The configuration of energy storage is key to maintaining the stability and flexibility of a high proportion of new energy power systems in a strategy of carbon peak and carbon neutrality. A robust model of energy storage considering ladder-type carbon trading and the time-of-use price is developed. The uncertainty effects of the source-load dual side are considered in the model, and the time smoothing constraint and spatial clustering constraint are used to narrow the source-load uncertainty set boundary and reduce the conservativeness of the model. The uncertainty constraint is converted into a deterministic constraint by Lagrangian inference, and the model is analyzed by an improved sparrow algorithm. The examples show that system economy will be significantly improved with the space-time coupling effect, and the decision-maker can balance system economy and robustness by choosing the confidence probability of uncertainty. Different energy storage planning schemes are proposed for different flexibility reformation stages, and it is pointed out that the system starts to have carbon benefits when the proportion of thermal power installed in the region falls below 43%. This work is supported by the National Natural Science Foundation of China (No. 51666017).