A Least-Squares Approach to Estimate Lagrange Multipliers in a Combined Method to Voltages Collapse Detection

Voltage stability is concerned with the ability of a power system to maintain acceptable voltages at all buses. A measure of the power system voltage stability is the distance to the saddle node bifurcation of the power flow equations, which is called the load margin. Two approaches are widely used to compute the critical load margin: Continuation and Optimization. The first approach uses tangent vectors of the power flow equations to determine the saddle node bifurcation, whereas the second approach formulates it as a non-linear optimization problem. This paper reviews both algorithms, and proposes a method to combine both techniques, obtaining the load margin-voltages curves, and the sensitivities of the critical load margin with respect to the active and reactive power dispatch. Starting from an approximation of the saddle node bifurcation, calculated by continuation method, a least-squares problem is formulated to obtain an approximation of the Lagrange multipliers. This approximation will be used as starting point on critical load margin calculation by optimization method. The performance of the method is illustrated with the CIGRE 32-buses test system.