Investigation of Transients in Grounding Grids

SAMY, B. M. e al. VOLUME: 22 |NUMBER: 4 |2024 |DECEMBER Resea ch A icle INVESTIGATION OF TRANSIENTS IN GROUNDING GRIDS Basma M. SAMY1, Ib ahim I. I. MANSY2, Eb ahim A. BADRAN2,3,∗ 1Highe Ins i u e o Enginee ing and Technology in El-Mahalla, El-Mahala El-kub a, Egyp 2Elec ical Enginee ing Depa men , Mansou a uni e si y, Mansou a, Egyp 3Mansou a Highe Ins i u e o Enginee ing and Technology (Mansou a Collage), El-Mansou a, Egyp basbosasam[email p o ec ed], [email p o ec ed], [email p o ec ed] ∗Co esponding au ho : Eb ahim A. Bad an; [email p o ec ed] DOI: 10.15598/aeee. 22i4.240412 A icle his o y: Recei ed Ap 26, 2024; Re ised Sep 08, 2024; Accep ed Oc 08, 2024; Published Dec 31, 2024. This is an open access a icle unde he BY-CC license. Abs ac . The g ounding g id o a powe sys em is e y impo an o abso bing he ha m ul o e ol ages and/o o e cu en s du ing ansien s. The ligh ning su ges equen ly causes o e ol ages and/o o e cu - en s ia he g ounding g id. This may ha e dange ous e ec s on pe sons and/o equipmen . The e o e, his pape e iews in de ail he ansien in g ounding g ids due o ligh ning su ges. The g ounding g id con igu a- ions and ma hema ical modeling a e explained. Many con igu a ions a e used in he analysis such as one, ou , six een meshes g ounding con igu a ions. Also, wo injec ion poin s a e analyzed: a he e minal and he middle o he g id. The analysis is ca ied ou using ATP/EMTP. Many ansien esponses o ol ages and cu en s a di e en poin s o he g ounding g id o di e en con igu a ions a e calcula ed and compa ed. The peak ol age and cu en alues a e compa ed o be he basis o sa e y design o he g ounding sys em. Keywo ds Ligh ning, O e ol age, O e cu en , Mi iga- ion, G ounding G ids, ATP/EMTP. 1. In oduc ion The amewo k o powe sys ems is s uc u ed a ound speci ic poin s like gene a o and ans o me neu al poin s [1]. G ounding g ids play a key ole in e- ducing o e ol age du ing sho -ci cui e en s. These g ids consis o conduc i e segmen s ac ing as g ound- ing uni s. G ounding sys ems in subs a ions a e essen ial o sa e y and eliabili y, aiming o main ain ouch and s ep ol ages wi hin es ablished s anda ds [2]. A g ounding g id includes in e connec ed ho izon al con- duc o s and ods, wi h he p ima y goal o mee - ing sa e y le els se by indus y s anda ds [3]. Va i- ous g ounding me hods a e s udied o enhance human sa e y a ound g ounding g ids and elec ical equipmen [4]. Imp o ing g ounding g id pe o mance in ol es ad- d essing wo key a eas: educing aul cu en and e- ining g id design [5]. Dec easing aul cu en is chal- lenging [6] bu can be achie ed by adjus ing he g id’s mesh and adding e ical g ounding ods [7, 8], enhanc- ing p o ec ion agains elec ic shocks [9]. G ounding sys ems ha e mul iple unc ions, such as neu al g ounding o ans o me s, dissipa ing o e - head g ound o e ol age, balancing cha ge be ween phases and g ound, and p o iding equipmen g ound- ing [10]. P ope g ounding is c ucial o de ense agains ligh ning, ensu ing ope a o and equipmen sa e y [11]. Inadequa e g ounding can lead o damage, da a and equipmen loss, plan shu downs, and sa e y isks [12]. Elec ic powe companies a e wo king o imp o e g ounding sys ems o sa e y and eliabili y [13]. G ounding sys em pe o mance is a ec ed by ac- o s such as g ounding cu en , so moni o ing and assessing g ounding condi ions is an ongoing a ea o esea ch [14]. Due o he di icul y o obse - ©2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 371 SAMY, B. M. e