Previous Year Question

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:

H is the inertia constant in seconds, ω_s is synchronous electrical angular speed, δ is rotor electrical angle relative to the synchronous reference, and P_m − P_e 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 P_e = P_max 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.