Formulations for the apparent and unbalanced power vectors in three-phase sinusoidal systems

Buchholz's apparent power and its derived unbalanced power, determined from the quadratic difference between the apparent power and the positive-sequence apparent power, are formulated in this paper in vector notation for three-phase sinusoidal systems. The proposed unbalanced power vector holds three components that measure the imbalance effects caused by the active and reactive currents, and the voltage imbalance effects, respectively. The total apparent and unbalanced powers of several subsystems (sources or loads) can be respectively obtained as the norm of the vector sums of their apparent and unbalanced power vectors, according to these new formulations. The correctness of the apparent and unbalanced power vector formulations are verified in a three-phase sinusoidal installation formed by two linear loads supplied from a 400 kVA delta/wye distribution transformer, as an application example.