Using numerical analysis, stabilization of the cyclic fluctuation (changes of several minutes or less) of PV (photovoltaics) was attempted by introducing governor-free control of a SOFC (solid oxide fuel cell), controlling air flow rate, and using a flywheel inertia system. The energy balance of the system element, mass balance, time lag, etc. were modeled, and the response characteristics of the proposed system were analyzed using MATLAB/Simulink 2013a. Consequently, the range of fluctuation in the electrical frequency within 0.2 Hz was controlled by introducing a flywheel inertia constant of 0.01 s. Interconnection electricity using PV with cyclic fluctuations can be supplied as high-definition electricity. That electricity is controlled using a flywheel and a proportional-integral-differential controller with suitable parameters by adjusting the governor-free control and rate of air flow in the SOFC. The SOFC and an inertia system provide a supply of backup power from renewable energy and serve to promote the increased use of clean energy. (C) 2015 Elsevier Ltd. All rights reserved.