Complex power in circuits with multiple reactive elements

ABSTRACT This paper provides a detailed discussion of how complex powers combine in circuits with multiple reactive or phase dependent elements. Reactive powers in different circuit elements are additive by simple addition if and only if either the currents or the voltages are in phase or 180° out; this condition is met by multiple elements on a given circuit branch, and by multiple circuit branches between common nodes. The phase condition is not met between individual reactive circuit elements on different circuit branches, therefore reactive power cannot be determined using simple addition; a more complex procedure is necessary. The results are of direct importance for properly determining energy storage between multiple circuit elements within an electrical grid.