A framework to study QV-constraint exchange points in the maximum loadability analysis

•The use of a predictor–corrector scheme to compute power flow solutions at QV-constraint exchange points.•The use of second-order information to estimate QV-constraint exchange points.•The determination of QV-constraint exchange points of the power flow equations by using an optimisation model.•The use Lagrange multipliers to verify the nature of the QV-constraint exchange points. This paper presents a framework to analyse critical levels of the power system loadability from the point of view of reactive power generation. Three main aspects are addressed: (1) the preliminary identification of the critical points of reactive power generation in terms of the power system loadability through a predictor scheme, (2) the solution of an optimisation problem to precisely determine these points in the corrector step, and (3) the classification of these critical points in terms of bifurcation type by using by-products of the optimisation process. The conventional power flow equations are expressed in rectangular coordinates, since this type of formulation allows both an accurate estimation of the power network variables in the predictor step and the computation of fast and robust solutions in the correction step. Numerical results obtained with two power networks are shown to illustrate the performance of the proposed methodology.