Optimal battery sizes for plug-in-hybrid electric vehicles

Plug-in-hybrid electric vehicles (PHEV) have recently been introduced into markets world-wide. They offer large shares of cheap electric driving without big expensive batteries. However, the question which battery size is cost optimal for a certain driver of group of drivers with their specific driving profiles is difficult to answer in general. Here, we derive explicit formulae for the optimal battery size for any driving profile and parameters such as fuel and battery costs by analytically minimizing the total cost of ownership for the driver(s). Our results are applied to realistic individual driving profiles as well as the distribution of German driving profiles (from a large-scale survey) and are also found to be in good agreement with numerical optimization of the same driving profiles. With the right-sized batteries, PHEVs can capture market share more easily. The present results can be directly applied to find the optimal PHEV battery size for any other country's population or group of drivers.