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 L_{2} and l_{2}
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 Tellegenâ€™s theorem with the Least effort problem and a novel
application is presented.