al. VOLUME: 22 |NUMBER: 4 |2024 |DECEMBER ing o e ol age di ec ly, nume ical simula ions like he Al e na i e/Elec oMagne ic T ansien P og am (ATP/EMTP) a e used o in es iga ion [15]. In his pape , a de ailed o e iew and b ie discus- sion o g ounding g ids a e in oduced. The g ounding g id con igu a ions and ma hema ical modeling a e ex- plained. Many con igu a ions a e used in he analysis such as one, ou , six een meshes g ounding con igu- a ions. Also, wo injec ion poin s a e analyzed: a he e minal and he middle o he g id. The analysis is ca ied ou using ATPD aw e sion o ATP/EMTP [16]. Many ansien esponses o ol ages and cu en s a di e en poin s o he g ounding g id o di e en con igu a ions a e calcula ed and compa ed. The peak ol age and cu en alues a e compa ed o be he basis o sa e y design o he g ounding sys em. The subsequen sec ions o he pape a e o ganized as ollows: Sec ion 2. co e s g ounding con igu a ion and modeling, Sec ion 3. del es in o he ansien beha io o g ounding g ids, Sec ion 4. p esen s simu- la ions o se e al illus a i e cases, and inally, Sec ion 5. summa izes he conclusions. 2. G ounding G id Con igu a ion And Modeling Va ious me hods ha e been used o e he yea s o analyze and op imize g ounding g id design and con- igu a ion [17]. Une en spacing o g id elemen s has demons a ed imp o ed pe o mance in some cases, wi h ac o s like aul cu en , soil esis i i y, and con- duc o leng h con ibu ing o lowe and mo e e enly dis ibu ed ouch ol ages [18]. An expe imen al app oach is p esen ed in one s udy [19], while ano he in oduced he concep o a "Com- p ession a io" conduc o [20, 21]. O he echniques based on gene ic algo i hms a e applied in di e en s udies [22, 23]. An e olu iona y app oach is o en p e e ed as i op imizes he g ounding g id’s layou wi hou elying on ixed s uc u es o p e ious expe i- ence. The g ounding g id is composed o ba s posi ioned a a speci ic dep h benea h he subs a ion loo , spanning he en i e subs a ion a ea. G ounding ods a e s a e- gically placed wi hin he mesh, ex ending downwa d o a eas like building and ans o me ounda ions [24]. Fig. 1a p o ides a de ailed iew o he g ounding g id componen s [25], while Fig. 1b illus a es he g ounding elec odes, including induc ances and esis- ances. The esis ance (R) and sel -induc ance (L) a e (a) The h ee-dimensional iew. (b) Pa ame e s o he g ounding elec odes model. (c) The equi alen ci cui o e ical od/spike. Fig. 1: Equi alen ci cui o he g ound G id. de e mined using equa ions (1) and (2). R=ρ π 2[Ω] (1) L=µ◦l 2πln 2l √2 h−1[H] (2) whe e lis he leng h o each cell, is he elec ode adius, ρcu is he ma e ial esis i i y, his he dep h and he pe meabili y is assumed as he acuum pe - meabili y, µ0= 4π10−7A/m [26]. Also, he g ounding esis ance, R and he capaci ance o g ound a e de- e mined by: R =ρ πl ln 2l √2 h−1[Ω] (3) C=πεl ln 2l √2 h −1 [F](4) In his con ex , he esis i i y o he soil (ρ)is a key pa ame e , and i ’s impo an o no e ha he ©2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 372 SAMY, B. M. e al. VOLUME: 22 |NUMBER: 4 |2024 |DECEMBER pe mi i i y (ε)is de ined as ε=ε0ε , whe e ε0= 8.859 ×10−12 F/m ep esen s he acuum pe mi i - i y, and ε deno es he ela i e pe mi i i y o he soil [26]. The equi alen ci cui o he e ical od/spike is shown in Fig. 1c. The esis ance, induc ance, and ca- paci ance unde ansien phenomenon a e calcula ed by: Ri=ρ liln 8li d−1[Ω] (5) Li= 2liln 4li d×10−7[H] (6) C=ε li 18 ln 4li d×10−9[F](7) whe e, ρis solid esis i i y (Ωm),liis he o al leng h o g ound od (m), dis he diame e o he g ound od (m), and ε is he ela i e pe mi i i y o solid. 