Independently operated energy storage can exploit arbitrage opportunities available due to inter-temporal variation of electricity prices. Storage can be utilised as a dispatchable or non-dispatchable asset. In this study, a new optimal scheduling algorithm is proposed to enable independently operated, locally controlled storage to accept dispatch instructions issued by independent system operators (ISOs). Storage in this case is referred to as dispatchable storage. In addition, a new index is proposed to measure the storage dispatchability. While the operation of locally controlled storage is optimally scheduled at the owner's end, using the proposed algorithm, storage is fully dispatchable at the ISO's end. Dispatchable storage units have great potential to enhance the flexibility of electric grids and are key elements envisioned to enable smart grid realisation. The proposed algorithm outperforms previous algorithms in which storage is either locally controlled at the owner's end and cannot optimally accept ISO's instructions; or storage is centrally controlled by the grid operator to achieve some technical objectives. The efficacy and feasibility of the proposed algorithm are validated using real-world data. It is demonstrated that the proposed algorithm can enable the storage to accept all ISO's instructions. Revenue values of dispatchable and non-dispatchable storage are computed and compared.