The Battery Swapping Station (BSS) is emerging as a viable means for fast energy refill of Electric Vehicles (EVs), in addition to many potential benefits in providing energy and ancillary services to the distribution grid. This paper focuses on developing a mathematical model for uncertainty-constrained BSS optimal operation that not only covers the random customer demands of fully charged batteries, but also leverages the available batteries to reduce its operation cost through demand shifting and energy sellback. The battery degradation is further modeled and formulated to ensure a practical solution. Numerical simulations on a test BSS demonstrate the effectiveness of the proposed model and show its viability in achieving the predefined objectives as discussed in this paper. (C) 2019 Elsevier Ltd. All rights reserved.