Solving Three-phase AC Infeasibility Analysis to Near-zero Optimality Gap

Abstract: Recent works have shown the use of equivalent circuit-based infeasibility analysis to identify weak locations in distribution power grids. For three-phase power flow problems, when the power flow solver diverges, three-phase infeasibility analysis (TPIA) can converge and identify weak locations. The original TPIA problem is non-convex, and local minima and saddle points are possible. This can result in grid upgrades that are sub-optimal. To address this issue, we reformulate the original non-convex nonlinear program (NLP) as an exact non-convex bilinear program (BLP). Subsequently, we apply the spatial branch-and-bound (SBnB) algorithm to compute a solution with near-zero optimality gap. To improve SBnB performance, we introduce a bound tightening algorithm with variable filtering and decomposition, which tightens bounds on bilinear variables. We demonstrate that sequential bound tightening (SBT) significantly improves the efficiency and accuracy of Gurobi's SBnB algorithm. Our results show that the proposed method can solve large-scale three-phase infeasibility analysis problems with >5k nodes, achieving an optimality gap of less than 10e-4. Furthermore, we demonstrate that by utilizing the developed presolve routine for bounding, we can reduce the runtime of SBnB by up to 97%.