GEOPHYSICAL RESEARCH LETTERS, VOL. 32, L18804, doi:10.1029/2005gl023255, 2005 Lightning current waves measured at short instrumented towers: The influence of sensor position Silvério Visacro and Fernando H. Silveira Lightning Research Center, Federal University of Minas Gerais, Belo Horizonte, Brazil Received 16 April 2005; revised 6 July 2005; accepted 1 August 2005; published 21 September 2005. [1] The influence of the current sensor position along short-instrumented towers on the contamination of measured lightning current waves was evaluated. The evaluation was performed by simulation, employing a hybrid electromagnetic model. Assuming certain simplifications, the dynamic behavior of lightning channel was considered, including core losses and corona sheath. The results showed that, for realistic front time values of negative downward strokes, the current wave measured at tower top and at its base is practically the same, for first and subsequent strokes. Therefore, for short towers, the wave amplitude is not dependent on the current sensor position. Citation: Visacro, S., and F. H. Silveira (2005), Lightning current waves measured at short instrumented towers: The influence of sensor position, Geophys. Res. Lett., 32, L18804, doi:10.1029/2005gl023255. 1. Introduction [2] The design of protection systems is very dependent on lightning current parameters. Most of the knowledge about such parameters comes from direct measurements taken at instrumented towers. In this respect, the most important database is that derived from Berger s measurements, taken at San Salvatore Station, Switzerland [Berger et al., 1975]. Instrumented towers, installed in several other countries, such as South Africa and Italy, provided additional data. [3] Depending on the specific measuring station, current measurement is taken at the tower base or top. In San Salvatore, the current sensor was positioned at tower top, while, in South Africa, it was placed at tower base. The technical literature considers the influence of elevated stricken objects on measured lightning current waves and discusses the current wave profile along the tower. A complete overview on this subject is presented by Rakov [2001]. [4] Some researchers state that measurements taken at the top of instrumented towers are subject to slight contamination, while those taken at the tower base have the current wave strongly disturbed. This influence is very clear for very tall structures, as shown by Rachidi et al. [2002]. Melander concluded that, even for short towers (60m), the amplitude of current wave measured near the bottom is estimated to exceed in 60% the value measured at the top [Melander, 1984]. Maybe, due to such work, it is usual to hear, as a general statement, that the amplitude of current wave measured at base is significantly larger than that taken Copyright 2005 by the American Geophysical Union. 0094-8276/05/2005GL023255$05.00 at top. Sometimes, this statement is referred to, in order to explain the difference on the amplitude of lightning currents measured in different regions. [5] As a matter of fact, even in a simplified electromagnetic approach, it is possible to confirm this conclusion for strikes to tall towers. Nevertheless, for short towers (less than 80 m long), this assumption does not seem reasonable, when typical front time values of lightning current waves are considered. This paper is specifically dedicated to the evaluation of current contamination effect for short towers. [6] The investigation is mainly motivated by the authors involvement with lightning current measurements at Morro do Cachimbo Station (MCS), in Brazil. At this station, current measurement is taken at the base of a 60 m instrumented tower. The 13-year local database shows that the median peak current for downward negative lightning strokes is around 48 ka [Visacro et al., 2004], a value around 50% larger than that found by Berger. 2. Basic Considerations [7] In order to correctly evaluate the question on focus, it is prudent to have an insight in the dynamics of return current establishment. The understanding of such fundamental aspect may allow a good representation of the physical system where current is measured and also a better computation of the process that determines the amplitude and waveform of measured current. Such dynamics is following commented with reference to Figure 1. [8] After the attachment is achieved, two current waves are established along the channel, one traveling upwards and the other one downwards. When the descending wave reaches tower top, it is partially reflected upwards and partially transmitted to the tower body. The transmitted wave follows towards the tower base and is reflected at soil level. The ascending reflected wave is once more reflected after reaching tower top. Following, a sequence of reflections occurs at tower base and top, while current wave travels along the tower. This transient process establishes the resulting current along the tower. 3. Developments 3.1. Introduction [9] Most current contamination evaluations apply reflection coefficients that are determined assuming certain conditions for the equivalent impedance of lightning channel. According to such evaluations, in 1984 Gorin and Shikelev estimated this impedance to vary from 600 to 2500 W from the comparison of current waves measured at tower top and tower base [Rakov, 2001]. It was estimated larger than 3 times the tower characteristic impedance L18804 1of5
