This paper is focused on conditioning the voltage and current waveform quality of a hybrid matrix converter that consists of a conventional nine-switch matrix converter and an auxiliary back-to-back voltage source converter. Upon critical evaluation of the existing methods for shunt and series compensation, the fundamental limitations for achieving superior results have been identified. A new strategy based on power averaging for obtaining the reference compensating current and voltage has been proposed. The effectiveness of the proposed method has been verified by the simulation results for both the shunt and series compensation with concurrent presence of the harmonic components in voltages and currents.