The IEEE Standard 1459, the CPC Power Theory, and Geometric Algebra in Circuits With Nonsinusoidal Sources and Linear Loads

An alternative circuit analysis technique and its associated power theory is compared to the IEEE Standard 1459 and the current´s physical components power theory. The comparison shows that elimination of the fundamental reactive power quantity Q₁ as defined by the Standard does not ensure supply current reduction. In contrast elimination of the reactive current as defined by the CPC power theory ensures supply current reduction. However, the balance principle of the reactive power cannot be applied to the CPC power theory as the definition of the reactive power is not a signed quantity. The alternative method which uses geometric algebra instead of complex numbers, multivectors in place of phasors and the Euclidian N-dimensional space instead of the frequency domain succeeds in defining a decomposition that accounts for the total nonactive power, and also satisfies conservation. The alternative circuit analysis technique allows viewing the flow of currents and energy/powers in the circuits under examination. Additionally, the paper provides 4 reasons why the present definition of apparent power defined as the product of the magnitude of current and voltage is unsuitable for nonsinusoidal circuits in the G_N domain.