Both discrete storage model (DSM) and continuous storage model (CSM) have been used in the power system planning literature. In this work, we conduct a sizing-error analysis for the use of CSM in generation expansion planning (GEP), which shows more reasonable storage sizing decisions are offered by the DSM in comparison to the CSM. However, when the DSM is considered in the context of interval optimization, the discrete status variables in mutually exclusive constraints and the strong temporal coupling in state-of-charge (SOC) constraints create significant challenges. To tackle this, a tailored interval optimization approach is proposed to consider both DSM and renewable energy uncertainty in GEP. Our approach is proved to cover all worst cases in a given uncertainty set, meanwhile running in an iteration-free manner. Moreover, to reduce the conservativeness of investment decisions, a bi-interval policy is designed to achieve a better trade-off between investment cost and system security.