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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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]