and

vertical elements joined at the nodes of the grounding device.The matrix of admittances

nY of the horizontal and vertical elements joined at the nodes

of the grounding device is as follows:


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The mutual impedance among elements in the grid can be presented by multiplication factor " F"from [15].

( ) 14ln4

2

1

+

+=

al

dlN

F s , (4)

where N the total number of rods in rodbed; ds the smallest distance between the adjacentrods, m; l the length of each conductor; and a radius of the conductor.

This Ffactor increases the resistance of each element of the grid or finally the value of voltage onthe grid. It happens because electromagnetic fields of all elements of the grid influence on each

other due to the small distance between them as shown in Figure 7. Thus, it artificially increasesthe value of resistance of each element.

Fig. 7. Influence of the elements on each other

Setting the value of the short circuit current injected in the grid Isc, the current distribution ofindividual elements and the voltage at the grid nodes can be determined.

There are two possible ways to calculate the current and voltage distributions through the

elements of the grounding device. First, determine nY after that, inverse matrix1

nY .

From the above-mentioned matrix, one can define the voltage drop from each of the groundingdevices nodes to the reference node d.

JYU n&& =

1, (5)

where J& is the matrix of currents injected in the grounding devices nodes. In this case, it is just


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one node (a) where we inject the short circuit currentIsc.

After determination of the matrixs

U& components, it is necessary to define inverse diagonal

matrix of the elements impedances1

bZ . This matrix is obtained from the above calculated

values of the elements resistances. So that the final equation for the current distributioncalculation can be written as follows:

= UMZI

T

bb&& 1

(6)

The second way of the currents determination is to create a combine matrix A as follows:

=

bZN

MA . (7)

The last step is to calculate current in the elements as follows:

JAIb&& =

1

. (8)

The results of current and potential distribution based on graphs theory and matrix analysis arepresented in Table 2 and Table 3 respectively.

The values in Table 2 and Table 3 represent voltages and currents in the grid of the groundingdevice in soil. Despite the fact that these values can have high magnitudes (kV) inside of the soil

there will be lower values on the top of the soil structure due to the resistivity of earth. They also

may appear to be dangerous for staff and equipment especially in case of damaged horizontalelements of the grid.

Node Potential, kV Node Potential, kV

a 29.283 i 0.975

b 7.150 j 0.975

c 7.150 k 0.602

e 1.838 l 0.421

f 2.827 m 0.502

g 1.838 n 0.421

h 0.602 - -

TABLE 2. Voltage Distribution in The Nodes of the Grounding Device


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Branch Number Current, kA Branch Number Current, kA

1 0.492 16 0.041

2 1.138 17 0.110

3 0.492 18 0.0124 0.118 19 0.010

5 0.278 20 0.038

6 0.096 21 0.016

7 0.027 22 0.019

8 0.071 23 0.027

9 0.019 24 0.071

10 0.004 25 0.010

11 0.023 26 0.038

12 0.096 27 0.020

13 0.118 28 0.004

14 0.278 29 0.02

15 0.041 30 0.012

- - 31 0.016

TABLE3.CURRENTS DISTRIBUTION THROUGH THE GROUNDING DEVICE ELEMENTS, KA

3.TOUCH STEP AND VOLTAGE ANALYSIS

The actual mesh voltageEm (maximum touch voltage) [1] can be evaluated as

m

Gimm

L

IKKE

=

. (9)

The geometrical factor Km, is as follows:

+

++

=

)12(

8ln

48

)2(

16ln

2

1 22

nK

K

d

h

dD

hD

dh

DK

h

iim

(10)

For grids with ground rods along the perimeter, or for grids with ground rods in the grid corners,

as well as both along the perimeter and throughout the grid area,

1=iiK , (11)

0

1hhKh +=

(12)

where h0 = 1m (grid reference depth).

Using four grid shape components, the effective number of parallel conductors in a given grid, n,


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can be made applicable to both rectangular and irregularly shaped grids that represent the numberof parallel conductors of an equivalent rectangular grid:

dcba nnnnn = , (13)

where

p

Ca

L

Ln = 2

(14)

and nb = 1 for square grids; nc = 1 for square and rectangular grids; nd= 1 for square, rectangular,

and L-shape grids.

Otherwise,

A

Ln

p

b

=4 , (15)

yx LL

A

yx

cA

LLn

=

7.0

, (16)

22yx

md

LL

Dn

+

=, (17)

where, LC is the total length of the conductor in the horizontal grid in m, Lp is the peripherallength of the grid in m,A is the area of the grid in m

2,Lx is the maximum length of the grid in the

x direction in m,Ly is the maximum length of the grid in the y direction in m,Dm is the maximum

distance between any two points on the grid in m,D is the spacing between parallel conductors in

m,His the depth of the grounding grid conductors in m, dis the diameter of the grid conductor inm.

