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This paper proposes a novel power compensation algorithm in three-phase four-wire systems by using p-q-r theory. The p-q-r theory is compared with two previous instantaneous power theories, p-q theory and cross vector theory. The p-q-r theory provides two-degrees of freedom to control the system currents by only compensating the instantaneous imaginary power without using any energy storage element. The definition of powers maintains power conservation, and agrees well with the general understanding of power. Simulation results show the superiority of p-q-r theory both in definition and compensation.