Dynamical homotopy transient-based technique to improve the convergence of ill-posed power flow problem

Abstract

This paper proposes a hybrid technique to solve the ill-posed Power Flow Problem (PFP), considering a homotopy approach. The primary proposal is to solve large-scale problems where the traditional Newton–Raphson (NR) fails to converge, as in the case of ill-posed systems. The method explores a dynamical homotopy transient-based technique to improve the convergence of the ill-conditioned problem instead of using the classical static method. Depending on the integration selected scheme and the integration step, the result furnished by the dynamical homotopy method has low accuracy. Then, the NR method is employed to refine the low-accuracy result and accurately determine the ill-posed PFP solution. The proposed approach can be implemented efficiently using only one Jacobian matrix computation and LU factorization per point of the homotopy path. In the static homotopy problem, a PFP using previous results must be solved per path point. In this case, some LU factorizations are necessary for each path point. The technique’s performance was evaluated through experiments, including a 70,000-bus large-scale system. The approximate dynamical homotopy result used as an initial estimate provided appropriate convergence quality for the NR method to determine a high-precision solution to the PFP.