Mitigation Methods to Improve the Lightning Performance of Hybrid Transmission Line

Transcription

1 Mitigation Methods to Improve the Lightning Performance of Hybrid Transmission Line Andrzej Mackow Mustafa Kizilcay Dept. of Electrical Eng. and Computer Science University Siegen Siegen, Germany Abstract EMTP simulations and lightning attachment models are performed to estimate backflashover performance of multicircuit transmission tower. Multi-circuit transmission tower has several systems on the tower and combines DC transmission over long distances with more flexible AC transmission. The outcome of simulations and calculations should give the range of backflashover withstand current and backflashover outage level. Maximum lightning current amplitude that does not cause backflashover across insulator string is estimated in response to first and subsequent strokes several flashover models. The paper presents a new unbalanced design of insulation. Latter should decrease backflashover rate for lines serving critical loads like HVDC lines. Index Terms-- backflashover, lightning stroke, multi-circuit transmission tower with AC and DC, modelling, flashover model I. INTRODUCTION Investigations in this paper have been done for two transmission lines that come into consideration of conversion to multi-circuit line with HVAC circuits and HVDC circuit (hereafter called hybrid line). Conversion to HVDC is most effective way to increase transmission capacity of existing AC lines [1]. The multi-circuit line with AC and DC systems offers diversified solutions for future transmission lines [1]- [3]. HVDC system could be accompanied by HVAC systems at various transmission voltage levels (e.g. 380 kv, 220 kv or 110-kV). The 380-kV circuit is substituted by a HVDC circuit on a tower. Some guidelines related to adaption of existing AC conductors and AC insulators are summarized in [1]. Available conductors of 380-kV circuit can be adapted to transfer DC power. Existing AC insulators has to be replaced by insulators intended for DC voltage. Composite longrod insulators are preferable choice due to adequate pollution performance. The outages that are caused by lightning strokes have two origins. One of them is backflashover. Lightning strokes that are intercepted by shield wires can afterwards cause backflashover across insulator strings. Lightning incidence (number of strokes to shield wire) is the first step to determine lightning performance of the transmission line. Estimation of equivalent interception radius reduces this task and is sufficient to determine lightning incidence of the line. Furthermore based on lightning incidence of hybrid line number of backflashovers can be estimated with aid of EMTP simulations. A backflashover analysis of hybrid line by means of electromagnetic simulations is presented in this work. This study was focused how new installed HVDC system affects lightning performance of multi-circuit towers. Backflashover withstand current and backflashover outage rate are calculated. Simulations in EMTP-ATP [4] consider effects like: footing resistance, number of phases and power frequency voltage, coupling from lightning current that flows through shielding wire, dependencies of lightning current parameters. Flashover across insulator string was implemented using MODELS [5]. II. BACKFLASHOVER OUTAGE RATE Lightning can cause flashover in two different manners. Either lightning strikes conductor directly and flashover occurs (shielding failure) or lightning flash terminates on tower or shield wire and causes a backflashover. The Backflashover Rate (BFR) indicates number of lightning strokes to shield wire that result in backflashover. BFR = 0.6 N f ( I) di (1) s IC where: N S is lightning incidence (backflashover /100 km/year), f(i) is the probability density function of the lightning crest distribution according to [6], I C is critical current (ka) (backflashover withstand current). The factor 0.6 is used in (1) to consider the effect the strokes within the span [6]. The BFR S is rate of subsequent strokes to shield wire causing backflashover can be expressed as BFR = 0.6 N P f ( I) di (2) S s S IC This work was supported by German TSO, Amprion.

