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

Transcription

1 ecent Advances in Intellient ontrol, Modellin and Simulation Earthin esistance Tester developed usin esonant ircuit Technoloy with No Auxiliary Electrodes Kazuo MUAKAWA, Hitoshi KIJIMA Technical Assistance and support center NTT East 1--5 Kamata-honcho, Ohta-ku, Tokyo, JAPAN Electrical Department Polytechnic University Hashimotodai Saamihara Kanaawa JAPAN Abstract: - This paper presents an earthin resistance tester that uses resonant circuit technoloy to operate with a simple earthin electrode and without auxiliary electrodes. The measurement mechanism is analyzed usin an earth return circuit model. The earthin electrode bein tested, a lead wire, a return wire and the soil itself comprise the earth return circuit ( serial circuit). The requirements for this measurement method are obtained from numerical simulations, takin the lenths of the lead wire and the return wire to be 1 m and m, and soil resistivity less than 1- s/m. The developed tester can measure the earthin resistance by evaluatin the loop impedance of the earth return circuit at its resonant frequency, usin a resonant frequency in the rane of 1 khz to 1.5 MHz. The return wire need only be placed on the soil surface without any termination. Earthin resistance measurements made by the developed tester and a conventional tester (3-pole method) differed by less than ±% for earthin resistance values between 5 Ω and 4 Ω. The developed tester is a ood way to test a simple earth electrode with an earthin resistance value of around 1 Ω. Key-Words: - eave one blank line after the Abstract and write your Key-Words (6-1 words) 1 Introduction Earthin is very important for both human and equipment safety in the case of power faults and lihtnin events, and is also is required for a sinal round, a voltae reference and so on. Examples of required resistance are 1 Ω and 1 Ω, values set by national reulations or international requirements. An earthin resistance value of 1 Ω is normally required for both human and equipment safety for low-voltae equipment in Japan. Many methods have been developed to measure the resistance of earth electrodes. The best known is the 3-pole method [1]. One pole is the earthin 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 voltae reference. However, it may be difficult to measure the earthin resistance value this way because the soil surface is usually covered by concrete or stones in developed areas. Therefore we have proposed an earthin resistance measurement method that requires no auxiliary electrodes []. The [3] [4] proposed method measures the loop impedance ISBN:

2 ecent Advances in Intellient ontrol, Modellin and Simulation at the resonant frequency of a circuit composed of the electrode itself, a return wire and the round itself. An insulated copper wire about m lon used as the return wire is simply laid out straiht on the soil surface, with no termination. A sophisticated network analyzer with a battery power supply was required to test the method because of the electrical noise in the field, includin radio waves and stray currents. In this paper, we would first like to explain our proposed earthin resistance measurement method, and also to show the voltae ratio technique. We also outline our development and testin of an earthin resistance tester based on our proposal. onventional measurement methods.1 3-pole method An existin earthin resistance measurement method is shown in Fi.1. Fi.1 (a) shows the measurement confiuration and Fi.1(b) the potential distribution. In Fi.1 (a), E is the earthin electrode bein tested, P is the auxiliary electrode for potential measurement, is the auxiliary electrode for current injection. A V(ω). V E P the vertical axis shows potential (voltae). V is the potential difference between electrodes E and P. The earthin resistance value at 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 paved, it is a difficult method to use.. oop impedance method The loop impedance method is shown in Fi.. Fi. (a) shows the measurement confiuration and Fi. (b) the potential distribution, as in Fi.1 (b). In Fi. (a), E is the earthin electrode bein tested, and is the auxiliary electrode for current injection. J is the current source, its frequency usually about 1 khz, V is a voltae meter. E, and the soil form the earth return loop, and the measurement is made by evaluatin the loop impedance. If the earthin resistance at electrode is smaller than that at E, the measured loop impedance is almost the same as the earthin resistance of electrode E, and the earthin resistance value of E is iven by the ratio of J and V. This method only uses electrode for current injection, and while it is often easy to measure earthin resistance, it is difficult to determine a low earthin resistance value for in the field. ommonly, the buildin earth is used as a electrode, but this is danerous when there are power faults in buildins. J(ω) Auxiliary earthin electrode Earthin electrode Soil E V (a) Measurement system Auxiliary earthin electrode Earthin electrode Potential V Soil (a) Measurement system E P (b) Potential distribution Fi.1. 3-pole method In Fi.1(a), V (ω) is a sinal enerator whose frequency is usually about 5 Hz, A is a current meter, V is a voltae meter. In Fi.1 (b), the horizontal axis shows distance, Potential E V (b) Potential distribution Fi. A loop impedance method ISBN:

