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Classifying Power System Stability and the Synchronous Machine Swing Equation

Power system stability is the study of a synchronous power system's dynamic response to disturbances, defined formally as the ability of a system, given an initial operating equilibrium, to regain a state of operating equilibrium after a disturbance with most system variables bounded. Because the underlying power system is a large, nonlinear, multivariable dynamic system, stability is classified by the physical nature of the instability—rotor angle, voltage, or frequency—driven respectively by real power imbalance between mechanical and electrical torque/power, reactive power imbalance, and imbalance between generation and load, with the rotor angle dynamics formally captured by the synchronous machine swing equation derived from Newton's second law for rotational motion.