A New Backward/Forward Method for Solving Radial Distribution Networks with PV Nodes

In this paper, a new backward/forward (b/f) methodology for the analysis of distribution systems with constant power loads is presented. In the proposed method, at each iteration, the loads are considered as constant impedances; in the backward sweep all the network variables (bus voltages and branch currents) are evaluated considering a scaling factor which is determined at the end of the backward phase. Indeed the forward sweep is eliminated and the node voltages calculation does not demand the sequentiality needed in the b/f methodology. The developed method, although deriving conceptually from the b/f methodology, presents only the backward phase in which all the network variables are evaluated considering a scaling factor. Moreover the load simulation as impedances is particularly important when the network shows PV nodes for which the voltage displacement and the reactive power are the unknowns. The condition of 90◦ displacement between the PV node voltage and the current injected by the apparatus for voltage regulation is not usually satisfied in networks solved by methods using constant current load models. The possibility to solve, at each iteration, a network made up of impedances allows to evaluate the reactance that must be inserted into the PV node in order to set the voltage at the prescribed value. In this way the value of this reactance is updated at each iteration and, at the end of the iterative process, whatever it is the displacement of the PV node voltage, the current circulating into the voltage regulating apparatus will be at 90◦ from it. In the paper, after a description of the PV nodes models reported in the b/f analysis literature, the new method is presented. The way in which the constant power loads are represented by means of a constant impedance model is also illustrated as well as the method for the evaluation of the unknown reactance to be installed at the PV nodes. The results of the executed applications show the efficiency of the model in terms of precision in the calculation of the reactive power required to sustain the voltage at the PV nodes.