3. G ounding G id Beha io Via T ansien s-Li a u e Re iew The indus ial sec o equi es a eliable and cos - e ec i e way o moni o he sa e y o g ounding g ids o p o ec people and equipmen . A moni o ing sys- em o assessing subs a ion sa e y was c ea ed in [27], inco po a ing elecom and senso echnology as pa o he sma g id ini ia i e. I uses a se equency o pe- iodically measu e ouch and s ep ol ages and elies on a da abase o e icien g ounding g id e alua ion. Fo be e equipmen p o ec ion, he plan should ex- pand o include addi ional senso s and indices. The g ounding design also ocuses on p o ec ing equipmen , wi h a hypo hesis sugges ing ha app op ia e ouch and s ep ol ages in a ious subs a ion loca ions indi- ca e good g ounding condi ions o equipmen p o ec- ion. Howe e , u he esea ch is needed o con i m his hypo hesis. The plan in ol es a senso ne wo k and da a collec ion, which poses challenges such as ne wo k c ea ion, main enance, and eliabili y, align- ing wi h he goals o sma g id esea che s ocused on in o ma ion and communica ion echnology (ICT). In e ms o g ounding g id design, he main aim is o educe g ounding esis ance, mesh ol age, and s ep ol age o accep able le els du ing a g ound aul . I ’s also essen ial o e alua e he g id’s pe o mance a - e a ligh ning s ike, as i beha es di e en ly unde impulse cu en compa ed o powe - equency ailu es. The ATP-EMTP so wa e assesses he g ounding g id’s e ec i eness du ing ligh ning s ikes. Va ious me hods o dec ease induced and ligh ning o e ol age in ol e modi ying he g id design by adding conduc o s o ods o inc ease he g id’s su ace a ea in con ac wi h he soil. One app oach, he IEEE me hod, in ol ed placing a single od o di e en leng hs a he poin o he ligh - ning wa e’s impac . An op imal od leng h o 3 me- e s has been ound, as longe leng hs inc ease induced o e ol age due o equency-dependen induc i e e - ec s [28]. An ex e nal g ound design in dis ibu ion sys ems aimed o imp o e ligh ning pe o mance by connec - ing an ex e nal g ound wi e and g ound od o o e - head wi es [29]. An ATP-EMTP model simula es ligh - ning pe o mance, including pole op ol age, c i ical cu en , and back lasho e a e (BFOR), using di - e en impulse esis ances and ligh ning cu en wa e- o ms. Ins alling an ex e nal g ound a ec s pole op ol age, c i ical cu en , and BFOR, depending on ac- o s such as ligh ning cu en wa e o m, wa e eloc- i y, and g ound od impulse esis ance. These indings guide ansmission line g ounding sys em designs and g ounding s anda ds e isions. Ano he s udy in oduced a ansien me hodology o calcula ing node ol ages and uses a gene ic algo- i hm o op imize g ounding g id size o s udying he e ec s o ligh ning s ikes [24]. Simula ion esul s wi h a ying mesh g id sizes p o ide insigh s in o he be- ha io and impedance o he g ounding sys em du ing ligh ning s ikes. The s udy examines g ound po en ial ise (GPR) and mesh g id size o enhance sa e y, ind- ing ha i egula g ounding g ids end o be mo e se- cu e, wi h lowe o al GPR compa ed o egula g ids. Ano he in es iga ion examined he ansien beha - io o g ounding sys ems unde ligh ning s ikes us- ing ci cui models [26]. These models include cu en - con olled ol age sou ces (CCVS) o ep esen in e - ac ions among g ounding elec odes and simula e com- plex g ounding g ids unde su ge condi ions. The models align wi h EMF heo y models despi e ap- p oxima ions ela ed o ci cui ep esen a ions du ing su ge