The irregularity factor, Ki, used in conjunction with the above defined n is:

nKi += 148.0644.0 . (18)

For grids with ground rods in the corners, as well as along the perimeter and throughout the grid,

the effective buried length,Lm, is:

R

yx

rCm L

LL

LLL

+

++=22

22.155.1, (19)

whereLris the length of each ground rod in m.

Substituting values in the above described equations one can obtain:


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12

m2.157391515

322.155.190

22=

+

++=mL

Since the shape of the grounding device example for calculation is not square: nd = 1; nc = 1;

1.11504

60=

=bn

,

360

902 ==an

, 3.3111.13 ==n ,

132.13.3148.0644.0 =+=iK ,

2.115.01 =+=hK ,

738.0

)13.32(14.3

8ln

2.1

1

02.04

5.0

02.058

)5.025(

02.05.016

5ln

14.32

1

22

=

+

+

++

=mK

The mutual impedance factor "F"

49.11)

008.034ln(

53

4

132

1 =

+

+=F ,

In (9) multiplication ofGI is voltage at the node of the grid. So by using the values from Table

1 and taking into account F factor one can obtain the maximum touch (mesh) voltage:

8.23149.12.157

132.1738.0283.29=

=mE

V.

By doing the same calculations for all nodes of the grid results can be presented in Table 4.Results are presented in both units and percentages.


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Node VTOUCH, V VTOUCH, % Node VTOUCH, V VTOUCH, %

a 231.8 100 i 7.7 3.3

b 56.6 24.4 j 7.7 3.3

c 56.6 24.4 k 4.7 2.0

e 14.6 6.3 l 3.2 1.5f 22.35 9.7 m 4.2 1.8

g 14.6 6.3 n 3.2 1.5

h 4.8 2.1 - - -

TABLE4.RESULTS OF THE TOUCH VOLTAGE CALCULATION AT NODES,V

The maximum Step Voltage values are obtained as the product of the soil resistivity (), the

geometrical factor Ks, the corrective/irregularity factor Ki, and the average current per unit of

buried length of grounding system conductor (IG/LS):

S

Giss

L

IKKE

=

. (16)

For the usual burial depth of 0.25 m < h < 2.5 m, then

+

++

=

)5.01(11

2

11 2nS

DhDhK

. (17)

For grids with or without ground rods, the effective buried conductor length, LS, is written asfollows:

RCS LLL += 85.075.0 (18)

By substituting values in (16), (17) and (18) and taking into account (4) one can obtain thefollowings.

65.1003985.09075.0 =+=SL m,

414.0)5.01(5

1

5.05

1

5.02

1

14.3

1 23.3=

+

++

=

SK ,

VES 2.20349.165.100

132.1414.0283.29=

=

By doing the same calculations for all nodes of the grid, the results are presented in Table 5 inboth units and percentages.


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Node VTOUCH, V VTOUCH, % Node VTOUCH, V VTOUCH, %

a 203.2 100 i 6.7 3.3

b 49.6 24.4 j 6.7 3.3

c 49.6 24.4 k 4.2 2.1

e 12.8 6.3 l 3.0 1.5f 19.7 9.7 m 3.6 1.8

g 12.8 6.3 n 3.0 1.5

h 4.2 2.1 - - -

TABLE5.RESULTS OF THE STEP VOLTAGE CALCULATION AT NODES

The calculation results VTOUCH and VSTEP can be presented as a graph in percentages of the

maximum voltage value (see Figure 8). The graph is a diagram where x-axis represents 0potential level. The y-axis (V) is relative magnitude of voltage in percentage. The curve in the

Figure 8 shows the voltage distribution throughout the grounding grid when the failure current isinjected in the corner mesh. As one can noticethis y-axis may be applied to both VTOUCHand VSTEP

in terms of percentages since both of them are functions of the same current. This example

represents the safety parameters distribution of the integral grounding grid without damagedelements in it.

During the experimental part with respect to the elements failures resistance, the current source Swas connected to two vertical steel elements buried in soil at 50 cm the horizontal grid depth, as

shown in Figure 9. Ends of both electrodes (7 cm) had a good contact with soil (generally it wasloam) while the rest of the electrodes length did not have any contact. A diameter of the

electrodes was 10 mm. A distance between electrodes was varied in a wide range from 1 cm up

to 60 cm.

Fig. 8. Touch and Step Voltage Distribution on the Surface of Soil


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These distances were chosen as possible values of the gap between two electrodes. Smaller valuesrefer to such factors as corrosion and freezing processes in the soil when the gap between

electrodes may have some centimetres value. Larger values (some dozens centimetres) may be

caused by possible mechanical accidents during construction works.

