propose a two-stage robust model for joint transmission and energy storage expansion planning in wind-farm-integrated power systems [19]; a polyhedral uncertainty set encapsulates all the possible values of wind power and demand. Nonetheless, it is generally acknowledged that the performance of stochastic optimization depends on the size of samples; limited data will injure the exactness of empirical distribution, while incorporating too many scenarios may toughen the solution, especially when the stage-independence in a multi-period problem is considered via the scenario tree [20]. Furthermore, the application of robust optimization is limited by its conservativeness, because the worst case will hardly happen [21]. Therefore, distributionally robust optimization is developed [22], which assumes that the probability distribution of uncertainty varies within an ambiguity set that is a close neighborhood of the empirical distribution. In this regard, this method compromises the conservativeness of stochastic programming and robust optimization. In the area of power systems, distributionally robust optimization has been used in co-optimization of energy and reserve dispatch [23], energy hub planning [24] and operation [25], and hydro-thermal-wind economic dispatch [26]. Furthermore, the existing literature related to storage rarely characterizes the impact of storage capacities on specific indices, such as operational economy, system flexibility, system security margin, renewable energy utilization, and so on. Here, we expect to derive the explicit relation between renewable energy curtailment and the power/energy capacities of ESUs, which will be useful in practical applications. To this end, we used multi-parametric programming, which is a systematic theory and technique that subdivides the parameter set into characteristic regions where the optimal values are given as explicit functions of the parameters [27]; hence, if we treat the power and energy capacities as parameters, such functions provide the decision-maker with insightful information about the impact of ESU on renewable energy curtailment. Multi-parametric programming has been used in some related works. In Reference [28], the impact of ESU on the operational economy of distribution network is discussed; similarly, Reference [29] focuses on the economic influence of ESU in energy hub; however, the complementarity constraints on the charging and discharging behaviors of ESUs are not imposed by binary variables in these two papers, which is not applicable in this paper, as illustrated in Section 2.3. The evaluation model in Reference [30] follows the scheme of robust optimization. This paper combines the distributionally robust optimization and multi-parametric programming, and proposes a distributionally robust multi-parametric mixed-integer linear program (DR-mp-MILP) to assess the impact of energy storages on renewable energy curtailment under distributional uncertainty. The DR-mp-MILP has a max-min form and is reformed as a canonical mp-MILP by duality theory; the results from the IEEE nine-bus system tests validate the effectiveness and performance of our proposed method, and provide insightful suggestions on storage sizing. The rest of this paper is organized as follows: In Section 2, the fundamental models of the power system are first introduced, followed by an illustrative example about the necessity to use binary variables to avoid simultaneous charging and discharging. In Section 3, the multi-parametric formulations are proposed. Section 4 presents the solution to mp-MILP, and Section 5 shows the results of case studies. Discussions are given in Section 6.