This paper analyzes instantaneous power compensation theory through comparing p-q theory and cross-vector theory which were proposed by Akagi and Nabae respectively in three-phase four-wire systems. The two compensation theories are identical when there is no zero-sequence voltage component in three-phase three-wire systems, However, when the zero-sequence voltage and/or current components exist in three-phase four-wire systems, the two compensation theories we different in definition on instantaneous real power and instantaneous imaginary power. Based on the analysis, this paper presents instantaneous power compensation method that can eliminate neutral current completely without using energy storage element when the zero-sequence current and voltage components exist in three-phase four-wire systems.