Vector space decomposition of reactive power for periodic nonsinusoidal signals

A vector space is used to represent periodic voltage and current signals in a single port electrical network. This representation is convenient for expressing time average power quantities, such as average power, apparent power, and certain definitions of reactive power. The vector representation for reactive power provides insight into the difficulty of finding a consistent definition for a scalar measure of reactive power when harmonics are present. Instead, a reactive power vector is defined and shown to obey conservation according to Tellegen's theorem. Projections of the reactive power vector are shown to obey conservation and can be used as signed, scalar measures of reactive power.