  Load forecasting at distribution networks is more challenging than load
forecasting at transmission networks because its load pattern is more
stochastic and unpredictable. To plan sufficient resources and estimate DER
hosting capacity, it is invaluable for a distribution network planner to get
the probabilistic distribution of daily peak-load under a feeder over long
term. In this paper, we model the probabilistic distribution functions of daily
peak-load under a feeder using power law distributions, which is tested by
improved Kolmogorov Smirnov test enhanced by the Monte Carlo simulation
approach. In addition, the uncertainty of the modeling is quantified using the
bootstrap method. The methodology of parameter estimation of the probabilistic
model and the hypothesis test is elaborated in detail. In the case studies, it
is shown using measurement data sets that the daily peak loads under several
feeders follow the power law distribution by applying the proposed testing
methods.

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