3 ecent Advances in Intellient ontrol, Modellin and Simulation 3 A measurement method without usin auxiliary electrodes As the loop impedance method explained in section. is quite a simple way to measure earthin resistance, we would like to consider a loop impedance method without a electrode, as shown in Fi.3. The difference between Fi. and Fi.3 is only the presence or absence of a electrode. In this new measurement system, a lead wire, a return wire, and an impedance meter are used, and the return wire is just placed on the round surface without any termination. conductor at x, where the potential is the potential from infinity (z = - ). S is the rectanular surface below the wire as shown in Fi.4, and is the contour of the surface S. P ( x, z) is a point on the contour. ε w μ σ w 1 ead wire z o V s onductor (φ: a) P(x,z) eturn wire(φ:h) I(x) V(x) Insulator x x+δx h x ead wire Impedance meter eturn wire Surface S ontour Earthin electrode ε e μ σ e Soil - Fi.4 Earth return model of new system Earthin electrode Soil 3. Earth return circuit analysis Where E r and H r are electric and manetic field vectors induced by the voltae oscillator Vs, the followin equation applies: Fi.3. Measurement system without usin auxiliary electrodes 3. 1 Earth return model To explain the measurement mechanism of the new method, an earth return model (6) (7) is shown in Fi.4. A return wire and a lead wire are placed on an infinite round soil; the electrode bein tested is buried in the soil. In Fi.4, both horizontal axis x and vertical axis z indicate distance. In Fi.4, a lead wire is connected to the electrode bein tested and to a voltae 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. In Fi.4, 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 h a h a { E z ( x + Δx, z) E z ( x, z)} dz { E z ( x, h) E z ( x, )} dx h a x+δx = j H y ( x, h) dxdz x ωμ...(1) 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 anular frequency. In Eq. (1), the term E z ( x, ) on the riht-hand side of Eq. (1) can be nelected because the electric field can be assumed to vanish at z =. Here, the potential of the wire conductor is iven by: h a V x) = Ez ( x, z) dz (...() When Δx, Eq.(1) can be written: dv ( x) h a + Z wi ( x) = jωμ H y ( x, z) dz...(3) dx 1 jωμ where Zw ( + ) is the impedance of the πa σ 8π w wire conductor (4). The riht hand side of Eq. (3) is a physical value related to manetic field contribution ISBN:

