> PAPER ID: 33< 1 Abstract—A new methodology based on the backward/forward (b/f) technique for the load flow solution in distribution systems is here proposed. The methodology takes efficiently into account the fixed voltage nodes and uses a reduced bus impedance matrix. In this way, it is possible to attain, for the unknowns at the PV nodes, the same values that are attainable solving the network with the methods adopted for transmission systems. With the same methodology it is possible to take into account also the meshes. If the network contains only meshes, the relevant model is linear and it is the one including the compensation currents. The presence of PV nodes introduces non linearity in the model and an iterative method is required to solve it. In this case, in the solution process, two cycles are present. An external main cycle connected to the b/f method and an internal cycle due to the presence of meshes and PV nodes. After the presentation of the used methods to take into account the presence of meshes and PV nodes, the new proposed method and its implementation are detailed. The results of the applications carried out show that the developed methodology presents, else than a high precision, good convergence properties and speed, qualities that are not dependent on the loading level and on the number of PV nodes. Index Terms—Backward/forward method, load flow distribution networks, PV nodes. I. INTRODUCTION HE most commonly used method in radial distribution networks analysis is the iterative backward/forward (b/f) technique ([1], [2], [3]). Its main points are: the computational ease, robustness, convergence (with heavy loading and under normal working conditions), possibility to keep into account any dependency of the loads on the voltage. With reference to the current summation method, the b/f technique is organised in two steps; in the first (the backward sweep), based on the loads currents, calculated starting from a known or fixed bus voltages profile and starting from the ending branches, the branches currents are calculated. In the second step, the forward sweep, starting from the source node with fixed voltage, all the bus voltages can be calculated. If the loads are constant current loads, the process ends with Manuscript received November 24, 2006. Antonino Augugliaro, Luigi Dusonchet, Salvatore Favuzza, Mariano Giuseppe Ippolito, Eleonora Riva Sanseverino are with the Dipartimento di Ingegneria Elettrica, Elettronica e delle Telecomunicazioni, Università di Palermo, 90128 Palermo, Italia (S. Favuzza + 39 091 6615221; fax: + 39 091 488452; e-mail: favuzza@diepa.unipa.it). the calculation of the bus voltages; differently, based on the dependency of the currents on the voltage, the new values of the currents can be calculated and another backward sweep is started. The iterative process stops when a prefixed convergence condition is met. In meshed structures, the solution procedure works on a system that is radialized by means of a certain number of cuts ([4], [5], [6]); for each couple of nodes created at each cut the injection of two equal and opposite currents is considered. The intensity of the currents is determined imposing the condition that the voltage difference between the two cut nodes is set to zero. This is the compensation currents method ([7]); it uses a reduced Thévenin impedance matrix and a known terms array containing the open circuit voltages between the cut nodes. The latter are the voltage values that are attained at the end of the forward sweep on the radialised system. Since the condition imposed by the cut nodes is linear (equality of voltages) the system to be solved is also linear and its solution is carried out through the inversion of the reduced Thévenin impedance matrix. The compensation currents method is used also to solve networks with PV nodes ([8], [9], [10]); in this case, some fictitious meshes are considered, these are attained connecting one null impedance branch between the PV node and the voltage reference node of the source node; an ideal voltage generator is then considered in the branch and its magnitude is the desired voltage at the PV node. The solution of the system having real and fictitious meshes associated to the PV nodes is made with the already described method, executing cuts in the meshes so as to radialize the network. The cuts on the fictitious meshes are executed so that the cut nodes are one, the PV node of the network; the other, the pole of the ideal voltage generator. The construction of the reduced Thévenin impedance matrix is carried out based on all the meshes, both real and fictitious . As far as the known terms are concerned, namely the voltage differences among couples of cut nodes, arises a problem for the couples of nodes of the fictitious meshes. Indeed, the voltage of a generic PV node of the network is that attained at the end of the forward sweep on the radial system and is expressed by a phasor having a given module and displacement taking as reference, for all the voltages and currents, the voltage of the ideal generator (usually the reference vector is the source node voltage, an imaginary number with null complex part). The voltage of the ideal generator at the PV node is known only in module, while its displacement is unknown. In the literature, many approaches have been proposed to solve this problem. In [8], A Multi-Port Approach to Solve Distribution Networks with Meshes and PV Nodes A. Augugliaro, L. Dusonchet, S. Favuzza, M. G. Ippolito, and E. Riva Sanseverino T