<\/p>\n
ELEKTR\u00ddK -ELEKTRON\u00ddK - B\u00ddLG\u00ddSAYAR M\u00dcHEND\u00ddSL\u00dd\u00d0\u00dd 10. ULUSAL KONGRES\u00dd\nB\u0130R \u00c7UBUK TOPRAKLAYICI \u00c7EVRES\u0130NDE POTANS\u0130YEL\nDA\u011eILIMININ SONLU FARKLAR Y\u00d6NTEM\u0130 \u0130LE HESABI\n\u00d6zcan KALENDERL\u01301\nErsan \u015eENT\u00dcRK2 Okan \u0130hsan \u00d6ZT\u00dcRK3\n1\u0130stanbul Teknik \u00dcniversitesi, Elektrik-Elektronik Fak\u00fcltesi, Elektrik M\u00fchendisli\u011fi B\u00f6l\u00fcm\u00fc\n2, 3Turkcell \u0130leti\u015fim Hizmetleri A.\u015e.\n1e-posta: ozcan@elk.itu.edu.tr\n2e-posta: ersan.senturk@turkcell.com.tr\n3e-posta: okan.ozturk@turkcell.com.tr\nAnahtar s\u00f6zc\u00fckler: Elektriksel Topraklama, Potansiyel Da\u011f\u0131l\u0131m\u0131, Sonlu Farklar Y\u00f6ntemi\nyerine \nsunulmu\u015ftur. Problemin \n\u00d6ZET\nBu \u00e7al\u0131\u015fmada, elektriksel topraklamada yayg\u0131n olarak\nkullan\u0131lan topraklay\u0131c\u0131 t\u00fcrlerinden biri olan \u00e7ubuk\ntopraklay\u0131c\u0131lar\u0131n \ngetirirken\ni\u015flevlerini \n\u00e7evrelerinde olu\u015fan potansiyel da\u011f\u0131l\u0131m\u0131n\u0131n say\u0131sal\nhesab\u0131 \nsay\u0131sal hesab\u0131,\nsilindirsel koordinatlarda, iki boyutlu sonlu farklar\nile geli\u015ftirilen bir bilgisayar program\u0131\ny\u00f6ntemi \nkullan\u0131larak yap\u0131lm\u0131\u015ft\u0131r. \u00c7al\u0131\u015fma, canl\u0131lar\u0131n can\ng\u00fcvenli\u011fi bak\u0131m\u0131ndan \u00f6nemli olan ad\u0131m ve dokunma\ngerilimlerinin boyutunu ve de\u011fi\u015fimini vermekte ve\n\u00e7evresinde potansiyel\nelektriksel \nda\u011f\u0131l\u0131m\u0131 hesaplar\u0131 i\u00e7in farkl\u0131 bir yakla\u015f\u0131m se\u00e7ene\u011fi\nsunmaktad\u0131r.\ntopraklay\u0131c\u0131lar \n1. G\u0130R\u0130\u015e\ntehlikeli \nelektrik devrelerini, \nnesneleri \nElektriksel topraklama, ba\u015fta insanlar olmak \u00fczere,\nelemanlar\u0131n\u0131 ve\ncanl\u0131lar\u0131, \nkulland\u0131\u011f\u0131m\u0131z \ngerilimlerden\nkorumada ve elektriksel sistemlerin i\u015fletilmesi i\u00e7in\ngereken toprak potansiyelini sa\u011flamada kullan\u0131lan bir\nelektrik \ntesisi,\ntopraklanacak yerin toprakla ba\u011flant\u0131s\u0131n\u0131 sa\u011flayan\ntopra\u011fa g\u00f6m\u00fclen\ntopraklama \ntopraklay\u0131c\u0131 ad\u0131 verilen iletkenlerden olu\u015fur. Koruma\ng\u00f6revini ar\u0131za ko\u015fullar\u0131nda olu\u015fan ak\u0131mlar\u0131, \u00e7evresi\ni\u00e7in tehlikeli gerilimler olu\u015fturmadan g\u00fcvenli bir\n\u015fekilde topra\u011fa ak\u0131tarak yerine getirir.\ntesisidir. Basit\u00e7e bir \niletkenlerinden ve \ntopraklama \nde\u011feri, \ntesisini \nBir topraklama tesisi \u00fczerinde ve \u00e7evresinde olu\u015facak\ngerilim \nolu\u015fturan,\ntopraklama \nmalzemenin \ntopraklay\u0131c\u0131n\u0131n\nt\u00fcr\u00fcne, boyutlar\u0131na, \ng\u00f6m\u00fclme ortam\u0131na ve ko\u015fullar\u0131na yak\u0131ndan ba\u011fl\u0131d\u0131r.\nAtlama, delinme, dokunma, ba\u011flanma gibi olaylar\nsonucu devrede veya elemanlarda meydana gelen k\u0131sa\ndevrelerde veya y\u0131ld\u0131r\u0131m gibi elektriksel bo\u015falman\u0131n\ntesisinden y\u00fcksek de\u011ferde\netkisinde \nak\u0131mlar ge\u00e7er. Bu ak\u0131mlarla topraklama tesisi ve ba\u011fl\u0131\noldu\u011fu yap\u0131larda ortaya \u00e7\u0131kacak gerilim d\u00fczeyi,\ntopraklama direncine veya genel anlamda topraklama\nempedans\u0131na ba\u011fl\u0131d\u0131r. Topraklama direnci ise topra\u011f\u0131n\nve topraklay\u0131c\u0131n\u0131n \u00f6zelliklerine ba\u011fl\u0131d\u0131r. Bu basit gibi\ng\u00f6r\u00fcnen ba\u011fl\u0131l\u0131k zinciri pek\u00e7ok ara\u015ft\u0131rmaya konu\nolmu\u015ftur [1 - 4]. Topraklay\u0131c\u0131n\u0131n geometrisine (\u00e7ubuk,\ntopraklama \n\u015ferit, \nboru,...), \nboyutlar\u0131na, \nlevha, \nderinli\u011fine, \nb\u00fcy\u00fckl\u00fc\u011fe ba\u011fl\u0131 olarak \nbelirlenmesi, \ndeneysel \u00e7al\u0131\u015fmalar\u0131n ilgi oda\u011f\u0131 olmu\u015ftur [1 - 6].\ng\u00f6m\u00fclme\ntopra\u011f\u0131n \u00f6z direncine gibi bir\u00e7ok\ntopraklama direncinin\ntopraklama konusunda kuramsal ve\nLiterat\u00fcrde, y\u00f6netmelik ve standartlarda topraklama\ndirencini hesaplamak i\u00e7in amprik, analitik ve say\u0131sal\nbir\u00e7ok form\u00fcl ve y\u00f6ntem, verilmekte; topraklama\ndirencini \u00f6l\u00e7erek belirlemek \ni\u00e7in bir\u00e7ok \u00f6l\u00e7me\ny\u00f6ntemi a\u00e7\u0131klanmaktad\u0131r [7, 8]. Sonu\u00e7ta belli bir\ndiren\u00e7 de\u011ferine sahip bir topraklay\u0131c\u0131dan bir ak\u0131m\nge\u00e7ti\u011finde, topraklay\u0131c\u0131da referans topra\u011fa g\u00f6re bir\ngerilim olu\u015fur ve topraklay\u0131c\u0131 ile referans toprak\naras\u0131nda bir potansiyel da\u011f\u0131l\u0131m\u0131 ortaya \u00e7\u0131kar (\u015eekil 1).