Induced and ground potential voltage components in analysis of separation distance for lightning protection in buildings

Transcription

1 Renaa MARKOWSKA 1 Poliechnika Białosocka, Wydział Elekryczny (1) doi: / Induced and ground poenial volage componens in analysis of separaion disance for lighning proecion in buildings Absrac. The paper presens numerical analysis of volages beween LPS and nearby elecrical equipmen, and separaion disances necessary o preven dangerous sparking during direc lighning srikes. The analysis is focused on he role of induced and ground poenial volage componens. The compuaion of volages was carried ou wih specialized sofware ha uses advanced numerical mehods based on elecromagneic field heory approach. Based on he resuls sparking disances were calculaed and compared wih separaion disances according o EN Sreszczenie. Arykuł przedsawia analizy numeryczne napięć pomiędzy LPS a pobliskim urządzeniem elekrycznym oraz odsępów izolacyjnych wymaganych w celu uniknięcia przeskoków podczas wyładowań piorunowych. Analizowano rolę dwu składowych napięcia: indukowanej i związanej z rozkładem poencjału w gruncie. Obliczenia napięć wykonano za pomocą oprogramowania wykorzysującego meody numeryczne opare na eorii pola. Na bazie wyników wyznaczono odległości przeskoku i porównano je z odsępami izolacyjnymi zgodnie z EN (Składowe napięcia indukowana i związana z rozkładem poencjału w gruncie w analizie odsępów izolacyjnych do celów ochrony odgromowej w budynkach). Keywords: lighning proecion in buildings, separaion disance, surge wihsand, numerical compuaions. Słowa kluczowe: ochrona odgromowa w budynkach, odsęp izolacyjny, wyrzymałość udarowa, obliczenia numeryczne. Inroducion According o he curren legi sae of echnical knowledge, he basic proecion measure agains direc lighning srikes o a building srucure is exernal Lighning Proecion Sysem (LPS). The recommendaions on he design, echnical realizaion, exploiaion and mainenance of LPS are included in curren inernaional sandards [1, 2]. The proper design and use of LPS is imporan for reducion of life hazard and physical damage o he srucure iself and o he conen of he srucure, including elecrical and elecronic equipmen and sysems. The role of LPS is o inercep lighning srikes and o lead down and dissipae lighning currens in ground safely for living beings, he proeced srucure and is conens. During his process, he shor-erm lighning curren componens cause wo major problems: 1) he flow of lighning curren in LPS conducors (or in building consrucion componens used as LPS) resuls in volage drops (mainly inducive) along hese conducors and in loops creaed by LPS and oher conducive insallaions; 2) he dissipaion of lighning curren in ground resuls in poenial differences beween LPS grounding sysem componens due o non-zero grounding impedance (nonzero impedance of sysem componens and finie soil conduciviy). The volage differences beween LPS componens of boh hese origins resul in surge volages beween he LPS componens and elecrical insallaions or equipmen locaed near o hese componens. The mos severe condiions (highes volages) should be expeced for he insallaions or equipmen locaed close o he poin of srike o LPS, since his poin would have he highes poenial wih respec o he common grounding poin of elecrical insallaions (main grounding erminal), which is locaed near he ground level. Such siuaion occurs ypically in case of insallaions or equipmen locaed on a building roof near a verical air erminaion rod [3]. The surge volage ha arises beween LPS conducor and nearby elecrical insallaion or equipmen may exceed he surge wihsand capabiliy of dielecric maerial (air, concree, wood ec.) in he place of proximiy. In he consequence, he unconrolled lighning curren flow may likely cause damage o he whole elecrical insallaion and equipmen conneced o he considered elemen. In order o preven dangerous volage sparking, he proper minimal disance should be mainained beween LPS and oher conducive insallaions. The minimal disance beween wo conducive pars a which no dangerous sparking