Fig.9. Experimental Study on the Failure Resistance.

From the experiment, one can see that the Ohmic value increases as the distance between

electrodes increases (see Table 6).

Distance between

electrodes, cmR, k

1 0.226

2 0.4454 0.100

6 0.120

26 1.100

60 4.260

TABLE6.RESISTANCE OF FAILURE

If there is a damaged element in the mesh of the grid it will result in increase of the potential atthis point since soil resistance in the gap can be substantially higher than the resistance of the

integral element. So it is vital to conduct such an analysis with damaged elements presence in thegrid. It will be helpful for prediction of possible dangerous variations of touch and step voltage.The results below provide information about the potential distribution ofVTOUCHand VSTEP in case

ofthe failure presence. By failure one can mean break or rupture of the horizontal element dueto mechanical, freezing, corrosion or other causes.

As a worst-case scenario the element 1 was chosen as a damaged one since it is one of the closest

elements to the point with the highest potential.


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Table 7 shows the results for the case with 90 failure. It is the Resistance of the gap in the

damaged element of approximately 0.6 cm due to corrosion. The values in the Table 7 arepresented for both touch and step voltage as a percentage of the potentials of the grid without

failures. The values in the table show fluctuation of the voltage in percentage of the initial voltage

without damaged elements.

Node Voltage Fluctuation, % Node Voltage Fluctuation, %

a +16.1 i -7.9

b +12.8 j -29.2

c -50.0 k -45.0

e +10.2 l -1.9

f -18.5 m -18.5

g -47.3 n -35.4

h +8.1

- -

TABLE7.RESULTS OF TOUCH AND STEP VOLTAGE DISTRIBUTION IN CASE OF ONE HORIZONTAL

ELEMENT FAILURE (R=90)

Results of the Table 7 are plotted as a graph in Figure 10.

Similar to Figure 8 the graph is a diagram where x-axis represents 0 potential level. The

vertical axis (V) is relative magnitude of voltage in percentage. The curve in the Figure 10 shows

the voltage distribution throughout the grounding devices grid when there is a damaged elementin the corner mesh element 1. The voltage distribution with the failure is shown in solid lines

when dashed curve means the case without damaged elements. As it may be observed themaximum voltage at the node a when the element #1 is damaged is 16.1% higher in

comparison with the voltage in case of the integral grid.


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Fig. 10. Touch and Step Voltage Distribution When Failure Resistance Equals 90

Another example of modelling with R=250 (the gap is more than 1 cm due to freezing or

mechanical causes) is presented in Table 8 and Figure 11 respectively.

NodeVoltage

Fluctuation, %Node

Voltage

Fluctuation, %

a +22.7 i -11.1

b +18.2 j -41.3

c -70.7 k -63.8

e +14.4 l -2.4

f -26.2 m -30

g -66.9 n -49.9

h +11.3 - -

TABLE8.RESULTS OF STEP VOLTAGE DISTRIBUTION IN CASE OF ONE HORIZONTAL ELEMENT FAILURE

(R=250)


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Fig. 11. Step Voltage Distribution When Failure Resistance Equals 250

As one can see from Figure 11, the voltage magnitude under such a scenario is 22.7% highercompared with the case without damaged elements in the grid.

By analyzing above-described calculations the main results can be summarized as follows:

1. Values of the main safety criteria at Electric Power Plants (step and touch voltages) may

vary depending on the features of malfunctions but it is vital to anticipate their possiblemagnitudes. Even if the grounding device was designed according to all safety criteria it

may happens that in some period of time due to corrosion and other reasons some damaged

element appearance will result in increase in touch and step voltage.

2. Due to high values of voltage in the grounding devices grids dangerous potentials on thesurface of earth may also appear.

3. Failures of the horizontal elements of grids may result in substantial increase of potentialsespecially at edge meshes of the grounding device. This increase may be up to some dozens

of percents compare with the scenarios without damaged elements.


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4.CONCLUSIONS

The mathematical model presented in this paper enables the evaluation of hazardous

voltage rise on the surface of earth with or without damaged horizontal elements. The

safety condition parameters in terms of touch and step voltage for worst scenario of

failures are described.

Graph theory and matrix analysis are used as the main basis for the mathematical

treatment. It is shown that the grounding device voltage and ground potential rise on the

surface above the grid are not the same due to soil impedance. But the surface potential

can be dangerous for staff in some cases especially due to damaged elements of the

earthing grid.

The mathematical analysis explains the case when there is one damaged horizontal

element in the corner mesh of the grounding grid. The results of the experimental

investigation of the failures possible resistance in the real outdoor conditions were used

for the mathematical model verification. It is shown that depending on the soil resistancein the area of failure hazardous voltage picks can be some dozens percent higher compare

to a similar situation but without damaged elements.

