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• A novel concept of mobile energy storage is proposed in this paper. • A detailed modeling of mobile compressed air energy storage with higher dispatchability and storage capacity is presented. • In concern to routing challenges, Google map's Application Programming Interface is used to find the target location. • A new heuristic-based technique that overcomes deficiencies of traditional constraint handling methods is proposed. • The proposed framework is tested through the IEEE 33-bus and 136-bus networks with different scenarios. • Various reliability indices and operating profits are measured to demonstrate the applicability of the proposed technology. Efficient energy storage technology is one of the key elements to enhance the flexibility, economy, and security of the power system. With the continuous development of energy storage technology, containerized mobile energy storage is coming into view, which has offered promising opportunities to improve distribution network (DN) performances and grid operating factors against emergencies. This paper proposes the concept of mobile compressed air energy storage (CAES) for an electric DN. The movable air storage tanks with stored energy are transported by trucks and placed at some distribution nodes/buses to improve DN performance. To overcome routing challenges for trucks, the configuration of the grid is mapped on the urban region of the city of Sydney, Australia, using Google map's Application Programming Interface. This approach can accurately model distances between current and targeted locations, unavailability of tanks during traveling, route congestions, and fuel consumptions. A new heuristic mathematical method is proposed in this paper to convert the constraints of the mobile CAES (MCAES) model into feasible search spaces, which significantly improves the convergence quality and speed. Operating results for both stationary and mobile CAESs are presented and compared. The methodology is applied to IEEE 136-bus DN in addition to IEEE 33-bus DN to demonstrate the competence of MCAES for larger-scale grids in optimizing the total operating profit, active power loss, energy not supplied, and voltage stability index of the grid. The crucial application of the proposed model can deal with natural disasters to avoid large-scale power outages and, eventually, mitigate the power system damages. [ABSTRACT FROM AUTHOR]