condi ions. Fu he esea ch is sugges ed o im- p o e pe o mance a lowe equencies and examine he model’s po en ial o simula ing complex g ound- ing a angemen s. While ci cui models a e limi ed by low- equency quasi-s a ic app oxima ions, EMF heo y models o - e mo e accu acy bu s uggle wi h complex geome- ies. Field heo y-based models o en o e look ioniza- ion e ec s. The ci cui app oach can be ex ended o highe equencies by di iding he elec ode ep esen a- ion in o basic cells, bu i may o e es ima e ansien ol ages due o quasi-s a ic assump ions [30]. ©2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 373 SAMY, B. M. e al. VOLUME: 22 |NUMBER: 4 |2024 |DECEMBER Las ly, a case s udy a he Al-Mos akbal subs a ion in Cai o, Egyp , e alua ed g ounding g id design un- de di e en condi ions, including g ound aul s and ligh ning s ikes [28]. The s udy highligh s he impo - ance o assessing g ounding g id pe o mance du ing ligh ning s ikes, whe e impulse cu en s cause di e - en beha io han powe - equency ailu es. Va ious s a egies a e examined o mi iga e induced o e ol age, ocusing p ima ily on changing g id de- sign o inc ease con ac su ace wi h he soil. The IEEE me hod ecommends using a 3-me e od a he poin o ligh ning impac o educe induced o e ol - age. ATP-EMTP simula ions assess he e ec i eness o hese me hods. Mo eo e , a s udy explo es g ounding sys em mod- eling o g ound po en ial ise (GPR) compu a ion, powe sys em simula ions, and insula ion coo dina ion [31]. I p oposed a me hod o p edic equi alen ci cui pa ame e s h ough ime-domain impulse esponse op- imiza ion. Equi alen ci cui s ha accu a ely ep e- sen g ounding sys ems while accoun ing o equency e ec s and soil ioniza ion a e de eloped. Nonlinea ci cui s imp o e esponse accu acy, educing e o s in GPR es ima ion o less han 4%. These ci cui s apply o sys emic analyses and GPR calcula ions conside ing ligh ning s ikes and sho ci cui s. While many elec omagne ic ansien (EMT) in es- iga ions ocus on o e ol age beha io ac oss a wide equency ange, o e cu en o g ounding g id’s e ec s ecei es less a en ion. 4. G ounding G id Simula ion and Analysis 4.1. G ounding G id Simula ion To examine he ansien esponse o g ounding g ids accu a ely, i is c ucial o conduc simula ions o hese g ids. In his esea ch, he ansien esponse o ligh - ning impulses using a ious es ed g ids: CS01, CS04, and CS16, as depic ed in Fig. 2 a e analyzed o many cases. The dimensions o hese es cases a e de ailed in Table 1. The ho izon al g ounding g id conduc o s ha e a adius o 10 mm and a e bu ied a a dep h o 0.6 m in soil wi h ε= 50 and ρ= 100Ωm [32]. The cu en impulse injec ed a poin A in each g id ol- lows he o mula p esen ed in equa ion (8). The peak alue o his cu en impulse is app oxima ely 12 kA. The peak cu en and he ime cons an s a e selec ed as gi en in [32] o compa ison pu pose. I( ) = 12000 e−27000 −e−5600000 (8) The i s poin o injec ion is poin A a he e minal o he g id, whe eas he second poin is poin B a he middle o he g id, as gi en in Fig. 2 Fig. 3 illus a es he ATPD aw model employed o hese es cases. Ta- ble 2 p o ides he RLC pa ame e s o he g ids unde in es iga ion, whe e R and C ep esen he esis ance and capaci ance o he g id, while L1 and L2 deno e he induc ance o he main wi e and he g id conduc o s. Fig. 4 p esen s he compa ison be ween he pub- lished in [32] and simula ed ol age wa e o m a he ou le poin o bo h one and ou meshes g ounding g id as esponse o he ligh ning impulse a poin A. I can be seen he closeness be ween he wa e o ms