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

Given a nonlinear system of equations with or without varying paramete rs, this paper presents a technique to solve the convergence problem a t singular or near-singular roots of the system. A theoretical basis s temming from bifurcation theory for the proposed technique is given. S pecial attention is given to saddle-node bifurcations points (nose poi nts) as found in power systems applications. It is also shown that a p revious method presented in the litterature to solve ill-conditioning load flow solutions falls into the framework presented in this paper a nd is thereby theoretically justified. Moreover, this paper develops a n efficient computational procedure to solve ill-conditioning load flo w solutions with the following features: (1) it locally removes the si ngularity of the corresponding Jacobian; (2) it only requires a simple modification of the standard load flow equations, with no added dimen sion; (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 c onvergence around singular solutions. This method achieves its simplic ity and efficiency by exploiting the special properties of linear para meter-dependence in load flow equations. Applications to compute nose points of power flow equations are demonstrated and simulated on a pra ctical power system.