Instantaneous Power Theory Revisited with Classical Mechanics

The paper revisits the concepts of instantaneous active and reactive powers and provides a novel definition for basic circuit elements based on quantities utilized in classical mechanics, such as absolute and relative velocity, momentum density, angular momentum and apparent forces. The discussion leverages from recent publications by the authors that interpret the voltage and current as velocities in generalized Lagrangian coordinates. The main result of the paper is a general and compact expression for the instantaneous active and reactive power of inductances, capacitances and resistances as a multivector proportional to the generalized kinetic energy and the geometric frequency multivector. Several numerical examples considering stationary and transient sinusoidal and non-sinusoidal conditions are discussed in the case study.