Abstract
In the restructured electricity industry, meaningful loss allocation methods are required in order to send correct signals to the market taking into account the location and characteristics of loads and generations, including the local sources forming the distributed generation (DG). This paper addresses the issues related to loss allocation in radial distribution systems with DG, with a three-fold focus. First, the key differences in the formulation of the loss allocation problem for radial distribution systems with respect to transmission systems are discussed, specifying the modeling and computational issues concerning the treatment of the slack node in radial distribution systems. Then, the characteristics of derivative-based and circuit-based loss allocation techniques are presented and compared, illustrating the arrangements used for adapting the various techniques to be applied to radial distribution systems with DG. Finally, the effects of introducing voltage-controllable local generation on the calculation of the loss allocation coefficients are discussed, proposing the adoption of a "reduced" representation of the system capable of taking into proper account the characteristics of the nodes containing voltage-controllable DG units. Numerical results are provided to show the time evolution of the loss allocation coefficients for distribution systems with variable load and local generation patterns.

Abstract
The allocation of the system losses to suppliers and consumers is a challenging issue for the restructured electricity business. Meaningful loss allocation techniques have to be adopted to set up appropriate economic penalties or rewards. The allocation factors should depend on size, location, and time evolution of the resources connected to the system. In the presence of distributed generation, the variety of the power flows in distribution systems calls for adopting mechanisms able to discriminate among the contributions that increase or reduce the total losses. Some loss allocation techniques already developed in the literature have shown consistent behavior. However, their application requires computing a set of additional quantities with respect to those provided by the distribution system power flow solved with the backward/forward sweep approach. This paper presents a new circuit-based loss allocation technique, based on the decomposition of the branch currents, specifically developed for radial distribution systems with distributed generation. The proposed technique is simple and effective and is only based on the information provided by the network data and by the power flow solution. Examples of application are shown to confirm its effectiveness.

Abstract
In this paper, the concepts related to loss partitioning among the phase currents in three-phase distribution systems are revisited in the light of new findings identified by the authors. In particular, the presence of a paradox in the classical loss partitioning approach, based on the use of the phase-by-phase difference between the input and output complex power, is highlighted. The conditions for performing effective loss partitioning without the occurrence of the paradox are thus established. The corresponding results are then used to extend the branch current decomposition loss allocation method for enabling its application to three-phase unbalanced distribution systems with distributed generation. Several numerical examples on a three-phase line with grounded neutral and on the modified IEEE 13-node test system are provided to assist the illustration and discussion of the novel conceptual framework. © 2008 IEEE.

Abstract
This paper highlights some specific aspects concerning the computational techniques for performing distribution system loss allocation including the impact of the distributed generation. The aspects addressed include the approximations related to the nearly-quadratic dependence of the total losses on the load power and the treatment of the voltage-controllable local generation. Examples showing the time evolution of the loss allocation coefficients with variable load and generation patterns are provided. © 2006 IEEE.

Abstract
In this paper, two factors typical of large photovoltaic (PV) arrays are investigated: one is the current-voltage (I-V) mismatch consequent to the production tolerance; the other is the impact of reverse currents in different operating conditions. Concerning the manufacturing I-V mismatch, the parameters of the equivalent circuit of the solar cell are computed for several PV modules from flash reports provided by the manufacturers. The corresponding I-V characteristic of every module is used to evaluate the behavior of different strings and the interaction among the strings connected for composing PV arrays. Two real crystalline silicon PV systems of 8 x 250 kW and 20 kW are studied, respectively. The simulation results reveal that the impact of the I-V mismatch is negligible with the usual tolerance, and the insertion of the blocking diodes against reverse currents can be avoided with crystalline silicon technology. On the other hand, the experimental results on I-V characteristics of the aforementioned arrays put into evidence the existence of a remarkable power deviation (3%-4%) with respect to the rated power, linkable to the lack of measurement uncertainty in the manufacturer flash reports.

Abstract
This study illustrates and discusses an original approach to classify the electricity consumers according to their daily load patterns. This approach exploits the notion of entropy introduced by Renyi for setting up specific clustering procedures. The proposed procedures differ with respect to typical methods adopted for electricity consumer classification, based on the Euclidean distance notion. The algorithms tested include firstly a classical method based on the between-cluster entropy and its slight variation. Then, a novel procedure is presented, based on the calculation of the similarity between centroids, with successive refinement to allow effective identification of the outliers. The outcomes of the classification carried out by using the proposed procedure are compared to the results of other available techniques, using a set of clustering validity indicators for ranking the clustering methods. On the basis of these results, it emerges that the novel procedure exhibits better clustering performance with respect to both the literature approaches and the classical entropy-based method, for different numbers of clusters. The results obtained are of key relevance for assisting the electricity suppliers in identifying a reduced number of load pattern-dependent classes, to be associated with distinct consumer groups for load aggregation or tariff purposes. © 2010 © The Institution of Engineering and Technology.