Rosehart, William D.Cañizares, Claudio A.2025-07-162025-07-161999-02-010142-0615https://doi.org/10.1016/S0142-0615(98)00037-4https://hdl.handle.net/10012/21999The final publication is available at Elsevier via https://doi.org/10.1016/S0142-0615(98)00037-4. © 1999. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper presents the bifurcation analysis of a detailed power system model composed of an aggregated induction motor and impedance load supplied by an under-load tap-changer transformer and an equivalent generator and transmission system. Different modeling levels with their respective differential-algebraic equations are studied, to determine the minimum dynamic model of the system that captures the most relevant features needed for bifurcation studies of power systems. An aggregated model of a realistic load is used to illustrate the ideas presented throughout the paper.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Saddle-node and Hopf bifurcationssystem modelingvoltage collapseArticle10.1016/s0142-0615(98)00037-4