4 ecent Advances in Intellient ontrol, Modellin and Simulation of the wire under the soil. Therefore, Eq. (3) can be expressed as follows. dv ( x) = Z( ω) I( x)... (4) dx Z( ω ) = Z + Z + jω... (5) w e di( x) = Y ( ω) V ( x)... (6) dx Y ω) = jω + Y e (... (7) Z eye γ e = jωμ( σ e + jωεeε)... (8) where is an inductance of the wire when the soil is assumed to be a perfect conductor, Ze is the impedance contribution of the wire conductor under the soil. is the capacitance of the wire when the soil is assumed to be a perfect conductor, Y e is the admittance contribution of the wire conductor under the soil. and are iven by: μ h = ln... (9) π a πε wε =... (1) h ln a as the frequency is less than 3 MHz and σ e is more than 1 3 (s/m) or 1, Ze can be written as follows. (4)(6) Z e jωμ 1+ γ eh ln... (11) π γ h e where the equivalent earth return circuit of the wire conductor over the soil can be expressed as shown in Fi.5. Z w Z e Y e Fi.5 An equivalent earth return circuit of the wire over the soil In this case, the transmission coefficient and the characteristic impedance shown in Fi.5 are as follows. γ = ( Z + Z + jω)( jω + Y )...(1) z w e e = Z + Ze + jω jω + Ye...(13) w Accordin to the equivalent circuit shown in Fi.5 and Eqs.(1) and (13), Fi.4 can be represented schematically as shown in Fi.6. In Fi.6, Z is the earth impedance of the earthin electrode bein tested. The sinal oscillator, the earth electrode bein tested and the end of the return wire are at x = - 1, x = and x=. In Fi.6, a is the additive inductance, and s is the stray capacitance of Vs. Fi.6 is assumed to be a transmission line model in which the left-hand side is terminated by and the riht-hand side is open. Numerical results based on the transmission line model show that the earthin resistance value can be obtained as the impedance at the resonant frequency of the transmission line (See Appendix). The resonant frequency depends on the lenth of the return wire, so in Fi.6, a must be added so that the resonant frequency is less than 3 MHz. x=- 1 x= x= V I z V s s a V I z Fi.6 Earth return circuit model for Fi Numerical results The additive inductance a, the lenths 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. (1) Additive inductance a impedance alculated earthin resistances with/without additive inductance are shown in Fi.7 (8) where 1 = 1 m and = m, h/a =, ε w =4, ε e = 1 and σ e = ISBN:

5 ecent Advances in Intellient ontrol, Modellin and Simulation 1 - s/m. Typical soil resistivity (1) is shown in Table.1. Table.1 Typical soil resistivity (1/conductivity) Soil Soil resistivity (ohm-m) 14 =m,h/a= Mini. Mid. Max. Surface soils, loam, etc Z (Ω) 1 e=3ω Ω 1Ω lay 1 Sand and ravel Surface limestone imestone 5 4* 1 3 Shale 5 1 5Ω 3Ω Ω frequency (Hz) (a) without inductance a 14 =m,h/a= e=3ω 13 Ω Z (Ω) 1 1Ω Sandstones *1 3 Granites, basalts 1 4 Decomposed eneisses 5 5*1 Slates, etc. 1 1 Pastoral, low hills, rich 3 soil Flat country, marshy, 1 densely wooded Pastoral, medium hills and forestation * 1 ocky soil, steep hills 1 5* Sandy, dry, flat, typical of coastal country 3* 1 5* Ω 3Ω Ω frequency (Hz) (b) with inductance a(=4μ H) Fi.7 a dependency of calculated earthin resistance Fi.7 (a) is the calculated result without the additive inductance a for, 3, 5, 1, and 3 Ω. Fi.7 (b) is the calculated result when the additive inductance a is 4 μh. In Fi.7 (a) and Fi.7 (b), the horizontal axis shows the frequency in Hz and the vertical axis the impedance in Ω. In Fi.7 (a), the resonant frequency is about 9 1 MHz, in Fi.7, frequencies where impedances are the lowest are the resonant frequencies. The rane is 55 6 KHz for Fi.7 (b). alculated earthin resistances are almost the same as the values iven. In earthin resistance measurements, it is important that the return wire should not function as an antenna. Therefore, the lenth of the return wire must be less than 1/1 or 1/ of a wavelenth. If the lenth of the return wire is set to m, the measurement frequency must be less than MHz. () eturn wire lenth dependency The calculated earthin resistance values when is set to 1,, 3, 5, 1, and m are shown in Fi.8, where 1 = 1 m, h/a =, ε w = 4, ε e = 1, σ e = 1 - s/m and = 1 Ω. Z (Ω) = m e=1ω, 1 =1m, h/a= 1m 5m 3m m frequency (Hz) Fi.8 dependency of calculated earthin resistance In Fi.8 (8), the resonant frequency is proportional to the return wire lenth, when is m, the resonant frequency is about 55-6 khz and the 1m ISBN:

