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