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More electric aircraft (MEA) architectures have increased in complexity leading to a demand for evaluating the dynamic stability of their advanced electrical power systems (EPS). The system interactions found therein are amplified due to the increasingly integrated subsystems and on-demand power requirements of the EPS. Specifically, dynamic electrical loads with high peak-to-average power ratings as well as regenerative power capabilities have created a major challenge in design, control, and integration of the EPS and its components. Therefore, there exists a need to develop a theoretical framework that is feasible and useful for the specification and analysis of the stability of complex, multi-source, multi-load, reconfigurable EPS applicable to modern architectures. This paper will review linear and nonlinear system stability analysis approaches applicable to a scalable representative EPS architecture with a focus on system stability evaluation during large-displacement events.