Figure 1. Representation of lightning channel and tower. [Beierl, 1992] and this result was later confirmed by Fuchs [1998]. [10] A quite different approach is adopted in the present evaluation, from the application of an elaborated hybrid electromagnetic model HEM [Visacro and Soares, 2005]. Based in the partition of the whole current path into a large number of short elements, this model develops an electromagnetic representation of the physical system (channel-tower-grounding electrodes), according to information about the geometrical configuration of this system and constants of involved media (air, conductors, channel and soil). The model finds the electromagnetic coupling relations among all the elements along current path, including the effects of corona sheath and core losses in the lightning channel, to determine current and voltage wave distribution along it [Visacro and Silveira, 2004]. [11] In this particular application, the HEM model is able to accurately compute the distribution of electromagnetic field in the vicinities of tower and channel. Most of models employed in similar evaluations assume a TEM mode for field propagation along the tower and channel. Due to the vertical position of tower and channel, in the presence of soil, the electric field lines are displaced from the typical transversal lines of this mode. In a distributed circuit approach, this effect corresponds to a variation of parameters along current path, with a diminishment of the capacitance per unit length, as height is increased. [12] Though this approach does not apply an equivalent impedance representation for the lightning channel, evaluations derived from the results of model application show that the estimates for such impedance are consistent with the cited experimental results by Gorin and Beierl, ranging from about 600W to more than 1200W, according to the conditions assumed for the channel. Considering its variation with height, the tower surge impedance is estimated from 120W to 300 W. 3.2. Representation of the Physical System [13] This model was applied to simulate lightning strikes to the MCS tower, considering its real configuration and dimensions. The first simulated system consists of the lightning channel, the tower (60 m high) and grounding electrodes, as shown in Figure 1. Attachment position was assumed 100 m above tower top. Simulations departed from the instant of attachment, assuming an external source to inject a ramp current wave at the attachment point (Figure 1). Different values were considered for the front time, in order to resemble the first and subsequent strokes. The waveshape is not a critical aspect, as the same wave generates the results at top and base of tower. The ramp was chosen in order to make the analysis of results clear. This position is not relevant in the current transient process along the tower. The main question is to assure the lightning channel is represented above tower top. Once the current front is transmitted to the tower body, the effect of channel is felt only after the transit time spent by the current front to travel downwards and to return to tower top after the reflection at the soil level (0.4 ms). [14] The evaluation followed two steps: [15] (i) First, a simplified representation of the current establishment dynamics was considered. The channel parameters were assumed not to vary during the process. Though for each simulation the parameters were considered constant, a sensitivity analysis was performed, assuming different conditions for such parameters (channel losses, corona and grounding impedance). [16] (ii) In a second step, a more realistic behavior was considered for the current dynamics. The variation of channel parameters was partially taken into account, assuming a transition for the physical characteristics of lightning channel. To represent such transition, the current wave injected at the attachment point was decomposed into two components, as indicated in section 3.3. The first one propagates at the beginning of the process along a low ionized path surrounded by a wide corona sheath. The second component begins a little later and is assumed to propagate along a channel modified by the flow of first current component. Such flow is responsible for promoting an increase on channel ionization level and a reduction of corona sheath. 