An Affine Arithmetic-Based Framework for Uncertain Power Flow and Optimal Power Flow Studies

This paper proposes a unified framework based on affine arithmetic for computing reliable enclosures of uncertain power flow (PF) and optimal power flow (OPF) solutions. The main idea is to formulate a generic mathematical programming problem under uncertainty by means of equivalent deterministic problems, and to identify the affine forms describing the data uncertainty by means of a signal processing technique based on principal components analysis. Compared to existing solution algorithms, this formulation presents greater flexibility, as it allows to find feasible solutions and inclusion of multiple equality and inequality constraints, and reduce the approximation errors to obtain better PF and OPF solution enclosures. Detailed numerical results are presented and discussed using a variety of realistic test systems, demonstrating the effectiveness of the proposed methodologies and comparing it to existing techniques for uncertain PF and OPF analysis.