Optimal Power Flow Algorithms

The ordinary power flow or load flow problem is stated by specifying the loads in megawatts and megavars to be supplied at certain nodes or busbars of a transmission system and by the generated powers and the voltage magnitudes at the remaining nodes of this system together with a complete topological description of the system including its impedances. The objective is to determine the complex nodal voltages from which all other quantities like line flows, currents and losses can be derived. The model of the transmission system is given in complex quantities since an alternating current system is assumed to generate and supply the powers and loads. In mathematical terms the problem can be reduced to a set of nonlinear equations where the real and imaginary components of the nodal voltages are the variables. The number of equations equals twice the number of nodes. The nonlinearities can roughly be classified being of a quadratic nature. Gradi-