Apparent power of three-phase four-wire system in sinusoidal asymmetric mode and energy effectiveness of shunt active filters

This paper shows that the vector of the three-phase current source which maximizes the energy consumption at the given asymmetric sinusoidal voltages and power losses in the four-wire cable must be proportional to the instantaneous phase voltage vector with partial decrease of zero-sequence component in accordance with the parameters of the power cable. As a result, the energy process in the three-phase four-wire power system is completely defined by three-dimensional complex vectors of phase current and voltage symmetrical coordinates with modified values of zero-sequence components. Inner and outer products of these vectors define all components of apparent power, and their real proportionality allows to get a unit power factor under asymmetric sinusoidal mode. These results were applied to compare the energy efficiency of shunt active filters using different control strategies. Also, the Fryze´s decomposition formula for the complex vector of three-phase currents under asymmetrical sinusoidal voltages has been refined.