Mahdi Izadi

An Analytical Second-FDTD Method for Evaluation of Electric and Magnetic Fields at Intermediate Distances from Lightning Channel

Evaluation of electric and magnetic fields due to lightning discharge is important in determination of lightning induced voltage and power system protection especially to the distribution system. In this paper, by using dipole method, Maxwell equations and second order finite-difference time domain (later referred as a 2nd FDTD method) on two realistic return stroke currents, an algorithm for evaluation of electric fields is proposed, which is based on numerical methods in the time domain. Besides proving greater accuracy, it also allows the evaluation of electric and magnetic fields away from lightning channel. In addition, the comparison between simulation results and measured fields wave shape showed that the proposed algorithm is in good agreement for evaluation of electric and magnetic fields due to lightning channel.

Evaluation of electromagnetic fields associated with inclined lightning channel using second order FDTD-hybrid methods

Evaluation of electromagnetic flelds caused by the lightning channel is an appealing topic in order to consider the indirect efiects of lightning on the power lines. A common assumption for the calculation of electromagnetic flelds at the observation point is a vertical lightning channel, but the fact is that in reality the lightning channel is seldom vertical on the ground surface. In this study, the electromagnetic flelds due to inclined lightning channel at various observation points with difierent angles and with respect to the image of lightning channel on the ground surface were explored. This study also proposes general equations that can estimate the electric flelds due to inclined lightning channel through the 2nd FDTD method. The proposed method supports the notion of vertical lightning channel while the channel angle with respect to z-axis is assumed to be zero. This method was validated through the data gathered from flve flelds: three at a close distance from inclined lightning channel and two at intermediate distances from vertical lightning channel. Similarly, due to inclined lightning channel, the efiects of geometrical and current parameters on the electromagnetic flelds are considered. This study substantiates difierent coupling models with FDTD structure directly at the time domain without a need for extra converters.

Numerical expressions in time domain for electromagnetic fields due to lightning channels

In this paper, by considering the factors that influence the charge height variation along the lightning channel and using Maxwells equations, general expressions in time domain for the evaluation of electromagnetic fields at an observation point are proposed. The lightning channel is assumed to be perpendicular to the ground surface and the ground conductivity is considered to be perfect. Our results showed that the proposed method has good agreement with the measured values, as we validated the outcome using fields measured at close and intermediate distances from the lightning channel. A set of general equations, which has the ability of evaluating any given channel base current function and current model in time domain is also derived.

Analytical Expressions for Electromagnetic Fields Associated with the Inclined Lightning Channels in the Time Domain

Abstract This article describes general analytical equations that are developed for the calculation of electromagnetic fields due to an inclined channel directly in the time domain. The input parameters of the model, angle of inclination of the lightning channel and the angle at the observation point can be varied through all possible values to produce the relevant electromagnetic fields. The proposed model is validated with eight electromagnetic waveforms measured at close range of the lightning channel. The results of the model show good agreement with the measured data. Furthermore, the proposed equations are compatible with different channel base current functions. The equations could easily be applied in the coupling models that calculate induced voltages in conductors in the presence of lightning-generated electromagnetic fields.

Evaluation of lightning return stroke current using measured electromagnetic fields

The lightning return stroke current is an important parameter for considering the efiect of lightning on power lines. In this study, a numerical method is proposed to evaluate the return stroke current based on measured electromagnetic flelds at an observation point in the time domain. The proposed method considers all fleld components and the full wave shape of the current without the use of a special current model as a basic assumption compared to previous methods. Furthermore, the proposed algorithm is validated using measured flelds obtained from a triggered lightning experiment. The results show a good agreement between the simulated fleld based on the evaluated currents from the proposed method and the corresponding measured fleld at a remote observation point. The proposed method can determine current wave shapes related to a greater number of lightning occurrences compared to the direct measurement of the current.

Considering on the Ground Reflection Effect on the Electromagnetic Fields due to Lightning Channel

Lightning electromagnetic fields are important issues for the evaluation of lightning induced overvoltage on power lines and for setting the appropriate protection level for power networks. Such electromagnetic fields are strongly dependent on lightning return stroke currents at different heights along the lightning channel. On the other hand, the ground reflection factor due to the difference between the return stroke channel impedance and the equivalent ground impedance at channel base can have an effect on the shape of the return stroke currents by entering additional reflected currents into the channel. In this paper, the effect of the ground reflection factor on the return stroke currents at different heights along a channel and the electromagnetic fields associated with the lightning channel at close distances are considered. Moreover, the behavior of the electromagnetic fields versus the reflection factor changes and the radial distance changes are considered and the results are discussed accordingly. The results illustrate that the reflection factor has a direct relationship with the values of the electromagnetic fields while this is usually ignored in earlier studies.

Evaluation of Electromagnetic Fields Due to Inclined Lightning Channel in Presence of Ground Reflection

In this paper, analytical fleld expressions are proposed to determine the electromagnetic flelds due to an inclined lightning channel in the presence of a ground re∞ection at the striking point. The proposed method can support difierent current functions and models directly in the time domain without the need to apply any extra conversions. A set of measured electromagnetic flelds associated with an inclined lightning channel from a triggered lightning experiment is used to evaluate the proposed fleld expressions. The results indicate that the peak of the electromagnetic flelds is dependent on the channel angle, the observation point angle as well as the value of the ground re∞ection factor due to the difierence between channel and ground impedances. Likewise, the efiect of the channel parameters and the ground re∞ection on the values of the electromagnetic flelds is considered and the results are discussed accordingly.

The analytical field expressions associated with lightning channel in presence of ground reflection at striking point

In this paper a general set of field expressions associated with a lightning channel are proposed to evaluate the electromagnetic fields due to lightning in the presence of a ground reflection at the channel base. The ground reflection factor is due to the difference between the channel and ground impedances and can enter additional reflected currents into the lightning channel. The proposed field expressions can support the widely used current functions and current models directly in the time domain without the need to apply any extra conversions. Moreover, the proposed expressions are applied on a sample of lightning current that has been obtained from a triggered lightning experiment and the evaluated electromagnetic fields are compared to the corresponding measured fields and the results discussed accordingly. The results illustrate that the simulated fields based on the proposed method are in good agreement with the measured fields. Moreover, the ground reflection factor can have a great effect on the values of the lightning electromagnetic fields. The proposed field expressions consider all field components directly in the time domain and vary appropriately to join with widely used coupling models to evaluate the lightning induced voltage on power lines without the need to apply any extra conversions.

Considering on return stroke current wave shape for tall objective cases

The return stroke current along the lightning channel for striking of the lightning to tall objective case is different from ground surface case with many factors affect this phenomenon. This study considers the engineering related to return stroke current models where the general equations are expressed and different models are generated. The results obtained will be compared and discussed.

Considering on charge density along return stroke lightning channel

Prediction of return stroke current wave shape along lightning channel is an important subject in evaluating the electromagnetic fields and induced overvoltage due to lightning channel at observation point and power line. This paper reviews the different return stroke current models, with the engineering current models is selected as the leading model, and evaluates the their current behaviors along the lightning channel. A comprehensive result on the charge density for each model will then be presented to conclude the findings.