2 where P S is the probability of backflashover from subsequent stroke (assumed that previous strokes has not caused backflashover). P S can be estimated by assuming no correlation between first and subsequent return-stroke currents, as I n 1 CS PS = P n 1 fs ( I) di (3) 2 0 where I cs (ka) is the critical current associated with subsequent strokes, P n is the probability that there are n strokes per flash, as given in [7]. That statistical distribution of number of strokes pro flash in [7] has been reviewed as overestimated in [8]. Moreover not all subsequent strokes strike the overhead line because new terminations channels may develop. Thus subsequent stroke may terminate hundred meters from transmission line [8]. f s (I) is the probability density function of the lightning crest current distribution for subsequent strokes according to [9]. The total backflashover rate, BFR T (backflashover/100 km/yr), that is the rate of lightning first and subsequent strokes to phase conductors causing backflashover, is given as BFR = BFR + BFR (4) III. T LIGHTNING INCIDENCE A. Lightning Incidence Lightning incidence is the first step to determine lightning performance of the transmission line. Estimation of equivalent interception radius reduces this task and is sufficient to determine lightning incidence of the line [10]. The basis formula of equivalent interception radius is (5). R S E eq = r h (5) where r and E are factors listed in Tab. II and h is height of conductor (m). After equivalent interception radius was calculated, the annual number of lightning strikes to shields wires per 100 km of a transmission line N s can be estimated with (6). Ns = 0.1 Ng(2 Req + b) (6) where N g is ground flash density ( strikes/km 2 /year), and R eq is the equivalent interception radius of shield wire (in meters), b is separation distance between shield wires (in meters). The average height of the shield wire in calculations is assumed as its height at the tower minus 2/3 of the sag [11]. Different models with various coefficients were proposed to estimate equivalent interception radius (Table II). IV. SIMULATION MODEL Multi-circuit towers have a height up to 60 m and have up to three conductors at each cross arm. EMTP-ATP simulations have been performed for two tower configurations (s. Fig. 1) coming into consideration for a multi-circuit line with AC/DC circuits. - + N GW W 380-kV AC W V U W V U 110-kV AC 110-kV AC TOWER A V U 2 x 380-kV AC V W W U V GW TOWER B N kV DC Figure 1. Layout of hybrid transmission towers A und B The upper two cross-arms of tower A carry on left side a 420-kV HVDC and on right side a 380-kV HVAC system. A 110-kV double circuit line is suspended from the lowest cross arm. The upper two cross-arms of tower B on the right side carry 420-kV HVDC. Tower B is 6.5 m higher than tower A. Single line diagram of simulation model in ATP Draw is presented in Fig. 2. The modelling method for the backflashover analysis used in this paper is based mainly upon [12]. All simulations were computed for section with 9 towers. The lightning stroke is applied to tower 5 that is located in the middle of investigated section. Footing impedance for all towers is 10 Ω according to [12] as typical value for EHV lines. All towers in investigated sections were assumed to have the same height. (7-km) (330m) (330m) (7-km) 420-kV DC 380-kV AC 2 x 110-kV AC shield wire FLASHOVER MODEL I(t) Zf=1000Ω Shield wire 2 x 110-kV AC 380-kV AC 420-kV DC Rf Rf Rf TOWER 1 TOWER 5 Figure 2. Single line diagram of simulation model in EMTP-ATP. LIGHTNIN G SOURCE TOWER 9

3 A. Tower Model Multistory model [13] is used to represent transmission towers. In multistory model each vertical tower section between cross arms is represented by lossless line connected in series with RL parallel circuit. This parallel circuit represents attenuation of traveling waves. Model and equations for all impedances were described in [13]. In Fig. 3 multistory model is shown. Formula for surge impedance is given as 1 R Zwaist = 60ln cot 0.5 tan (7) h where rh 1 2+ rh 2 + rh 3 1 R = (8) h h = h 1 + h 2 (9) R1 R2 R3 R4 ZT1,h1,vt ZL1 ZT2,h2,vt ZL2 ZT3,h3,vt ZL3 ZT4,h4,vt ZL4 Figure 3. Tower model with additional RL-circuits. For the tower A with 50 m and tower B with 56.5 m equation (1) delivers the surge impedance Z waist_a = 204 Ω and Z waist_b = 208 Ω, respectively. B. Transmission Lines Total 9 towers are represented including all line circuits the model [2] at f = 400 khz. Span lengths have m. The investigated section with 9 towers is terminated at both ends with 7 km long additional (constant parameters distributed line) model that has the same electrical parameters as spans between investigated towers 1-9. These additional sections should prevent impact of reflected waves. The investigated section is connected to voltage sources (via additional line section) in order to take into account the effect on the AC and DC steady-state voltage of the lines on a lightning surge. C. Flashover Models Electromagnetic transients programs allow investigating flashover phenomena in more detailed way. Various flashover models are based on diverse assumptions and have been developed based on different experimental tests. In this study several flashover models are applied for comparison purposes. First model is related to flashover voltage-time characteristic of insulators. A more sophisticated way to represent flashover is achieved by representing the physical process of flashover. Several flashover models have been developed in order to represent the flashover progression process across insulator gaps directly. These models are called Leader Progression Models (LPM). Models 2-6 are various implementation of leader progression model. 