Parameterizations of the load-flow equations for eliminating ill-conditioning load flow solutions

Given a nonlinear system of equations with or without varying parameters, the authors present a technique to solve the convergence problem at singular or near-singular roots of the system. A theoretical basis stemming from bifurcation theory for the proposed technique is given. Special attention is given to saddle-note bifurcation points (nose points) as found in power system applications. It is also shown that a previous method of solving ill-conditioning load flow solutions falls into the framework presented and is thereby theoretically justified. An efficient computational procedure is developed to solve ill-conditioning load flow solutions. It has the following features: it locally removes the singularity of the corresponding Jacobian; it only requires a simple modification of the standard load flow equations, with no added dimension; it adds just a few nonzero elements to the sparse Jacobian matrix of the load flow equations; and it enlarges the region of convergence around singular solutions. This method achieves its simplicity and efficiency by exploiting the special properties of linear parameter-dependence in load flow equations. Applications to compute nose points of power flow equations are demonstrated and were simulated on a practical power system