During any disturbance, the rotor decelerates or accelerates with respect to the synchronously rotating air gap magnetomotive force, creating relative motion.
[1] During this period the rotor moves at synchronous speed ωs in rad/s.
The electric torque Te corresponds to the net air-gap power in the machine and thus accounts for the total output power of the generator plus I2R losses in the armature winding.
The angular position θ is measured with a stationary reference frame.
Representing it with respect to the synchronously rotating frame gives: where, δm is the angular position in rad with respect to the synchronously rotating reference frame.
Therefore, the term dδm/dt represents the deviation of the rotor speed from synchronism in rad/s.
and multiplying both sides by ωm, where, Pm , Pe and Pa respectively are the mechanical, electrical and accelerating power in MW.
The coefficient Jωm is the angular momentum of the rotor: at synchronous speed ωs, it is denoted by M and called the inertia constant of the machine.
Since Pm, Pe and Pa are given in MW, dividing them by the generator MVA rating Srated gives these quantities in per unit.