An optimal structural design model of residential cogeneration systems with a battery is developed using an MILP (mixed-integer linear programming) approach. A battery is introduced as a device candidate to increase operational flexibility of cogeneration units without electric power export. In this model, the selection from device candidates and multi-period operation of selected devices, in which various operational restrictions are considered, are simultaneously optimized so as to minimize annual primary energy consumption. For a battery, not only charging and discharging losses and an upper limit of charging and discharging electric power but also charging-discharging status and electric power consumption in a built-in bidirectional inverter are uniquely incorporated into the model. In addition, the solution method for this MILP problem is improved using a simple decomposition approach. The developed model is then applied to the structural design of a residential cogeneration system with a battery for simulated energy demands in Japan. The results reveal the effectiveness of the simple decomposition approach and the increase in the energy-saving effect of the residential cogeneration system by the introduction of the battery, as a consequence of the increase in the electric capacity factor of the cogeneration unit by the charge of surplus electric power. Moreover, it is shown that this increase strongly depends on the battery performances. (C) 2015 Elsevier Ltd. All rights reserved.