Homotopy methods for solving decoupled power flow equations

Explores the application of probability-one homotopy algorithms for solving the load flow equations under the decoupling assumption. The existence of solutions and convergence properties of homotopy methods are interpreted within the power systems framework, via an analogy between nonlinear resistive circuits in steady state and power systems. These ideas are further related to system stability. The effectiveness and performance of various homotopy functions are presented through simulation results for several small examples of power systems.