LAUSR

This paper proposes a novel method termed HEAP for fast and reliably computing nose points, tracing the entire P-V curve, and assessing static stability limits. HEAP uses an arc-length parametrization and piecewise approximants and enjoys a favorable feature that can pass through the nose without numerical difficulties. Another feature of HEAP is its computational efficiency by enabling the accurate approximation over long intervals because of the large convergence region of HEAP. Existing methods for similar tasks usually suffer from several issues including empirical criteria for detecting noses, small convergence regions of correctors, numerous intermediate points, and large memory consumption. These issues are addressed by HEAP. To check its numerical performance, HEAP is tested on models with up to 70,000 buses, and numerical results substantiate its outstanding features. Depending on intended applications (e.g., only locating the nose or fully tracking the curve), tailored approaches are devised to effectively deriving numerical solutions. In comparison with the continuation-based power flow (CPF) method, HEAP attains speedups of 3x to 300x and notably achieves speedups of at least 19x for all large cases with 10,000 or more buses. While the CPF fails in several large cases, however, all of which are successfully solved by HEAP.