A Novel FFHE-Inspired Method for Large Power System Static Stability Computation

Abstract

This article proposes a novel method termed HEAP for fast and reliably computing nose points, tracing the entire PV curve, and assessing static stability limits. Here, the prefix “HE” in HEAP refers to (fast and flexible) <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</u> olomorphic <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</u> mbedding, and “AP” is short for <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</u> rc-length <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</u> arametrization. This novel method uses an arc-length parametrization and piecewise approximants that enable it to have the favorable feature of Continuation Power Flow that can pass through the nose point without numerical difficulties. Another outstanding feature of the proposed method HEAP is its computational efficiency by enabling the accurate approximation over a long interval of the parameter (i.e., a large step size). This is because of the large convergence region of HEAP. The existing methods for similar tasks usually suffer from several issues such as empirical criteria for detecting nose points, small convergence regions of correctors, numerous intermediate points, and large memory space consumption. These issues are well addressed by HEAP. To examine its numerical performance, HEAP is tested on various power system models with as many as 70,000 buses, and numerical results substantiate the outstanding features of HEAP. Depending on intended applications (e.g., only locating the nose point or fully tracking the curve), two tailored approaches are devised to effectively derive numerical solutions. In comparison with the continuation-based power flow method, HEAP attains speedups of 3x to 300x and notably attains speedups of at least 19x for all large test cases with 10,000 or more buses. The continuation-based power flow method fails in several large test cases, however, all of which are successfully solved by HEAP. After enforcing the generator reactive power limit, HEAP also produces the same accurate results as the continuation-based power flow method.