| This paper is devoted to the problems of nd-ing the power ow feasibility, saddle node and Hopf bifur-cation boundaries in the space of power system parameters. The rst part contains a review of the existing relevant approaches including not so well-known contributions from Russia. The second part presents a new robust method for nding the power system load ow feasibility boundary on the plane deened by any three vectors of dependent variables (nodal voltages), called the-plane. The method exploits some quadratic and linear properties of the load ow equations and state matrices written in rectangular coordinates. An advantage of the method is that it does not require an iterative solution of nonlinear equations (except the eigenvalue problem). Besides beneets for visualization, the method is a useful tool for topological studies of power system multiple solution structures and stability domains. Although the power system application is developed, the method can be equally eecient for any quadratic algebraic problem.