M, The Power Definition in Geometric Algebra that Unveils the Shortcomings of the Nonsinusoidal Apparent Power S

The circuit analysis approach based on geometric algebra and M , the power definition based on the geometric product between the voltage and the current multivectors, are used here to demonstrate the shortcomings of the traditional definition of the non-sinusoidal apparent power S . The shortcomings of S are illustrated in three ways. Firstly, by showing an example of how the norm of M contains S . Secondly, through six experiments that involve compliance with: Kirchhoff’s circuit laws, Tellegen’s theorem, the principle of conservation of energy, the equivalency of two terminal networks and the concept of reactive power compensation. Lastly, by showing how the use of S leads the current’s physical component power theory astray. The experiments show contradictions between the aforementioned circuit theory fundamentals and the results attained with S but a compelling harmony with the results attained with M . The evidence reveals two unprecedented discoveries: (1) that mathematical models aimed at explaining energy flow in non-sinusoidal circuits shouldn’t be based on the decomposition of S —as traditionally done— and, (2) the inappropriateness of extrapolating definitions from sinusoidal conditions to non-sinusoidal settings.