De-noising the CN Tower lightning current signal using short term Fourier transform-based spectral substraction

The CN Tower is a transmission tower and it is not unexpected that recorded lightning current signals be corrupted by noise. The existence of noise may affect the calculation of current waveform parameters (current peak, 10-90% risetime to current peak, maximum steepness, and pulse width at half value of current peak). But accurate statistics of current waveform parameters are required to design systems for the protection of structures and devices, especially those with electrical and electronic components, exposed to hazards of lightning. Since more electrical devices are used nowadays, lightning protection becomes more important. So to determine accurate statistics of current waveform parameters, the interfering noise must be removed. In this thesis we describe a technique for de-noising the CN Tower lightning current by modifying its Fourier Transform (FT) where a simulated current waveform (Heidler function) is used to represent the lightning current signal.The limitations of Discrete Fourier Transform (DFT) for removal of non-stationary noise signals, including the noise connected with CN Tower lightning current signals and its properties are discussed. The Short Term Fourier Transform (STFT) is explored to analyze non-stationary signals and to deal with the limitations of DFT. Last of all, an STFT-based Spectral Subtraction method is developed to denoise the CN Tower lightning current signal. In order to evaluate the Spectral Subtraction method, a simulated current derivative waveform ( obtained by differentiating Heidler function) is artificially distorted by a noise signal measured at the CN Tower in the absence of lightning. The Spectral Subtraction method is then used to de-noise the distorted waveform. The de-noised waveform proved to be very close to the original simulated waveform. A signal-peak to noise-peak ratio (SPNPR) of the CN Tower lightning current signal is defined and calculated before and after the de-noising process. For example, for a typical measured current derivative signal, the SPNPR before de-noising is 7.27, and after de-noising it becomes 151.30. Similarly for its current waveform (obtained by numerical integration) the SPNPR before de-noising is 20,16 and it becomes 361.39 after de-noising. Statistics of current waveform parameters are obtained from the de-noised waveforms. The Spectral Subtraction method is also applied for de-noising the electric and magnetic field waveforms generated by lightning to the CN Tower which enables the calculation of their waveform parameters.

Characterization of noise in the lightning current derivative signals measured at the CN tower

Simultaneous measurements of parameters of CN Tower lightning strikes have been performed since 1991. The current derivative signals measured, are corrupted by a 100 kHz oscillating interference. This noise has caused substantial limitations on the usage of the CN Tower lightning current data. As a result, we became motivated to characterize it and search for its source. Furthermore identifying the low-frequency noise is expected to help in its removal and avoid it altogether in future installations. This thesis proves that the low-frequency noise corrupting the lightning current derivative signals is the Loran-C radionavigation signal. This finding is a major contribution not only for the CN Tower lightning project but also for any other research related to measurement of lightning at tall structures. Researchers and experimentalists should be aware of the existence of the Loran-C signal and take the necessary precautions to avoid its interference effect.

Modelling of tall-structure lightning return-stroke current using the Electromagnetic Transients Program

The main aim of this PhD work is to advance tall-structure lightning return-stroke current modelling. The Alternative Transients Program (ATP), a version of the Electromagnetic Transients program (EMTP), is used to model the lightning current distribution within a tall structure and the attached lightning channel. The tall structure, namely the CN Tower, is modeled as three or five transmission line sections connected in series. The lightning channel is represented by a transmission line with a continuously expanding length. The presented model takes into account reflections within the tower and within the lightning channel. Locations of reflections, current reflection coefficients and the parameters of the current simulation function are calculated based on the time analysis of the current derivative signal, measured at the tower. The decay parameters of the simulation function are first determined by curve fitting the decaying part of the current obtained from measurement. The other parameters are determined by curve fitting the measured initial current derivative impulse with the derivative of the simulation function, before the arrival of reflections. The simulation results substantially succeeded in reproducing the fine structure of the measured current derivative signal. The model allows for the computation of the lightning current at any point along the current path (the tower and the attached channel), which is required for the calculation of the associated electromagnetic field. Using the three-section model of the tower, the presented return-stroke current model enables the determination of a discrete return-stroke velocity profile, demonstrating that the velocity generally decays with time. Furthermore, based on the five-section model, the proposed approach enables taking into account the existence of upward-connecting leaders, which allowed, for the first time, the determination of upward-connecting leader lengths and return-stroke velocity variation profiles with more details. The return-stroke velocity profile is found to initially increase rapidly with time, reaching a peak, and then decrease less rapidly. The proposed model is also experimentally verified based on the comparison between the computed and measured electromagnetic fields. The simulated electric and magnetic field waveforms are found to reproduce important details of the measured fields, including initial split peaks that appear due to channel-front reflections in the presence of upward-connecting leaders.

