A major transition in the operation of electric power grids is the replacement of synchronous machines by distributed generation connected via power electronic converters. The accompanying "loss of rotational inertia" and the fluctuations by renewable sources jeopardize the system stability, as testified by the ever-growing number of frequency incidents. As a remedy, numerous studies demonstrate how virtual inertia can be emulated through various devices, but few of them address the question of "where" to place this inertia. It is, however, strongly believed that the placement of virtual inertia hugely impacts system efficiency, as demonstrated by recent case studies. In this article, we carry out a comprehensive analysis in an attempt to address the optimal inertia placement problem. We consider a linear networkreduced power system model along with an H 2 performance metric accounting for the network coherency. The optimal inertia placement problem turns out to be non-convex, yet we provide a set of closed-form global optimality results for particular problem instances as well as a computational approach resulting in locally optimal solutions. Further, we also consider the robust inertia allocation problem, wherein the optimization is carried out accounting for the worstcase disturbance location. We illustrate our results with a three-region power grid case study and compare our locally optimal solution with different placement heuristics in terms of different performance metrics.
Primal-dual gradient methods have recently attracted interest as a set of systematic techniques for distributed and online optimization. One of the proposed applications has been optimal frequency regulation in power systems, where the primal-dual algorithm is implemented online as a dynamic controller. In this context however, the presence of external disturbances makes quantifying input/output performance important. Here we use the H2 system norm to quantify how effectively these distributed algorithms reject external disturbances. For the linear primal-dual algorithms arising from quadratic programs, we provide an explicit expression for the H2 norm, and examine the performance gain achieved by augmenting the Lagrangian. Our results suggest that the primal-dual method may perform poorly when applied to largescale systems, and that Lagrangian augmentation can partially (or completely) alleviate these scaling issues. We illustrate our results with an application to power system frequency control by means of distributed primal-dual controllers.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.