  Traditional power theories and one of their most important concepts
--apparent power-- are still a source of debate and, as shown in the
literature, they present several flaws that misinterpret the power-transfer
phenomena under distorted grid conditions. In recent years, advanced
mathematical tools such as geometric algebra (GA) have been applied to address
these issues. However, the application of GA to electrical circuits requires
more consensus, improvements and refinement. In this paper, power theories
based on GA are revisited. Several drawbacks and inconsistencies of previous
works are identified and modifications to the so-called geometric algebra power
theory (GAPoT) are presented. This theory takes into account power components
generated by cross-products between current and voltage harmonics in the
frequency domain. Compared to other theories based on GA, it is compatible with
the traditional definition of apparent power calculated as the product of RMS
voltage and current. Also, mathematical developments are done in a
multi-dimensional Euclidean space where the energy conservation principle is
satisfied. The paper includes a basic example and experimental results in which
measurements from a utility supply are analysed. Finally, suggestions for the
extension to three-phase systems are drawn.
