Single-phase illuminated transmission line model including corona effect

This paper presents a model for a single-phase transmission line in the presence of corona effect and induced voltages, the latter due to external electromagnetic fields. The solution of the transmission line equations is proposed through the method of characteristics, which is based on the partial differential equations (PDEs) theory. Based on that theory, the Telegrapher´s equations, consisting on a system of two PDEs, are transformed into ordinary differential equations (ODEs). The resultant nonlinear system of ODEs is numerically integrated along the characteristic curves, which implicitly fulfill the Courant-Friedrichs-Lewi (CFL) condition. In the modeling of corona, the capacitance has been taken as static, i.e., it does not depend on the rate of change of the voltage. This permits to use charge-voltage (qv) curves to represent the nonlinear phenomenon of corona. The induced voltages along the line have been calculated by using an incident nonuniform field. This field has two components, one in the direction of the ground and the second being orthogonal to the ground.