General equations of lumped parameter ladder circuits and a special approach to analyzing electrical line transient states

The presented analytical procedure gives the equations that can be named as the General Equations of Lumped Parameter Ladder Circuits. The procedure is based on representing an electrical line through its lumped parameter model, applying the principle of superposition, and summation of the finite and infinite geometric series. The developed analytical procedure results in relatively simple analytical expressions for the relationship between currents and voltages at different points of transmission line models in both transient and steady state conditions. Also, the developed analytical procedure follows one by one all the phases of the actual physical process occurring during transient states in transmission lines. As such, this procedure is convenient for determination of power frequency over-voltages during a transient state of a transmission or distribution line. As an illustration of this, the paper presents a numerical example of determination of switching over-voltage at the open end of a transmission line.