PARAMETERIZATIONS OF THE LOAD-FLOW EQUATIONS FOR ELIMINATING ILL-CONDITIONING LOAD FLOW SOLUTIONS

Given a nonlinear system of equations with or without varying parameters, this paper presents 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-node bifurcations points (nose points) as found in power systems applications. It is also shown that a previous method presented in the litterature to solve ill-conditioning load flow solutions falls into the framework presented in this paper and is thereby theoretically justified. Moreover, this paper develops an efficient computational procedure to solve ill-conditioning load flow solutions with the following features: (1) it locally removes the singularity of the corresponding Jacobian; (2) it only requires a simple modification of the standard load flow equations, with no added dimension; (3) it adds just a few non-zero elements to the sparse Jacobian matrix of the load flow equations; and (4) 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 simulated on a practical power system.