3.3. Results and Analyses [17] As a first result of simulations, Figure 2 shows the current waves observed at tower top and base for the condition of step (i). [18] It was assumed a 2 m corona sheath equivalent radius. This condition corresponds to a velocity around 0.6c for the current propagation [Visacro and Silveira, 2004]. Different values were considered for the resistance of channel core, in order to represent different levels of core losses: R = 0.56 and 1 W/m. Channel was also represented as a copper conductor. For the real configuration of grounding electrodes, two values of soil resistivity were assumed (100 and 2500 W.m), in order to consider extreme conditions for grounding impedance. Two values of front time were simulated (0.5/50 and 2/50 ms) in order to represent fast current waves respectively associated to subsequent and first negative strokes. The results for the assumed conditions are following commented. [19] As expected, for the lower grounding impedance condition, the amplitude of both currents is a little larger. The current amplitude is also larger for faster waves. The effect of assuming more pronounced core losses is a reduction in the current wave amplitude. In all cases, the differences are very small. [20] In spite of such differences, when the waves observed at the top and at the base are compared for the same condition, the amplitude is practically the same. The only difference is a small increase of the wave front slope for the wave considered at tower base. This is also an 2of5
Figure 4. Composition of the injected current wave. Figure 2. Current wave at tower top and base. expected result due to the simultaneity of incident and reflected waves at the tower base. [21] Figure 3 refers to the same results, but concentrates on the effect of tower grounding impedance. In this case, the same current velocity was assumed (same corona sheath) and core losses were computed by a 0.56 W/m resistance per unit length of channel. The grounding impedance was varied about 25 times by increasing the soil resistivity and little effect is observed. Though the current amplitude tends to increase as grounding impedance is reduced and larger amplitudes are found for the faster wave, practically no differences are observed between the current waves at tower top and base. Only a moderate increase of front wave slope is perceived for the wave measured at tower base. The results, shown for the 0.5/50 ms current wave, are similar for a 2/50 ms wave. [22] Following, the simulations contemplated the evolution of channel conditions, as described in step (ii). Figure 4 indicates the two components the injected current is divided into. Both waves depart from the attachment point and reach the tower top at little different instants. They were supposed to travel along channels with different parameters. The first wave propagates at low velocity (v = 0.6c) along a low ionized core surrounded by a large corona sheath (assumed conditions: R = 0.56 W/m, equivalent corona radius: 2 m). For the second wave, the corona sheath is reduced to a 0.5 m equivalent radius (v = 0.72c) and the core losses are significantly reduced (R = 0.035 W/m). This approach tries to resemble the dynamic nature of channel parameters during the process of current establishment and makes the reflections at tower top closer to reality in relation to the assumptions considered in step (i). [23] Figure 5 presents the results for fast and slow waves. The results are quite similar to those obtained for the conditions assumed in step (i) and demonstrate that the dynamic behavior of channel parameters has little influence. [24] The results lead to the conclusion that for short instrumented towers, such as the ones of Morro do Cachimbo, South Africa and San Salvatore stations (60m), the current wave measured at the tower top and at tower base would practically be the same. Therefore, the Figure 3. Current wave at tower top and base: the effect of grounding impedance. Figure 5. Current wave at tower top and base (dynamic behavior of channel parameters). 3of5
general idea that measurements at the tower base would generate larger amplitudes is not consistent. [25] This result contradicts the conclusions presented in [Melander, 1984], but seems quite reasonable in the perspective of the electromagnetic propagation theory. The Melander s overestimate of current contamination at tower base is basically attributed to the short wave front time (lower than 0.2 ms) assumed in her evaluations, in conditions of a large equivalent impedance for lightning channel. Also the assumed low propagation velocity of current along the tower and the neglect of circuit parameters variation along the tower are expected to have given small contributions. [26] Due to the relevance of the results, the authors decided to expand the evaluations to some other situations, as following commented. [27] For the first evaluation, the same conditions of step (ii) were assumed, but the tower was supposed to be 250 m high. The results of simulations are shown in Figure 6. As it is shown, the current profile is quite different for the waves measured at tower top and base. While the wave at base has a smooth variation of its front, the reflection is very explicit for the wave at the top. Nevertheless, the peak values are similar. Only for the fast wave, the peak value of wave at the top is about 10% larger. Naturally, this difference is expected to increase for waves with shorter front time. [28] Also some situations considered in simulations reported by literature were evaluated for a short tower (60m) [Guerrieri et al., 1988]: (i) the current was supposed to be injected directly at tower top by an ideal current source and the lightning channel was not considered