Impact of Inertia Variability on the Transient Stability of Interconnected Power Systems: A Methodology for the Estimation of Transient Stability Margins

The aim of this paper is to study the impact of the variability of inertia of interconnected electrical systems on transient stability. In the first part of the paper, after formulating the transient stability problem as a boundary value problem, we demonstrate how to evaluate the transient stability margin, considering the impact of the randomness of inertia, with reference to a single area connected to an infinite power grid. In the second part of the paper, we determine the distributional properties of the transient stability margin for two interconnected areas, considering the correlation of the area’s inertias, described as random variables. To demonstrate the robustness of the procedure, two case studies are analyzed. In the first case, the random variables are described as correlated lognormal random variables, while in the second they are considered as correlated gamma random variables. The numerical analyses reported in the final part of the paper show an almost linear dependence of transient stability margin from inertia while correlation coefficient affects mainly the transient stability random variable’s dispersion rather than its magnitude. Some useful considerations are performed regarding the applicability and validity of the linearized probabilistic method instead of the Monte Carlo method. The Monte Carlo method allows considering the non-linearity of the model, which is more pronounced in the tails. This could affect, in some critical cases, the priority of access to production in the logic of the free market. In such a case, greater accuracy allows for a more transparent mechanism of access to production.