{'fraction_non_alphanumeric': 0.01881467544684854, 'fraction_numerical': 0.0037629350893697085, 'mean_word_length': 5.52760736196319, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Augmented system for detecting the steady‐state voltage stability margin

This work provides an augmented system (AS), constructed based on a modified tangent vector Index, i.e. the full derivative of the uncontrollable parameter with respect to the voltage magnitude of critical bus of the system, to directly detect steady-state voltage stability margin (SSVSM). The Newton iteration produced by the AS is illustrated to be able to approach the equilibrium manifold until converging to the saddle node bifurcation, given that the initial point is approaching to the corresponding branch. With the special searching direction, limit induced dynamic bifurcations or limit induced static bifurcation that appear along the equilibrium manifold are able to be located with expected precision by the proposed corrections. Several cases in a 2000-bus synthetic grid exemplify the effectiveness and high efficiency of the algorithm, compared with standard continuation power flow and the predicter-corrector primal dual interior point algorithm for detecting the SSVSM.