A Hilbert Space Interpretation of the Power Theory

The definition of the reactive power in nonsinusoidal conditions has been a controversial topic since the experiment published by C. P. Steinmetz in 1892. Where among Electrical Engineers there is no consensus on how to compute the reactive power in non-sinusoidal conditions. Therefore, in this paper it is used the mathematical concept of a Hilbert space, namely the L₂ and l₂ spaces, and the Least effort problem to obtain the definition of the generalized reactive power. Then, the obtained definition of the generalized reactive power is compared against some of the main power theories. Finally, it is used that definition to study the relation between the Tellegen’s theorem with the Least effort problem and a novel application is presented.