A New Approach to Measure Earthling Registrant of a Digital Telephone Exchange

Statistical Approach to Find an Empirical Relationship Between the Grounding Resistance and Length of Buried Electrode in the Soil

M. A. Salam, A. A. Maqrashi, Nazar Mohammed, Zia Nadir and *M. Shahidullah Department of Electrical & Computer Engineering College of Engineering Sultan Qaboos University P. O. Box: 33, Muscat 123, Oman

*Department of Electrical & Electronic Engineering Chittagong University of Engineering and Technology Chittagong-4349, Bangladesh

Abstract finding coupling coefficient, he used another In this paper, an empirical relationship between the formula. Chow et al [7] proposed a formula to grounding resistance and length of buried electrode calculate the grounding resistance. They divided the in the soil is proposed by regression analysis based n number of meshes of the grid and also compared on experimental data. the results with others researchers results. Joy et al [8] proposed a graphical method for calculating Keywords: Grounding resistance, buried electrode, earthing resistance of the substation grounding regression analysis, layered soil. system. Nagar et al [9] proposed a computer-aided method to allow the design engineer to bypass many Introduction assumptions that are necessary in the other methods to simplify the solution. The calculation process of The main objective of the grounding system is to grounding resistance of a grid depends on the provide a path with minimum value of grounding segmentation of the grid into n-segments. The resistance. The minimum value of grounding method of images is applied on each segment. Other resistance is <1Ω. The good grounding system can researchers [10-11] have used numerical technique to assure the safety of the persons, to protect the low calculate the resistance of the substation grounding voltage electrical and electronic equipment, system, for practical grid and soil parameters. household appliances without interruption of power supply. In order to attain these targets, the apparent In this paper a statistical approach is used to find the value of the grounding system should be low enough empirical relationship between the grounding to guarantee the supply system and its appliances. resistance and length of the buried electrode in the soil based on experimental data’s. Recently, Farag et al [1] discussed that the lightning currents are independent of polarity, and propagate Experimental Procedures into the soil according to the typical laws of conducting means. The value of grounding resistance The experiment was carried out for the soil should be kept low to ensure better safety to the low consisting of a mixture of sand and small rock. voltage equipment and personnel from the dangerous ground potential due to lightning discharge into the The grounding electrode was driven vertically to the ground [2]. In these studies the influence on the ground. The ‘Earth Tester’ instrument (HIOKI, behavior of grounding electrodes in transient Model 3/50, JAPAN) was used in the experiment to conditions of the involved parameters has been measure the grounding resistance directly. investigated. Gómez-Calviño et al [3] presented a numerical approach for grounding analysis The standard auxiliary electrodes of about 0.4m long embedded in stratified soils and its implementation in were connected with the tester by the specified a high-performance parallel computer. The feasibility connection wires of prescribed length. The distances of this system is also studied with the application of between the electrodes were kept fixed for specified an analysis of a real grounding system in a layered length of the connecting wires during measurement. soil. Takahashi et al [4] started from Tagg’s formula The instrument displays the direct reading of and developed a generalized formula for n-soil based grounding resistance in ohms. Figure 1 shows the on the same assumption used by Tagg. Blattner [5] schematic diagram for measuring grounding developed an empirical formula for calculating the resistance at various electrode lengths in the soil. value of soil resistivity taken at depths of up to two The different values of grounding resistances were meters. Extrapolation process is used to get the recorded during electrode buried to the soil. effective resistivity at depths of up to ten times the measurements’ depths. Costic [6] proposed a The measurement results were summarized in the mathematical expression for finding equivalent Tables 1 and 2. resistance of a foundation grounding system. For Resistance Scale Earth Tester

M M E Earth 1 2

Earth The above experiments were conducted during the 6m Level 1 months of March and December in 2001. These months are representing very dry and rainy season 6m Auxiliary electrodes Level 2 respectively. of about 0.4 m long

6m Level 3 Table 1. Values of Grounding Resistances measured Level 4 by Earth Tester in March 2001 6m

Earthing electrode Length Resistances 6m Level 5 (meter) ()