De-noising the CN Tower lightning current signal using short term Fourier transform-based spectral substraction

The CN Tower is a transmission tower and it is not unexpected that recorded lightning current signals be corrupted by noise. The existence of noise may affect the calculation of current waveform parameters (current peak, 10-90% risetime to current peak, maximum steepness, and pulse width at half value of current peak). But accurate statistics of current waveform parameters are required to design systems for the protection of structures and devices, especially those with electrical and electronic components, exposed to hazards of lightning. Since more electrical devices are used nowadays, lightning protection becomes more important. So to determine accurate statistics of current waveform parameters, the interfering noise must be removed. In this thesis we describe a technique for de-noising the CN Tower lightning current by modifying its Fourier Transform (FT) where a simulated current waveform (Heidler function) is used to represent the lightning current signal.The limitations of Discrete Fourier Transform (DFT) for removal of non-stationary noise signals, including the noise connected with CN Tower lightning current signals and its properties are discussed. The Short Term Fourier Transform (STFT) is explored to analyze non-stationary signals and to deal with the limitations of DFT. Last of all, an STFT-based Spectral Subtraction method is developed to denoise the CN Tower lightning current signal. In order to evaluate the Spectral Subtraction method, a simulated current derivative waveform ( obtained by differentiating Heidler function) is artificially distorted by a noise signal measured at the CN Tower in the absence of lightning. The Spectral Subtraction method is then used to de-noise the distorted waveform. The de-noised waveform proved to be very close to the original simulated waveform. A signal-peak to noise-peak ratio (SPNPR) of the CN Tower lightning current signal is defined and calculated before and after the de-noising process. For example, for a typical measured current derivative signal, the SPNPR before de-noising is 7.27, and after de-noising it becomes 151.30. Similarly for its current waveform (obtained by numerical integration) the SPNPR before de-noising is 20,16 and it becomes 361.39 after de-noising. Statistics of current waveform parameters are obtained from the de-noised waveforms. The Spectral Subtraction method is also applied for de-noising the electric and magnetic field waveforms generated by lightning to the CN Tower which enables the calculation of their waveform parameters.

Lightning Return-Stroke Transmission Line Modelling Based on the Derivative of Heidler Function and CN Tower Data

One of the most important parameters in a lightning flash that is of interest to researchers is the lightning return-stroke current as it causes most of the destructions and disturbances in electrical and telecommunication networks. In most cases, the lightning return-stroke current can not be directly measured and current characteristics are determined from measured electric and magnetic fields through the use of lightning return-stroke models. The main objective of this work is the development of a lightning return-stroke model for an elevated object. Also, an important objective is the correlation of the wavefront parameters (peak, maximum rate of rise and risetime) of the return-stroke current with the wavefront parameters of its associated lightning electromagnetic pulse (LEMP), measured 2 km north of the tower. The developed field-current parameter relationships for CN Tower lightning return strokes are compared with those obtained from measurements conducted at the Peissenberg Tower in Germany. A 3-section transmission line (TL) model of the CN Tower, along with the derivative of the modified Heidler function, is used to simulate the measured current derivative signal. Then, the spatial-temporal distribution of the lightning current along the CN Tower and the lightning channel, during the lightning return-stroke phase, is determined. The presented model simulates the measured current derivative signal instead of the current as has been used by other researchers. The use of the derivative of the modified Heidler function to simulate the lightning current derivative proved to be superior than simulating the lightning current. For the quantitative assessment of the proposed model, a comparison between the simulated field, obtained through the usage of Maxwell’s equations and the simulated current, and the measured field is performed. The developed 3-section TL model based on the measured current derivative and the derivative of the modified Heidler function produced a simulated magnetic field that is much closer to the measured field in comparison with previous models. The developed field-current parameter relationships as well as the experimentally verified lightning return-stroke model can contribute to solving the inverse-source problem, one of the most challenging problems in lightning research, where the lightning current characteristics are estimated based on the characteristics of the measured LEMP.

Modeling of the Lightning Return Stroke Current at a Tall Structure Using the Derivative of the Heidler Function

Traditionally tall structures have been modeled as simple lossless transmission lines. This model is inadequate for the CN Tower, which may be modeled as a series of transmission lines with different characteristic impedances resulting in a reflection coefficient at each discontinuity. Analysis shows that these vary significantly and are related to the ratio of the current derivative peak to the current derivative 10%-90% risetime, suggesting that they are frequency dependent. The magnitude of the reflection from the return stroke front, if it does exist, is much smaller that was previously proposed. An alternative approach to modeling, based on modeling the current derivative, is proposed and it is found to provide a better match with the measured waveforms. The CN Tower is modeled as a series of uniform lossless transmission lines and the channel is represented by the MTLL model. The features of the measured magnetic field waveform are well reproduced.

