Earthing Resistance Tester developed using Resonant Circuit Technology with No Auxiliary Electrodes

Earthing Resistance Tester developed using Resonant Circuit Technology with No Auxiliary Electrodes Kazuo MURAKAWA, Masanobu MACHIDA, Hideshi OHASHI, Hitoshi KIJIMA Electrical Department Polytechnic University 4-1-1 Hashimotodai Sagamihara 9-1196 Kanagawa JAPAN hkijima@uitec.ac.jp Abstract: This paper proposes an earthing resistance tester that uses resonant circuit technology to operate without auxiliary electrodes. The measurement mechanism is analyzed using an earth return circuit model. The earthing electrode being tested, a lead wire, a return wire and the soil itself comprise the earth return circuit (LRC serial circui. The developed tester can measure the earthing resistance by evaluating the loop impedance of the earth return circuit at its resonant frequency in the range of 1 khz to 1.5 MHz. The return wire need only be placed on the soil surface without any termination. Earthing resistance measurement deviation between the new tester and a conventional tester is less than ±% for earthing resistance value of around 1Ω. Key-Words: Earthing resistance, Earth return circuit, Tester, Auxiliary electrodes, Resonant circuit 1 Introduction Many methods have been developed to measure the resistance value of earth electrodes. A popular method is so that called 3-pole method [1]~[4]. One pole is the earthing electrode to be tested, and the other two are auxiliary electrodes. The auxiliary electrodes must be directly connected to the soil itself for current injection and voltage reference. However, it may be difficult to measure the earthing resistance value because the soil surface is usually covered by concrete or stones in developed areas. Therefore we have proposed an earthing resistance measurement method that requires no auxiliary electrodes [5]. The proposed method measures the loop impedance at the resonant frequency of a circuit composed of the electrode itself, a return wire and the ground. An insulated copper wire about m long used as a return wire is simply laid out straight on the ground surface, with no termination. In this paper, we would like to expalin the outline of the development of the new earthing resistance tester. Problem in the case of using conventional measurement method so that called 3-pole method Fig.1 (a) shows the measurement configuration and Fig.1(b) shows the potential distribution. In Fig.1 (a), E is the earthing electrode being tested, P is the auxiliary electrode for potential measurement, C is the auxiliary electrode for current injection. Potential A V(ω). V E P C Auxiliary earthing electrode (a) Measurement system V Soil E P C (b) Potential distribution Fig. 1 conventional measurement method so that called 3-pole method ISBN: 978-1-6184-6-6 14

In Fig.1(a), V (ω) is a signal generator whose frequency is usually about 5 Hz, A is a current meter, V is a voltage meter. In Fig.1 (b), the horizontal axis shows distance, the vertical axis shows potential (voltage). V is the potential difference between electrodes E and P. The earthing resistance value of E is defined as the ratio of V and A. This is the most widely used method in the world. However, when the soil is stony or covered by concrete, it is difficult to use. z ε w μ σ w Return wire(φ:h) L 1 Lead wire V s o Conductor (φ: a) P(x, Insulator L I(x) x x+δx V(x) h x 3 Problem Solution applying Resonant Circuit Technology with No Auxiliary Electrodes 3.1 A measurment method without using auxiliary electrodes Fig. shows a measurement system without using auxiliary electrodes. In this new proposed measurement system [5], a lead wire, a return wire, and an impedance meter are used, and the return wire is just placed on the ground surface without any termination. Lead wire Impedance meter Return wire Fig. Measurement system without using auxiliary electrodes Soil To explain the measurement mechanism of the new method, an earth return model [5]~ [7] is shown in Fig.3. A return wire and a lead wire are placed on an infinite ground soil; the electrode being tested is buried in the soil. In Fig.3, both horizontal axis x and vertical axis z indicate distance. In Fig.3, a lead wire is connected to the electrode being tested and to a voltage oscillator (Vs), and the return