above the tower; (ii) the current was injected directly at tower top by an ideal current source but a lightning channel was connected to the tower, assuming 2 m equivalent radius for corona sheath and R = 0.56 W/m. Figure 7 shows the results of model application for a fast and a slow current wave. [29] The results denote that, only for the first assumption (no lightning channel connected to the tower), there is a substantial difference between the current waves at the tower top and base. Even though, such difference is really significant for the fast wave. The assumption of current injection directly at tower top could be reasonable for subsequent strokes as the attachment is very close to the tower in this case. Nevertheless, the absence of a lightning channel corresponds to a non-realistic physical representation, as verified by the cited results of Gorin and Beierl. Figure 6. Current wave at tower top and base (tower height: 250 m, dynamic behavior of channel parameters). Figure 7. Current wave at tower top and base (current injected at tower top). Therefore, in all developed evaluations, the only case that the current waves at tower top and base are substantially different for short towers is not representative of the physical process involved in lightning current establishment. 4. Conclusions [30] This work presented evaluations about the influence of the current sensor position on the contamination of lightning current waves for measurements taken at short instrumented towers. An accurate electromagnetic representation of tower was adopted. [31] The results denoted that the current waves measured at top and base of the tower are quite similar, when typical values of lightning current wave front are considered. For representative conditions assumed for lightning channel, the amplitude of such waves are practically the same. The only difference is a moderate increase of wave front slope for the current measured at tower base. [32] The authors naturally expected these results for short towers. The measurements taken at MCS indicate median values for current front time (T d10 ) around 7 ms and 0.9 ms, respectively for first and subsequent strokes [Visacro et al., 2004]. Even without applying elaborated models, it is not difficult to conclude from electromagnetic theory that, for short towers (less than 80 m) and realistic front time values, the contaminated current wave at the top and base should be very similar, once the transit time along the tower is around 0.2 ms. For typical first strokes, it is natural not to expect any influence on current amplitude, though for subsequent ones a slight difference could be expected. Also the increase of the wave front slope was a reasonable expectation, once the wave reflected at tower base is added with no delay to the incident wave. Of course, if extreme values are assumed for wave front, such as 0.1 ms, differences would naturally be expected. [33] Therefore, the difference on median peak values for negative lightning currents determined from database obtained by measurement at short towers in different parts of the world should not be attributed to the position of the sensor along the tower, as it is very commonly assumed. References Beierl, O. (1992), Front shape parameters of negative subsequent strokes measured at Peissenberg tower, paper presented at International Conference on Lightning Protection, Berlin. Berger, K., R. B. Anderson, and H. Kröninger (1975), Parameters of lightning flashes, Electra, 41, 23 37. 4of5
Fuchs, F. (1998), On the transient behavior of the telecommunication tower at the Mountain Hoher Peissenberg, paper presented at International Conference on Lightning Protection, Birmingham, U. K. Guerrieri, S., C. A. Nucci, M. Ianoz, F. Rachidi, and M. Rubinstein (1988), On the influence of elevated strike objects on directly measured and indirectly estimated lightning currents, IEEE Trans. Power Delivery, 13(4), 1543 1555. Melander, B. G. (1984), Effects of tower characteristics on lightning arc measurements, paper presented at International Conference on Lightning and Static Electricity, Orlando, Fla. Rachidi, F., V. Rakov, C. A. Nucci, and J. L. Bermudez (2002), Effect of vertically extended strike object on the distribution of current along the lightning channel, J. Geophys. Res., 107(D23), 4699, doi:10.1029/ 2002JD002119. Rakov, V. (2001), Transient response of tall object to lightning, IEEE Trans. Electromagn. Compat., 43(4), 654 661. Visacro, S., and F. H. Silveira (2004), Evaluation of current distribution along the lightning discharge channel by a hybrid electromagnetic model, J. Electrost., 60/2(4), 111 120. Visacro, S., and A. Soares Jr. (2005), HEM: A model for simulation of lightning-related engineering problems, IEEE Trans. Power Delivery, 20(2), 1026 1208. Visacro, S., M. A. Schroeder, A. Soares Jr., L. C. Cherchiglia, and V. J. Sousa (2004), Statistical analysis of lightning current parameters: Measurements at Morro do Cachimbo station, J. Geophys. Res., 109, D01105, doi:10.1029/2003jd003662. F. H. Silveira and S. Visacro, Lightning Research Center, Federal University of Minas Gerais, Belo Horizonte, 31270-901, Brazil. (lrc@cpdee.ufmg.br) 5of5