Determination of the bifurcation points of the power flow equations through optimisation-based methods

This paper describes the determination of quadratic turning points of the non-linear parameterised power flow equations using two optimisation-based approaches. The first is based on the trust region concept combined with sequential quadratic programming. The second uses tensor calculations as an extension of Newton's method. It is shown that the use of these algorithms imparts robustness to the iterative process, providing fast and reliable solutions. Numerical results obtained for problems with thousands of variables are used to illustrate the main features of the approaches, emphasising the robustness of the trust region-based approach.