6 ecent Advances in Intellient ontrol, Modellin and Simulation calculated earthin resistance value is 15 Ω. However, when is 1 m, the resonant frequency is 1.8 MHz and the calculated earthin resistance value is 1 Ω. (3) Soil conductivity σ e dependency alculated earthin resistance values when σ e is set to 1-4, 1-3,1 -, 1-1,and 1 s/m are shown in Fi.9, where 1 = 1 m, = m, h/a =, ε w = 4, ε e = 1 and = 1 Ω. When soil conductivity σ e is less than 1-3 s/m, the calculated earthin resistance is more than 14 Ω, and the error is more than 4%. However, when soil conductivity σ e is hiher than 1 -, the calculated earthin resistance is about Ω. In eneral, in an urban area, soil conductivity is usually hiher than 1 - s/m, which means that the new method can be used in a wide variety of environments. Z (Ω) e=1ω, 1 =1m, =m,h/a= 1-4 s/m 1-3 s/m 1,1-1,1 - s/m frequency (Hz) Fi.9 σ e dependency of calculated earthin resistance 4. Development of earthin resistance tester 4.1 S parameter method (S 11 ) In eneral, earthin resistance measurement is not easy because there exists electrical noises in the field and round soil. For examples, under 3MHz, radio waves, amateur radio wave, electric power noises, electric fault currents. The network analyzer can evaluate impedance under the test by usin S 11 measurement mode. The network analyzer has a bride for impedance measurements as shown in Fi.1, and its characteristic impedance is set to 11Ω in this case. The network analyzer has two terminals for a lead wire and a return wire as shown in Fi.1. After doin open, short and standard (11Ω) corrections at the two terminals, we can obtain impedances between two terminals of the lead wire and the return wire by usin S 11 at each frequency. ead wire terminal Display Network analyzer Bride eturn wire terminal Fi.1 A developed network analyzer for measurement powered by batteries 4. New Tester A network analyzer is a powerful piece of equipment for evaluatin impedance in noisy environments. However, for our purposes it must be modified to be simple, portable and not heavy in real on-site measurement. There are several methods to evaluate impedances: (1) esonance method () () Bride method (3) I-V method (4) F I-V method (5) Other (S parameter method) Meter i Meter Noise (a) without noise (a) with noise Fi.11 Measurement systems for resonant method For the loop impedance measurement of an earth return circuit, the resonance method (1) is suitable in this case. A measurement system usin the resonance method is shown in Fi.11. Fi.11(a) is i n i ISBN:

