A Deterministic Method to Identify Multiple Local Extrema for the AC Optimal Power Flow Problem

This paper presents a deterministic approach to compute multiple local extrema for AC Optimal Power Flow (ACOPF) problems. An elliptical representation of the sphere-confined Fritz John conditions is constructed from a quadratic formulation of the ACOPF problem. Application of a branch tracing method to the elliptical formulation enables the calculation of multiple solutions. Further, a monotone search strategy enhances the computational efficiency of finding multiple local solutions with improved objective values. The proposed approach is first illustrated using two small examples with known feasible spaces. Then, four additional local solutions to a 39-bus system are found using the proposed approach.