Backward solution of PV nodes in radial distribution networks

Abstract

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 constant power) 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 the methods developed up until now for the solution of such systems, PV nodes are taken into account at the end of each iteration by evaluating, based on the known quantities of the network, the unknowns associated with PV nodes. In the methodology developed here the unknowns relevant to PV nodes are considered within the search process together with the unknown state variables. The proposed method at 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 shunt impedances of the terminal buses. In order to solve such a system, a simple and efficient technique has been established. It allows the determination during the backward sweep of all the unknowns. The main and most important feature of the simulation of PV nodes with shunt reactance is the high precision of results related to reactive power injection at PV nodes. The applications indeed show that precision does not differ from that related to the use of the classical Newton–Raphson method; furthermore, also the number of iteration is similar with reduced CPU times. After having reported the models of PV nodes already existing in the literature in the field of b/f analysis methods, the general methodology for solving a radial network made up of impedances is briefly presented. The new analysis method and its implementation are then presented in detail. The results of the applications carried out show the good performance of the model in terms of both speed of convergence and, mainly, of precision.