Extension of the CPC power theory to four-wire power systems with non-sinusoidal and unbalanced voltages

A modification of the CPC power theory to four-wire power systems with non-sinusoidal and unbalanced voltage supply is presented. The reasons behind the introduced modification are thoroughly explained by referring to Buchholz's apparent power definition. By applying Cauchy-Schwarz-Bunyakovsky inequality it is proved that the differences between the corresponding power quantities given by the original and proposed CPC definitions depend on the presence of voltage unbalance. In the case of load compensation to unity power factor the presented theory gives the smallest possible line losses for the same active power transferred to the load. In order to determine where the proposed definition stands among other power definitions, quantitative differences between the corresponding power quantities for the cases of different harmonic and unbalance levels in power system voltages are investigated by means of numerous computer simulations. This analysis includes also the definitions given by the IEEE and DIN standards, and Conservative Power Theory. Finally, the proposed CPC theory is extended for the cases when the supplying line has neutral conductor which resistance differs from the resistance of phase conductors.