Stability of power networks with time-varying inertia

A major transition in modern power systems is the replacement of conventional generation units with renewable sources of energy. The latter results in lower rotational inertia which compromises the stability of the power system, as testified by the growing number of frequency incidents. To resolve this problem, numerous studies have proposed the use of virtual inertia to improve the stability properties of the power grid. In this study, we consider how inertia variations, resulting from the application of control action associated with virtual inertia and fluctuations in renewable generation, may affect the stability properties of the power network within the primary frequency control timeframe. We consider the interaction between the frequency dynamics and a broad class of non-linear power supply dynamics at the presence of time-varying virtual inertia and provide suitable conditions such that stability is guaranteed. In particular, we impose two conditions; a decentralized passivity-related condition on the power supply dynamics and a condition that associates the maximum rate of growth of virtual inertia with the local power supply dynamics. The presented conditions are locally verifiable and applicable to arbitrary network configurations. In addition, in case of linear power supply dynamics, they can be efficiently verified by solving suitable linear matrix inequalities. Our analytic results are validated with simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system, where we demonstrate how varying virtual inertia may induce large frequency oscillations and show that the application of the proposed conditions yields a stable response.