Being one of the most spectacular events in nature, lightning is basically a transient high current electric discharge in the atmosphere, which extends up to kilometres. Cloud to ground discharge is the most hazardous one as far as ground based structures are considered. Among the different phases of a lightning flash, return stroke is considered to be the most energetic phase and is basically responsible for most of the damages. Hence, much emphasis has been given to return stroke modeling. A more realistic modeling of return stroke is very essential to accurately study the interaction of return stroke with the structures on ground. As return stroke is dominated by electromagnetic phenomenon, an electromagnetic model will be the most suitable one. It does not call for any assumption on the mode of wave propagation, as well as, electromagnetic coupling between the different channel portions. There are mainly two approaches adopted for electromagnetic models i.e. frequency domain and time domain approach. Time domain approach is more reliable as it can handle, in principle, the nonlinear processes in the lightning channel. It is also free of numerical frequency domain to time domain inversion problem, which are found to be quite severe. However, most of the previous works on time domain electromagnetic models suffered from following two serious limitations - (i) the initial charge on the channel, which forms the true excitation for the problem, is not considered and (ii) instead of the non-linearly rising conductivity of the channel, a constant resistance is employed. For a realistic simulation of the interaction between the channel and any intercepting system, a time domain model with the above two major aspects being fully represented is very essential. In an earlier work, all these aspects have been fully considered but a domain based numerical modelling was employed. Consequently, it was difficult to consider the down conductor and further the number of unknowns was considerably large. In view of this, the present work is taken up and its scope is defined as to develop a boundary based numerical time domain electromagnetic model in which the initial charge on the channel and the non-linearly evolving channel conductance are fully considered. For the electrical engineering applications, electromagnetic aspects of the lightning phenomena is more important than the other associated physical processes and hence, importance is given only to the electromagnetic aspects. In other words, the light emission, thunder, chemical reactions at the channel etc. are not considered. Also, for most of the electrical engineering applications, the critical portion of current would be the region up to and around the peak and hence, modeling for this regime will be given prime importance. Owing to the complexity of the problem, some simplifying assumptions would be very essential. The literature indicates that these assumptions do not affect the adequate representation of the phenomena. Lightning channel is considered to be vertically straight without any branches. Earth is considered to be perfectly conducting. Explicit reference to dynamically varying channel radius, temperature and the air density is not made. However, it is assumed that the arc equation employed to describe the temporal changes in conductivity would adequately take care of these parameters. Lightning channel is represented by a highly conducting small core, which is surrounded by a weakly conducting corona sheath. The initial charge on the channel is deduced by solving for electrostatic field, with leader portion set to possess an axial gradient of 60 V/cm and the streamer portion to 5 – 10 kV/cm. The radius of the corona sheath is set iteratively by enforcing a gradient of 24 kV/cm up to its radial boundary. As analytical solution for the problem is impractical, suitable numerical solution is sought. Since the spatial extension of this time marching problem is virtually unbound and that the significant conduction is rather solely confined to an extremely small cross section of the channel core, a boundary-based method is selected. Amongst the numerical methods, the present work employs the moment method for the solution of the fields associated with the return strokes. A numerical solution of the Electric Field Integral Equation (EFIE) for thin structures has been developed in the literature. The same approach has been employed in the present work, however, with suitable modifications to suit the lightning problem. The code was written in MATLAB and integrations involved in the EFIE were solved using MATLAB symbolic computation. Before introducing the channel dynamic conductance and the initial charge on the channel, the code developed is validated by comparing the results for a center fed dipole antenna with that given in the literature. Also, NEC (Numeric Electromagnetic Code) simulations for various cases of monopole and dipole antenna were performed. The results from the code developed are shown to have good matching with that obtained from NEC based time domain results. In an earlier work, the dynamic conductance of the return stroke channel core, which is a high current electric arc, was represented by a first order arc equation. The same approach is employed in the present work also. Similarly, the transition from streamer to leader was modeled by Braginskii’s spark law and the same has been considered in the present work. A value of 10-5 S/m was used for minimum value of streamer conductance. For numerical stability, upper (Gmax = 3 S/m) and lower bounds (Gmin = 0.0083 S/m) for the channel conductance are forced. Preliminary simulations were run with and without dynamic channel conductance. The initial charge distribution along the channel formed the excitation. Results clearly show that without the dynamically varying channel conductance, no streamer to leader transition and hence, no return stroke evolution can occur. In other words, the non-linearly evolving channel conductance is mainly responsible for the evolution of the return stroke. In order to consider the charge neutralization by the return stroke, the charge deposited by it is diffused into the corona sheath. A fixed value of the corona sheath conductance is employed and the diffusion process is modeled by an equation derived from the continuity equation. To study the effect of corona sheath, simulations were run with and without corona. From the simulation results it was observed that the corona sheath causes increase in peak value of the stroke current, as well as, time to front and a decrease in the velocity of propagation. For the validation of the model, the basic characteristics of the return stroke current like the current wave shape, temporal variation of stroke current at different