What is a swing equation in a power system?

The swing equation describes the motion of the rotor angle (or phase angle) of a synchronous generator. It is derived from the fundamental physical principles of energy balance in the machine. The equation takes into account the mechanical power input, the electrical power output, and the damping effects.

The general form of the swing equation for a single-machine infinite-bus system is:

M * d²θ/dt² = Pm - Pe - D * dθ/dt

Where:

M represents the moment of inertia of the generator rotor.

θ denotes the rotor angle, which represents the relative position of the rotor with respect to the synchronous reference frame.

t is the time variable.

Pm is the mechanical power input to the generator.

Pe is the electrical power output from the generator.

D is the damping coefficient, which represents the inherent damping characteristics of the generator.

The left-hand side of the equation represents the acceleration of the rotor angle, while the right-hand side represents the net torque acting on the generator. The swing equation describes how the rotor angle changes over time in response to disturbances in the system.

Transient stability analysis utilizes the swing equation to assess whether a power system can maintain synchronism and return to a stable operating condition after experiencing disturbances such as faults, sudden changes in load, or generator outages. By simulating the swing equation, engineers can evaluate the stability limits of the system and design appropriate control measures to enhance stability and prevent system collapse.