Chapter 9

Extension of d–q Theory to Unbalanced Operation

9.1    Introduction

Balanced three-phase sinusoidal steady-state, studied in Chapter 4 is only an ideal, rarely achieved condition for either a motor or a generator. For example, in a power system, phase balance depends upon precise loading of distribution networks feeding various parts of a load network. The presence of non-linear loads such as rectifiers, computer power supplies, and the like also contribute harmonics which, while they may be filtered, continue to flow in small percentages in the phases of a large generator. Motors are generally tied to a distribution system which also has single phase loads, thereby producing unbalanced voltages across the lines of the motor. Harmonics ...

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