Reliable Solution of DC Power Flow Equations for Uncertain Topology Networks

Many operational tools for power system resilience analysis in the presence of multiple contingencies require the solution of a large number of DC power flow equations. The combinatorial nature of this process renders the exhaustive analysis of all possible contingencies extremely demanding, or even unfeasible, especially for large-scale networks. This manuscript proposes a tractable approach based on affine arithmetic, which allows direct computation of a reliable enclosure of the exhaustive solution set by introducing the concept of uncertain topology network. This formulation allows the system state variables to be expressed by affine forms, which explicitly represent the impacts on system operation of any combinations of the vulnerable components state. As a result, repetitive power flow solutions for different component operation states are avoided, drastically reducing the complexity of exhaustive multiple contingency analysis. Detailed simulation results obtained on both IEEE test networks and a real large-scale power system are presented and discussed in order to prove the effectiveness of the proposed method in reliably identifying the effects of multiple contingencies in realistic operation scenario.