## 1 Introduction
However, current storage costs and electricity market policies do not provide sufficient incentives for deploying a demand-side energy storage [20]. Incentive mechanisms for user-side energy storage are thus indispensable. [PERSON] et al. [23] evaluated two financial incentive mechanisms to promote energy storage investment. These mechanisms involved providing tax credits based on the installed storage capacity or the amount of energy delivered from the storage. [PERSON] et al. [24] investigated the impact of fiscal incentives, specifically production tax credits and investment tax credits, on investment behavior in the energy storage sector. [PERSON] et al. [25] proposed a multi-level incentive electricity prices mechanism for demand response and energy storage systems to address the operational risks of the virtual power plant participating in the short-term electricity market. [PERSON] et al. [26] designed an incentive mechanism for agents strategically investing in solar and battery storage systems to provide incentives to each user involved in the energy-sharing scheme. However, most existing research has studied incentive mechanisms from an energy or power perspective. Few studies have proposed incentives directly from the perspective of carbon. Therefore, in the context of the decarbonization of energy systems, designing energy storage incentive mechanisms from a carbon perspective is in line with the development trend and has important research significance. Due to the demand-side energy storage capacity planning, it is necessary to clarify the demand-side carbon emission responsibility. [PERSON] et al. [27] pioneered the carbon emission flow (CEF) theory, which established a strong theoretical basis for designing demand-side energy storage incentive mechanisms from a carbon perspective. [PERSON] et al. [28] proposed an improved CEF theory considering line power losses. The CEF theory can well track the flow of virtual carbon emission in the power system and thus gained popular applications. [PERSON] et al. [29], [PERSON] et al. [30],[PERSON] et al. [31], and [PERSON] et al. [32] applied CEF theory to the research problem of planning and operation of power or multi-energy coupled systems. Therefore, based on the CEF theory, it is feasible to construct an incentive mechanism for energy storage planning that considers demand-side carbon emission responsibility. In short, international scholars have made important contributions to demand-side energy storage planning and incentive mechanisms. Still, the design of demand-side energy storage incentive mechanisms from a carbon perspective has not been sufficiently studied. To fill the research gap, this article has conducted some studies with the following main contributions. 1. Based on the CEF theory, a dynamic carbon incentive mechanism (DCIM) for demand-side energy storage is proposed. The proposed DCIM can effectively guide the demand-side energy storage carbon-oriented configuration and operation based on dynamic carbon intensities and prices. 2. A hierarchical two-stage robust planning model for demand-side energy storage integrating the proposed DCIM is developed in this paper. The first level is obtaining the bus caron intensities through the economic dispatch and CEF model. The second level is a two-stage robust energy storage planning model considering the uncertainties of wind turbine output and power demand. 3. Based on the nested column and constraint generation (N-C&CG) algorithm, the model is transformed into a mixed integer linear programming (MILP) problem, and a commercial optimization solver is invoked to solve it. The validity and advantages of the proposed model are then illustrated by numerical analysis of cases.