Calculating multiple loadability points in the power flow solution space

Abstract

Calculating loadability margins is indispensable for maintaining secure and stable operations of electric power grids. Loadability margins closely resemble boundedness placed by the Power-Flow (PF) equations solution space. Estimating these limits is a computationally demanding task linked to the non-convex structure of the PF solution space, technological constraints, and intricate grid topology. Furthermore, multiple loadability points exist within the PF solutions space due to the non-convex topology, representing either a structural change in the number of equilibria or the disappearance of all system equilibria. To address the problem of accurately estimating loadability margins, we present a computationally robust two-stage algorithmic framework that guarantees to identify all isolated loadability points within the PF solution space for a given set of parameters. Numerical results from different test cases validate the proposed algorithmic framework computational performance and also illustrate the convoluted structure of the PF solution space with disjoint sections.