This research paper presents a new approach to power definitions in multiphase AC systems in the frequency domain from a purely geometric approach. The theoretical foundation is based on Geometric Algebra (GA) framework, which enables the representation of harmonic voltages and currents as multidimensional vectors in Euclidean space. The use of the geometric product allows to compute the geometric power multivector. The proposed method is a generalization and extension of previous works that have focused on single- phase and balanced three-phase systems. This paper introduces a complete analysis of new power terms in arbitrary multi- phase electrical systems entirely rooted on Geometric Algebra and Symmetrical Components. Several synthetic and real-world examples are presented to illustrate the novelty, effectiveness and accuracy of the proposed approach. The results of this study contribute to the development of a new geometric foundation for the power theory in electrical engineering.