1 A Contribution to the Direct Measurement of Lightning Currents by Means of Resistive Transducers Antonia. N. Gómez Silvério Visacro José Luiz Silvino LRC - Lightning Research Center Federal University of Minas Gerais Av. Antônio Carlos, 6627, 31.270-901, Belo Horizonte, MG, Brazil, Lrc@cpdee.ufmg.br. Abstract This paper discusses certain relevant aspects related to the measurement of lightning current by means of shunt resistors, including an analysis of inductive effects. The distortion in voltage waves measured by shunt resistors is explored. The paper emphasizes the need to correct the measured voltage wave to recover the original current instead of obtaining it directly from the shunt considered as pure resistor. Experimental results are presented, including the measurement of current of a recent strike to the mast of the Morro do Cachimbo Station in Brazil. Index Terms Lightning, Lightning Current, Lightning Current Measurement, Shunt Resistor, Instrumented Tower. 1 HISTORICAL NOTE The measurement of lightning currents by means of shunt resistors has been applied for many years [1]. The most traditional database, obtained by Berger from measurements taken at an instrumented tower on Monte San Salvatore, adopted such devices (shunt resistances: 0.8 Ω and 50 mω) [2]. This device was also employed by Garbagnati in Italy [3], at Fukui chimney in Japan (10 mω and 2 mω) [4], at Gaisberg tower in Austria (0.25 mω) [5, 6] and at Ilyapa tower in Colombia (0.52 mω) [7]. Shunt devices have also been used to measure currents in triggered lightning experiments (1 mω) [8]. 2 BASIC CONSIDERATIONS Presently, most of the plants dedicated to lightning current measurements employ Pearson and Rogowski coils since such devices present very good performance to measure the impulsive parcel of lightning current. Nevertheless, they have poor response to slow frequency components of current and, commonly, the measurement is restricted to a narrow window of time that is usually shorter than 1 ms. Shunt resistors are still used not only to measure the impulsive current but the continuing current component as well. Very frequently the physical arrangement show in figure 1 is adopted to allow measuring lightning currents in different ranges of amplitude. Figure 1 Typical arrangement of shunts Usually, the two shunt resistors have quite different values of low frequency resistance: around 1 Ω and 1mΩ. The air gap is calibrated to spark around 5 kv, allowing a maximum current peak around 5 ka to cross shunt 1 (larger resistance). Above this voltage value the spark avoids corresponding currents to flow across such shunt, preventing damages due to the dissipated power. On the other hand, the whole current crosses the low resistance shunt. The power dissipated in this shunt is moderate due to the resistance value. It is usual assumed that the lightning current wave that crosses the shunt resistors can be recovered simply dividing the detected voltage by the value of shunt
2 resistance. Though this procedure may be appropriate for devices with significant values of resistance (~1Ω) employed to measure low intensity currents, the use of this device to measure intense impulsive currents requires careful processing of the measured data in order to recover the lightning current waveform due to inductive effects, as considered below. Heating concerns determine two practices. First, only materials having low coefficient of temperature are used to build shunts in order to limit the variation of electrical resistivity due to the temperature increase promoted by current flow. Also, the value of the low frequency resistance is limited. This explains the resistance value around 1 mω for measuring the largest lightning currents. The development and application of shunts for measurement of lightning current presents some complexities that are poorly reported by literature. One of the relevant aspects refers to the inductive characteristic of the shunt for fast impulsive currents and the increase of its internal impedance due to skin effect. The deviation of current waveform from the measured voltage wave may be very significant, once the inductive behavior is considerable for the typical frequencies of the wave front. Thus, the usual practice of simply dividing the detected voltage by the shunt resistance to obtain the current wave may lead to significant errors. This is the focus of the present paper. 3 THE DEVELOPMENT OF SHUNT DEVICE 3.1 The design The authors have developed a system to measure lightning current that includes shunt resistors. The system was developed to measure both the impulsive and continuing current components. It has been installed at Morro do Cachimbo Station, in Minas Gerais, Brazil [9, 10] in order to complement the local measurement. The former system installed there was able to measure up to 15 strokes in a flash but the interval of each stroke register was limited to a 400 µs window. A sketch of the measuring system is shown in figure 2. A magnetic field sensor placed at the top of the shielded shelter turns on the measuring system circuit when a thunderstorm approaches the station (detection of field radiated from cloud-to-ground strikes closer than 10 km). The voltage drop across the shunt device caused by the current of a lightning strike to the mast is measured by the system and is converted into a light signal that is transferred to the shelter. There, it is converted again to an electrical signal that is recorded at a Personal Computer. 60 m High Tower O/E Current transducer E/O Measurement part Battery Fiber optic cable E/O Magnetic Field Sensor O/E Electronic circuit PC Recording part Figure 2 - Sketch of the measuring system installed in MCS. Wave Memory 12 Bit 128k buffer 4 channel The device, shown in figures 3, was designed with a special geometric configuration that assures a very reduced value for its inductance. The very defined geometry of this device that comprises two coaxial cylinders, whose radii have close values, allows calculating accurately such inductance. Built of a Nikrotal plate (Ni80%Cr20%), whose thickness is 0.6 mm, the shunt resistor has 162.5 mm of external radius and 262 mm of length. Its low frequency impedance value (resistance) is 0.75 mω. Figure 3 - External view of the current transducer Figure 4 shows an internal view of the device that includes a refractory concrete layer to assure thermal insulation to the electric-optical converter and other electronic components installed inside. The cylindrical shape minimizes the inductive field these components are submitted to [11].
