  The aim of this work is to present major upgrades to existing power theories
based on geometric algebra for single-phase circuits in the frequency domain.
It also embodies an interesting new approach with respect to traditionally
accepted power theories, revisiting power concepts in both sinusoidal and
non-sinusoidal systems with linear and nonlinear loads for a proper
identification of its components to achieve passive compensation of true
non-active current. Moreover, it outlines traditional power theories based on
the apparent power $S$ and confirms that these should definitively be
reconsidered. It is evidenced that traditional proposals based on the concepts
of Budeanu, Fryze and others fail to identify the interactions between voltage
and current harmonics. Based on the initial work of Castro-N\'u\~nez and
others, new aspects not previously included are detailed, modified and
reformulated. As a result, it is now possible to analyze non sinusoidal
electrical circuits, establishing power balances that comply with the principle
of energy conservation, and achieving optimal compensation scenarios with both
passive and active elements in linear and non-linear loads.
