The penetration of solar photovoltaic (PV) systems in residential areas contributes to the generation and usage of renewable energy. Despite its advantages, the PV system also creates problems caused by the intermittency of renewable energy. As suggested by researchers, such problems deteriorate the applicability of the PV system and have to be resolved by employing a battery energy storage system (BESS). With concern for the high investment cost, the choice of a cost-effective BESS with proper sizing is necessary. To this end, this paper proposes the employment of a vanadium redox flow battery (VRB), which possesses a long cycle life and high energy efficiency, for residential users with PV systems. It further proposes methods of computing the capital and maintenance cost of VRB systems and evaluating battery efficiency based on VRB electrochemical characteristics. Furthermore, by considering the cost and efficiency of VRB, the prevalent time-of-use electricity price, the solar feed-in tariff, the solar power profile and the user load pattern, an optimal sizing algorithm for VRB systems is proposed. Simulation studies are carried out to show the effectiveness of the proposed methods.