6m Level 6 6 26.5 12 13.6 18 6.7 24 4.8 Figure 1. Measurement of grounding 30 4.2 resistance of buried electrode in the soil. 36 3.1 y= ln( p ) b= ln( q ) Table 2. Values of Grounding Resistances measured a= ln( m 1) by Earth Tester in June 2001 r= x

a Length Resistances The constants and b of equation (3) can be (meter) () determined by using least square method. We therefore wish to minimize the quantity as [12], 6 13.3 n S=[ y - ( ax + b )]2 (4) 12 5.5 i i i=1 18 3.4 24 2.2 This is accomplished by setting the derivatives with 30 1.5 respect to a and b equal to zero. Performing these 36 1.1 operations, there results are, Relationship Development nb+ a邋 xi = y i (5) In the experiment it is found that the value of grounding resistance decreases with increasing the 2 b x+ a x = x y (6) length of the buried electrode in the soil. Depending 邋i i i i on the experimental data. Consider the regression equation is an exponential form as, Solving equations (5) and (6) simultaneously gives

r1 r 2 n x y- x y p= qm1 m 2 ...... (1) 邋i i( i)( i ) a = 2 (7) n x2 - x The above equation can be modified by taking 邋i( i ) natural logarithm of each side, 2 (邋yi) x i- ( 邋 x i y i)( x i ) lnp= ln( q ) + r1ln( m )...... 1 (2) b = 2 (8) 2 n邋 xi- ( x i ) Comparing equation (2) with the following equation, Let us assume that a suitable correlation between y y= b + ax (3) and x has been obtained by either least squares analysis or graphical curve fitting. We want to know Where: how good this fit is and the parameter, which conveys this information is the correlation coefficient R defined by, ] Ω [

s e c n a

2 s 轾 i s y, x s R =犏1 - (9) e R

2 犏 s g 30 y n

臌 i d n

u R(Expt) o

r 25 y R(Statistical) where s y is the standard deviation of given as, G 20 1/ 2 n 轾 2 15 犏 (yi- y m ) 犏 s = i=1 (10) 10 y 犏 n -1 犏犏 5 臌 1/ 2 0 轾n 2 0 10 20 30 40 犏 (yi- y ic ) 犏 s = i=1 (11) Length of buried electrode in the soil [m] y, x 犏 n - 2 犏犏 Fig 2. Variation of grounding resistance with 臌 different lengths of buried electrode for the month of March The y are the actual value of y and the y are the i ic in Fig. 1. Similarly, for the month of June the values computed from the correlation equation for coefficient of buried electrode and constant was x the same value of . The division by n - 2 results calculated base on experimental data’s. from the fact that we have used the two derived The value of coefficient of length is 0.08 and variables a and b in determining the value of y . 2 ic constant is 2.81. In this analysis, the value of R is We might say this removes 2 degrees of freedom found 96.5% that is closer to 1 than the value of 2 from the system of data. The determination of R coefficient or correlation coefficient R may also be for the month of March. The experimental and written as, regression analysis results for the month of December are plotted together as shown in Fig. 2. In Fig. 2, it is found that the value of grounding s2- s 2 R2 = y y, x resistance 0.93 Ω at 36m length of buried electrode 2 (12) s y by regression analysis. This value of grounding resistance can be considered proper value for good grounding system. Low value of 2 indicating poor fit and high value R Depending on the value of the correlation coefficient, indicating good fit of the curve. the second model can be considered as generalized model for finding the relationship between the Results

The measurement of grounding resistances was ] Ω

carried out near the vicinity of telephone exchange [

s both in the dry and rainy season. The objective of the e c n a test was to measure the grounding resistances with t s i s

different values of length of the buried electrode in e r

the soil g n

i 14 d n

u R(Expt) o

G R(Statistical) The measurement values of grounding resistances are 10 analyzed by statistical software MINITAB 14. 8 For the month of March, the experimental values of 6 resistances are converted to other values using natural log (i.e. lnR). After that the converted values 4 of resistances are set as in the response and length of buried electrode as predictors. The coefficient of 2 length and constant was calculated as 0.069 and 3.45 0 respectively using the software. The determination of 0 10 20 30 40 coefficient is also calculated and the value is 2 Length of buried electrode in the soil [m] R = 92.9 %. For better correlation the closer value of R2 to unity. The experimental values of grounding Fig. 3. Variation of grounding resistance with resistances and statistical analysis results are plotted different lengths of buried electrode for the month of December grounding resistance and length of buried electrode Design of Earthing Systems for Electrical in the soil. Substations in Non-Homogeneous Soil Models, The empirical relationship between the grounding IEEE International Conference on Parallel resistance and buried electrode in the soil for dry and Processing, ICPP 2000. rainy seasons are, [4] T. Takahashi, T. Kawase, “Calculation of Earth -0.069L Resistance for a Deep Driven Rod in a Multi-Layer Rdry = 31.5 e (13) Earth Structure”, IEEE Trans. Power Delivery, Vol. 6, pp. 608-614, 1991. -0.08L Rrainy = 16.6 e (14) [5] C. J. Blattner, “Prediction of Soil Resistivity and Ground Rod Resistance for Deep Ground Electrode”, Conclusion IEEE Trans. Power Apparatus & Systems, Vol. PAS- 99, No. 5, pp. 1758-1763, Sep/Oct. 1980. 1. Two empirical relations have been proposed for [6] M. B. Costic, “Analysis of Foundation Systems dry and rainy seasons using regression analysis with External Loops and Rods”, IEEE Trans. Power software based on experimental data’s. Delivery, Vol. 140, No. 2, pp. 73-76, March 1993.

2. In this analysis the determination of coefficients [7] Y. L. Chow, M. M. A. Salama, “A Simplified are also calculated. The value R2 is found 96.5% for Method for Calculating the Substation Grounding the second empirical formula that is closer to 1. Drid Resistance”, IEEE Trans. on Power Delivery, Vol. 9, No. 2, pp. 736-742, April 1994. 3. Depending on the lower value of grounding resistance and correlation coefficients, second [8] E. B. Joy, N. Poik, T. E. Brewer, R. E. Wilson, empirical formula is considered as a generalized “Graphical Data of Grounding Grid Analysis”, IEEE relationship between the grounding resistance and Trans. on Power Apparatus & Systems, Vol. PAS- length of buried electrode in the soil. 102, No. 9, pp.3038-3048, September 1983.

Acknowledgement [9] R. P. Nagar, R. Velazquez, M. Leoloeian, D. Mukhedkar, Y. Gervais, “Review of Analytical The authors acknowledge the technicians of BIT, Methods for Calculating the Performance of Large Chittagong for their valuable technical assistance. Grounding Electrode, Part I: Theoretical Consideration”, IEEE Trans. Power Apparatus & References Systems, Vol. PAS-104, No. 11, pp. 3124-3132, 1985. [10] F. Dawalibi, D. Mukhedar, “Influenced of [1] A. S. Farag, T. C. Cheng, D. Penn, “Ground Grounding Rods on Grounding Grids”, IEEE Trans. Terminations of Lightning Protective Systems”, Power Apparatus & Systems, Vol. PAS-98, No. 6, IEEE Trans. Dielectrics and Electrical Insulation, pp.2089-2097, 1979. Vol. 5, No. 6, pp. 869-877, December 1998. [11] F. Dawalibi, N. Barbetio, “Measurements and [2] Robert L. Casio, “Safe Measurement of Ground Computations of the Performance of Grounding Resistance”, Society for Mining, Metallurgy and System Buried in Multilayer Soils”, IEEE Trans. Exploration (SME) Symposium, Phoenix, Arizona, Power Delivery, No. 6, pp. 1483-1490, 1991. 27 February 1992. [12] J. P. Holman, “Experimental Methods for [3] J. Gómez-Calviño, I. Colominas, F. Navarrina Engineers”, Seventh edition, Mcgraw-Hill and M. Casteleiro, “Parallel Computing Aided International Edition, 2001.