A Study on Steady-State Resistances of Horizontal Grounding Mesh and Conducting Plates

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1 THE SCIENCE AND ENGINEEING EVIEW OF DOSHISHA UNIVESITY, VOL. 55, No. July 14 A Study on Stedy-Stte esistnces of Horizontl Grounding Mes nd Conducting Pltes Teo FUJIWAA*, Keisue NAKAMUA*, Aiiro AMETANI*, Noto NAGAOKA*, Yosiiro BABA* (eceived Mrc 1, 14) Tis pper investigtes te stedy-stte resistnces of orizontl grounding electrodes bsed on experimentl mesurements FDTD( Finite-Difference Time-Domin) simultions nd nlyticl formul. Te resistnce of grounding mes is compred wit tt of orizontl conducting plte considering te re nd te spe. Finlly n pproximte formul to estimte grounding resistnce is developed. Grounding electrodegrounding mesconducting pltestedy-stte resistncefdtd simultion FDTD * * * * 1) (),3) (Finite-Difference Time-Domin Metod : FDTD ) 4) *Fculty of Science nd Engineering, Dosis University, Kyoto Telepone: , FAX: , E-mil: metni@mil.dosis.c.jp ( 17 )

2 11 藤原健生中村圭佑雨谷昭弘長岡直人馬場吉弘 Fig. 1 Sunde ) r l r r r ln l r l l l r [m], l [m] r l (1) r d [m]fig. 1 ρ [Ωm] d [m] (1) r d d ln l (1)(4) d l ln 1 l r 1 d 1 l (1) () (3) r (4) ρ [Ωm] ρ [Ωm] r l d l [m] Fig. 1. A buried conductor. ρ [Ωm] 1,) d d 1 l l Imge electrode d [m] d Ert surfce Ert electrode ( / 4er)rcsin( e) (5) e 1 l r (6) el[m]r[m] (5) l = Plte Plte 8r (7) A [m ] r (7) r A (8) ) Plte 4 1 4d r (9) ρ : [Ω m]r : (8) [m]d : [m] Fig. (1) Fig..1 m.6 m.3 m (KHD 1.75) Pulse Genertor (NoiseKen INS-4) 4 m (3DV) 5 Ω Fig ns 1 A 1 A ( 18 )

3 水平網状および平板状接地電極の定常接地抵抗に関する研究 m Wenner 4 1) KEW416 ( ).5 m 1 4 Ωm 5 Ωm Coxil cble 5 I Current led wire V 4 m Pulse genertor 5 m Connecting wire of. m Horizontl grounding electrodeof..5 m 4 Ωm 6 Lio.1 m.6 m.3 m σ = 1-1 [S/m] ε r = 1 5 Ω 3 1 A 15 ns Fig.. Experimentl setup. Current led wire Current [A] Simultion Experiment Time [s] 5 3 V I Connecting wire Horizontl grounding electrode Fig. 4. Anlyticl spce..5m Fig. 3. Injected current. () DPO (Tetronix ) DC ~ 1 GHz P6139A (Tetronix ) P6139A DC ~ 5 MHz 8 pf P51 (Tetronix ) DC ~ 5 MHz.75 pf AC CT -1 (Tetronix ) CT-1 5Hz ~ 1GHz 5 mv/ma Fig. 4 Δs.5 m X, Y, Z 6. m Fig. 5 FDTD t = 3 ns 416 VFDTD 46 V Sunde (4) 44 V 3 % Voltge [V] 4 Simultion 3 1 Experiment Time [ns] Fig. 5. Comprison of mesured nd FDTD simultion results. ( 19 )

4 11 藤原健生中村圭佑雨谷昭弘長岡直人馬場吉弘 FDTD FDTD FDTD D d torus D Dln4 D d c (1) (1)(13) c (7) p b b c A M 1 P (3) (11)(1) M mes mes b (14) (15) Fig. 7 s 1,) 1 r 1 s s s s (16) Fig. 6 M r llnl d 1 (17) (1) Fig. 6 S M M (7) M c D M P 1 (11) [Ω](4)ρ[Ωm]s [m]r[m]l[m]d [m] / M / M MD P = (7) [Ω] () M l M A [m ] l M A M 1 (1) l r Fig. 6. Eqully spced grounding mes. s [m] s [m] s [m] r M (13) rm l M Electrode Fig. 7. prllel conductors on te sme plne. ( )