can occur is called separaion disance [2]. For he purpose of his work, anoher erm, sparking disance, is defined. I is he maximal disance beween wo conducive pars a which sparking can occur. Hence, he separaion disance should be greaer han he sparking disance. According o he sandard EN [2] he separaion disance s can be calculaed using he following formula: i (1) s kc l km k where: k i coefficien dependen on he class of LPS (equal o 0.08 for class I, 0.06 for class II and 0.04 for class III and IV), k m coefficien dependen on he elecrical insulaion of maerial presen a he place of proximiy (equal o 1 for air and 0.5 for concree, brick or wood), l lengh of he shores pah along LPS conducors from he considered place of proximiy o he neares equipoenial bonding poin or earh erminaion (in m), k c coefficien dependen on he curren share in he individual LPS conducors of he pah l. For mesh air erminaion sysem or many inerconneced ring conducors he formula (1) is exended o [2]: k k i (2) s k l k l... k l... m c1 1 c2 2 ci i where: l i, k ci respecively, lengh and coefficien of curren share associaed wih i-h elemen of he pah l. For meshed air erminaion sysem on he roof, he coefficien k c may be deermined as shown in figure 1 [2]. The formulas (1) and (2) were originally inroduced in 1980s based on resuls of simplified calculaions performed for very simple srucures, due o limied compuaion power available [4, 5]. The simplificaion of he formulas relies on he approach ha he dependency of he separaion disance on he waveform and peak value of surge volage beween wo conducive pars is subsiued by simple dependency on he curren sharing beween LPS conducors. PRZEGLĄD ELEKTROTECHNICZNY, ISSN , R. 92 NR 12/

2 Laely, some more complex numerical compuaions have been underook using a compuer code ha solves complee Maxwell s equaions (CONCEPT) [4]. The main objecive of he work [4] was o verify he sandard EN formulas in case of complex LPS, i.e. mesh air erminaion on he roof and srucures represening meal roof as naural LPS componen. The evaluaion of separaion disances in [4] was based on numerical compuaions of volages induced in loops. Based on hese volages he separaion disances were calculaed using he early esablished consan area crierion [4, 6]. Fig. 1. Deerminaion of coefficiens k c of lighning curren share o individual LPS conducors (based on [2]) Indeed, modern compuer simulaion codes available nowadays make i possible o perform numerical compuaions of complex elecromagneic problems in very complex srucures. They use circui, ransmission line or elecromagneic field heory approaches [7, 8, 9, 10, 11]. In case of separaion disance calculaion, he elecromagneic field heory approach seems o be he mos suiable. I allows for sraighforward aking ino accoun all he elecromagneic couplings and phenomena in complex wire srucures [4, 9, 10, 11]. However, even now mos of he analyses performed using such sofware is limied o eiher only aboveground [4, 10] or only underground [9] srucures. This is also in he case of separaion disance compuaions presened in [4], where furhermore, ground was assumed as ideal, perfecly conducive plane. The compuaions in [4] were performed for srucures of differen size and heigh for only one lighning curren waveform 0.25/100 s, which is he sandard (EN [1]) represenaion of subsequen reurn sroke curren. This paper presens resuls of numerical compuaions of surge volages and sparking disances wih using consan area crierion and specialized sofware (CDEGS) based on elecromagneic field heory approach. In hese compuaions, however, boh aboveground and underground pars of he srucure in concern have been aken ino accoun and realisic (non-zero impedance) ground has been assumed. The analysis presened in he paper concerns also four differen curren waveforms represening differen lighning curren componens. The paper is a coninuaion of earlier auhor s works on separaion disance compuaion [12, 13, 14, 15, 16]. The supreme goal of all hese works as well as he presen paper is o find beer soluions for esimaion of separaion disances for engineering-design purposes han provided in he sandard [2]. This need is jusified by [4, 13, 14, 15, 16], where i was shown ha he separaion disances evaluaed using sandard [2] definiions may be under- or overesimaed compared o numerical analysis. In [12] some preliminary resuls of numerical analysis regarding he curren waveform 10/350 s (sandard [1] represenaion of firs posiive reurn sroke) are presened. Work [13] shows he firs aemp o simplify he calculaion for he curren waveform 0.25/100 s (sandard represenaion of subsequen negaive reurn sroke). In work [15] he exac numerical compuaion resuls for boh 10/350 s and 0.25/100 s as well as wo more differen curren waveforms for simple inducive loop were presened. Works [14, 16] consider he influence of cable rouing (simple inducive loops and complex srucures) and lighning curren waveform on he separaion disance. Compuaion mehodology The compuaions of surge volages a he considered places of proximiy were performed using HIFREQ sofware. The program is a par of large specialized sofware package CDEGS, which offers grea possibiliy of numerical compuaions of curren and poenial disribuions in complex wire srucures (including heir above- and under-ground pars), elecric and magneic fields in and around he srucures as well as some oher auxiliary compuaions, e.g. Fourier ransformaions. The compuaion mehod employed in HIFREQ [17] is based on wo-poenial (scalar and vecor) elecric field inegral equaions (derived from full Maxwell s equaions) solved numerically using mehod of momens [17, 18]. The wo-poenial equaions are formulaed for a user-defined 3- dimensional nework of inerconneced hin, cylindrical conducors (subdivided in segmens of appropriae lengh and radius), locaed in muli-layered media (air and/or one or more layers of soil). The elecrical parameers (resisiviy, permiiviy, permeabiliy) of he conducors and of he media are defined by he user [17]. The elecric filed inegral equaions are formulaed in frequency domain and so he compuaions in HIFREQ. The ime-domain soluions are obained based on Fas Fourier Transform (FFT) of he source signal (curren, volage or elecromagneic field), performing he frequency domain compuaions in HIFREQ for harmonic sources and subjec he resuls for Inverse Fas Fourier Transform (IFFT). The operaions of Forward and Inverse FFT have been performed using FFTSES [19], which is also a par of CDEGS sofware package. The source signal for he compuaions was he imedomain lighning curren waveform injeced ino he srucure a he poin of srike using an ideal curren source. The curren waveform a he aachmen poin was assumed as arbirary (as inroduced in he sandards [1, 2]). The influence of curren disribuion in lighning channel was disregarded in he compuaions. Simple calculaion wih using 10 m long conducor aached o he poin of srike (wih he curren source a he op) showed ha he peak values of obained volages differ no more han 8 % compared o he case wihou he conducor. Only in case of curren waveform 0.25/100 s he difference was larger, abou 30 %. The observed differences can be associaed mainly wih he change of lighning curren wave a he aachmen poin due o reflecion phenomena. These effecs of curren disribuion in lighning channel are no in he scope of he paper, however furher sudies are needed. The lighning curren waveform was described using he following sandardized formula of EN [1]: (3) i I e where: I peak value of he curren wave, correcion facor, 1 fron ime consan, 2 ail ime consan. The values of he parameers used in formula (1) were se according o he sandard [1] requiremens (for LPS PRZEGLĄD ELEKTROTECHNICZNY, ISSN , R. 92 NR 12/2016

3 class IV) or adjused so ha o obain he following impulse curren waveforms: 1) 10/350 s, 100 ka sandard [1] represenaion of firs posiive reurn sroke curren, 2) 4/200 s, 75 ka represenaion of reurn sroke curren of moderae fron ime, 3) 1/200 s, 50 ka sandard [1] represenaion of firs negaive reurn sroke curren, 4) 0.25/100 s, 25 ka sandard [1] represenaion of subsequen negaive reurn sroke curren. According o he hin wire approach applied in HIFREQ, he considered building srucures were composed of cylindrical conducors. I was assumed ha naural building componens (reinforcemen and foundaion grounding) are used as LPS. These componens were modeled as galvanized seel conducors of approximae radius, according o [17]. Elecrical insallaions were defined as copper insulaed conducors, and equipmen chassis as aluminium wires a he edges. The verical air erminaion rod on he roof was se as copper conducor. A single layer ground model was chosen and soil was assumed as poor, dry or moderaely humid, wih resisiviy 500 m, relaive permiiviy 10 and relaive permeabiliy 1. The conducors of he considered srucures were subdivided in segmens wih lenghs no exceeding /10, where is he wavelengh of he highes considered frequency. The highes frequency corresponding o 0.25 s impulse curren fron ime was 32,768 MHz, which resuls in he wavelengh of abou 9 m in air and 2.5 m in soil. Hence, he segmen maximum lenghs were se o 0.9 m and 0.25 m respecively. Once he ime domain surge volages a he considered places of proximiy in he srucures had been compued, he sparking disances were deermined using consan area crierion [4, 20]. According o he crierion, he spark beween wo elecrodes subjeced o unipolar surge volage will occur if paricular value of inegral A is reached (Fig. 2): In his work, he sparking disance d was compued numerically based on equaions (4), (5) and (7) using ime domain surge volages a he places of proximiy. Examined configuraions The considered building srucure is a large hall wih dimensions of 48 x 24 m and heigh 12 m. I is composed of naural LPS (class IV) wih naural ype A earh erminaion sysem. Elecrical equipmen in he building is supplied wih underground power line from MV/LV ransformer locaed in abou 60 m disance. On he roof of he building an examined elecrical equipmen is locaed. The equipmen is proeced agains direc lighning srikes by verical air erminaion rod. Direc lighning srike o he air erminaion rod is assumed. The analysis is focused on evaluaion of separaion disance beween he verical air erminaion rod and he proeced equipmen (Fig. 3). a) Configuraion A b) Configuraion B (4) A 2 u 1 U d where: U 0 saic (DC) volage breakdown. 0 c) Configuraion C Fig. 2. Illusraion of consan area crierion The relaions beween A, U 0 and sparking disance d (disance a which spark/discharge under impulse or DC volage occurs) are well esablished based on experimenal ess and are widely known in lieraure [20, 21, 22, 4]: (5) A 590 d (6) U 630 d 0 (7) U d for 0.25 d 2.5 where: A (kvs), U 0 (kv), d (m). Fig. 3. Locaions of he proeced equipmen on he building roof and configuraions of is PE wire pah (dash line) inside he building The analysis was carried ou for hree differen pahs, along which he power supply cable o he proeced equipmen was laid down (Fig. 3). For simpliciy only he PE PRZEGLĄD ELEKTROTECHNICZNY, ISSN , R. 92 NR 12/

4 (Proecive Earh) wire of he cable was included in he simulaion model. Hence, he PE wire pahs corresponded o differen mechanisms, by which he surge volage was produced: magneic inducion in loops associaed wih ground poenial difference beween exreme foundaion grounding elecrodes (configuraions A and B, Fig. 3a, 3b), and magneic inducion in loop only wih no ground poenial difference (configuraion C, Fig. 3c). The aim of his sudy was o deermine he wors case condiions for surge volage sparking exposures relaed o cable rouing and o he main origin of heir generaion, i.e. magneic inducion in loops and ground poenial rise due o finie soil conduciviy, which may have significan influence on he separaion disance, as i was shown in [12, 13]. Surge volage compuaion resuls The compued ime-domain volages beween he air erminaion rod and he proeced equipmen for configuraions (A, B and C) from figure 3 and for differen lighning curren waveforms are presened in figure 4. The compuaion resuls show ha for every considered lighning curren impulse he volages produced in configuraions A and B of he PE wire have very similar waveforms. They differ only in he peak value. These differences, however, are significan only for longer riseime curren impulses (10 s and 4 s) and become less pronounced in case of shor rise-ime currens (0.25 s). The volage generaed in configuraion C is generally differen han ha produced in he oher wo (A and B). The waveform of configuraion C volage for longer rise-ime currens (10 s) corresponds well wih he waveforms produced in configuraions A and B. However, for shor riseime currens (1 s and 0.25 s) he volage waveforms obained for configuraion C are deformed by oscillaions. These oscillaions arise due o ravelling wave phenomena in he relaively long PE wire, abou 150 m ( = 156, Fig. 3c). The resonan frequency can be seen in figure 4c. I is abou 500 khz, which corresponds o 600 m wavelengh. The lengh of he PE wire is a quarer of his wavelengh. I should be noed also ha he half cycle of he oscillaion, 1 s, corresponds o he impulse curren rise-ime. Illusraion of his siuaion is shown in figure 5. The volage generaed in configuraion C is mainly of inducive naure. I is produced in large loop formed by he LPS down conducor locaed direcly beneah he verical air erminaion rod and he PE wire. From figure 4a and 4b i can be seen ha his volage is of negaive polariy wih respec o he volages produced in configuraions A and B. The volage generaed in case of configuraion A and B is a superposiion of wo componens: 1) volage induced magneically in he loop formed by he LPS down conducor beneah he verical air erminaion rod, ground and he PE wire, 2) ground poenial difference beween he wo foundaion earh elecrodes locaed beneah he air erminaion rod and he main grounding erminal. For a given lighning curren impulse, he componen relaed o ground poenial difference is he same for boh configuraions, A and B. If o assume ha he inducion componen is of opposie polariy o ground poenial componen (as i was obained for configuraion C, Fig. 4a, 4b), he lower volage produced for configuraion A compared o B can be explained by is higher inducion componen (larger loop) wih respec o he same value of ground poenial componen. The differences in he peak values of volages produced for configuraions A and B are less pronounced in case of shor rise-ime curren impulses (Fig. 4c, 4d) compared o longer rise-imes. This can be explained by smaller effecive area of lighning curren dissipaion by grounding sysem in case of shorer rise-ime curren pulses. Hence, he ground poenial componen for shor rise-ime currens is much higher han for long rise-ime. Consequenly, he inducion componen is much less visible in he oal volage. a) b) c) d) Fig. 4. Volages beween he air erminaion rod and he proeced equipmen for differen lighning currens: a) 10/350 s 100 ka, b) 4/200 s 75 ka, c) 1/200 s 50 ka, d) 0.25/100 s 25 ka 268 PRZEGLĄD ELEKTROTECHNICZNY, ISSN , R. 92 NR 12/2016

5 sandard ways of calculaion of coefficien k c of curren share in he individual LPS down conducors. The firs way of k c calculaion is shown in figure 1. In case of lighning srike o he corner, he oal lighning curren is equally divided beween 3 conducors (wo edges of he mesh air erminaion and he down conducor beneah he sriking poin). Hence he curren share in he LPS down conducor beneah he air erminaion rod equals o k c = This is valid in case of all of he considered configuraions (A, B, and C). The oher way o deermine he curren share coefficien is using he following formula [2]: Fig. 5. Illusraion of volage ravelling wave in PE wire observed in configuraion C for 1/200 s lighning curren (Fig. 4c) Sparking and separaion disance calculaion resuls Calculaion of sparking disance in case of oscillaory ype volage waveforms (configuraion C in figures 4c and 4d) is problemaic, since consan area crierion generally applies o unipolar impulses. However, for he purpose of rough approximaion in his work such calculaion was done. In he approximaion, i was assumed ha each subsequen oscillaory pulse of he same polariy as he firs one (larger han saic DC volage breakdown U 0 ) was inegraed and added up o he oal value of area A (Fig. 2). Furhermore, his calculaion was done separaely for oscillaory pulses of posiive and negaive polariy and he larger value from hese wo was aken as he final value of sparking disance. The illusraion of he compued sparking disances for he considered lighning curren impulses and for he examined configuraions (Fig. 3) are presened in figure 6. These resuls generally reflec he feaures and characerisics of he compued volages observed in he previous secion. In paricular, he resonance effecs observed for shor lighning curren fron imes (1 s and 0.25 s) resul in sudden increase of sparking disance for hese curren waveforms. Fig. 6. Sparking disance d for differen lighning currens esimaed using consan area crierion based on compued volages (Fig. 4) The deailed resuls of calculaion of sparking disances are shown in able 1. The las column in he able presens he values of separaion disance calculaed according o sandard EN [2] formulas (1) and (2). There are wo values of separaion disance in able (1), associaed o wo EN k c n (8) 3 where: n oal number of down conducors, c disance of he down conducor o he nex down conducors, h spacing (or heigh) beween ring conducors. In all he considered configuraions (A, B and C) n = 8, c = 18 m (average from 24 m and 12 m) and h = 12 m. Hence, k c = According o formula (2), k i = 0.04 (class IV), k m = 1 (air insulaion), k c1 = 1, l 1 = 1 m, l 2 = 12 m. Hence, s = 20 cm (for k c2 = 0.33) and s = 23 cm (for k c2 = 0.39). Table 1. Compued sparking disances for differen lighing curren impulses and differen configuraions of he PE wire (Fig. 3) Sparking disance d Separaion disance s Lighning curren (cm) (cm) parameers A B C acc. o EN / ka / ka (k c2 acc. o Fig. 1) 1/ ka (k c2 acc. o (8)) 0.25/ ka Wors case In order o avoid sparking, he necessary separaion disance s should be larger han he compued sparking disance d. The shaded areas in able 1 show he cases, in which his condiion is no fulfilled (if he EN sandard formulas are o be used). In some of he cases, he compued disance d, a which sparking may occur, is nearly wice as large as he separaion disance s calculaed based on he sandard formulas. Conclusions The paper presened he analysis of ime domain volages produced beween he verical air erminaion rod and he proeced equipmen locaed on he roof of a large building during direc lighning srike o he rod. Along wih and based on hese volages, sparking disances were also esimaed using consan area crierion. The sparking disances were analyzed in connecion o he problem of proper evaluaion of separaion disances necessary o mainain in order o preven dangerous sparking. The analysis was focused on he role of wo componens of he oal volage a he considered place of proximiy: 1) volage induced in loops formed by LPS down conducors, ground and he PE wire of he cable supplying he proeced equipmen, 2) ground poenial difference as a resul of non-ideal (non-zero) grounding impedance. The analysis was an aemp o deermine he wors case condiions ha may occur in he considered building srucure, depending on he PE wire pah inside. The wors case was generally urned o be associaed wih he c h PRZEGLĄD ELEKTROTECHNICZNY, ISSN , R. 92 NR 12/

6 configuraion B, for which boh he main componens of surge volage (inducive and ground poenial) was presen, and for which he PE wire was locaed close o he ground level. However, he resuls obained for configuraion C clearly show ha he general observaions may be misleading if resonance and ravelling wave phenomena appear. Such siuaion occurs when he pah of he ravelling wave (doubled PE wire lengh) is comparable o he half of he wavelengh ha corresponds o he rise-ime of he curren impulse (oscillaion frequency). The confronaion of he compued sparking disances wih he separaion disances evaluaed based on EN sandard mehods shows ha he sandard mehods migh someimes lead o underesimaion of he necessary separaion disance. The wors case value of he compued sparking disance was nearly wice as large as he sandard-based separaion disance. In all he cases analyzed in he paper, as well as in