ABSTRACT
This chapter first explores the result of applying the operator, 'a', to a phasor-quantity. Second, it expresses each of the operators such as 'j-operator', '120º-operator', and 'a-operator', in polar, and rectangular, form. Third, the chapter provides solution to three-phase problems for both balanced and unbalanced loads. Next, it also provides solution to unbalanced load, three-wire load, and star-connected load through Millman's Theorem. The 'a-operator' or '120º-operator', makes solving three-phase unbalanced-load problems easier than by constructing and analysing three-phase phasor diagrams. An unbalanced load is one in which the phase currents are different in both magnitude and phase angle. Even though the load is unbalanced, it emphasises that the supply voltages are symmetrical because they are determined by the supply system and not by the load. This means that, although the phase and line currents may vary, the line and phase voltages are always symmetrical. The exception to this general rule regarding symmetrical voltages is the three-wire and star-connected loads.