and hence he a ailabili y o he p oposed model using ATPD aw. Tab. 1: RLC o each g id con igu a ion. R(Ω) L1(H)C(F)L2(H) CS01 6.499 2.396e-005 6.802e-09 5.529e-006 CS04 5.665 2.396e-005 7.803e-09 5.529e-006 CS16 1.071 1.412e-004 4.125e-08 3.301e-005 4.2. Analysis o G ounding G id’s Vol ages The analysis o g ounding g id’s ol age is ca ied ou ia he in es iga ion o he g id esponse when he in- jec ion is applied a wo poin s; e minal poin A and middle poin B. 1) Injec ion a he e minal poin A The ligh ning impulse is applied in his case a poin A. The wa e o ms o he ansien ol ages in esponse o a ligh ning impulse o di e en g ounding g id con igu- a ions a e illus a ed. In Fig. 5, he ol age wa e o ms a he ou le poin o one, ou , and six een g ounding g id meshes a e obse ed. Also, Fig. 6 shows he ansien ol age wa e o ms a poin s B2 and B3 a one mesh con igu a ion and he same poin a a ious g id con igu a ions in esponse o he ligh ning impulse. Addi ionally, Fig. 7 displays he ansien ol age wa e o ms a se e al poin s o each g id con igu a ion in esponse o he same ligh ning impulse. The abo e analysis is ca ied ou again when he h ee e minals o he g ound g id a e ea hed ia he e ical od. Fig. 8 illus a es he ansien ol age wa e o ms a he h ee e minals o bo h one and ou meshes’ g ound g id con igu a ions. Fu he mo e, Fig. 9 shows he compa ison be ween he ol age o he same e minal poin o he h ee g ound g id con i- u a ions unde s udy. ©2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 374 SAMY, B. M. e al. VOLUME: 22 |NUMBER: 4 |2024 |DECEMBER Fig. 2: Di e en numbe o meshes o squa e g ids. (a) CS01. (b) CS04. (c) CS16. Fig. 3: ATPD aw simula ion models o di e en cases. (a) Published. (a) B2 a one mesh. (b) B3 a one mesh. Fig. 6: The ol age wa e o ms a e minal poin s o di e en g ids as esponse o he ligh ning impulse a poin A wi hou ea hing he e minals. (b) Simula ed. Fig. 4: Compa ison be ween he published and simula ed ol - age wa e o m a he ou le poin o bo h 1 and 4 meshes as esponse o he ligh ning impulse. Fig. 5: The ol age wa e o m a he ou le poin o 1, 4, and 16 meshes as esponse o he ligh ning impulse a poin A. (a) 1 mesh. ©2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 375 SAMY, B. M. e al. VOLUME: 22 |NUMBER: 4 |2024 |DECEMBER (b) 4 meshes. (c1) 16 meshes. (c2) 16 meshes. (c3) 16 meshes. Fig. 7: The ol age wa e o ms a se e al poin s o di e en g id con igu a ions as esponse o he ligh ning impulse a poin A wi hou ea hing he e minals. Fig. 10 shows he compa ison be ween he ansien ol age wa e o ms a many poin s o he ou meshes con igu a ions when he h ee e minals a e ea hed. Also, Fig. 11 shows he compa ison be ween he an- sien ol age wa e o ms a many poin s o he sex- een meshes con igu a ions when he h ee e minals a e ea hed. I can be seen ha nonlinea i y o ol ages wa e o m and he peaks. Also, he ea hing o he main e minals educes he peak alues. 2) Injec ion a he e minal poin B Again o mo e in es iga ion o he esponse o he g ounding g id o he ligh ning impulse, he injec ion o he ligh ning is applied in his case a poin B. The wa e o ms o he ansien ol ages in esponse o a ligh ning impulse o di e en g ounding g id con igu- a ions a e illus a ed. (a) 1 mesh. (b) 4 meshes. Fig. 8: The ol age wa e o m a he h ee e minal poin s o 1 and 4 meshes as esponse o he ligh ning impulse a poin A wi h ea hing o he h ee e minals. (a) B2. (b) B4. (c) B3. Fig. 9: The ol age wa e o ms a e minal poin s o he one mesh and hei equi alen s o di e en g ids as esponse o he ligh ning impulse