\nBurada \ntoprak kavram\u0131,\npotansiyel\ntopraklay\u0131c\u0131 \nda\u011f\u0131l\u0131m\u0131nda potansiyelin teorik olarak s\u0131f\u0131r kabul\nedildi\u011fi \nbir\ntopraklay\u0131c\u0131dan yakla\u015f\u0131k 20 m uzakl\u0131ktaki toprak\nb\u00f6l\u00fcm\u00fc referans toprak olarak kabul edilir.\nb\u00f6l\u00fcm\u00fcd\u00fcr. Uygulamada \ns\u00f6z\u00fc edilen \n\u00e7evresinde \nreferans \nolu\u015fan \ntoprak \nbir \nU (V)\nUa\n3\n2\nUtk\n1\nx (m)\n4\n\u015eekil 1. Topraklay\u0131c\u0131 \u00e7evresindeki potansiyel da\u011f\u0131l\u0131m\u0131.\n U (V): Gerilim ekseni\n x (m): Uzakl\u0131k ekseni\n Utk: Topraklay\u0131c\u0131 gerilimi\n Ua: Ad\u0131m gerilimi\n1. Potansiyel da\u011f\u0131l\u0131m\u0131\n2. Toprak\n3. Topraklay\u0131c\u0131\n4. Referans toprak\nBir topraklay\u0131c\u0131 \u00e7evresindeki potansiyel da\u011f\u0131l\u0131m\u0131,\ndokunma ve ad\u0131m gerilimlerinin b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc belirler.\nDokunulan yer ile ondan 1 m uzakl\u0131ktaki nokta\naras\u0131ndaki potansiyel fark\u0131, dokunma gerilimi olarak;\n1 m uzunlu\u011fundaki bir ad\u0131mda iki ayak aras\u0131ndaki\npotansiyel fark\u0131 da ad\u0131m gerilimi olarak adland\u0131r\u0131l\u0131r.\n197\n\fELEKTR\u00ddK -ELEKTRON\u00ddK - B\u00ddLG\u00ddSAYAR M\u00dcHEND\u00ddSL\u00dd\u00d0\u00dd 10. ULUSAL KONGRES\u00dd\nHer iki gerilimin de tehlikeli olmayacak s\u0131n\u0131rlarda\nolmas\u0131 gerekir. Bu gerilimler hakk\u0131nda bir\u015fey\ns\u00f6yleyebilmek \ni\u00e7in potansiyel da\u011f\u0131l\u0131m\u0131n\u0131 bilmek\ngerekir. Uygulamada bu bilgiyi elde etmek i\u00e7in\nde\u011fi\u015fik form\u00fcller kullan\u0131lmaktad\u0131r [7 - 8].\n1(1j,iV1j,iV\n++\n+\u2212\n+\nj,1iV)\n+\n+\nh\nr2\nh\nr2\n1(\n\u2212+\nj,iV4j,1Vi\n)\n\u2212\n\u2212\n=\n0\n(2)\nBu \u00e7al\u0131\u015fmada, uygulamada yayg\u0131n olarak kullan\u0131lan\ntopraklay\u0131c\u0131 \n\u00e7ubuk\ntopraklay\u0131c\u0131 \u00e7evresindeki potansiyel da\u011f\u0131l\u0131m\u0131, sonlu\nfarklar y\u00f6ntemi ile hesaplanm\u0131\u015ft\u0131r.\nt\u00fcrlerinden biri olan bir \nolacakt\u0131r [9]. A\u011f\u0131n potansiyeli bilinmeyen her d\u00fc\u011f\u00fcm\u00fc\ni\u00e7in yaz\u0131lan bu denklemde, h a\u011f\u0131n g\u00f6z geni\u015fli\u011fi veya\nad\u0131m b\u00fcy\u00fckl\u00fc\u011f\u00fc, r ise denklemin yaz\u0131ld\u0131\u011f\u0131 d\u00fc\u011f\u00fcm\u00fcn\nkoordinat\u0131d\u0131r.