A Practical Mathematical Model of Corona for Calculation of Transients on Transmission Lines

Overvoltage protection and insulation coordination are based to a large degree on the knowledge of the magnitudes and waveforms of voltages. Two kinds of significant phenomena affect the attenuation and distortion of overvoltages propagating along overhead transmission lines: (a) variations of transversal parameters due to corona and (b) frequency dependence of longitudinal parameters caused by imperfect ground return and skin effect of conductors. Through many years´ efforts, satisfactory results have been achieved in the study of frequency dependence. Owing to the complexity of the physical phenomena of corona, a satisfactory approach to include corona effect in the calculation of travelling waves has not been developed, although many attempts have been made. The main problem is the lack of a sophisticated and practical corona model. The techniques proposed in the literature to include corona effect in the transmssion line transients calculations may be classified into two methodologies. In the first methodology, a number of mathematical-physical models have been developed on the basis of the physical mechanism of corona to obtain charge versus voltage characteristics in line transients computations. Papers published using the second methodology do not deal with the physical mechanism of corona. They have a common difficulty of predicting the q-v characteristics of the line beforehand. A practical model using the image method to calculate the dynamic capacitance of the line in corona is presented in this paper. Time-varying spatial electromagnetic fields propagating along fixed cross-section power lines are basically parallel plane fields even during corona.