all he previous auhor s works [12, 13, 14, 15, 16], he highes values of sparking disance was associaed o 1/200 s 50 ka lighning curren impulse, i.e. he sandard represenaion of firs negaive reurn sroke curren. Auorzy: dr hab. inż. Renaa Markowska, Poliechnika Białosocka, Wydział Elekryczny, ul. Wiejska 45d, Białysok, r.markowska@pb.edu.pl. REFERENCES [1] EN :2011 (IEC :2010, modified), Proecion agains lighning - Par 1: General principles [2] EN :2011 (IEC :2010, modified), Proecion agains lighning - Par 3: Physical damage o srucures and life hazard [3] Sowa A. W., Analysis of separaion disances beween LPS and devices on he building roof, Przegląd Elekroechniczny (Elecrical Review), ISSN , R. 86 (2010), nr. 3, [4] Heidler F., Zischank W., Kern A., Analysis of separaion disances for lighning proecion sysems including naural componens, Proceedings of 28h ICLP, Kanazawa, Japan, (2006), [5] Beierl O., Seinbigler H., Induziere Überspannungen im Bereich von Ableiungen bei Blizschuzanlagen mi maschenförmigen Fanganordnungen, Proceedings of 18h Inernaional Conference on Lighning Proecion, ICLP, München, Germany, (1985), Paper 4.1. [6] Kind D., Die Aufbaufläche bei Soßbeanspruchung echnischer Elekrodenanordnungen in Luf, Ph. D. Thesis, TH München, 1957 [7] Zou J., Lee J., Ji L., Chang S., Zhang B., He J., Transien simulaion model for a lighning proecion sysem using he approach of a coupled ransmission line nework, IEEE Transacions on EMC, vol. 49, (2007), [8] Wang S., He J., Zhang B., Chen S., Yu Z., Numerical elecromagneic analysis of lighning proecion sysem over lossy ground, 2008 Pacific Symposium on EMC & 19h Inernaional Zurich Symposium on EMC, Singapore, (2008), [9] Geri A., Visacro S. F., Grounding sysems under surge condiions: comparison beween a field model and a circui model, Proceedings of 26h Inernaional Conference on Lighning Proecion, Cracow, Poland, (2002), [10] Aniserowicz K., Analiza efeku dyspersji w modelu anenowym kanału wyładowania amosferycznego z rozłożoną indukcyjnością, Przegląd Elekroechniczny (Elecrical Review), ISSN , R. 92 (2016), nr. 2, 5 7, doi: / [11] Markowska R., Wiaer J., Kompuerowe meody analizy impulsowych narażeń elekromagneycznych, Przegląd Elekroechniczny (Elecrical Review), (2007), nr. 9, [12] Markowska R., Przeskoki iskrowe do insalacji i urządzeń umieszczonych na dachach podczas wyładowań piorunowych w budynki, Przegląd Elekroechniczny (Elecrical Review), ISSN , R. 88 (2012), nr. 2, (in Polish) [13] Markowska R., Danger of flashovers o elecric equipmen locaed on roofs of buildings sruck by lighning, Przegląd Elekroechniczny (Elecrical Review), ISSN , R. 88 (2012), nr. 8, [14] Markowska R., Influence of cable rouing on he flashover disance beween lighning proecion sysem and elecrical equipmen on a building roof, Proceedings of XXII Inernaional Conference on Elecromagneic Disurbances (EMD 2012), Vilnius, Lihuania, (Sepember 2012), [15] R. Markowska, Wyznaczanie odsępów izolacyjnych do celów ochrony odgromowej w budynkach, Przegląd Elekroechniczny (Elecrical Review), ISSN , R. 88 (2012), nr. 11b, [16] Markowska R., Influence of lighning curren waveshape on he separaion disance required beween elecrical equipmen and lighning proecion sysem, Elekronika ir Elekroechnika (Elecronics and Elecrical Engineering), ISSN , vol. 19, (2013), no. 4, 15 18, hp://dx.doi.org/ /j01.eee [17] HIFREQ User s Manual, Safe Engineering Services & Technologies Ld., Monreal, Canada, (2000) [18] Compuaion of elecromagneic fields creaed by recilinear curren sources in a sraified medium, Safe Engineering Services & Technologies Ld., Monreal, Canada (Maerials unpublished) [19] FFTSES user s manual, Safe Engineering Services & Technologies Ld., Monreal, Canada, (2000) [20] Beyer M., Boeck K., Moller K., Zaengl W., Hochspannungsechnik, Springer-Verlag, (1986), 362 [21] IEEE Sd , IEEE Sandard Techniques for High-Volage Tesing [22] Sowa A. W., Separaion disances in lighning proecion of roof fixures, Proceedings of GROUND 2010, Salvador, Brazil, (2010), PRZEGLĄD ELEKTROTECHNICZNY, ISSN , R. 92 NR 12/2016