\n3. \u00c7UBUK TOPRAKLAYICI ve SONLU\nFARKLAR MODEL\u0130\nBir topraklay\u0131c\u0131 \u00e7evresindeki potansiyel da\u011f\u0131l\u0131m\u0131n\u0131\nhesaplamak amac\u0131yla model olarak 16 mm \u00e7ap\u0131nda 2\nm boyunda bir \u00e7ubuk \ntopraklay\u0131c\u0131 g\u00f6z \u00f6n\u00fcne\nal\u0131nm\u0131\u015ft\u0131r. Referans toprak kavram\u0131na uygun olarak bu\ntopraklay\u0131c\u0131dan 20 m uzakta bulunan her noktada\npotansiyel de\u011ferinin s\u0131f\u0131r volt oldu\u011fu kabul edilmi\u015ftir.\nBu \u015fekilde d\u00fc\u015f\u00fcn\u00fclerek olu\u015fturulmu\u015f olan model \u015eekil\n3\u2019te g\u00f6sterilmi\u015ftir. Her bir kare g\u00f6z\u00fcn kenar\u0131 h = 2\nmetre al\u0131nm\u0131\u015ft\u0131r. Bu \u015fekilde problemin incelendi\u011fi\n\u00e7\u00f6z\u00fcm b\u00f6lgesi, 90 kare g\u00f6z ve 112 d\u00fc\u011f\u00fcmden\nmeydana gelmi\u015ftir.\n20 m\n2. SONLU FARKLAR Y\u00d6NTEM\u0130\nSonlu farklar y\u00f6ntemi (SFY), potansiyel da\u011f\u0131l\u0131m\u0131\nhesaplar\u0131nda da kullan\u0131lan bir say\u0131sal y\u00f6ntemdir [9].\n\u0130lkesi, potansiyel da\u011f\u0131l\u0131m\u0131 Laplace veya Poisson\ndenklemiyle verilmi\u015f kapal\u0131 bir b\u00f6lgede say\u0131sal\n\u00e7\u00f6z\u00fcmlemedeki say\u0131sal \nt\u00fcrev konusundan bilinen\nt\u00fcrevler i\u00e7in sonlu fark denklemlerini kullanarak\npotansiyel da\u011f\u0131l\u0131m\u0131n\u0131 hesaplamaya dayan\u0131r. Bunun\ni\u00e7in \u00f6rne\u011fin \ninceleme\nb\u00f6lgesi kare, dikd\u00f6rtgen veya \u00fc\u00e7gen g\u00f6zleri olan bir\na\u011fa b\u00f6l\u00fcn\u00fcr (\u015eekil 2).\niki boyutlu problemlerde, \ny j+2\nyj+1\ny j\nyj-1\nyj-2\nh\nV i, j+1 2\nVi-1,j\n3\nVi,j\nVi+1,j\n0\n1\nVi,j-1 4\nh\nx i-2\nx i-1\nx i\nx i+1\nxi+2\n\u015eekil 3. Kartezyen koordinatlarda, iki boyutlu, kare\ng\u00f6zl\u00fc sonlu farklar y\u00f6ntemi a\u011f\u0131 \u00f6rne\u011fi.\nbilinen \nA\u011f\u0131n d\u00fc\u011f\u00fcm noktalar\u0131nda Laplace veya Poisson\ndenklemleri yerine sonlu fark denklemleri yaz\u0131l\u0131r.\nB\u00f6ylelikle \nd\u00fc\u011f\u00fcm\nve \npotansiyellerini i\u00e7eren bir lineer denklem tak\u0131m\u0131 elde\nedilir. Bu denklemlerde, s\u0131n\u0131r ko\u015fullar\u0131 veya bilinen\nd\u00fc\u011f\u00fcm potansiyelleri kullan\u0131larak \nlineer denklem\ntak\u0131m\u0131 \u00e7\u00f6z\u00fcl\u00fcr ve bilinmeyen d\u00fc\u011f\u00fcm potansiyelleri\nbulunur.