The Swing Equation for transient stability of generators describes the relative motion between the rotor and the synchronously rotating stator axis with respect to time.
Swing Equation for transient stability of generators is very helpful in analyzing the stability of connected machines.
A power system consists of a number of synchronous machines operating synchronously under all operating conditions.
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis does not change.
During any disturbance, the rotor decelerates or accelerates with respect to the synchronously rotating air gap magnetomotive force, therefore creating relative motion.
Swing equation describes the relative motion. This equation is a non-linear second order differential equation that describes the swing of the rotor of synchronous machine.
As we know that in a synchronous generator the speed of rotor axis and stator filed axis is equal to synchronous speed (N = 120f/P) during normal operating condition. This simply means that the relative speed between rotor axis and stator field axis is zero.
Thus, the rotor field axis and stator filed axis maintains a constant angle δunder normal operating condition. This angle δ is known as Load Angle or Torque Angle.
Below equation represents the dynamics of a rotational mechanical system:
Above dynamics of rotational mechanical system and the attached document help to derive swing equation as below:
The generator rotor angle stability depends on rotation speed of generator (w-omega), inertia constant (H) and difference between mechanical power (Pm) and electrical power (Pe).
