Many residential houses combine residential fuel cell (FC) systems with photovoltaic (PV) systems. Under Japan's Feed-in Tariff Program, utilities must purchase electricity generated by PV systems at high prices. As a result, most generated power is sold, not used in homes, and FC system output follows demand. The currently high purchase price of generated electricity is not likely to continue indefinitely, however. This paper proposes a new method for determining the optimal FC system output that minimizes primary energy consumption. We verify the effectiveness of the proposed method in comparison with primary energy consumption using conventional methods.