\nbilinmeyen \nBu \u00e7al\u0131\u015fmada kare g\u00f6zlere sahip bir a\u011f yap\u0131s\u0131\nkullan\u0131lm\u0131\u015ft\u0131r. \n\u0130ncelenen problemin geometrisine\nuygun olarak sonlu fark denklemleri silindirsel\nkoordinatlarda yaz\u0131lm\u0131\u015ft\u0131r. Silindirsel koordinatlarda\niki boyutlu Laplace denklemi;\n2\nV\n\u2202\n2\nr\n\u2202\n+\n1\nr\nV\n\u2202\nr\n\u2202\n+\n2\nV\n\u2202\n2\nz\n\u2202\n=\n0\n(1)\n\u015eekil 3. \u00c7ubuk topraklay\u0131c\u0131 SFY modeli.\n\u015eekil 3\u2019te g\u00f6sterilen ve \u015eekil 4\u2019te d\u00fc\u011f\u00fcm numaralar\u0131\nverilen modelin kare g\u00f6zlere b\u00f6l\u00fcnm\u00fc\u015f olan\nkesiminde yer alan d\u00fc\u011f\u00fcmlerden 1, 12, 23, 34, 35, 45,\n55, 56, 65, 74, 83, 84, 91, 92, 93, 94, 98, 99, 100, 101\nve 112 numaral\u0131 d\u00fc\u011f\u00fcmlerdeki potansiyel de\u011ferleri;\nbu d\u00fc\u011f\u00fcmlerin herbirinin 11 ve 102 d\u00fc\u011f\u00fcmleri aras\u0131na\nyerle\u015ftirilmi\u015f, 2 metre boyundaki bak\u0131r \u00e7ubuk elektrot\ntopraklay\u0131c\u0131dan 20 metre uzakta olmas\u0131ndan dolay\u0131,\ns\u0131f\u0131r volttur. Potansiyel de\u011ferleri belli olan 1, 11, 12,\n23, 34, 35, 45, 55, 56, 65, 74, 83, 84, 91, 92, 93, 94,\n98, 99, 100, 101, 102 ve 112 numaral\u0131 d\u00fc\u011f\u00fcmlerin\nd\u0131\u015f\u0131ndaki d\u00fc\u011f\u00fcmlerin potansiyel de\u011ferleri bilinme-\nmektedir.\ndir. Burada, r ve z silindirsel koordinatlar, V = V(r, z)\npotansiyeldir. (1) denkleminin sonlu farklar ifadesi,\nBu \n\u00e7al\u0131\u015fmada potansiyel de\u011ferleri bilinmeyen\nd\u00fc\u011f\u00fcmlerin potansiyel de\u011ferlerinin Sonlu Farklar\n198\n\fELEKTR\u00ddK -ELEKTRON\u00ddK - B\u00ddLG\u00ddSAYAR M\u00dcHEND\u00ddSL\u00dd\u00d0\u00dd 10. ULUSAL KONGRES\u00dd\nY\u00f6ntemi (SFY) ile hesaplanmas\u0131 ama\u00e7lanm\u0131\u015ft\u0131r. Her\nd\u00fc\u011f\u00fcme ili\u015fkin sonlu farklar denklemi (2) numaral\u0131\nifadede oldu\u011fu gibi ayr\u0131 ayr\u0131 yaz\u0131lm\u0131\u015f ve elde edilen\ntak\u0131m\u0131 MATLAB 6.0 program\u0131\nlineer denklem \nkullan\u0131larak \nd\u00fc\u011f\u00fcmlerin\npotansiyel de\u011ferleri bulunmu\u015ftur.\nbilinmeyen \n\u00e7\u00f6z\u00fclerek \nHesaplamalarda kullan\u0131lan denklemlerin olu\u015fturulmas\u0131\nve olu\u015fturulan bu denklemlerin d\u00fczenlenmesi g\u00f6z\n\u00f6n\u00fcnde bulundurularak MS EXCEL program\u0131nda\nVisual Basic tabanl\u0131 bir program haz\u0131rlanm\u0131\u015f ve\ndenklemlerin d\u00fczenlenmesi sonras\u0131nda elde edilen\nmatrisin hatas\u0131z ve kullan\u0131ma uygun olarak elde\nedilmesi sa\u011flanm\u0131\u015ft\u0131r. Elde