Introducing hypernion numbers for the analysis of electric networks driven by nonsinusoidal sources

Abstract

The most common method of analysis and design of AC circuit driven by sinusoidal sources, i.e., the symbolic method, is based on using complex numbers. A system of hypercomplex numbers is created for obtaining a new complex number method. This system expands the concept of numbers and gives meanings to equations and transforms with discontinuous functions and makes it possible to describe various non-Euclidean spaces. The proposed method of analyzing linear electric networks with nonsinusoidal voltages and currents enables numerical calculations to be made for complex circuits by using standard software.