Power flow algorithm using a second-order differentation approach

Load flow is the key tool for most of the studies related with electric power systems operation and planning. For a given electric network and power dispatch, power flow provides the state variables of the system, i.e. bus voltages magnitude and angle. In most of the cases, power flow must be run several times to cover different dispatches, topologies, outages, etc. Therefore, power flow algorithms must be fast and robust. This paper presents a second-order formulation of the Newton-Raphson method applied to the power flow problem. Power flow equations are reformulated as a homotopy that undergoes a manifold between initial point and the solution. The updating vector at each iteration is computed using first and second-order derivatives. The performance of the algorithm is illustrated using the IEEE 39 buses test network.