heights, velocity of propagation and the vertical electric fields at various radial distances were compared with available field/experimental data. A good agreement was seen and based on this, it is concluded that the present work has successfully developed a boundary based time domain numerical model for the lightning return stroke. Natural lightning being a stochastic process, the values of the parameters associated with it would differ in every event. On other hand, any deterministic model like the one developed in the present work predicts a fixed pattern of the simulated quantities. Therefore, it was felt that some of the model parameters must be permitted to vary so that a range of results could be obtained rather than a single pattern of results. Incidentally, the model parameters like arc time constant, settling value of arc conductivity/gradient, bounds for channel conductivity, streamer gradient, radius of the core etc. are not precisely known for the natural lightning environment. Further, some of them are known to vary within an event. Considering these and that simplicity is very important in already complex model, the above-mentioned parameters are taken as tunable parameters (of course to be varied within the prescribed range) for deducing the return stroke currents with some desired characteristics. A study on the influence of these parameters is made and suggestions are provided. Simulations for the nominal range of stroke currents are made and results are presented. These simulations clearly show the role of cloud potential, which in turn dictates the length of final bridging streamer, on the return stroke currents. The spatio-temporal variation of the current, charge deposited by the return stroke and the channel conductivity are presented which, reveal the dynamic processes leading to the evolution of return stroke current. Subsequently, simulations for two cases of stroke to elevated strike object are attempted. The upward leader was modeled quite similar to the descending one. Many interesting findings are made. In summary, the present work has successfully developed a boundary-based time domain numerical electromagnetic model for the lightning return stroke, wherein, the initial charge deposited on the channel and the non-linearly rising channel conductance have been appropriately considered. Simulation using the model clearly depicts the dynamic evolution of the return stroke. The characteristics of the simulated return strokes are in good agreement with the field data. Some of the parameters of the model are suggested as tunable parameters, which permit simulation of strokes with different characteristics.

Lightning is a natural phenomenon involving transient high current discharge in the atmosphere. Cloud-to-ground lightning, wherein the discharge occurs between the cloud and the ground is quite hazardous to systems on the ground. Apart from threat to life, the devastating effects of lightning can be mainly of thermal, mechanical and electromagnetic origin. Many a times, thermal and electromagnetic effects are of main concern. A direct hit, wherein the system under consideration becomes a part of the lightning path, could be quite catastrophic to many vulnerable systems like oil rigs, chemical factories, missile/satellite launch pads. From the safety and operational point of view, lightning is of serious concern for electrical systems including transmission lines and substations, nuclear power stations, telecommunication station and data banks. Lightning cannot be avoided, however, by employing a suitable Lightning Protection System (LPS), adequate protection against a direct hit can be provided to ground based systems. A typical lightning protection system involves: 1) Air termination network, which is responsible for stroke interception, 2) Down conductor system, which provides to the stroke current a minimal impedance path to the ground and 3) Earth termination network, for safe dissipation of current into the ground. Similarly, for the indirect effects, which are basically of electromagnetic origin, suitable protection can be designed. The key factors in a protective action involve interception of the dangerous strokes, minimization of the consequential potential rise on down conductors, as well as, at earth termination and keeping the field in the protective volume within an acceptable level. The last aspect can be generally categorized into secondary level protection. For critical systems, the lightning protection system is generally isolated from it. In such designs, potential rise on LPS governs the physical isolation required between the protected and protection system. For a given level of bypass strokes, cost of the LPS increases with the amount of physical separation employed. All most all of the earlier works have concentrated on lightning surge response of power transmission line towers. Apart from their relatively moderate heights, the intention was to arrive at a model, which can be incorporated in circuit simulation software like EMTP. Consequently, they envisage or approximate the mode of propagation to be TEM. In reality, for down conductors of height greater than say 30 m, only TM mode prevails during the initial critical time period. Hence the earlier models cannot be extended to general lightning protection schemes and for down conductor of larger lengths. Only limited literature seems to be available on the characteristics of general down conductor configurations. The problem in hand is very important and some serious research efforts are very much essential. In view of the above, the present work aims to evaluate the rise in potential as well as current injected into the soil at the base for: (i) practical range of down conductor configurations involving single down conductor (with height exceeding 30 m) and (ii) pertinent values of stroke current parameters. The protection schemes considered are isolated vertical down conductor, isolated tower (both square and triangular cross-section) and, tower with insulated lightning mast carrying ground wires. The parameters under consideration are: (i) height and cross section for the down conductor, (ii) clearance between the down conductor and the protected system, (iii) channel geometry, wherein only inclination is to be considered, (iv) velocity of current along the channel and (v) wave shape and rise time for the stroke current. For the evaluation of lightning surge response of transmission line towers, many theoretical and experimental approaches are found in the literature. However, works considering the TM mode of current propagation is relatively limited. In that both experimental and theoretical approaches have been adopted. Theoretical approach invariably adopted numerical field computation in frequency