The Optimal Power Flow Operator: Theory and Computation

Optimal power flow (OPF) problems are mathematical programs to determine how distribute over networks subject and operational constraints. In this article, we treat an OPF problem as operator that maps user demand generated power, allow the parameters take values in some admissible set. We formalize theoretic approach, define characterize restricted parameter sets under which mapping has a singleton output, independent binding constraints, is differentiable. show for any network, these analytical properties hold almost all operating conditions can thus be relied upon applications. further provide closed-form expression Jacobian matrix of describe various derivatives computed using recently proposed scheme based on homogenous self-dual embedding. contrast related work optimization literature, our results have clear physical interpretation.