General equations of the line represented by discrete parameters. I. Steady state [power transmission lines]

An original analytical procedure is presented which results in a new mathematical form of the well-known general, i.e. fundamental, line equations. The procedure is based on representing the line by an arbitrary number of discrete or lumped parameters, using the principle of superposition, and on the summation of finite and infinite geometric series. This results in relatively simple analytical expressions for the interrelationship of currents and voltages at different points along transmission lines in steady-state operation. This procedure opens up the possibility of using a new approach for the interpretation and explanation of resonant phenomena on transmission lines and their models with lumped parameters