domain using Numerical Electromagnetic code (NEC-2). Fourier Transform techniques are employed to extract the time domain quantities. This approach is very economical, free from experimental errors and least time consuming. Hence it is selected for the present work. However, there are certain limitations in this approach. In NEC simulation, there is a restriction on the size and the arrangement of individual elements. Therefore, although fairly complex tower structures can be simulated, some simplification in the geometry is unavoidable. Such an approximation has been reported to cause insignificant error. NEC is not accurate for calculations in low frequency regime. But in the present work, the initial time regime is of concern wherein the high frequency components dominate. Therefore the above said limitation is not of any serious concern. In order to validate the approach, potential rise is computed for 120 m tall cylindrical down conductor and tower. Results are compared favorably with earlier works, which are based on potential lead wire method. A careful re-look into the ’potential rise’ on the down conductors reveal several things. The electric field in the region between the protection system and protected system is the root cause for the breakdown/flashover. For a given geometry, the integral of the electric field along the shortest path between the two systems must be representing the overall stress on the air gap. Further, for the later time periods, this integral coincides with the well-known quasi-static potential. All the available data and models for breakdown of long air gaps are basically in terms of this quasi-static potential. In view of this, the above path integral is defined as ’equivalent potential rise’ (which will be hereafter termed as ’potential rise’), and taken as the index for surge response. Further, observation of the computed spatio-temporal radial electric field around the down conductor reveals some additional features, which are not common in the quasi-static regime. Electric field reverses its polarity in space, which is due to the opposite current flowing in the lightning channel. Therefore, ’potential rise’, which is taken as the representative for the dielectric stress on the air, should not be evaluated for larger distances. Considering this and noting that the protected system generally lies well within a distance of 50% of the H, height of the down conductor, potential rise is evaluated by integrating electric field within this distance (12.5%H, 25%H, 50%H). Three heights (100%H, 75%H, 50%H) are considered for the evaluation of the potential. The influences of various down conductor and lightning channel parameters are analyzed. Finally vertical channel with full velocity for current propagation is arrived for the investigations. Also, the influence of neighboring conducting objects is briefly studied. It is argued that it needs to be ignored for the general study. Analysis is carried out for a range of down conductor configurations of heights ranging from 45 m to 120 m. Cylindrical down conductor is selected for the detailed study on the overall characteristics and its dependency on pertinent parameters. The characteristics of potential rise are found to be significantly different from that given by the commonly employed uniform transmission line model. In the regime of very fast front currents, down conductor of comparable heights have comparable potential rise. For the larger time to crest, behavior tends more to wards that for quasi-static regime. The dependency of the potential rise on radius of the down conductor seems to be logarithmic in nature. Surge response of isolated towers of both square and triangular cross sections is studied for heights ranging from 45 m to 120 m. The overall characteristics are found to be similar to cylindrical down conductor. Dispersive propagation is found to exist on towers. As a result, the base currents are slightly lower and potential rise exhibits less oscillations. Data curves on potential rise at three different heights and for three different spatial extents are generated for the range of down conductor heights with rise time of the stroke current as the variable. Several interesting observations have been made. Next the investigation is taken up for the insulated mast scheme. The parameters of the study are taken as the number of ground wires, grounding location of ground wires and length of the insulation cylinder. Potential across the insulation, tower base currents, and ground wire end currents are deduced. The basic characteristics of the potential rise are shown to be quite similar to that for the transmission line. For fast front currents the temporal variation is bipolar with a smooth decay. In other words, oscillations are sustained for considerably longer duration. Voltage stress across the insulation surface for one ground wire design is found to be higher by 1.4 - 2.4 times than that for isolated tower. The highest amplification of the ground end current, which occurs for fast front currents, is about 1.8 times. Potential difference across the insulation for two-ground wire design is higher by a factor of 1.3 - 1.85 than that for isolated tower. For the design with four ground wires, potential across the insulation is comparable with that for the tower. However, the mechanical strength of the insulating support should also be considered in the selection of number of ground wires. There exists, especially for fast front strokes, significant induction to the supporting tower. The height of the insulation seems to possess no appreciable influence on the potential rise and base currents. Several issues need to be considered before selecting this design. The contribution made by the present work can be summarized as follows. It basically deals with lightning surge response of isolated down conductors of height in the range 45 - 120 m. The configurations considered are, cylindrical down conductor, tower with both square and triangular cross section and insulated mast scheme. It makes a careful study on the ’potential rise’ on down conductors and a suitable definition for the same is proposed. Basic characteristics of potential rise and ground end currents are studied for the above-mentioned designs. Their salient features are enumerated. For the towers, design data curves are provided for relevant range of stroke current rise time. The issues that need to be considered in the insulated mast scheme are discussed along with the data on potential rise and base currents. The findings of this work are believed to be very useful for the design of lightning protection scheme involving isolated down conductor. Further the results are useful in analyzing the consequential lightning generated threat of being close to tall towers.