Estimating feasible nodal power injections in distribution networks

This paper proposes a set-theoretic method to estimate feasible nodal injections (generation or load) in a distribution network, while respecting power system performance requirements. In the setting that we study, performance requirements are constraints in the form of interval ranges on the values that line flows can take, which are modelled by a convex poloytope. At its core, the proposed method relies on the solution of a linearly constrained least-squares optimization problem, which is formulated using sensitivity factors computed by linearizing the power flow equations around the operating point. Since this optimization problem admits a linear closed-form solution, the polytope of permissible line flows is propagated through the solution, via set operations, to obtain the set of feasible nodal injections.