Application of geometric algebra for power factor improvement

Abstract-The main contribution of this paper is to demonstrate how the framework of geometric algebra can be used to systematically design optimal compensators to increase the power factor in circuits that operate under nonsinusoidal conditions and possess significant source impedances. We demonstrate how the mathematical tools of geometric algebra can be used to construct a physically meaningful orthogonal decomposition of apparent power in terms of a power multivector. This power multivector, which in the sinusoidal case is analogues to complex power, provides the means to encode all the necessary information to find an optimal compensator in both the sinusoidal and nonsinusoidal case. Some simple examples are used to illustrate the method.