The calculation of power flow in power systems with the presence of harmonics has been properly studied in the scientific literature. However, power flow calculation considering interharmonic components is still an open question. Traditional methods based on the IEEE1459 standard have proven to be valid and accurate only for linear and sinusoidal systems, but have been criticized for non-linear and non-sinusoidal systems because they are not able to explain correctly the current and voltage interactions beyond the active power. This paper proposes the use of a novel mathematical framework called geometric algebra (GA) to study the power flow considering the interaction of current and voltage harmonics and interharmonics. The use of GA enables the precise determination of the direction and magnitude of the total and single active power flow for each component, as well as other power elements related to the non-active power due to cross interaction. Moreover, this paper makes a novel contribution to the definition of interharmonics in geometric algebra space that has not been done before. To test the validity of the method, both linear and non-linear circuits are proposed and solved by applying voltages and currents with harmonic and interharmonic components. The results obtained show that power flow can be analyzed under the prism of the principle of energy conservation (PoCoE) in a way that allows a better understanding of the power spectrum due to the interaction of harmonics and interharmonics of voltage and current.

Non-linear loads in circuits cause the appearance of harmonic disturbances both in voltage and current. In order to minimize the effects of these disturbances and, therefore, to control over the flow of electricity between the source and the load, they are often used passive or active filters. Nevertheless, determining the type of filter and the characteristics of their elements is not a trivial task. In fact, the development of algorithms for calculating the parameters of filters is still an open question. This paper analyzes the use of genetic algorithms to maximize the power factor compensation in non-sinusoidal circuits using passive filters, while concepts of geometric algebra theory are used to represent the flow of power in the circuits. According to the results obtained in different case studies, it can be concluded that the genetic algorithm obtain high quality solutions that could be generalized to similar problems of any dimension.