Transmission Functions and its application to the analysis of time uncertainties in Protection Engineering

In this paper we explore the concept of transmission Functions and its application to the resolution of the problem posed by the uncertainty in the time to take manual protective actions due for instance to different operator abilities. This time uncertainty is a very special kind of uncertainty with obvious relevance in Protection Engineering problems. Tackling it involves a large amount of simulations of transients associated to sequences of system transitions, resulting from those actions, where the only difference from one simulation to another is the time interval between transitions, the evolution laws being always the same. In order to solve such type of problems, a new formalism is proposed based on the concept of transmission Function. We prove that for a large class of Multiple Input-Multiple Output (MIMO) piecewise linear systems, the output may be obtained as additive contributions of each interval of the sequence, each one characterized via a Transmission Function. We then provide efficient methods to compute Transmission Functions of sequences of canonical Single Input-Single Output (SISO) piecewise systems, and to find the locus of protective action times that lead to damage (damage domain).