Application of the transfer matrix approach to direct lightning studies of overhead power lines with underbuilt shield wires. Part I: Theory

This work is devoted to the analysis of voltages produced on overhead distribution lines hit by direct lightning. We will consider arbitrary terminations at both line ends and, also, arbitrary positioning of the pole being struck. We will deal with lines protected by shield wires, placed either above or below the phase conductors. The analytical tools chosen to deal with such complex system are the transfer matrix method and the theory of multiconductor transmission lines with periodic grounding. The innovation of an artificial symmetrical unit cell has been introduced to eliminate the need of two characteristic wave impedance matrices and to ease computation flow.