The UNFCCC has stated that energy policies and measures to address climate change should be cost-effective to ensure global benefits at the lowest possible cost. To mitigate the bulk of carbon emission from the electricity sector, a large market penetration of renewable energy technologies with as low cost as possible is a key research topic. The energy-related R&D policy in Japan aims to achieve a green economy. In our study, based on this context, we demonstrated how to optimize the timing of public R&D investment within the framework of a bottom-up partial equilibrium model. The developed optimization model represents the Japanese electricity sector and minimizes the total system cost subject to an accumulated carbon emission constraint. Our main research focus is the role of R&D activity, especially in the innovation stage of renewable technologies. We employ a two-factor learning curve and quantify the impact of the learning effect on the dynamic diffusion of major renewable technologies. The study shows a dynamic technology transition in the Japanese electricity sector and the optimized R&D investment schedule for each renewable technology. With the first-best energy policy, an R&D budget of more than 2000 million USD would be allocated to PV in 2050, which corresponds to 45% of the energy-related Japanese R&D budget in 2050. Because some have criticized the uncertainty problems with dynamic simulations and learning models, supplemental sensitivity analyses are included.