This study introduces a novel method for optimising the size and control strategy of grid-connected, utility-scale photovoltaic (PV) systems with battery storage aimed at energy arbitrage and frequency containment reserve (FCR) services. By applying genetic algorithms (GA), the optimal configurations of PV generators, inverters/chargers, and batteries are determined, focusing on maximising the net present value (NPV). Both DC- and AC-coupled systems are explored. The performance of each configuration is simulated over a 25-year lifespan, considering varying pricing, solar resources, battery ageing, and PV degradation. Constraints include investment costs, capacity factors, and land use. A case study conducted in Wiesenthal, Germany, is followed by sensitivity analyses, revealing that a 75% reduction in battery costs is needed to make AC-coupled PV-plus-battery systems as profitable as PV-only systems. Further analysis shows that changes in electricity and FCR pricing, as well as limits on FCR charging, can significantly impact NPV. The study confirms that integrating arbitrage and FCR services can optimize system profitability.