Characterization of noise in the lightning current derivative signals measured at the CN tower

Simultaneous measurements of parameters of CN Tower lightning strikes have been performed since 1991. The current derivative signals measured, are corrupted by a 100 kHz oscillating interference. This noise has caused substantial limitations on the usage of the CN Tower lightning current data. As a result, we became motivated to characterize it and search for its source. Furthermore identifying the low-frequency noise is expected to help in its removal and avoid it altogether in future installations. This thesis proves that the low-frequency noise corrupting the lightning current derivative signals is the Loran-C radionavigation signal. This finding is a major contribution not only for the CN Tower lightning project but also for any other research related to measurement of lightning at tall structures. Researchers and experimentalists should be aware of the existence of the Loran-C signal and take the necessary precautions to avoid its interference effect.

Modeling of the Lightning Return Stroke Current at a Tall Structure Using the Derivative of the Heidler Function

Traditionally tall structures have been modeled as simple lossless transmission lines. This model is inadequate for the CN Tower, which may be modeled as a series of transmission lines with different characteristic impedances resulting in a reflection coefficient at each discontinuity. Analysis shows that these vary significantly and are related to the ratio of the current derivative peak to the current derivative 10%-90% risetime, suggesting that they are frequency dependent. The magnitude of the reflection from the return stroke front, if it does exist, is much smaller that was previously proposed. An alternative approach to modeling, based on modeling the current derivative, is proposed and it is found to provide a better match with the measured waveforms. The CN Tower is modeled as a series of uniform lossless transmission lines and the channel is represented by the MTLL model. The features of the measured magnetic field waveform are well reproduced.

Modelling of tall-structure lightning return-stroke current using the Electromagnetic Transients Program

The main aim of this PhD work is to advance tall-structure lightning return-stroke current modelling. The Alternative Transients Program (ATP), a version of the Electromagnetic Transients program (EMTP), is used to model the lightning current distribution within a tall structure and the attached lightning channel. The tall structure, namely the CN Tower, is modeled as three or five transmission line sections connected in series. The lightning channel is represented by a transmission line with a continuously expanding length. The presented model takes into account reflections within the tower and within the lightning channel. Locations of reflections, current reflection coefficients and the parameters of the current simulation function are calculated based on the time analysis of the current derivative signal, measured at the tower. The decay parameters of the simulation function are first determined by curve fitting the decaying part of the current obtained from measurement. The other parameters are determined by curve fitting the measured initial current derivative impulse with the derivative of the simulation function, before the arrival of reflections. The simulation results substantially succeeded in reproducing the fine structure of the measured current derivative signal. The model allows for the computation of the lightning current at any point along the current path (the tower and the attached channel), which is required for the calculation of the associated electromagnetic field. Using the three-section model of the tower, the presented return-stroke current model enables the determination of a discrete return-stroke velocity profile, demonstrating that the velocity generally decays with time. Furthermore, based on the five-section model, the proposed approach enables taking into account the existence of upward-connecting leaders, which allowed, for the first time, the determination of upward-connecting leader lengths and return-stroke velocity variation profiles with more details. The return-stroke velocity profile is found to initially increase rapidly with time, reaching a peak, and then decrease less rapidly. The proposed model is also experimentally verified based on the comparison between the computed and measured electromagnetic fields. The simulated electric and magnetic field waveforms are found to reproduce important details of the measured fields, including initial split peaks that appear due to channel-front reflections in the presence of upward-connecting leaders.

Lightning Return-Stroke Transmission Line Modelling Based on the Derivative of Heidler Function and CN Tower Data

One of the most important parameters in a lightning flash that is of interest to researchers is the lightning return-stroke current as it causes most of the destructions and disturbances in electrical and telecommunication networks. In most cases, the lightning return-stroke current can not be directly measured and current characteristics are determined from measured electric and magnetic fields through the use of lightning return-stroke models. The main objective of this work is the development of a lightning return-stroke model for an elevated object. Also, an important objective is the correlation of the wavefront parameters (peak, maximum rate of rise and risetime) of the return-stroke current with the wavefront parameters of its associated lightning electromagnetic pulse (LEMP), measured 2 km north of the tower. The developed field-current parameter relationships for CN Tower lightning return strokes are compared with those obtained from measurements conducted at the Peissenberg Tower in Germany. A 3-section transmission line (TL) model of the CN Tower, along with the derivative of the modified Heidler function, is used to simulate the measured current derivative signal. Then, the spatial-temporal distribution of the lightning current along the CN Tower and the lightning channel, during the lightning return-stroke phase, is determined. The presented model simulates the measured current derivative signal instead of the current as has been used by other researchers. The use of the derivative of the modified Heidler function to simulate the lightning current derivative proved to be superior than simulating the lightning current. For the quantitative assessment of the proposed model, a comparison between the simulated field, obtained through the usage of Maxwell’s equations and the simulated current, and the measured field is performed. The developed 3-section TL model based on the measured current derivative and the derivative of the modified Heidler function produced a simulated magnetic field that is much closer to the measured field in comparison with previous models. The developed field-current parameter relationships as well as the experimentally verified lightning return-stroke model can contribute to solving the inverse-source problem, one of the most challenging problems in lightning research, where the lightning current characteristics are estimated based on the characteristics of the measured LEMP.