Battery energy storage systems （BESS）with bidirectional fast response capabilities can provide dynamic frequency responses to electricity grids

alleviating imbalances caused by fluctuating renewable power outputs.In order to ensure the economic effectiveness of BESS participating in frequency response services

it is necessary to reasonably optimise BESS capacity configurations together with operating strategies.From the perspective of the UK's Dynamic Moderation frequency response service market

this paper develops a closer-to-real-time energy management for BESS through dynamic adjustment of operational baselines so as to ensure that BESS comply with the market's State of Energy Management Rules （SoEMRs）and have sufficient energy footroom and headroom to completely cope with low-and high-frequency events.Furthermore

the techno-economic operation of BESS throughout its service life is simulated and translated into an equivalent annual annuity which is maximised to determine the best BESS capacities and operating strategy variables.Simulation results show that the optimised BESS can fully respond to all the frequency events and follow the SoEMRs for the majority of the time.The paper provides deep insights into the energy storage-friendly frequency response service markets in the UK that protects the benefits of energy-limited participants

which have reference significance and practical values for the development of ancillary service markets and the operation of BESS in China.