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Application of a three-phase to single-phase matrix converter for a 1 kW household gas engine cogeneration system is proposed. The matrix converter connects a three-phase permanent magnet synchronous generator of the cogeneration system to single-phase utility. Application of the matrix converter has the following advantages: (a) the generator efficiency will be improved because power factor control of the generator with the matrix converter can reduce reactive current which increases copper losses in the windings and harmonic current which causes harmonic torques of the generator, (b) The converter efficiency will be also improved because the conducting losses of switching devices can be reduced by employing reverse-blocking (RB) devices such as RB-IGBTs. However, since the matrix converter has no energy storage component inside itself, power pulsation due to single-phase power appears directly in the three-phase side. In order to treat this power pulsation, we have proposed a novel method that realizes modulation of the instantaneous three- phase power of the generator synchronized with the single- phase power, and the power pulsation is absorbed with inertia of the rotor of the generator and a gas engine, which is large enough to regard the rotor speed as constant. The proposed method is demonstrated through numerical simulation and primary experiments using a motor/generator set and an IGBT matrix converter.