Calculation Of Lightning Electromagnetic Field And Lightning-Induced Overvoltages On Overhead Transmission Lines

Recently, with the widespread application of sensitive electronic devices in many areas, such as data-transmission networks and power system, the economic losses caused by lightning accidents increase rapidly. It is generally acknowledged that lightning-induced surge voltage and current are the two main factors which cause electronic equipment failure. To analyze the surge voltage and current, there are two problems needed to be solved:(1) establishing an effective numerical method to calculate lightning electromagnetic fields affected by finitely conducting ground, (2) founding telegrapher equations to describe the behavior of conductors illuminated by lightning electromagnetic fields and the numerical technique to solve these equations.Generally, the vertical electric field and magnetic field generated by lightning are obtained by the dipole technique, and the horizontal electric field generated by lightning can be calculated from the Cooray-Rubinstain formula. But the dipole technique and the Cooray-Rubinstain formula are based on the hypotheses of perfectly conducting ground and plane waves refracting nearly perpendicularly at the air-earth interface respectively, which cannot be satisfied in practice. When using the current field-to-transmission line coupling models to predict the overvoltages on one line in a multiconductor power lines system, overvoltages on all the lines have to be evaluated, which is quite inefficient as the computational time increases with the number of the lines. Besides, the sags of the lines are ignored in the evaluation of lightning-induced overvoltages. To overcome these shortcomings, the relevant researches are carried out and the results obtained are showed as follows:(1) A general expression for the calculation of the horizontal electric field is developed. The general expression is based on the Norton equations, and discards the hypotheses that plane waves refract nearly perpendicularly and parallel at air-earth interface in the Cooray-Rubinstain and Wait formulae respectively. By comparing the horizontal electric fields obtained by the dipole technique, the general expression, the Cooray-Rubinstain formula and the Wait formula respectively, it can be found that the general expression gives the highest accuracy result; the dipole technique gives the poorest result; the Cooray-Rubinstain formula gives the underestimated result; and the Wait formula gives the overestimated result. In the evaluation of the underground horizontal electric field and lightning-induced overvoltages, underestimated field and overestimated overvoltages are obtained by Cooray-Rubinstain formula; the results obtained by the general expression have higher accuracy. Thus, the validity of the general expression is confirmed.(2) A decoupling method based on modified Agrawal model is developed, which can be used to evaluate the overvoltages on one line in a multiconductor transmission lines system independently and efficiently. By comparing lightning-induced overvoltages obtained by the decoupling method and the modified Agrawal model, the validity and efficiency of the proposed method are confirmed.(3) In the evaluation of lightning-induced overvoltages on the overhead transmission lines, the lines are regarded as straight lines, i.e. the sags of the lines are ignored, in the current telegrapher equations. However, overvoltages are affected by the sags intensely. In this paper, generalized telegrapher equations are deduced for evaluating overvoltages on the nonuniform overhead transmission lines illuminated by lightning electromagnetic fields, and are verified by numerical examples. The parameters of the lines affected by length are analyzed and the overvoltages influenced by sags are investigated.(4) The lightning electromagnetic fields' frequency spectra under different conductivities and dielectric constants are analyzed by using numerical method to solve the Norton equations. The results show that the vertical electric field and magnetic field vary with conductivity very little, except horizontal electric field; the lightning electromagnetic fields rarely vary with dielectric constant. Two inverse algorithms for estimating the lightning current from vertical electric field and magnetic field are discussed respectively.