The rapid advancement of battery technology has drawn attention to the effective dispatch of distributed battery storage systems. Batteries offer significant benefits in flexible energy supply and grid support, but maximising their cost-effectiveness remains a challenge. A key issue is balancing conflicts between intentional network services, such as energy arbitrage to reduce the overall electricity costs, and unintentional services, like fault-induced unintentional islanding. This paper presents a novel dispatch methodology that addresses these conflicts by considering both energy arbitrage and unintentional islanding services. First, demand profiles are clustered to reduce uncertainty, and uncertainty sets for photovoltaic (PV) generation and demand are derived. The dispatch strategy is originally formulated as a robust optimal power flow problem, accounting for both economic benefits and risks from unresponsive islanding requests, alongside energy loss reduction to prevent a battery-induced artificial peak. Last, this paper updates the objective function for adapting possible long-run competition changes. The IEEE 33-bus system is utilised to validate the methodology. Case studies show that, by considering the reserve for possible islanding requests, a battery with limited capacity will start to discharge after a demand drop from the peak, leading to the profit dropping from USD 185/day (without reserving capacity) to USD 21/day. It also finds that low-resolution dynamic pricing would be more appropriate for accommodating battery systems. This finding offers valuable guidance for pricing strategies.