Electrical three phase circuit analysis using quaternions

Nowadays, reactive power and power factor in unbalanced circuits and/or with the presence of harmonics are still being investigated by several researchers. In this context, quaternions, whose use has recently been intensified in the electrical engineering field, is presented as an alternative tool to analyze electrical quantities in single and three-phase circuits. However, studies solving three-phase circuits by quaternions are not yet in literature, nor a complete electrical description with this tool. This article, therefore, presents single and balanced three-phase quantities expressed as quaternions. Results of an analysis of a series RLC single and balanced three-phase circuits are presented. It is important to notice that this tool can also be employed to represent three-phase power under unbalanced situations and with the presence of harmonics.