Computation of load flow problems with homotopy methods

Load flow comptations are the basis for voltage security assessments in power systems. All of the flow equation solutions must be computed to explore the mechanisms of voltage instability and voltage collapse. Conventional algorithms, such as Newton's methods and its variations, are not very desirable because they cannot be easily used to find all of the solutions. This paper investigate homotopy methods which can be used for numerically computing the set of all isolated solutions of multivariate polynomial systems resulting from load flow computations. The results significantly reduce the number of paths being followed.