7 ecent Advances in Intellient ontrol, Modellin and Simulation the measurement system without noise, where i indicates the circuit current. Fi.11 (b) is a measurement system with noise, where i is the circuit current and i n is the current induced by noise. In Fi.11, is a resistance that represents the earthin resistance, is the inductance and is the capacitance of the earth return circuit. Meter is an impedance meter that can vary in frequency. At the resonant frequency, is iven where Meter shows the minimum resistance at the resonant frequency in Fi.11 (a). However, in real on-site measurement, there is noise, as shown in Fi.11 (b), such as radio waves and electrical fault currents, so it is not easy to evaluate. To overcome these problems, we propose the tester circuit shown in Fi.1. Fi.1(a) is the tester circuit, Fi.1(b) is an equivalent circuit. In Fi.1, S.G. is a sinal enerator, is 5 Ω, a is the additive resistance 5 Ω, a is the additive inductance 4 μh, Mix. is an analo mixer with two input ports, one dc-out port and one earth port. PF is a low pass filter; V is a dc voltmeter as shown in Fi.1 (a). In Fi.1 (b),, and comprise the loop impedance of the earth return circuit bein tested. is the earthin resistance of the electrode bein tested. a is the additive resistance, where a >> and. S.G. V o A return wire terminal a 1 a Mix. 3 E V 1 V PF V V ( ω, t) / V = V ( ω, t) = + Vn ( t) (15) 1 a + + j{ ω( + a ) } ω Where V ( ω, t) is a sinal enerator producin a sinusoidal wave with an anular frequency ω. In Eq.(15), V n (t) represents the noise as a function of time. We define the followin time interal: 1 α = V1 ( ω, t) * V ( ω, t) dt T...(16) Eq.(16) shows the correlation between V1 ( ω, t) and V ( ω, t) 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 followin equations hold at the resonant frequency. 1 V ( ω, t) α open = dt T...(17) 4 α 1 V ( ω, t) = a + T 4 dt...(18) where V ( ω, t) V ( t) dt...(19) n = Then we can write the followin equation, α β = =...() α + open a and we can finally obtain the resistance of the earth electrode bein tested as follows. βa =...(1) 1 β A lead wire terminal (a) A tester circuit a a V 1 V (b) Equivalent circuit Fi.1 A tester circuit In Fi.1(b), V 1 and V can be written as follows. 4.3 Experimental results We have developed an earthin resistance meter provided by HIOKI.E.E OP. as shown in Fi.13 with the test circuit shown in Fi.1. Fi.13 (a) 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. Fi.13 (b) shows the new tester, and also shows the lead and return wires (1 m and m respectively) connected to the terminals. (, ) 1 ( Vo ω t V1 = V ω, t) =... (14) ISBN:

8 ecent Advances in Intellient ontrol, Modellin and Simulation (a) Outlook of a new tester (b) A return wire is put on an asphalt road ead wire eturn wire (b) A new tester and a return wire and a lead wire (rolled) Fi.13 A developed new tester (c) A return wire is put on tiles Fi.14 Experiment situations By chanin the depth of the electrode, the earthin resistance can be controlled. Measurement results are shown in Fi.15. The horizontal axis is the value determined by the existin method (3pole method) and the vertical axis is the value determined by the new tester. Solid squares represent measured data, and the solid line is an approximated curve. The broken line is the ideal curve, which would be obtained if the measured by the existin 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 earthin resistances above Ω because the condition that a >> is not satisfied. Therefore, the new tester requires a correction table (values shown in Fi.15). The corrected measurements are shown in Fi.16. With corrections, the deviation between the methods is less than ±% (Fi.16). The new tester can be used for earthin resistance measurements between 1-3 Ω, as shown in Fi.16. We have examined the performance of the new tester at about sites in Japan. Several of the experimental setups are shown in Fi.14. Fis.14 (a) and (b) show the return wire placed on asphalt road, Fi.14(c) shows the return wire on tiles. We use an earth electrode.8 m lon and.14 m in diameter, which is driven to the soil. Asphalt road eturn wire A new tester Existin earth meter Existin earth meter Earthin electrode Earthin electrode (a)a return wire is put on an asphalt road 1 ISBN:

9 ecent Advances in Intellient ontrol, Modellin and Simulation of proposed method (ohm) orrection values Ideal curve Approximated curve existin methods were not small, but that by usin correction tables, the new tester can be used to measure earthin 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 earthin resistances, perhaps down to the 1-3 Ω rane. of proposed method (ohm) of 3 pole method (ohm) Fi.15 Experiment results without corrections of 3 pole method (ohm) Fi.16 Experiment results with corrections 5. onclusions This paper proposes an earthin resistance measurement method without auxiliary electrodes. A theoretical analysis of the proposal was conducted usin 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, usin a 1 m lead wire and a m return wire. The soil resistivity must be less than 1 - s/m, so the new method is applicable in urban or rural areas except where sand or stone creates hih soil resistivity. Therefore, a new earthin resistance tester was developed based on voltae ratio measurements. The new tester was tried at more than sites across Japan, includin places where the soil surface was covered by asphalt, tiles, stones and sand. It was found that measurement deviations between the new tester and eferences [1] Section 5 of Earthin and bondin : ITU-T handbook, 3. [] Y. Kobayashi, H. Ohashi, K. Murakawa, T. Kishimoto, H. Kijima: Earthin resistance measurement, EMJ98-78,pp.45-5, [3] H. Oohashi, Y. Kobayashi, K. Murakawa, T. Kishimoto, H. Kijima: A New Earthin resistance Measurement Method usin a resonant circuit, 13th Int. Zurich Symp. and Tech. Exhibit. on EM, No.6J4, pp , 1999 [4] F.M. Tesche, M.V. Ianoz, T. Karlson : EM analysis methods and computational models: hapter 8, Wiley, New York, 1989 [5] S. amo, J.. Whinnery, T.V. Daser : Field and waves in communication electronics, nd Ed., Wiley, New York, 1989 [6] E.D.Sunde: Earth conduction effects in transmission system, Dover Pub, Inc., New York, 1949X [7] S. Bour, B. Sacepe, T. Debu : Deep earth electrodes in hihly resistive earth: frequency behavior, 1995 IEEE International Symposium on EM, pp , Au [8] K. Murakawa, H. Ohashi, H. Yamane, M. Machida, H. Kijima: Proposal of earthin resistance measurement method without auxiliary electrodes, IEEJ Trans. FM, Vol.14, No.9, pp , 4. APPENDIX alculation of earthin resistance The transmission equations in Fi.6 can be represented as follows. x x V x Ve ( ) γ γ re 1 γ + Ve + =...(A1) γ x x x I e γ re 1 + γ ( ) = I e I γ x x V x Ve γ ( ) re + γ = + Ve...(A)...(A3) ISBN:

10 ecent Advances in Intellient ontrol, Modellin and Simulation γ x x x I e γ ( ) re + γ = I e I... (A4) where the time function is exp( jω t) and is omitted in Eqs.(A1-A4), V and I are the voltae and current in the lead wire at x =, and V and I are the voltae and current in the return wire at x =, and r and r are the reflection coefficients of the lead wire and the return wire at each termination. Termination conditions of each wire are iven as follows. where V ( ) 1+ r I( V ( ) 1+ r = Z =... (A6) I ( ) 1 r V V Z = Z 1 = Z = Z... (A5) 1) 1 r =... (A7) I I =... (A8) 1 + jω εeε 1 =... (A9) π l F( ) a follows. γ 1+ re Z( ω) Z + Z 1 γ re... (A13) When ε e is 1, σ e is.1 s/m, the lenth of the earth electrode is.8 m, and its diameter is.14 m, then is about.3 nf.when is 1 Ω and the frequency is 1 MHz, accordin to Eq.(A8), the earth impedance is estimated to be 96.3 j18. 9 Ω. Therefore Eq.(13) can be rewritten as follows if the frequency is less than 1 MHz. Z( ω) 1+ re + jx + Z 1 r e γ γ... (A14) where X is the imainary part of the earth electrode s impedance. If the followin resonant frequency condition is satisfied by chanin the frequency, γ 1+ re γ 1 re jx + Z = or <<... (A15) the earthin resistance of the earth electrode can be iven as follows. Z(ω )...(A16) 1 1 ) + 1 F ( x) = ln( x + 1+ x +... (A1) x x where Z,,, l and a are the earth electrode impedance, and its real part Z, its capacitance Z, the earth electrode lenth and the diameter of the earth electrode (7), respectively. In this case, Z(ω) at the sinal enerator Vs is iven as the sum of the impedances of the lead wire and the return wire as follows. V( x) V( x) Z( ω ) = +... (A11) I ( x) I ( x) x= x= Eq.(A.11) can be rewritten usin Eqs.(A1)-(A4). + γ e 1 + γ 1 e γ e γ e 1+ r 1+ r Z( ω) = Z + Z... (A1) 1 r 1 r When γ 1 << 1, Eq.(A1) can be represented as ISBN: