This paper addresses a central challenge of jointly considering shorter-term (e.g. hourly) and longer-term (e.g. yearly) uncertainties in power system planning with increasing penetration of renewable and storage resources. In conventional planning decision making, shorter-term (e.g., hourly) variations are not explicitly accounted for. However, given the deepening penetration of variable resources, it is becoming imperative to consider such shorter-term variation in the longer-term planning exercise. By leveraging the abundant amount of operational observation data, we propose a scenario-based robust planning framework that provides rigorous guarantees on the future operation risk of planning decisions considering a broad range of operational conditions, such as renewable generation fluctuations and load variations. By connecting two-stage robust optimization with the scenario approach theory, we show that with a carefully chosen number of scenarios, the operational risk level of the robust solution can be adaptive to the risk preference set by planners. The theoretical guarantees hold true for any distributions, and the proposed approach is scalable towards real-world power grids. Furthermore, the column-and-constraint generation algorithm is used to solve the two-stage robust planning problem and tighten theoretical guarantees. We substantiate this framework through a planning problem of energy storage in a power grid with deep renewable penetration. Case studies are performed on large-scale test systems (modified IEEE 118-bus system) to illustrate the theoretical bounds as well as the scalability of the proposed algorithm.