1) Disruptive criterion according to Kind [14] 2) LPM according to Pigini [15] 3) LPM according to Motoyama 1996 [16] 4) LPM according to Motoyama 1998 [17] 5) LPM according to CIGRE Working Group [6] 6) LPM according to Wang [18] They were implemented using MODELS [5]. Parameters and flashover criteria are precisely described in [6] and [14]-[18]. Insulation levels are correspondingly adapted for all systems. All insulators are composite insulator strings with longrod design. Gap length D of composite insulator strings for 110-kV is ca mm, 380-kV AC and HVDC is ca mm. Each flashover model connected across insulator strings controls switch. After fulfillment of breakdown condition, surge current flows into failure conductor. The definition of the lightning strength of insulators is based on tests with standard lightning (SI) impulse waveforms (1.2/50 µs). In reality wave shapes of lightning surge voltages across insulators differ from standard lightning wave shapes [18]. The waveform of lightning surge voltage across insulators differs from standard lightning impulse due to reflections from adjacent towers and footing impedance. Testing of insulation under all possible lightning overvoltages would be very time consuming and is therefore not economical. Some models were developed to consider short tail lightning impulse lightning voltage (STLI) (1.45/11 µs) [16], [18]. As pointed in [1] constant DC voltage may be higher than the instantaneous voltage on any of the AC phase conductors on hybrid tower. Thus the composite overvoltage across insulator string of DC may be higher than across insulator of AC circuit. The DC insulator dimensioning and selection are based on the pollution performance, the flashover performance level and the environmental stress [1]. Proper classification of candidate insulators require flashover pre-calculations considering breakdown characteristics with different surge polarities. Due to air clearances restrictions from original HVAC multi-circuit tower new HVDC insulator strings have the same length as 380-kV insulator strings.

4 D. Ligthning Source The lightning stroke is modelled by a current source and a parallel resistance, which represents the lightning path surge impedance. Lightning surge impedance is selected as 1000 Ω according to [12]. TABLE I. LIGHTNING CURRENT PARAMETERS [8] Parameter First stroke Subsequent stroke Peak current I I, initial 27.7 ka 11.8 ka Maximum steepness S m 23.3 ka/µs 39.9 ka/µs Front time t d30/ µs 0.67 µs Tail time to half value t h 77.5 µs 30.2 µs Fig. 4 shows the representation of first and subsequent stroke current waveforms with CIGRE lightning waveform [8], considering the median values according to Berger s conditional distributions [9] for subsequent strokes and global distribution according to [6] for first strokes. investigate overhead lines (OHL). In latter r and E coefficients were validated with field observation data from [21] as well as recently observed lightning incidence for high transmission towers [22]. Methods with smallest deviations were used in this study and are based on EGM by Armstrong and generic models according to Rizk and Petrov. Results by means of EGM by Armstrong are employed in this study. TABLE II. EQUIVALENT INTERCEPTION RADIUS AND LIGHTNING INCIDENCE Author Req Tower A Tower B ELECTROGEOMETRIC MODELS strokes to shield wires in year over 100 km OHL Young [23] 14.3 h Love [24] 13.9 h Armstrong, Whitehead [25] 33.7 h Brown, Whitehead [26] 30.1 h Wagner, Hileman [27] 11.0 h Whitehead [28] 14.2 h GENERIC MODELS Rizk [29] 18.9 h Petrov [30] 6.2(h+15) Ait-Amar & Berger [31] 33.0 h Figure 4. Lightning currents with median values. According to [8] the front time t f and steepness S m depend on the peak value of the lightning current for first stroke. For subsequent stroke the front time t f is constant, whereas S m depends on the peak value of the lightning current. In this paper was used simplified representation of first stroke. Features like: initial concavity, subsequent abrupt rise and several peaks were neglected. Representation of first and subsequent stroke has only one peak and smooth shape. B. Backflashover Simulations EMTP-ATP simulations were performed to compare the behavior of insulators in response to lightning surge voltage impulses. Some researchers pointed out that waveforms of lightning voltages across insulator strings are closer to STLI than LI [18], [32]. Therefore flashover model 3 