General theory of average power for multi-phase systems with distortion, unbalance and direct current components

An approach to the instantaneous power theory for multi-phase systems with distortion, unbalance and direct current components and in which each wire resistance could take any value was derived in a companion paper through the properties of linear algebra in vector space. Extending the linear algebra that was applicable to instantaneous components only, an approach is developed now that is valid also in the average power domain for any m-wire system with wires of any resistance under conditions of distortion (non-sinusoid), unbalance and dc offset. The approach demonstrates a clear link between instantaneous power and average power in both mathematical derivation and interpretation. The result of the analysis is a calculation method for apparent power and power factor that is quick and simple. The calculation distinguishes compensation that can be provided by energy transfer between phases from the compensation requiring energy storage.

► Extends linear algebra used in the instantaneous domain to the average power domain.
► Shows mathematical consistency between instantaneous and average power.
► Derived components of non-active power have real meanings.
► Simple calculation of compensation with and without energy storage.
► Supports a new definition of apparent power consistent with proposals by others.