Effects of Variable Inertia on Synchronous Machine Transient Dynamics

To ensure reliable power system operation, frequency and voltage profiles are actively regulated. Frequency is tied to the rotational velocity of the synchronous machine rotor which is maintained through balanced torque between the prime mover and counter-torque from the stator. When a disturbance occurs, a temporary torque imbalance is created leading to a frequency deviation inversely proportional to the moment of inertia of the machine. This behavior is described by the classical swing equation that forms the basis for most synchronous machine dynamic models. This paper considers the effects of a variable moment of inertia (vMOI) on the frequency dynamics of a synchronous generator in relation to a power system to which it is connected. A mathematical framework for a vMOI synchronous machine is derived using first principles by rederiving the classical swing equation to consider a vMOI. This paper shows that vMOI systems exhibit better frequency response characteristics than fixed inertia machines. To demonstrate this principle, the paper simulates the behavior of a vMOI synchronous machine in a candidate multi-area power system model. The vMOI is characterized using proportional, first-order, and second-order first-principles physics models, and a range of system parameters are used to present different system behaviors and explore their implications for system design.