Abstract: The power flow problem has several  solutions, among which are the common ​“high-voltage solution” and the ​“low-voltage solution.” In transient stability analysis, these power flow solutions represent equilibria of the classical model. To evaluate the stability boundary of the stable equilibrium point, all the type-1 unstable equilibrium points are needed, which requires solving multiple power flow solutions.

In this talk, I will explore different methods to solve power flow solutions and provide the fastest way to find these solutions with elliptical formulation and the holomorphic embedding technique. Then, we will extend this method to solve multiple OPF local extrema, which can be further applied to any bounded QCQP problems. With the help of the proposed numerical tool, ongoing research on the influence of load modeling for transient stability analysis will be discussedd. It is shown that the algebraic manifolds (as well as the type-1 UEPs) of the classical power system DAE model can be topologically changed with different load models. I will also touch on a few other interesting topics in natural gas networks and nonlinear oscillations for synchronous machines if time allows.