5 水平網状および平板状接地電極の定常接地抵抗に関する研究 113 m mes mes // m (18) Fig. 8 Fig. 9 Tble 1. m 4 mm 1 m 1 m 1 mm Fig. 9 1 m 1 Ωm 6 Ωm m m Coxil cble 5 I Current led wire V 4 m Pulse genertor 5 m Connecting wire of. m Horizontl grounding electrode Fig. 8. Experimentl setup wit connecting wire. r [m] [m] [m] [m] [m] () Squre plte (b) Mes (M = 4) (c) Circulr plte Fig. 9. Vrious grounding electrodes. Tble 1 t = 3 ns Fig. 1().85 m ( Cse B-1 ) ( Cse A ) 1(b)( Cse B )( Cse C ) t = 1 ns 6 V 3) Tble 1 t = 3 ns % ( KEW 416) ( ± 3% )Cse B-1 (9) 49 Ω 6 % t = 3 [ns] Voltge [V] 6 Cse B-1 Cse A-1 4 Cse A Time [ns] Voltge [V] () squre plte nd mes 6 Cse B-1 4 Cse B- Cse C Time [ns] (b) Squre nd circulr pltes Fig. 1. Mesured results of trnsient voltges. Tble 1 ( Cse A ).85 m ( Cse B-1 )Cse A-1 15 % Cse A-.4 % ( 1 )

6 114 藤原健生中村圭佑雨谷昭弘長岡直人馬場吉弘 ( Cse C ) Cse B-1 % M = 4 M 4 = m.85 m.85 m.85 m.85 m () Cse D-1 (b) Cse D- (c) Cse D-3.85 m Tble 1. Experimentl conditions nd mesured resistnces corresponding to Fig. 9. Cse Type [m] r *[m] Size[m ] Vs G **[Ω] A-1 Mes A- Mes B-1 Squre Plte B- Squre Plte C Circulr Plte ρ=ωm,applied current : rise time T f 15ns,mplitude I 1A *r : equivrent equivlent rdius given by eq.(.1) Vs :Voltge t t=3[ns] ** G :mesured result wit fll of potentil metod V:Simultion t 3[ns] Fig m.85 m ( M = 4, 9, 16 ). m 7Ωm Tble M = 4 %M = 9 % M = 16 1 %.85 m FDTD (1) Tble (16)(18) (16) 7 % (18) 14 % [m] [m] (d) Cse E (e) Cse F Fig. 11. Vrious electrodes used in experiments. Tble. Experimentl conditions nd mesured resistnces corresponding to Fig. 11. Cse Type r *[m] r M Vs G **[Ω] G Cse D-1 Mes Cse D- Mes Cse D-3 Mes Cse E SQ-Plte Cse F Circle ρ : 7 Ωm, Size:.7m M : te number of mes cells in te orizontl grid *r : equivrent equivlent rdius given by A/πV s : mesured result t t=3[ns] G : mesured result wit fll of potentil metod () FDTD Fig. 1 Δs. m X 6 m, Y 6 m, Z 6.m. m Ωm m m M = (16) (18) FDTD Tble 4 M Fig. 13 FDTD (16) 3 %(9) 11 % Fig. 13 ( )

7 水平網状および平板状接地電極の定常接地抵抗に関する研究 m V Fig. 1. Anlyticl spce for n FDTD simultion. Tble 3. Mesured result G nd clculted results by equtions (16) nd (18). Tble 4. FDTD simultion result V s nd clculted results by equtions (16) nd (18). I Current injected wire Cse ρ [Ωm] [m] M G [Ω] Eq.(16) Eq.(19) (18) A A D D D M : te number of te mes cells in grid, te grid G : mesured result wit te fll of te potentil metod Type M V s Eq.(16) Eq.(19) (18) Mes Plte Size of te grid : m m, Ert resittivity : Ωm M : te number of te grid cellsmes, in te Vgrid, s : te Vs voltge : te voltge vlue vlue t t = t3 t = 3 ns ns FDTD (1) () (3) 1) ( 1993)pp.1-14 ) E.D.Sunde, Ert conduction effects in trnsmission system, (Dover Publictions, Inc., New Yor, 1968), pp ) B131() 5-14 (11) 4) FDTD (1998)pp.1-74 esistnce [] 5 45 FDTD simultion 4 Eq.(16) 35 Eq.(18) Number of cells te mes in te grid M Fig. 13. FDTD simultion results nd teoreticl results s function of M. ( 3 )

Chapter 6 Electrostatic Boundary Value Problems. Dr. Talal Skaik

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