wire is connected to Vs with the other end of the return wire open. ε w (about 3-5) is the permeability of these wires insulators, and σ w is the conductivity of the wires. ε e (about 1-8) and σ e are the permeability and conductivity values for the soil. Surface S Contour C ε e μ σ e Soil Fig.3 Earth return model of new system - In Fig.3, a is the diameter of the wire conductors, h is the distance from the soil surface to the wires centers; these two wires are covered with PE insulation, so they do not contact to the soil directly. V (x) and I (x) are the potential and current of the wire conductor at x, where the potential is the potential from infinity (z = - ). S is the rectangular surface below the wire as shown in Fig.3, and C is the contour of the surface S. P ( x, is a point on the contour C. 3. Earth return circuit analysis Where E r and H r are electric and magnetic field vectors induced by the voltage oscillator Vs, the following equation: h a h a { E + Δ z ( x x, Ez ( x, } dz { E z ( x, h) Ez ( x, )} dx h a x+δx = j ωμ H y ( x, h) dxdz (1) x where E z and H y are the z component of electric field E r and the y component of H r. j is a complex number, ω is an angular frequency. In Eq. (1), the term E z ( x, ) on the right-hand side of Eq. (1) can be neglected because the electric field can be assumed to vanish at z =. Here, the potential of the wire conductor is given by: h a V ( x) = Ez ( x, dz () When Δx, Eq.(1) can be written: dv ( x) h + = a Z wi( x) jωμ H y ( x, dz (3) dx 1 jωμ where Zw ( + ) πa σ 8π w is the impedance of the wire conductor [8]. The right hand side of Eq. (3) is a physical value related to magnetic field contribution of the wire under the soil. Therefore, Eq. (3) can be expressed as follows. ISBN: 978-1-6184-6-6 15

dv ( x) = Z( ω) I( x) dx (4) Z( ω ) = Zw + Ze + jωl (5) di( x) = Y ( ω) V ( x) dx (6) Y ( ω) = jωc + Y e (7) Z eye γ e = jωμ( σ e + jωεeε) (8) where L is an inductance of the wire when the soil is assumed to be a perfect conductor, Z e is the impedance contribution of the wire conductor under the soil. C is the capacitance of the wire when the soil is assumed to be a perfect conductor, Ye is the admittance contribution of the wire conductor under the soil. L and C are given by: μ h L = ln π a (9) πε wε C = (1) h ln a as the frequency is less than 3 MHz and σ e is more than 1 3 (S/m) or 1 (S/m), Ze can be written as follows. [8] Ze jωμ 1+ γ eh ln π γ eh (11) where the equivalent earth return circuit of the wire conductor over the soil can be expressed as shown in Fig.4. Z w Z e L R g x=-l 1 x= L x=l V L I L z V s C s L a V R I R z Fig.5 Earth return circuit model for Fig.3 In Fig.5, L a is the additive inductance, and Cs is the stray capacitance of Vs. Fig.5 is assumed to be a transmission line model in which the left-hand side is terminated by R g and the right-hand side is open. Numerical results based on the transmission line model show that the earthing resistance value can be obtained as the impedance at the resonant frequency of the transmission line. The resonant frequency depends on the length of the return wire, so in Fig.5, L a must be added so that the resonant frequency is less than 3 MHz. 3.3 Numerical calculation results The additive inductance L a, the lengths of the lead wire and the return wire, and the soil conductivity are very important parameters for the proposed new measurement method. In this section, the requirements for these parameters are examined. 14 L =m,h/a= C Y e 13 Re=3Ω Ω 1Ω Fig.4 An equivalent earth return circuit of the wire over the soil In this case, the transmission coefficient and the characteristic impedance shown in Fig.4 are as follows. γ = ( Z + Z + jωl)( jωc + Y ) (1) w e e z = Z + Ze + jωl jωc + Ye (13) w According to the equivalent circuit shown in Fig.4 and Eqs.(1) and (13), Fig.4 can be represented schematically as shown in Fig.5. In Fig.5, R g is the earth impedance of the earthing electrode being tested. The signal oscillator, the earth electrode being tested and the end of the return wire are at x = -L 1, x = and x = L. 1 5Ω 3Ω 11 1 5 16 (a) without inductance La 14 13 1 Re=3Ω Ω 1Ω 5Ω 3Ω Ω 11 15 1 6 (b) w ith inductance La(=4μ H) Fig.6 L a dependency of calculated earthing resistance Ω L =m,h/a= ISBN: 978-1-6184-6-6 16

(1) Additive inductance L a dependence Calculated earthing resistances with/without additive inductance are shown in Fig.6 where L 1 = 1 m and L = m, h/a =, ε w =4, ε e = 1 and σ e = 1 - S/m. Fig.6 (a) is the calculated result without the additive inductance L a for, 3, 5, 1, and 3 Ω. Fig.6 (b) is the calculated result when the additive inductance L a is 4 μh. In Fig.6 (a) and Fig.6 (b), the horizontal axis shows the frequency in Hz and the vertical axis shows the impedance in Ω. In Fig.6 (a), the resonant frequency is about 9 1 MHz, in Fig.6, frequencies where impedances are the lowest mean the resonant frequencies. The range is 55 6 KHz for Fig.6 (b). Calculated earthing resistances are almost the same as the values given. In earthing resistance measurements, it is important that the return wire should not function as an antenna. Therefore, the length of the return wire must be less than 1/1 or 1/ of a wavelength. If the length of the return wire is set to m, the measurement frequency must be less than.75-1.5 MHz. () Return wire length L dependency The calculated earthing resistance values when L is set to 1,, 3, 5, 1, and m are shown in Fig.7, where L 1 = 1 m, h/a =, ε w = 4, ε e = 1, σ e = 1 - S/m and Rg = 1 Ω. In Fig.7, the resonant frequency is proportional to the return wire length, when L is m, the resonant frequency is about 55-6 khz and the calculated earthing resistance value is 15 Ω. However, when L is 1 m, the resonant frequency is 1.8 MHz and the calculated earthing resistance value is 1 Ω. R g = 1 Ω. When soil conductivity σ e is less than 1-3 S/m, the calculated earthing resistance is more than 14 Ω, and the error is more than 4%. However, when soil conductivity σ e is higher than 1 - S/m, the calculated earthing resistance is about 13-15 Ω. In general, in an urban area, soil conductivity is usually higher than 1 - S/m, which means that the new method can be used in a wide variety of environments. 14 13 1 Re=1Ω, L 1 =1m,L =m,h/a= 1-4 s/m 1-3 s/m 1,1-1,1 - s/m 11 1 5 1 6 Fig.8 σ e dependency of calculated earthing resistance 4 Development of new earthing resistance tester We would like to propose the tester circuit shown in Fig.9. Fig.9(a) is the tester circuit, Fig.9(b) is an equivalent circuit. 14 Re=1Ω,L 1 =1m, h/a= A return wire terminal R R a L a 13 S.G. V o R 3 1 Mix. E V 1 V LPF V 1 1m A lead wire terminal L = m 1m 5m 3m m (a) A tester circuit 11 1 5 16 Fig.7 L dependency of calculated earthing resistance (3) Soil conductivity σ e dependency Calculated earthing resistance values when σ e is set to 1-4, 1-3,1 -, 1-1,and 1 S/m are shown in Fig.8, where L 1 = 1 m, L = m, h/a =, ε w = 4, ε e = 1 and V 1 R a V L a R g (b) Equivalent circuit Fig.9 A tester circuit In Fig.9, S.G. is a signal generator, R is 5 Ω, R a is the additive resistance 5 Ω, La is the additive inductance L C ISBN: 978-1-6184-6-6 17

4 μh, Mix. is an analog mixer with two input ports, one dc-out port and one earth port. LPF is a low pass filter; V is a dc voltmeter as shown in Fig.9 (a). In Fig.9 (b), R g, L and C comprise the loop impedance of the earth return circuit being tested. R g is the earthing resistance of the electrode being tested. R a is the additive resistance, where R a >> R and R g. In Fig.9(b), V 1 and V can be written as follows. (, ) 1 ( Vo ω t V1 = V ω, = (14) RgV ( ω, / V = V ( ω, = + Vn ( 1 Ra + Rg + j{ ω( L + La ) } ωc (15) Where V ( ω, is a signal generator producing a sinusoidal wave with an angular frequency ω. In Eq.(15), V n ( represents the noise as a function of time. We define the following time integral: 1 α = V1 ( ω, * V ( ω, dt (16) T Eq.(16) shows the correlation between V1 ( ω, and V ( ω, where T is a finite duration. When the lead wire and the return wire are not connected, then are connected, to the earth return circuit, the following equations hold at the resonant frequency. 1 V ( ω, α open = dt (17) T 4 R g 1 V ( ω, α R g = dt (18) Ra + Rg T 4 where V ( ω, Vn ( dt = (19) Then we can write the following equation, α R R g g β = = () α open Ra + Rg and we can finally obtain the resistance of the earth electrode being tested as follows. βra R g = (1) 1 β We have developed an earthing resistance tester provided by HIOKI.E.E CORP. as shown in Fig.1. Lead wire Fig.1 A developed new tester Return wire Fig.1 shows a view of the new tester powered by 4 x 1.5 V dry cells. The tester has a power switch, a dial that can vary the oscillation frequency between 5 khz and 1.5 MHz, and also has a lead wire terminal and a return wire terminal. We have examined the performance of the new tester at about sites in Japan. Several of the experimental setups are shown in Fig.11. Asphalt road Return wire A new tester Existing earth meter Existing earth meter (a) A return wire is put on an asphalt road 1 (b) A return wire is put on an asphalt road (c) A return wire is put on tiles Fig.11 Experiment situations Figs.11 (a) and (b) show the return wire placed on asphalt road, Fig.11(c) shows the return wire on tiles. We use an earth electrode.8 m long and.14 m in diameter, which is driven to the soil. By changing the depth of the electrode, the earthing resistance can be controlled. Measurement results are shown in Fig.1. The horizontal axis is the R g value obtained by the conventional method (3-pole method) and the vertical axis is the R g value determined by the new tester. Solid squares represent measured data, and the solid line is an ISBN: 978-1-6184-6-6 18

approximated curve. The broken line is the ideal curve, which would be obtained if the R g measured by the conventional method were equal to that from the new tester. The actual measurements show some deviation between the methods, which is small around 1-15 Ω, but increases for earthing resistances above Ω because the condition that R a >> R g is not satisfied. Therefore, the new tester requires a correction table (values shown in Fig.1). The corrected measurement results are shown in Fig.13. With corrections, the deviation between the methods is less than ±% (Fig.13). The new tester can be used for earthing resistance measurements between 1-3 Ω, as shown in Fig.13. R g of proposed method (ohm) R g of proposed method (ohm) 4 3 1 4 3 1 Ideal curve Correction values 1 3 4 R g of 3 pole method (ohm) Approximated curve Fig.1 Experiment results without corrections 1 3 4 A theoretical analysis of the proposal was conducted using earth return circuit models. In this method, insulated lead and return wires are simply placed on soil surfaces without any termination. Numerical simulations of measurements were used to explore the expected outcomes, using a 1 m lead wire and a m return wire. The new tester was tried at more than sites across Japan, including places where the soil surface was covered by asphalt, tiles, stones and sand. It was found that the new tester can be used to measure earthing resistance where the value lies between 1 3 Ω. The new tester is a very simple measurement tool that can be very useful in the field, especially when auxiliary electrodes cannot be used. In the future, we would like to improve the measurement accuracy for low earthing resistances, perhaps down to the 1-3 Ω range. References: [1] Y. Kobayashi, H. Ohashi, K. Murakawa, T. Kishimoto, H. Kijima: Earthing resistance measurement, EMCJ98-78, pp.45-5, 1998. [] Toshiyuki Katayama, Research on the grounding characteristic of the electrode constructed by the perpendicular dislocation ground, Institute of Electrical Installation Engineers of Japan, p65, 6 [3] T Makita, H Suzuki, Grounding property of mesh electrode buried near vertical fault, Nihon University, Report-of-research Vol.39, No. pp1-7, 6 [4] Takehiko Takahashi, The recent method of a grounding electrode design, South Korean Illuminating Engineering Institute, Autumn scientific convention, Special Lecture, 7 [5] K. Murakawa, H. Ohashi, H. Yamane, M. Machida, H. Kijima: Proposal of earthing resistance measurement method without auxiliary electrodes, IEEJ Trans. FM, Vol.14, No.9, pp.83-811, 4 [6] S. Ramo, J.R. Whinnery, T.V. Daser : Field and waves in communication electronics, nd Ed., Wiley, New York, 1989 [7] S. Bourg, B. Sacepe, T. Debu: Deep earth electrodes in highly resistive earth: frequency behavior, 1995 IEEE International Symposium on EMC, pp.584 589, Aug. 1995 [8] F.M. Tesche, M.V. Ianoz, T. Karlson : EMC analysis methods and computational models: Chapter 8, Wiley, New York, 1989 R g of 3 pole method (ohm) Fig.13 Experiment results with corrections 5 Conclusions This paper proposed an earthing resistance measurement method without auxiliary electrodes. The advantages of this new technology are as follows. ISBN: 978-1-6184-6-6 19