edilen bu denklem\ni\u00e7in MATLAB 6.0 program\u0131\ntak\u0131m\u0131n\u0131n \u00e7\u00f6z\u00fcm\u00fc \nkullan\u0131lm\u0131\u015ft\u0131r. Olu\u015fturulan \ntak\u0131m\u0131nda\ndenklem \nbilinmeyen d\u00fc\u011f\u00fcmlerin potansiyel ifadelerinin ba\u015f\u0131nda\nbulunan katsay\u0131lar\u0131n olu\u015fturdu\u011fu katsay\u0131lar matrisi\n[A], potansiyel de\u011ferleri bilinmeyen d\u00fc\u011f\u00fcmlerin\npotansiyellerinin olu\u015fturdu\u011fu matris [x] ve potansiyel\nde\u011ferleri bilinen d\u00fc\u011f\u00fcmlerin potansiyel de\u011ferlerinin\nolu\u015fturdu\u011fu matris [B] olarak g\u00f6sterildi\u011finde; bu\nmatrisler aras\u0131nda [A] . [x] = [B] \u015feklinde bir ba\u011f\u0131nt\u0131\nelde edilir. Bilinmeyen d\u00fc\u011f\u00fcm say\u0131s\u0131 88 adet oldu\u011fu\ni\u00e7in olu\u015fturulmas\u0131 gereken katsay\u0131lar matrisinin\nboyutu 88 x 88 olacakt\u0131r.\n102\n103\n104\n105\n106\n107\n108\n109\n110\n111\n112\n11\n22\n33\n44\n54\n64\n73\n82\n90\n97\n101\n10\n21\n32\n43\n53\n63\n72\n81\n89\n96\n100\n9\n8\n7\n6\n5\n4\n3\n2\n1\n20\n31\n42\n52\n62\n71\n80\n88\n95\n99\n19\n30\n41\n51\n61\n70\n79\n87\n94\n98\n18\n29\n40\n50\n60\n69\n78\n86\n93\n17\n28\n39\n49\n59\n68\n77\n85\n92\n16\n27\n38\n48\n58\n67\n76\n84\n91\n15\n26\n37\n47\n57\n66\n75\n83\n14\n25\n36\n46\n56\n65\n74\n13\n24\n35\n45\n55\n12\n23\n34\n\u015eekil 4. Topraklama sistemi SFY \u00e7\u00f6z\u00fcm a\u011f\u0131.\nDenklem sistemi \u00e7\u00f6z\u00fcld\u00fckten sonra sonlu farklar\na\u011f\u0131n\u0131n d\u00fc\u011f\u00fcm noktalar\u0131nda elde edilen potansiyel\nde\u011ferleri \u015eekil 5\u2019te g\u00f6sterilmi\u015ftir. \u015eekil 5'ten\ng\u00f6r\u00fcld\u00fc\u011f\u00fc gibi 11 ve 102 numaral\u0131 d\u00fc\u011f\u00fcmlerin\ncinsinden\npotansiyelleri, \nde\u011ferlendirmek ve ba\u011f\u0131l olarak di\u011fer gerilim\nde\u011ferlerine ge\u00e7i\u015fi normalize ederek kolayla\u015ft\u0131rmak\namac\u0131yla 100 Volt olarak kabul edilmi\u015ftir.\n\u00e7\u00f6z\u00fcm\u00fc \ny\u00fczde \n(%) \n100\n81,0671 67,7645 56,7853 47,0328 38,0457 29,6045 21,6069 14,0187 6,8363\n0\n100\n82,771\n68,9501 57,5002 47,48\n38,3541 29,8448 21,8161 14,2058 6,9696\n0\n79,2723 72,7284 63,734\n54,5486 45,6359 37,0624 28,8178 20,8966 13,339\n6,2889\n0\n68,0944 65,0695 58,9175 51,4519 43,513\n35,4673 27,4736 19,6018 11,9199 4,7487\n0\n60,6368 58,7962 54,226\n48,0115 40,9054 33,3571 25,6061 17,72\n9,5115\n0\n0\n54,9952 