Geometric Algebra: A Powerful Tool for Representing Power Under Nonsinusoidal Conditions

Geometric algebra is used in this paper for a rigorous mathematical treatment of power in single-phase circuits under nonsinusoidal conditions, as complex algebra for sinusoidal conditions. This framework clearly displays the multidimensional nature of power, which is represented by a multivector. The power multivector with its three attributes (magnitude, direction and sense) provides the means to encode all the necessary information in a single entity. This property, in conjunction with the fact that there is a one-to-one correspondence between the terms of this multivector, the instantaneous and the apparent power equation, distinguishes it as a highly efficient mathematical tool. In this way one can successfully describe power phenomena and handle practical problems (e.g., power factor improvement). Two simple examples show some of these features. In short, the power multivector under nonsinusoidal situations can be perceived as the generalization of the complex power under sinusoidal situations