and 6 are based on experiments with STLI. Flashover models were embedded in simulation model from Fig. 2. Fig. 5 presents lightning surge voltages across insulator string that result in backflashover. V. LIGHTNING CALCULATIONS A. Lightning Incidence Lightning incidence is calculated with various values of coefficients for R eq and results are shown in Table II. N g is based on [19] and amounts to 4.2 strikes/km 2 /year. Results are similar among all interception models and are higher for higher tower B. Lightning incidence based on generic models is higher than results based on electrogeometric model (EGM). According to comparison of lightning incidence factors r and E from [20] some of them were graded to Figure 5. Lightning surge voltages across insulator string of HVDC plus pole. (1)-Kind, (2)-Pigini, (3) - Motoyama 1996, (4)- Motoyama 1998, (5)- CIGRE, (6)-Wang These waveforms are from first negative lightning stroke to shield wire on the tower top. Since voltage of plus pole is constant (+420kV), time instant of lightning stroke is not

5 relevant. Backflashover withstand currents are shown in Fig. 6, simulated for all flashover models (1-6). These backflashover withstand currents vary considerably among the flashover models. The difference between highest and lowest current is up to 170 %. Higher critical currents were obtained for LPM. In particular LPM based on STLI experiments result in critical current over 200 ka. Further computed backflashover critical currents for towers A and B are simulated by means of LPM according to CIGRE WG [6]. That flashover models enables to consider design of insulator string (longrod or cap-and-pin) and polarity of impulse voltage. backflashover occur across two insulators of 110-kV circuit (power frequency voltage is equal on affected conductors) for 72 ka first negative stroke. That crest value of lightning stroke exceeds backflashover withstand current of both 110- kv circuit and causes backflashover in each 110-kV circuit. Voltage waveform across insulator at positive conductor (1) of HVDC sags shortly after first backflashover around 12 µs across 110-kV insulator. Figure 7. Overvoltages across the upper insulator string of positive pole (1), return pole (2) and two 110-kV phases (3), (4) in response to first stroke on tower top (72 ka). Figure 6. Critical backflashover current causing bachflashover across insulator string of HVDC plus pole Considerable deviations due to flashover modelling were also found for flashover models (1-3) in simulations of the critical current causing backflashover in a 110 kv circuit of a multi-circuit line [33]. Moreover minimum shielding failure flashover current for first and subsequent lightning strokes to conductor depend strongly on flashover model as demonstrated in [34]. C. Backflashover Outage Rate of Tower A The power frequency voltage is considered by calculating the backflashover withstand current I C (refer to (1)) for instantaneous power frequency voltages estimated for each of twelve 30 steps of phase angle. Thus sinusoidal waveform of 110-kV and 380-kV AC voltages is considered. Flashover occurs firstly on the lowest cross arm almost simultaneously across two 110-kV voltage insulators. In fact, higher voltage difference across insulator is to be expected for the positive conductor (plus pole) of the HVDC system as pointed in [1]. 110-kV insulators are three times shorter. This is crucial for higher susceptibility to backflashover of 110-kV systems. The value of backflashover withstand currents of 110-kV insulators vary from 68 to 77 ka depending on time instant of lightning stroke. Twelve estimated critical currents resulting from different power frequency instantaneous voltages are inserted in (1) as lower integration limit. Overvoltages across two insulator strings of 110-kV (of different circuits, both phases in voltage maximum) and across insulator of plus pole (upper cross-arm) and return pole (middle cross-arm) are presented in Fig. 7. Two Influence of backflashovers is more visible for higher lightning stroke current. In Fig. 8 the same overvoltages are presented in response to 150-kA first negative stroke. Two simultaneous backflashover occur across two insulators of 110-kV circuit around 11 µs (power frequency voltage is equal on affected conductors). In voltage waveform across plus pole insulator (1) on the upper cross-arm and return pole insulator (2) on the middle cross-arm considerable voltage sag is visible due to previous backflashovers across 110-kV insulator strings. That voltage sag hinders efficiently rise of surge voltage across insulators and avoids subsequent backflashovers across other insulator strings respectively. Figure 8. Overvoltages across the upper insulator string of positive pole (1), return pole (2) and two 110-kV phases (3), (4) in response to first stroke on tower top (150 ka). After backflashover other 110-kV sound phases were disconnected (3-phase auto reclosing). Amplitude of the lightning current was further increased up to 200 ka with corresponding front time t f and steepness S m according to [8].

