arXiv:2610.35815v1 Announce Type: new Abstract: The security region (SR) specifies a joint feasible region in the operational space involving various installations within the power system. It enables dynamic allocation of capacity among these energy units, thereby unlocking additional grid potential for power delivery and mitigating congestion. By constructing a convex hull from a set of vertices to form a polytope, the SR can be effectively represented with an acceptable accuracy loss. However, the SR computation inevitably generates many low-quality vertices, which contribute little to the overall hypervolume and can be discarded. By introducing SR compression, the SR data size can be reduced, which in turn facilitates the memory-efficient computation of SR and time-efficient solution of SR-related optimization problems. Accordingly, this paper proposes a vertex pruning approach that mixes local and backward search policies to achieve effective SR compression. In particular, the backward search strategy allows previously pruned vertices to be recycled when they are re-identified as critical. Subsequently, we incorporate this approach to enhance computational efficiency in the aforementioned applications. Numerical validations are conducted on two realistic medium-voltage Dutch grid cases. The results demonstrate at most 1.65% hypervolume loss with over 96.0\% SR data size reduction after applying the proposed compression approach. Empowered by this compression, the 8-dimensional (8D) SR becomes computationally tractable. Moreover, in relevant grid-aware computation challenges, the solving time can be reduced by at least 52.9% with at most an 1.36% optimality loss. All above validate both the efficacy and values of the proposed SR compression approach.