Correct answer: A — describe the rotor dynamics of synchronous machine
Power imbalance and rotor motion
A synchronous machine stores kinetic energy in its rotating mass. At steady operation, mechanical input and electrical output are balanced after losses are accounted for. A disturbance changes this balance, causing the rotor to accelerate or decelerate relative to the synchronously rotating reference.
For the classical model with damping neglected and powers expressed per unit on a consistent machine base, the swing equation is:
(2H/ωs) d²δ/dt² = Pm − Pe
H is the inertia constant in seconds, ωs is synchronous electrical angular speed, δ is rotor electrical angle relative to the synchronous reference, and Pm − Pe is accelerating power. Positive accelerating power speeds up the rotor; negative accelerating power slows it down.
Connection to stability
In a simple generator–infinite-bus model, electrical output takes the form Pe = Pmax sin δ. Substitution makes the swing equation a nonlinear second-order differential equation. Solving it shows how rotor angle changes after a disturbance and whether the machine remains in synchronism.
A linear equation can be obtained for small deviations around an operating point, but that is an approximation. The general equation describes rotor dynamics and is central to transient-stability analysis.