53,6233 49,8955 44,4699 37,9494 30,7839 23,2767 15,5893 7,8219\n0\n50,3966 49,2151 45,8764 40,8313 34,5894 27,5954 20,2344 12,7042 5,5226\n0\n46,4521 45,2994 41,9806 36,8693 30,4896 23,2715 15,8827 7,9407\n0\n0\n42,9517 41,6615 37,8777 31,9569 24,7747 16,2924 9,3672\n0\n0\n39,828\n38,1322 32,8824 24,0289 15,2977 0\n0\n0\n37,2401 34,6522 25,1043 0\n0\n0\n0\n0\n0\n\u015eekil 5. D\u00fc\u011f\u00fcmlerin SFY ile bulunan volt cinsinden\npotansiyel de\u011ferleri\nElde edilen bu potansiyel de\u011ferleri ile \u00e7izilecek toprak\ny\u00fczeyindeki potansiyel da\u011f\u0131l\u0131m\u0131, ad\u0131m ve dokunma\ngerilimlerinin hesaplanmas\u0131 a\u00e7\u0131s\u0131ndan b\u00fcy\u00fck \u00f6nem\nta\u015f\u0131maktad\u0131r. \u015eekil 6\u2019da yap\u0131lan SFY \u00e7\u00f6z\u00fcmlemesi ile\nelde edilen toprak y\u00fczeyindeki potansiyel da\u011f\u0131l\u0131m\u0131\ng\u00f6sterilmi\u015ftir.\nU (V)\n120\n100\n80\n60\n40\n20\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\nUzakl\u0131k (m)\n\u015eekil 6. Bir \u00e7ubuk topraklay\u0131c\u0131 \u00e7evresinde toprak\ny\u00fczeyindeki potansiyel da\u011f\u0131l\u0131m\u0131\n4. SONU\u00c7LAR\ntopraklamada yayg\u0131n kullan\u0131lan bir\nElektriksel \ntopraklay\u0131c\u0131 \ni\u00e7in\nt\u00fcr\u00fc olan \u00e7ubuk \na\u00e7\u0131klanan ve yap\u0131lan bu hesaplardan g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi\nbir topraklay\u0131c\u0131 \u00e7evresindeki potansiyel da\u011f\u0131l\u0131m\u0131 sonlu\ntopraklay\u0131c\u0131 \n199\n\fELEKTR\u00ddK -ELEKTRON\u00ddK - B\u00ddLG\u00ddSAYAR M\u00dcHEND\u00ddSL\u00dd\u00d0\u00dd 10. ULUSAL KONGRES\u00dd\n[2] Takahashi T., Kawase T., \"Calculation of Earth\nResistance for a Deep-Driven Rod in a Multi-\nLayer Structure\", IEEE Transactions on Power\nDelivery, Vol. 6, No. 2, April 1991.\n[3] Meliopoulos A. P. S., Xia F., Joy E. B.,\nCokkinides G. J., \"An Advanced Computer\nModel for Grounding System Analysis\", IEEE\nTransactions on Power Delivery, Vol.8, No. 1,\nApril 1993.\n[4] Dawalibi F., Mukhedkar D., \"Influence of\nGround Rods on Grounding Grids\", IEEE\nTransactions on Power Apparatus and Systems,\nVol. PAS-98, No.6, Nov.\/Dec. 1979, pp. 2089-\n2098.\n[5] Y\u0131ld\u0131r\u0131m, H., Kalenderli, \u00d6., T\u00fcrkay, B.,\n\u00c7elikyay, M., \"Topraklama a\u011flar\u0131n\u0131n bilgisayar\ndestekli \n- Elektronik\nM\u00fchendisli\u011fi 6. Ulusal Kongresi, Bursa, s. 130-\n133, 11-17 Eyl\u00fcl 1995.