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A probabilistic methodology is presented, conceived to assist the electric system planning engineers in the selection of the distribution substation locations, taking into account the hourly load changes or the daily load cycle. The hourly load centers, for each of the different hourly load scenarios, are calculated deterministically. These location points, properly weighted according to their correspondent load magnitude, are used to calculate the best fit probability distribution. This distribution is used to determine the maximum likelihood perimeter of the area where the substation should preferably be located by the planning engineers, taking into account, for example, the availability and the cost of the land lots, which are factors of special relevance in urban areas, as well as other obstacles that may be present in the final selection of the substation site. Results are presented and discussed for the application of the methodology to a real case, assuming three different bivariate probability distributions: the Gaussian distribution, a bivariate version of Freund's exponential distribution, and the Weibull probability distribution.
Khodr et al. (2003) studied this question.