Fully EVs (electric vehicles) and PHEVs (plug-in hybrid electric vehicles) have attracted much attention in recent years. Towards an increasing share of EVs, their economic feasibility and impact on the electricity distribution have been studied in detail. However, little has been achieved in investigating the impact on the electricity generation systems. This paper presents a MILP (mixed-integer linear programming) unit commitment model with focus on the effect of EVs on the generation side. The most important advantage of the proposed method is the ability to solve systems with a very large number of EVs. The algorithm is demonstrated on a benchmark system, which has been widely used in the literature and has been used here for all scenarios. It is demonstrated that optimized charging (centrally controlled) is cheaper and allows for higher EV penetration, compared to random charging. Simulations were also run for two scenarios based on the advancement in the charging infrastructure: (1) perfect infrastructure, with opportunity for charging everywhere and (2) moderate infrastructure, where charging is possible only at the owners' homes. In both cases the generation cost increases by 1% for every 10% of additional EV penetration, the modest infrastructure case being slightly more expensive.