\nanalizi\", Elektrik \n[6] Hasse, P., Overvoltage Protection of Low\nVoltage Systems, IEE Power and Energy Series\n33, United Kingdom, 2000,\n[7] ANSI\/IEEE Std 80-1986, IEEE Guide for Safety\nin AC Substation Grounding, 1986.\n[8] Elektrik \nTesislerinde \nTopraklamalar\nY\u00f6netmeli\u011fi, TMMOB, Elektrik M\u00fchendisleri\nOdas\u0131 Bursa \u015eubesi, Bursa, 2001 (21 A\u011fustos\n2001 tarih ve 24500 say\u0131l\u0131 Resmi Gazete'de\nyay\u0131mlanm\u0131\u015ft\u0131r).\n[9] Kalenderli, \u00d6., Elektrik M\u00fchendisli\u011finde Sonlu\nElemanlar Y\u00f6ntemi Ders Notlar\u0131, \u0130.T.\u00dc., 2003.\nile \nsay\u0131sal olarak kolayl\u0131kla\nfarklar y\u00f6ntemi \nbulunabilir. Bilgisayarda yap\u0131lan bu hesaplarla\npotansiyel da\u011f\u0131l\u0131m\u0131n\u0131 hem dokunma hem de ad\u0131m\ngerilimi bak\u0131m\u0131ndan, hem do\u011fru hem h\u0131zl\u0131 bir \u015fekilde\netmek olanakl\u0131d\u0131r.\nhesap \nedilen \nsonu\u00e7lar\u0131 \nElde \nincelendi\u011finde\ntopraklay\u0131c\u0131dan uzakla\u015ft\u0131k\u00e7a potansiyelin ve birim\nuzunluk ba\u015f\u0131na d\u00fc\u015fen potansiyel fark\u0131n\u0131n azald\u0131\u011f\u0131\ng\u00f6r\u00fclmektedir. Hesaplar farkl\u0131 topraklay\u0131c\u0131 uzunluklar\u0131\ni\u00e7in yap\u0131larak topraklay\u0131c\u0131 boyunun, farkl\u0131 g\u00f6m\u00fclme\nderinlikleri i\u00e7in yap\u0131larak da g\u00f6m\u00fclme derinli\u011finin\netkisi g\u00f6r\u00fclebilir. Bunun yay\u0131lma direncini ve ad\u0131m\ngerilimini azalt\u0131c\u0131 etkileri oldu\u011fu bilinir. Bu y\u00f6ntemle\nyap\u0131lan \npotansiyel\nda\u011f\u0131l\u0131m\u0131n\u0131n ve potansiyel farklar\u0131n\u0131n s\u00f6z\u00fc edilen\nb\u00fcy\u00fckl\u00fcklerle de\u011fi\u015fimini elde etmek ve g\u00f6rmek\nolacakt\u0131r.\n\u00e7al\u0131\u015fman\u0131n \nayr\u0131cal\u0131\u011f\u0131 \nise \nSonu\u00e7 olarak, bu \u015fekilde \nboyutlarda ve derinliklerdeki \npotansiyel \nhesab\u0131 \nde\u011ferlendirilebilir, g\u00fcvenli ve do\u011fru \ntasar\u0131m\u0131 yap\u0131labilir.\nfarkl\u0131 geometrilerde,\ni\u00e7in\ndavran\u0131\u015flar\u0131\ntopraklama\ntopraklay\u0131c\u0131lar \nda\u011f\u0131l\u0131m\u0131 \nile \nKAYNAKLAR\n[1] Bogensperger J. H., Frei J., Pack S., \"Resistance\nof Grounding Systems Stationary and Transient\nBehaviour\", Ninth International Symposium on\nHigh Voltage Engineering, August \n28-\nSeptember 1, 1995.\n200\n\f<\/pre>\n
\n