The growing market share of electric vehicles embodies the remarkable progress of transportation electrification. Battery swapping station serves as a critical infrastructure for efficient electric vehicles refueling. To coordinate the scheduling of a battery swapping station and a microgrid managed by non-cooperative entities, we develop two shadow price-based coordination methods, namely peer-to-peer method and leader-follower method. The context is of great importance for mitigating potential barriers of integration of battery swapping stations and microgrids. The peer-to-peer method only requires the exchange of individual shadow price and power trading requests between two entities. This mechanism is the first-of-its-kind solution that allows for co-ordination between two systems without releasing proprietary information. An iterative heuristic algorithm is developed to obtain outcomes of the co-ordination mechanism. For the leader-follower method, microgrid entity gets access to proprietary information of battery swapping station that is managed by an independent entity. A bi-level optimization model is developed to model the gameplay between two non-corporative entities, which is solved by a modified nested column-and-constraint generation algorithm. For both methods, we use an AC optimal power flow model to optimize operation of microgrid while battery swapping station operation is determined by a mixed-integer linear programming model. This work is also the first-of-its-kind study that incorporates AC power flow equations into relevant research. We demonstrate the effectiveness of both methods using an integrated system comprising a standard IEEE 33-bus system and a battery swapping station serving multiple private electric sedans or public electric buses. Nearly 10% of total operational cost saving can be attained if the proposed methods are applied for coordinating two systems, compared to implementing a baseline method.