a poin A wi h ea hing o he h ee e minals. ©2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 376 SAMY, B. M. e al. VOLUME: 22 |NUMBER: 4 |2024 |DECEMBER Fig. 10: The ol age wa e o ms a se e al poin s o he ou g id con igu a ion as esponse o he ligh ning impulse a poin A wi h ea hing o he h ee e minals. Fig. 11: The ol age wa e o ms a se e al poin s o he sex een g id con igu a ion as esponse o he ligh ning impulse a poin A wi h ea hing o he h ee e minals. Fig. 12: The ol age wa e o ms a he e minal poin s o di e - en g ids as esponse o he ligh ning impulse a poin B wi hou ea hing o he e minals. Fig. 13: The ol age wa e o ms a se e al poin s o he ou meshes’ g id as esponse o he ligh ning impulse a poin B wi hou ea hing o he e minals. Fig. 14: The ol age wa e o ms a se e al poin s o he sexi- een meshes’ g id as esponse o he ligh ning impulse a poin B wi hou ea hing o he e minals. Fig. 15: The ol age wa e o ms a he e minal poin s o di e - en g ids as esponse o he ligh ning impulse a poin B wi h ea hing o he e minals. ©2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 377 SAMY, B. M. e al. VOLUME: 22 |NUMBER: 4 |2024 |DECEMBER Fig. 12 shows he ansien ol age wa e o ms a he eminal poin s o a ious g id con igu a ions in esponse o he ligh ning impulse a poin B. Addi- ionally, Figs. 13 and 14 display he ansien ol age wa e o ms a se e al poin s o each o ou and sexi- een g id con igu a ion in esponse o he same ligh - ning impulse. The abo e analysis is ca ied ou again when he h ee e minals o he ound g id a e ea hed ia he e ical od. Fig. 15 illus a es he ansien ol age wa e o ms a he h ee e minals o bo h one and ou meshes’ g ound g id con igu a ions. Fu he mo e, Fig. 16 shows he compa ison be ween he ol age o he same e minal poin o he h ee g ound g id con iu- a ions unde s udy. 4.3. Analysis o G ounding G id’s Cu en s The analysis o g ounding g id’s cu en s is ca ied ou ia he in es iga ion o he g id esponse when he in- jec ion is applied a wo poin s; e minal poin A and he middle poin B. Also, he e minals o he main sides a e no g ounded and hen g ounded as wo case s udies as gi en be o e. 1) Injec ion a he e minal poin A The injec ion o he ligh ning impulse is applied in his case a poin A. The wa e o ms o he ansien cu - en s in esponse o a ligh ning impulse o di e en g ounding g id con igu a ions a e illus a ed. The e minals o he main sides a e no g ounded Fig. 17a shows he cu en s o he ou b anches o he one mesh g ounding g id con igu a ion (CS01). Fig. 17b shows he cu en s o he b anches o he i s mesh o ou meshs g ounding g id con igu a ion (CS04). Also, Fig. 17c shows he cu en s o he b anches o he i s mesh o sexi een meshs g ound- ing g id con igu a ion (CS16). The cu en s o he wo b anches connec ed o he injec ion poin a e inc eased wi h he inc easing o he g ounding g id meshes. I is inc eased o he one, ou , six een meshes as 1598 A, 3954 A, and 6766A, espec i ely. The e o e, i can be concluded ha he g ound g id cu en s a he i s mesh a e inc eased as he numbe o meshes inc eased. Fig. 18 illus a es he dis ibu ion o cu en s in se - e al pa hes o he ou meshes con igu a ion o he igh pa h (I1, I7, I21, and I17), he le pa h (I3, I9, I11, and I15), and he wo middle pa hes; middle pa h1 (I1, I23, I13, and I15) and middle pa h 2 (I3, I5, I19, and I17). I can be no ice ha he oscilla o y beha iou o he cu en inc eases a he end o each pa h whe e he cu en go o he ea h. Fig. 19 illus a es he dis ibu ion o cu en s in se e al pa hes o he six een meshes con igu a ion il- lus a es