6 Subsequent flashovers across sound conductors of 380-kV circuit and of HVDC circuit do not occur after backflashover across 110-kV insulators. Whereas backflashover from subsequent strokes are unlikely to occur across HVDC insulators, they can occur across 110-kV insulators. Subsequent strokes higher than 42 ka (average backflashover withstand current) may result in backflashover across insulator strings of 110-kV circuit. Converting of tower A into AC/DC multicircuit tower has not changed lightning backflashover performance of the line. Results of backflashover simulations show that lightning strokes first of all affect 110-kV circuits. First lightning strokes as well as subsequent strokes may cause backflashover across insulators on the lowest cross arm. The backflashover withstand level of the HVDC system is much higher and influenced strongly by the lightning performance of 110-kV systems. BFR T for tower A has not changed due to conversion in hybrid line and amounts to 5.08 backflashover/100km/yr. The BFR T consists of backflashover caused by first strokes as well as by subsequent strokes. D. Backflashover Outage Rate of Tower B Tower B from Fig. 1 has been chosen for comparison of backflashover behavior of 420-kV HVDC and 380-kV HVAC systems. The new HVDC composite insulators have the same length as 380-kV composite insulators. The minimal lightning current that causes backflashover has been determined for 380-kV AC and HVDC systems. The overvoltages across several insulators are presented in Fig. 9 in response to first stroke on tower top (150 ka). That value is backflashover withstand current for insulator string of plus pole. The backflashover across insulator string of positive pole occurs firstly. Higher positive voltage of 420-kV HVDC positive pole causes higher surge voltage across the insulator for a lightning stroke of negative polarity. This assumption is valid as long as both systems have composite insulators of equal length. occur after first backflashover across insulator string of plus pole. To what extent has conversion of 380-kV circuit into HVDC-circuit changed BFR, is investigated with original configuration of tower B (three 380-kV circuits). The power frequency voltage is considered by calculating the backflashover withstand current I C (refer to (1)) for instantaneous power frequency voltages estimated for each of twelve 30 steps of phase angle. Thus sinusoidal waveform of 380-kV AC voltage is considered. Only one backflashover occurs up to 200 ka. Backflashover withstand current and backflashover locations are variable and depend on power frequency voltage in 380-kV circuits and distance to tower top. Average backflashover withstand current is 171 ka. Subsequent strokes to tower top are hazardous neither for 380-kV insulators nor for HVDC insulators. The total BFR has risen from 0.18 to 0.34 backflashover/100km/yr due to conversion into hybrid line. Conversion of towers with 380- kv double circuit into hybrid line increases the probability of occurrence of backflashover. Constant +420-kV voltage of plus pole makes upper insulator at plus pole more prone to backflashover in comparison with the original 380-kV circuit. An unbalanced insulation design to prevent the backflashover across insulator string of HVDC system that serves critical loads can be realized in two manners: Whereas original 380-kV conductors are unchanged, substitution of AC insulators may be considered. Porcelain longrod insulators are more prone to flashovers than composite longrod insulators. Substitution of composite insulator for porcelain insulators could change backflashover behavior on the tower. CIGRE flashover model considers only insulator design (longrod). Additional test of dielectric strength of longrod porcelain insulator strings are required to revise this issue. This approach would necessitate