Power System Operation and Control

4.8 THE SWING EQUATION

The relative position of the rotor axis and the stator magnetic field axis is fixed under normal operation. The angle between the two is known as the load angle or torque angle denoted by δ and depends upon the loading of the machine. Larger the loading, larger is the value of torque angle δ. The equation describing the relative motion of the rotor (load angle δ) with respect to the stator field as a function of time is known as the swing equation. The net torque causing acceleration is,

 

T_a = T_S − T_e    where Te = electromagnetic torque

                Ts = shaft torque

T_a is positive if T_s > T_e for the generator

If T_e > T_s the motor will accelerate. Multiplying both sides of the above equation with angular velocity ...