Properties of the generalised power theory: universality and partitioning/augmentation properties

The power theory, which can be applied to a power system with transmission/distribution lines with unequal resistances, has useful properties of universality and partitioning/augmentation. Its definitions for apparent power and power factor are consistent from a sinusoidal single-phase system to a non-sinusoidal multi-line system. This study shows that a power system can be partitioned into sub-power systems if some conditions are satisfied and further, it is shown that the sub-power systems can be combined into a large power system. The application area of the concept of apparent power and power factor can be extended with consistency from a single system to a large combined system. The usefulness of the properties in analysing and designing combined power systems is illustrated using examples.