An optimal coordinated operation model of comprehensive energy storage and conversion devices was built by considering interdependency in a multi-vector energy community, to achieve an overall optimum. The model determined the storage size, the operation strategies of energy storage and conversion devices and scenario analysis was further conducted. The proposed sequential method solved the complex mixed-integer nonlinear programming (MINLP) problem by decomposing the multi-energy system into a subsystem of conversion devices and a PV-battery subsystem, which reduced the computation complexity. Firstly, electricity, heat and gas networks were modelled in an integrated manner and with a suitable level of detail for operational purposes. The integrated electrical-hydraulic-thermal-gas flow equations imposed by multi-energy networks were formulated as equality constraints in the optimization. The optimal operation of conversion technologies with increasing net-load variability on the consumer load profiles was determined. Secondly, the design and operation of PV-battery systems was investigated to provide economic incentives for storage owners. The total costs, the self-consumption ratio (SCR), the internal return rate (IRR) of PV-battery systems were calculated. In scenario analysis, interactions between multi-energy network operation limits as well as the impact of energy conversion devices on PV-battery systems were demonstrated. It showed that the option of Combined Heat and Power (CHP) was advantageous without considering PV-battery systems using 2016 financial data. However, considering the profit of PV-battery systems and the declining grid electricity carbon intensity, the option of heat pumps was advantageous and may be a favorable option in the long term.