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Tie-line power exchanges among regional power systems facilitate renewableaccommodations. Power exchanges can be calculated via a tie-line securityregion that provides the feasible region of the coupling parameters amongregional power systems. However, a tie-line security region is a high-dimensionpolytope due to multiple time periods and border buses inherently in powersystem operations, leading to the considerable computational burden. A fastcalculation method for tie-line security regions in high dimension is studiedin this paper. The high-dimension polytope across all the time periods isdecomposed as a Cartesian production of lower-dimension polytopes at each timeperiod by leveraging dispatch levels of generations. For each lower-dimensionpolytope, the computational burden brought by multiple border buses isalleviated by aggregating tie-line power. Also, minimum renewable curtailmentsare preserved by incorporating an additional dimension in the tie-line securityregion. For the coupling parameters located within our tie-line securityregion, a feasible decision of the regional power system exists. Finally, thetie-line security region is used to reduce renewable curtailments in aninterconnected power system under a decentralized and non-iterative framework.The performance of the presented methods is corroborated in the IEEE 9-bussystem, a 661-bus utility system and a five-region system.

Tie-line Security Regions in High Dimension for Renewable Accommodations