Backward solution of PV nodes in radial distribution networks

In this paper an iterative backward methodology to solve radial distribution networks with fixed voltage(PV) nodes and with constant power loads or mixed loads (with at least one component with constantpower) is proposed. The method developed, although deriving conceptually from the backward/forward(b/f) methodology, presents only the backward phase in which all the network variables are evaluated.In themethods developed up until nowfor the solution of such systems, PV nodes are taken into accountat the end of each iteration by evaluating, based on the known quantities of the network, the unknownsassociated with PV nodes. In the methodology developed here the unknowns relevant to PV nodes areconsidered within the search process together with the unknown state variables. The proposed methodat each iteration requires the solution of a network made up only of impedances; for such a system,supplied only at one node, the susceptances of the PV nodes are unknown as well as the currents in shuntimpedances of the terminal buses. In order to solve sucha system, a simple and efficient technique has beenestablished. It allows the determination during the backward sweep of all the unknowns. The main andmost important feature of the simulation of PV nodes with shunt reactance is the high precision of resultsrelated to reactive power injection at PV nodes. The applications indeed showthat precision does not differfrom that related to the use of the classical Newton–Raphson method; furthermore, also the number ofiteration is similar with reduced CPU times. After having reported the models of PV nodes already existingin the literature in the field of b/f analysis methods, the general methodology for solving a radial networkmade up of impedances is briefly presented. The new analysis method and its implementation are thenpresented in detail. The results of the applications carried out show the good performance of the modelin terms of both speed of convergence and, mainly, of precision.