Three-Phase Infeasibility Analysis for Distribution Grid Studies

With the increase of distributed energy resources in the distribution grid, planning to ensure sufficient infrastructure and resources becomes critical. While well-studied at the transmission grid level, planning at the distribution grid level is limited by the complexities of optimizing unbalanced systems. In this paper we develop a three-phase infeasibility analysis that identifies weak locations in a distribution network. This optimization is formulated by adding slack current sources at every connected node and minimizing their norm subject to distribution power flow constraints. Through this analysis we solve instances of power flow that would otherwise be infeasible and diverge. Under conditions when power flow is feasible, the solution of this approach is equivalent to standard three-phase power flow; however, for cases where power flow simulations fail, the slack injection currents compensate the missing power by injecting nonzero currents into the system. We develop two forms of this formulation: one using least squares and another with an L1 norm objective. The L1-approach implicitly returns a sparse solution vector that identifies locations in the grid that are power deficient or voltage unstable. We show the efficacy of this approach on realistic unbalanced taxonomy feeders for scenarios with a high penetration of electric vehicles.