Probabilistic models for daily peak loads at distribution feeders

Abstract

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.Index Terms-load forecasting, daily peak load probabilistic model, power law distribution, empirical load modeling, probabilistic forecasting I.

Medium-Term Load Forecasting Using Support Vector Regression, Feature Selection, and Symbiotic Organism Search Optimization

“…Using feature selection method, 10 features related to past loads are selected i.e., 1,2,3,4,6,7,8,14,26 and 28 days before the forecasting day. In addition, some other features such as holidays, day type of a week, and month of a year have been taken into account in inputs by binary features.…”

“…Thus, the forecasting results in VSTLF and STLF have usually led to fairly accurate results. On the other hand, studies in long term load forecasting (LTLF) tend to implement probabilistic modelling instead of point estimation [2]. In this condition, medium-term load forecasting (MTLF) requires more attentions, considering its vital applications in the operation, control, and planning of power systems at generation, transmission, distribution, and marketing levels.…”

Sensitivity of the General Linear Model to Assumptions

“…Minimum Variance Unbiased (MVU) and Maximum Likelihood (ML) estimators are usually difficult to determine without being represented by a general linear model [1]- [3]. [4] emphasizes the optimal estimators in linear model allows everyone to analyze the problem within the model due to its unique properties.…”

“…Based on our GLM from equation 2and 3, we considered the line fitting of the model using the observation from equation (3).…”

On the performance of forecasting models in the presence of input uncertainty

“…In addition, in statistical inference, bootstrapping is an efficient numerical method which is used to infer statistical parameters of population from a sample [21]. If the sample is drawn properly, bootstrapping is able to extract a fairly good approximation of the population's statistics like mean or standard deviation [22].…”