The Ossanna's Theorem for the Analytical Determination of a Two-Bus System PV Curve and Voltage Collapse Point

In the technical literature, the PV curves of the electrical lines are generally computed by only considering their electrical parameters as lumped. This model approach allows finding PV curve formulations without a large computational burden. Notwithstanding, such approximations bring to large inaccuracies for long transmission lines (especially insulated cables), for distribution ones (high r/x ratios) and for low power factor supply conditions. Starting from the Ossanna's theorem, novel and original PV curve and the voltage collapse point formulations for any electrical line are obtained. Moreover, PV curve analytical formulation considering the generator reactive power limits is formulated. Eventually, numerical results on the real-world case studies illustrate the differences with the proposed formulation with the classical ones found in the technical literature.