3 Figure 4 - Internal view of the current transducer 3.2 The relevance of inductive effect for fast current waves In spite of the special design, the inductive effect is still very pronounced at the wave front for fast currents. Figure 5 illustrates the register of a low amplitude fast impulsive current measured by a Rogowsky coil and also the corresponding voltage wave measured by the shunt device. 3.3 Other laboratorial tests In order to evaluate the behavior of the device in hard thermal, it was submitted to long duration currents (low frequency) to obtain the same heating caused by very high impulsive currents and long continuous current components. Even exceeding extreme conditions (in relation to the heating caused by typical lightning currents), the resistance value was not significantly affected. Impulsive current waves of moderate and large amplitude were also measured in laboratory, including 8/20µs and 4/10µs waveforms from 20 to 85 ka, and the results were quite good [12]. Figure 7 illustrates the comparison between measurements performed by a Pearson coil and by the shunt, after the wave was recovered by the transfer function. Figure 6 - Comparison of current waves measured by Rogowski Coil and recovered by the transfer function. Figure 5 - Comparison between voltage and current waves. This aspect motivated the derivation of a transfer function that is able to accurately recover the current wave from the detected voltage wave. This accuracy is assured by the knowledge of the exact values of the device impedance in the whole range of frequencies of interest. This impedance includes a resistance, an internal and an external inductance. Both internal parameters are very frequency dependent. The device was tested in laboratory with both low and high current amplitudes and showed very good results. Figure 6 shows the good agreement between the measured current and that recovered from the measured voltage after the application of the transfer function. Figure 7 Comparing measurements of intense impulsive current performed by the device and by a Pearson coil. The most relevant aspect denoted by figures 5 to 7 is not the accuracy of the measurements, but the very pronounced inductive effect that is expressed by the significant advance of the detected voltage wave in relation to the current wave.
4 4 APPLICATION TO A REAL CASE Experimental laboratorial tests provide substantial support for evaluations related to real phenomenon. Nevertheless, they are not able to replace the real tests in field conditions. The measuring system including the shunt device was installed in Morro do Cachimbo Station at the base of a 60 m high mast that is sustained by insulated guy ropes, as shown in Figure 8. 1700 µs. The digital recording process allows recovering data before the detection of current flow. Thus, differently of traditional measurements that require a threshold value to start recording (e.g. 2 ka in Berger's measurements [2]), the beginning of front wave is clearly perceived and allows determining the front time as the interval to reach the peak value. The mentioned front time was determined in this way. The front time derived from T d30 and T d10 [1, 2] have the same value: 10 µs. Figure 9 - Measurement of a real lightning current Figure 8 View of the shunt device installed at the base of a 60 m high mast in Morro do Cachimbo Station. Figure 9 shows the register of a real lightning current measured recently in Morro do Cachimbo Station using the developed measuring system (2006, March 1 st, 16:21:03hs GMT). Also the detected voltage waveform is included in the figure. The current wave had 46.4 ka peak value, 14.5 µs front time and a 66.7 µs half-wave time. Data corresponding to this measurement was first presented in reference [13] with an error due to edition mistakes. The register window was 1s and the flash duration was This real register seems very rich to denote how the inductive effect was able to distort the voltage wave in relation to the current one even for a relatively slow current wave. Just after the first instants, while the current increases slowly, there is a fast increase of measured voltage wave that remains until it reaches the peak. The deviation between current and voltage waves is very significant. In this specific case, if the current was recovered from the measured voltage directly from the low frequency resistance, the front time (T d30 ) would be 4.8 µs instead of the values 10 µs. Also the estimated current peak would be significantly higher. 5 CONCLUSIONS The fundamental aspects related to the design of a special resistive transducer to be used for measurement of fast impulsive currents were presented. The low frequency resistance of shunts used to measure intense lightning current is low, around 1 mω. In the frequency range that is representative of typical lightning current wave front time, there is always significant inductive effect. The difference between the waveform of current and voltage in the real presented case denotes this aspect.
