A mathematical model of load flow equations for an electrical grid having a chain of busses is embedded in a holomorphic embedding using a first embedding parameter s. The holomorphic embedding is transcribed into software for use in a computer processor. Voltages for each bus are calculated as an algebraic curve parameterized by the first embedding parameter. A second embedding parameter z is defined wherein the first embedding parameter s is a function of the second embedding parameter z. The holomorphic embedding is re-parameterized using the second embedding parameter z, such that the re-parameterized embedding provides an elimination polynomial equation relating parameters s and z. The roots of the elimination polynomial equation are determined by solving the for zero, which roots are used to compute bus voltages for each bus of the chain of busses. The bus voltages are displayed as the solution to the load flow equations.