The swing equation describes the electromechanical dynamics of a synchronous machine's rotor as a second-order differential equation relating rotor angular acceleration to the imbalance between mechanical input torque/power and electrical output torque/power, expressed in terms of the machine's inertia constant and a damping coefficient proportional to the rotor's slip from synchronous speed. This principle underlies the single-machine-infinite-bus model used in power system transient stability analysis, in which a synchronous generator connected through an external reactance to a very large system (approximated as an ideal, invariant voltage source) exchanges power with that bus as a function of the sine of the power (torque) angle between internal and bus voltages. The theory extends to reducing multi-machine systems to equivalent single-machine models via inertia-constant conversion to a common system base and aggregation of coherent (co-swinging) machines.
The swing equation describes the electromechanical dynamics of a synchronous machine's rotor as a second-order differential equation relating rotor angular acceleration to the imbalance between mecha…