5 Unless this effect is compensated for by any methodology, such as the transfer function adopted in the system developed by the authors, the current wave recovered from the measured voltage may present significant error. This error affects mainly the front wave but also the estimated current peak. The effect is expected to lead to an underestimate of the current front time (to around its half-value, in the presented real case) and to a significant overestimation of the current peak value. 6 ACKNOWLEDGEMENT The authors express their gratitude to CNPq - Brazilian Research Council for the financial support and to Mr. Alisson L. Senna Filho (LRC-UFMG) for his contributions during the construction of the developed device. 7 REFERENCES 1. S. Visacro, Lightning: An Engineering Approach, in Portuguese, Sao Paulo: Artliber Ed., 2005. 2. K. Berger, "Novel observations on lightning discharges: Results of research on Mount San Salvatore," J. Franklin Inst., 283, pp. 478-525, 1967. 3. E. Garbagnati, F. Marinoni, and G. B. Lo Piparo, "Parameters of lightning currents. Interpretation of the results obtained in Italy," in Proc. 1981 16th International Conference on Lightning Protection ICLP198, pp. 1-17. 4. K. Miyake, T. Suzuki, and K. Shinjou, "Characteristics of lightning current on Japan sea coast," IEEE Transactions on Power Delivery, vol. 7, pp. 1450-1450, July. 1992. 5. G. Diendorfer, M, Mair, W, Schulz, and W. Hadrian, "Lightning current measurements in Austria Experimental setup and first results," in Proc. 2000 25th International Conference on Lightning Protection ICLP 2000, pp. 44-47. 6. G. Diendorfer, M, Mair, and W, Schulz, "Detailed brightness versus lightning current amplitude correlation of flashes to the Gaisberg tower," in Proc. 2002 26th International Conference on Lightning Protection ICLP 2002, pp. 8-13. 7. H. Torres, O. Trujillo, F. Amortegui, G. Pinzon, C. Quintana, D. Gonzales, D. Rondon, M. Salgado and D. Avila, "Design, construction and calibration of three device to measure directly lightning parameters," in Proc. 1999 10th International Symposium on High Voltage Engineering IHS1999. 8. V. A. Rakov, and M. A. Uman: Lightning: Physics and Effects, Cambridge University. Ed., 2003. 9. S. Visacro, A. Soares, M.A. Schroeder, L.C.L Cherchiglia and V. Sousa, "Statistical Analysis of Lightning Current Parameters: Measurements at Morro do Cachimbo Station", Journal of Geophysical Research, vol. 109, no. D01105, pp. 1 11, January 2004. 10. S. Visacro, "A Representative Curve for Lightning Current Waveshape of First Negative Stroke", Geophysical Research Letters, vol.31, L07112, doi:10.1029/2004.gl019642, April 2004. 11. A. N. Gomez, S, Visacro, J. L. Silvino, P. Resende, A. L F. Senna and W. J. Rocha, "A special transducer for lightning current measurement", in Proc. 2004 International Conference on Grounding and Earthing - GROUND 2004, pp. 51-54. 12. A N. Gomez, S. Visacro, J. L. Silvino, and R. Hostt, "A contribution to the measurement of lightning currents by means of resistive transducers", in Proc. 2005 International Symposium on Lightning Protection SIPDA2005, pp. 213-217. 13. A. G. Navarro, S. Visacro, J. Silvino, R. Hostt and L. C. Rocha "Analysis of Lightning Current Measurement by Means of Resistive Transducers", In Proc. 2006 28th International Conference on Lightning Protection ICLP 2006, pp. 75-78.