he igh pa h (I1, I2, I4, I6, I23, I24, I59, I77), he middle igh pa h (I1, I2, I4, I19, I27, I55, I73, I74), he middle pa h (I1, I2, I15, I29, I51, I67, I70, I74), he middle le pa h (I1, I11, I31, I37, I38, I55, I73, and I74), he le pa h (I9, I32, I43, I61, I62, I68, I70, and I74), he le -middle pa h (I9, I32, I43, I48, I52, I56, I77). I can be no iced ha he oscilla o y beha iou o he cu en inc eases a he end o each pa h whe e he cu en goes o he ea h. The e minals o he main sides a e g ounded Fig. 20a shows he cu en s o he ou b anches o he one mesh g ounding g id con igu a ion (CS01). Fig. 20b shows he cu en s o he b anches o he i s mesh o ou meshes g ounding g id con igu a- ion (CS04). Also, Fig. 20c shows he cu en s o he b anches o he i s mesh o six een meshes g ounding g id con igu a ion (CS16). The cu en s o he wo b anches connec ed o he injec ion poin a e inc eased wi h he inc easing o he g ounding g id meshes. I is inc eased o he one, ou , six een meshes as 9059 A, 13857 A, and 24448 A, espec i ely. The e o e, i can be concluded ha he g ound g id cu en s a he i s mesh a e inc eased as he numbe o meshes inc eased. Fig. 21 illus a es he dis ibu ion o cu en s in se - e al pa hes o he ou meshes con igu a ion o he igh pa h (I1, I7, I21, and I17), he le pa h (I3, I9, I11, and I15), and he wo middle pa hes; middle pa h1 (I1, I23, I13, and I15) and middle pa h 2 (I3, I5, I19, and I17). I can be no ice ha he oscilla o y beha iou o he cu en inc eases a he end o each pa h whe e he cu en go o he ea h. Fig. 22 illus a es he dis ibu ion o cu en s in se e al pa hes o he six een meshes con igu a ion il- lus a es he igh pa h (I1, I2, I4, I6, I23, I24, I59, I77), he middle igh pa h (I1, I2, I4, I19, I27, I55, I73, I74), he middle pa h (I1, I2, I15, I29, I51, I67, I70, I74), he middle le pa h (I1, I11, I31, I37, I38, I55, I73, and I74), he le pa h (I9, I32, I43, I61, I62, I68, I70, and I74), he le -middle pa h (I9, I32, I43, I48, I52, I56, I77). ©2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 378 SAMY, B. M. e al. VOLUME: 22 |NUMBER: 4 |2024 |DECEMBER I can be no iced ha he oscilla o y beha iou o he cu en inc eases a he end o each pa h whe e he cu en goes o he ea h. (a) Fou meshes’ g id. (b) Sex een meshes’ g id. Fig. 16: The ol age wa e o ms a se e al poin s o he meshes’ g id as esponse o he ligh ning impulse a poin B wi h ea hing o he e minals. (a) 1 mesh. (b) 4 meshes. (c) 16 meshes. Fig. 17: Cu en s o all b anches o he i s mesh o di e en g id con igu a ions as esponse o he ligh ning impulse a poin A. (a) The igh pa h. (b) The le pa h. (c) The middle pa h 1. (d) The middle pa h 2. Fig. 18: Cu en s o all b anches o ou meshes g id as esponse o he ligh ning impulse a poin A. A. Injec ion a he e minal poin B Again o mo e in es iga ion o he esponse o he g ounding g id o he ligh ning impulse, he injec ion o he ligh ning is applied in his case a poin B. The wa e o ms o he ansien cu en s in esponse o a ligh ning impulse o di e en g ounding g id con igu- ©2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 379 SAMY, B. M. e al. VOLUME: 22 |NUMBER: 4 |2024 |DECEMBER [31] ANDRADE, A. F., e al. Modeling G ounding Sys ems Response o Cu en Impulses Consid- e ing Nonlinea E ec s. IEEE T ansac ions on Powe Deli e y. 2021, ol. 36, no. 6, pp. 3858- 3866. DOI: 10.1109/TPWRD.2021.3049908. [32] GOUDA, O. E., G. M. AMER, T. M. EL-SAIED. Fac o s A ec ing T ansien Response o G ound G id Sys ems. MEPCON Con e ence. 1998. ©2024 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 386