substitution of all insulator strings. Another way is to increase critical backflashover current in case of a HVDC insulator. This solution is also more economical because only HVDC insulator has to be replaced due to conversion. Elongation of composite insulator of HVDC to 3600 mm would result in backflashover across 380-kV insulator string. Figure 9. Overvoltages across the upper insulator string of positive pole (1), return polse (2) and two 3800-kV phases (3),(4) in response to first stroke on tower top (150 ka). Amplitude of the lightning current was further increased up to 200 ka with corresponding front time t f and steepness S m according to [8]. Subsequent flashovers across sound conductors of 380-kV circuit and of HVDC circuit do not VI. CONCLUSIONS The EMTP-ATP simulations have been performed for two tower configurations coming into consideration for a multicircuit line with AC/DC circuits. Furthermore subsequent lightning strokes were also considered in this investigation. Conversion of tower A with 380-kV and 110-kV doublecircuit on the same tower into AC/DC multi-circuit line does not increase lightning backflashover performance of the line. First lightning strokes as well as subsequent strokes cause first backflashover across 110-kV insulators on the lowest cross arm. The backflashover withstand level of the HVDC

7 system is much higher and influenced strongly by the lightning performance of 110-kV systems. Conversion of tower B with 380-kV circuits into AC/DC multi-circuit line increases the probability of occurrence of backflashover. Constant +420-kV voltage of plus pole makes upper insulator at plus pole more prone to backflashover in comparison with the original 380-kV circuit. Conversion of an AC system into bipolar DC system increases outage rate for the converted circuit. Subsequent strokes are not critical for the operation of HVDC and 380-kV systems. An unbalanced insulation design to protect the HVDC system that serves critical loads can be realized in two manners. The backflashover performance is estimated by means of several flashover models. They perform differently depending on the lightning waveform and investigated tower. Flashover model can influence strongly lighting outage rates of OHL. Additional test of dielectric strength of insulator strings and field observations are required to revise existing flashover models. This issue concerns particularly some of Leader Progression Models (LPM), since they are partially based on air gap breakdown of rod-rod field tests. ACKNOWLEDGMENT The authors like to thank Amprion for their expert advices. REFERENCES [1] CIGRE WG B 2.41, Guide to the conversion of existing AC lines to DC operation, 2014 [2] J. Lundkvist, I. Gutman and L. Weimers, "Feasibility study for converting 380 kv AC lines to hybrid AC/DC lines, in Proc. of 2009 EPRI's High Voltage Direct Current & Flexible AC Transmission Systems Conference. [3] C. Neumann, B. Rusek, S. Steevens and K.-H. Weck, Design and layot of AC-Dc hybrid lines, in Proc. of 2013 CIGRE Symposium, Auckland, Neuseeland, [4] Canadian/American EMTP User Group, ATP Rule Book, revised and distributed by EEUG Association, [5] L. Dube, Users guide to MODELS in ATP, 1996 [6] CIGRE WG 01 SC 33, Guide to procedures for estimating the lightning performance of transmission lines, 1991 [7] Lightning and Insulator Subcommittee of the T&D Committee, "Parameters of lightning strokes. A review", IEEE Trans. Power Delivery, vol. 20(1), pp , [8] CIGRE WG C4.407, Lightning Parameters for Engineering Applications, [9] K. Berger, R. B. Anderson, H. Kroninger, "Parameters of the Lightning Strokes," ELECTRA, vol. 41, pp , July [10] IEEE WG, "Estimating lightning performance of transmission lines II- Updates to analytical models," IEEE Trans. Power Delivery, vol. 8, pp , Jul [11] A. J. Eriksson, "An improved