The geometric algebra as a power theory analysis tool

In this paper, a multivectorial decomposition of power equation in single-phase circuits for periodic n-sinusoidal /linear and nonlinear conditions is presented. It is based on a frequency-domain Clifford vector space approach. By using a new generalized complex geometric algebra (GCGA), we define the voltage and current complex-vector and apparent power multivector concepts. First, the apparent power multivector is defined as geometric product of vector-phasors (complex-vectors). This new expression result in a novel representation and generalization of the apparent power similar to complex-power in single-frequency sinusoidal conditions. Second, in order to obtain a multivectorial representation of any proposed power equation, the current vector-phasor is decomposed into orthogonal components. The power multivector concept, consisting of complex-scalar and complex-bivector parts with magnitude, direction and sense, obeys the apparent power conservation law and it handles different practical electric problems where direction and sense are necessary. The results of numerical examples are presented to illustrate the proposed approach to power theory analysis.