•Price arbitrage operation of distributed battery storage is examined.•Local energy system and national power system interactions are considered.•Reformulated bilevel optimisation as a single level mixed integer linear problem.•Comparison of centralised and bilevel optimisations of distributed battery storage.•Influence of retail contracts on value of distributed battery storage investigated. Battery storage provides flexibility to the power system and supports the increased integration of renewable energy sources. Distributed battery storage systems that are behind the meter are operated by their local owners, whose objectives may not align with those of the national power system. This paper presents a Bilevel optimisation approach to investigate the exchange of electricity between distributed battery storage and the national power system. The independent operating objectives of the battery storage systems are explicitly considered to assess their impact on the operation of the national power system. A comparison with a Centralised optimisation approach, that assumes a single objective function for the whole system, shows that the Bilevel optimisation approach captures the independencies of distributed battery storage objectives, while accounting for its interactions with the wider power system. The results show that the Centralised optimisation approach tends to overestimate the value of distributed battery storage for the power system. The results also highlight the influence of the retail contract structure in maximising the value of distributed battery storage for the national power system.