Conditioning step on the initial estimate when solving ill-conditioned power flow problems

Abstract

This short communication describes a conditioning step applied to the initial estimate used in the numerical iterative method to resolve the ill-conditioned power flow problem (PFP). The conditioning step consists of modifying the iterative method’s initial estimate through a process involving the Jacobian matrix and the mismatch of the balance equations, both of which are calculated for the initial estimate. The Jacobian matrix is then used to form a perturbed linear system, which has a resultant perturbed matrix with a better condition number. Three options to implement the perturbed form are proposed. One of them is based on a positive-definite matrix composed accordingly to create a linear system based on the initial mismatch of the equations. This linear system’s solution is called the ’modified initial estimate.’ Finally, the result is used to solve the ill-conditioned PFP via an iterative method. The technique was investigated considering the classical Newton-Raphson (NR) and the Heun-King-Werner (HKW) method and some variants. Experiments in four ill-conditioned power system models with a flat start guess, including a 70 k-bus test system, demonstrate that the methods investigated with this modified initial estimate, including a frozen Jacobian version of the NR solver, achieve convergence with a reduced number of iterations.