The use of geometric algebra in circuit analysis and its impact on the definition of power

Abstract

Geometric algebras of the Euclidean 2-dimensional and 3-dimensional spaces have been used to analyze electric circuits with linear and harmonic generating loads (HGLs). It is shown in this paper that with both loads, time domain signals may be transformed to the G n domain such that the resulting multivectors permit circuit analysis through rotations and dilation-contractions of the excitation signal. The power equation, in particular, is created by applying the geometric product of the voltage and current multivectors and is suitable for linear and nonlinear loads. This is in contrast to commonly used frequency analysis methods where the reactive power cannot be obtained in correspondence with its definition in the time domain and it fails at providing a unified power equation for linear and HGLs. We interpret the proposed power equation in the frequency and time domains and introduce an analogous quantity to the reactive power Q, the CN-power, for circuits with nonlinear loads. A power factor equation applicable to both loads is also presented. The resulting one-to-one correspondence between the time domain and the G n domain avoids eliminating any component from the power equation in the time domain. Single-phase circuit examples are provided.