electrogeometric model for transmission line shielding analysis," IEEE Trans. Power Delivery, vol. PWRD-2, pp , Dec [12] A. Ametani und T. Kawamura, "A method of a lightning surge analysis recommended in Japan," IEEE Trans. Power Delivery, vol. 20, pp , [13] M. Ishi, T. Kawamura, T. Kouno, T. Ohsaki, E. Shiokawa and K. Murotani, Multistory transmission tower model for lightning surge analysis, IEEE Transactions on Power Delivery, pp , [14] Kind, The volt-time area in the case of impulse stressing of technical electrode arrangements in air( orginal title in German: Die Aufbauflächse bei Stoßspannungsbeanspruchung technischer Elektrodenanordungen in Luft, ETZ-A, pp , [15] A. Pigini, G. Rizzi, E. Garbagnati, A. Porrino and G. Pesavento, Performance of large air gaps under lightning overvoltages: Experimental study and analysis of accuracy of predetermination methods, IEEE Transations on Power Delivery, pp , Apr [16] H. Motoyama, Experimental Study and Analysis of Breakdown Characteristics of Long Air Gaps with Short Tail Lightning Impulse, IEEE Transactions on Power Delivery, pp , Apr [17] H. Motoyama, K. Shinjo, Y. Matsumoto, N. Itamoto, Observation and analysis of multiphase back flashover on the Okushishiku Test Transmission Line caused by winter lightning, IEEE Transactions on Power Delivery, vol. 13 pp , Apr [18] X. Wang, Z. Yu und J. He, Breakdown Process Experiments of 110- to 500-kV Insulator Strings Under Short Tail Lightning Impulse, IEEE Transactions on Power Delivery, pp , Oct [19] BLIDS: Flash Information Service by SIEMENS, x, [online]. [20] P. N. Mikropoulos and T. E. Tsovilis, Estimation of lightning incidence to overhead transmission lines, IEEE Transactions on Power Delivery, vol. 25 pp , July [21] A. J. Eriksson, "The incidence of lightning strikes to power lines," IEEE Trans. Power Delivery, vol. PWRD-2, pp , Jul [22] J. Takami and S. Okabe, Observational results of lightning current on transmission towers, IEEE Transaction on Power Delivery, pp , [23] F. S. Young, J. M. Clayton und A. R. Hileman, Shielding of Transmission Lines, IEEE Trans. on P A&S, pp , [24] E. R. Love, Improvements in lightning stroke modeling and applications to design of EHV and UHV transmission lines, M.Sc. dissertation, Univ. Colorado, 1973 [25] H. R. Armstrong und E. R. Whitehead, Field and Analytical Studies of Transmission Line Shielding, IEEE Trans. on P. A&S, pp , Januar [26] G. W. Brown und E. R. Whitehead, Field and Analytical Studies of Transmission Line Shielding, IEEE Trans. on p A&S, pp , [27] C. F. Wagner, The Relation Between Stroke Current and the Velocity of the Return Stroke, IEEE Trans. on PA & S, pp , Oktober [28] E. R. Whitehead, CIGRe survey of the lightning performance of EHV transmission lines, ELECTRA, vol. 33. pp , [29] F. A. Rizk, Modelling of transmission line exposure to direct lightning strokes to overheadlines, IEEE Trans. Power Del., pp , [30] N. I. Petrov, G. Petrova und R. T. Waters, Determination of attractive area and collection volume of earthed structures, in Proc. of 25th ICLP, Rhodes, Griechenland, [31] S. Ait-Amar und G. Berger, A modified version of the rolling sphere method, IEEE Trans. Dielectr. Electr. Insul., pp , Jul [32] A. Ancajima, A. Carrus, E. Cinieri und C. Mazzetti, Behavior of MV Insulators Under Lightning-Induced Overvoltages: Experimental Results and Reproduction of Volt-Time Characteristics by Disruptive Effect Models, IEEE Transactions on Power Delivery, pp , January 2010 [33] M. Kizilcay und C. Neumann, Backflashover analysis for 110-kV lines at multi-circuit overhead transmission line towers, in Proc. o IPST, Kyoto, Japan, 2009 [34] J Datsios, P. N. Mikropoulos and T. Tsovilis, " Estimation of the minimum shieldinh failure flashover current for first and subseqeunt lightning strokes to overhead transmission lines," Electric Power System Research, pp , 2014.