Even if the grounding device initially was made in accordance with all the standards

permissible requirements it can have damaged horizontal elements with passage of time

and be the source of a hazard.

REFERENCES

[1] IEEE Std.80-2000:IEEE Guide for Safety in AC Substation Grounding. The Institute ofElectrical and Electronic Engineers, New York, 2000.

[2] Haddad, A. Warne, D. F. Advances in High Voltage Engineering. The Institution ofElectrical Engineers, London, United Kingdom, 2004.

[3] Skiling, H. H. Electrical Engineering Circuits, 2 edition, NewYork :Wiley, 783 p., 1967;[4] Skiling H. H. Electric Networks, New York: Wiley, 483 p., 1974.

[5] Giannini, R., Dzapo, H. Earth Surface Potentials Measuring Device for Large GroundingSystem Testing. Proceedings of the Instrumentation and Measurement TechnologyConference, IMTC 2004, pp. 2132-2136.

[6] Grcev, L.D. Computer Analysis of Transient Voltages in Large Grounding Systems. IEEE

Transaction on Power Delivery, v. 11(2), pp. 815-823, 1996.[7] Dzapo, H., Giannini, R. Program. Support for Earth Surface Potentials Measuring System.

Measurement Science Review, 3(3), pp. 25-28, 2003.[8] Yang, H. Pan, D. A Numerical Calculation Method of Substation Grounding Grids Based

on a New Mathematical Model. Proceedings of the IEEE 8th International Symposium on

Antennas, Propagation and EM Theory, ISAPE 2008, pp. 807-810.[9] Li, Z., Chen, W., Fan, J., Lu, J. A Novel Mathematical Modeling of Grounding System

Buried in Multilayer Earth. IEEE Transactions on Power Delivery, v. 21(3), 2006.[10] Selby, A., Dawalibi, F. Determination of Current Distribution in Energized Conductors for

the Computation of Electromagnetic Fields. IEEE Trans. on Power Delivery, v. 9(2), pp.1069-1078, 1994


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[11] Grigsby L.L., The Electric Power Engineering Handbook, 1. Electric Power Production,2001 by CRS Press LLC, Auburn University, Auburn, Alabama.

[12] IEEE Std.81-1984: IEEE Guide for Measuring Earth Resistivity, Ground Impedance, andEarth Surface Potentials of a Ground System, IEEE Press, New York, 1984.

[13] IEEE Std. 142-1991 (2007): IEEE recommended practice for grounding of industrial and

commercial power systems, IEEE Press, New York, 1991, GREEN BOOK.[14] Yacobs, A. I. (1981). Electrical safety in agriculture, Moscow: Kolos.

[15] El Sherbiny M., Simple Formulas for Calculating the Grounding Resistance of RodbedBuried in Non-Uniform Soil. Proceedings of the 37th Midwest Symposium on Circuits and

SystemsUniversity of Waterloo, Waterlo, Ontario, Canada N2L 3Gl, 1954, pp. 1281-1284.

Authors

Y. Chikarovobtained his first degree in Electrical Engineering from Far Eastern Transport University(Khabarovsk), Russia in 2001. He had worked at the same University from 2001. In 2006, he graduated

with a Master in Electrical Engineering from Far Eastern Transport University (Khabarovsk), Russia. He

was a Lector, Senior Lector and Assistant Professor at the University conducting classes and scientific

research in power engineering. He is currently pursuing his Ph.D. degree at Auckland University of

Technology, New Zealand. His major interests are power system study, safety and automatics.

T. T. Lie(S89-M92-SM97) received his B.S. degree from Oklahoma State University, USA in 1986.He then obtained his M.S. and Ph.D. degrees from Michigan State University, USA in 1988 and 1992,

respectively. He had worked in Nanyang Technological University, Singapore. Dr. Lie is now a Head of

Department and a Professor in the Dept. of Electrical and Electronic Engineering, Auckland University of

Technology, New Zealand. His research interests include power system control, deregulated powersystems and renewable energy systems.

Nirmal-Kumar C. Nair (S01M04SM10)received his BE in E.E. from M.S. University, Baroda,

India and ME in E.E with specialization of High Voltage Engineering from Indian Institute of Science,

Bangalore, India. He received his Ph.D. in E.E. from Texas A&M University, College Station, USA.

Presently, he is a Senior Lecturer at the Department of Electrical & Computer Engineering in University

of Auckland, New Zealand. His current interest includes power system analysis, protective relaying &

optimization in the context of smart grids, electricity markets and integration issues of DG/renewable

sources.

safety parameters of grounding devices at an electric power plant

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