A Modal-Based Initial Estimate for the Newton Solution of Ill-Conditioned Large-Scale Power Flow Problems

Based on a modal approach, this letter identifies the primary cause for the ill-conditioning of a Power Flow Problem (PFP) and proposes a method to circumvent this numerical weakness. The technique consists in modifying the ill-conditioned PFP Jacobian matrix for the standard Newton method initial iterate by moving away just its smallest magnitude eigenvalue from near zero. The state deviations for this modified condition is then efficiently computed. This procedure is performed by adding a 1-rank perturbation matrix to the Jacobian matrix, but just for the first iteration and removing it for all others. Experiments performed in two ill-conditioned large-scale systems demonstrate the method's efficiency.