Two-step hybrid-based technique for solving ill-conditioned power flow problems

This paper presents a hybrid method to calculate the power flow problem (PFP) solution for ill-conditioned and large-scale power system models. The hybrid approach is composed of two steps. The first consists of calculating a partial solution of the PFP from a flat start estimate, which is characterized by low precision mismatches and a small computational burden. The calculations are performed by a homotopy technique, where each point of the homotopy path is determined using the classical Newton-Raphson (NR) method. The computed states in this first step are used in the second one as an estimate for an iterative method (IM), which determines the accurate and final solution of the PFP. Some IMs were investigated, including the NR solver and its fast-decoupled version (FDXB), besides other techniques considered appropriate to solve well-and ill-conditioned PFP. Results of experiments performed in four ill-conditioned power system models, including a 70k-bus system, demonstrate the efficiency and high-performance convergence quality identified in the proposed hybrid technique and its suitability even using simplified methods such as FDXB.