As the penetration rate of renewable energy increases in the electric power system, the issues of renewable power curtailment and system inertia shortage become more severe. Innovative solutions such as Cloud Energy Storage (CES) can be employed to address this challenge. However, the energy storage resources aggregated by the traditional CES business model mainly concentrate on Electrical Energy Storage (EES), which is still limited and expensive. It necessitates the exploration of new approaches to enhance the flexibility and cost-effectiveness of energy storage utilization, in which using District Heating System (DHS) as an equivalent energy storage resource of the power system is an effective method. Therefore, this paper proposes an optimal planning strategy of energy storage system under the CES model considering inertia support and electricity-heat coordination. Firstly, the system components and business model of the CES are described, and the framework of energy storage planning problem from the perspective of CES operator is formulated. Then the evaluation methods of energy storage utilization demand from CES users are proposed, including the evaluation of the renewable power curtailment, system minimum inertia requirement, and the equivalent energy storage ability of DHS. Based on this evaluation results, a bi-layer optimal energy storage planning model for the CES operator is established, where the upper-layer model determines the installed capacity of lithium (Li-ion) battery station and the lower-layer model determines the optimal schedules of the CES system. The numerical tests based on the operation profile of a typical city in China are carried out to demonstrate the effectiveness of the proposed method. The simulation result shows that the annual profit of the CES system can be improved by 15.26% after installing the energy storage system whose capacity is determined by the proposed method.