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This lecture covers the transient stability of power systems, focusing on the ability of synchronous machines to maintain synchronism after severe disturbances. Topics include voltage stability, power flow calculations, and the resolution of differential-algebraic equations. The instructor explains the different operating states of a power system, the phenomena of electromechanical oscillations, and the importance of maintaining synchronism. Various methods for analyzing transient stability, such as direct methods and simultaneous approaches, are discussed in detail.