Homotopy-based method numerical solution of the load flow problem in large-scale ill-conditioned power system models
Power flow problem; Newton-Raphson method; ill-conditioned systems; Homotopy; MATPOWER.
This doctoral thesis proposal presents a study on load flow solvers for poorly conditioned systems. The proposed idea is based on a hybrid technique facilitated by homotopy concepts to solve the Load Flow Problem (PFP) in ill-conditioned systems, where the standard Newton-Raphson (NR) method does not converge starting from a flat start estimate. The method uses transient-based dynamic homotopy concepts to initiate iterations through an integration scheme to obtain a low-precision voltage estimate. Then, with this initial estimate closest to the solution, the NR method refines the result to obtain a high-precision approximation with an error of 1 × 10−8. The method was tested for large-scale test systems, including 70,000 and 109k buses, and a high-precision solution was obtained. After this work, we intend to continue with homotopy-based solvers applied to systems with more than one slack bus while considering equipment limits and then present the thesis in December.