In recent years, there has been rapid advancement in new energy technologies aimed at mitigating greenhouse gas emissions stemming from fossil fuels. Nonetheless, uncertainties persist in both the power output of new energy sources and load. To effectively harness the economic and operational potential of an Integrated Energy System (IES), this paper introduces an enhanced uncertainty set. This set incorporates N-1 contingency considerations and the nuances of source–load distribution. This framework is applied to a robust optimization model for an Electric Vehicle Integrated Energy System (EV-IES), which includes Electric Vehicle Battery Swapping Station (EVBSS). Firstly, this paper establishes an IES model of the EVBSS, and then proceeds to classifies and schedules the large-scale battery groups within these stations. Secondly, this paper proposes an enhanced uncertainty set to account for the operational status of multiple units in the system. It also considers the output characteristics of both new energy sources and loads. Additionally, it takes into consideration the N-1 contingency state and multi-interval distribution characteristics. Subsequently, a multi-time-scale optimal scheduling model is established with the objective of minimizing the total cost of the IES. The day-ahead robust optimization fully considers the multivariate uncertainty of the IES. The solution employs the Nested Column and Constraint Generation (C&CG) algorithm, based on the distribution characteristics of multiple discrete variables in the model. The intraday optimal scheduling reallocates the power of each unit based on the robust optimization results from the day-ahead scheduling. Finally, the simulation results demonstrate that the proposed method effectively reduces the conservatism of the uncertainty set, ensuring economic and stable operation of the EV-IES while meeting the demands of electric vehicle users.