Probabilistic characterisation of the aggregated residential load patterns

The electrical load pattern representing the residential consumption is subject to different types of uncertainty, depending on family composition, lifestyle, number and type of use of the electrical appliances, thus requiring a dedicated analysis within a probabilistic framework. A comprehensive approach to the probabilistic characterisation of aggregated residential consumers supplied by the same feeder or substation, from the point of view of the electricity supplier, is presented. Starting from the result of a statistical study carried out on single-house extra-urban residential consumers, the time evolution of the average value and the standard deviation of the aggregated load power are presented. In addition, a dedicated goodness-of-fit analysis has been carried out to identify the most suitable probability distributions representing the daily aggregated load pattern at different times, referred to a set of typical days. This analysis includes a novel characterisation of the critical error of the Kolmogorov-Smirnov test on various probability distributions (beta, gamma, Gumbel, log-normal, Rayleigh and Weibull) for which the critical errors are not specifically available in publications. The gamma and log-normal probability distributions have emerged as the most promising solutions for several time intervals of analysis and for different numbers of aggregated consumers.

[1]  Kishor S. Trivedi.  Probability and Statistics with Reliability, Queuing, and Computer Science Applications , 1984 .

[2]  R. Herman,et al.  Load Models for Mixed-class Domestic and Fixed, Constant Power Loads for use in Probabilistic LV Feeder analysis. , 2003 .

[3]  Joanicjusz Nazarko,et al.  Estimation of diversity and kWHR-to-peak-kW factors from load research data , 1994 .

[4]  D.H.O. McQueen,et al.  Monte Carlo simulation of residential electricity demand for forecasting maximum demand on distribution networks , 2004, IEEE Transactions on Power Systems.

[5]  Friedrich Sick,et al.  Photovoltaics in Buildings: A Design Handbook for Architects and Engineers , 1996 .

[6]  Ralph B. D'Agostino,et al.  Goodness-of-Fit-Techniques , 2020 .

[7]  Veronica Irastorza,et al.  New Metering Enables Simplified and More Efficient Rate Structures , 2005 .

[8]  A. Molina,et al.  Implementation and assessment of physically based electrical load models: Application to direct load control residential programmes , 2003 .

[9]  L. H. Miller.  Table of Percentage Points of Kolmogorov Statistics , 1956 .

[10]  Irvin C. Schick,et al.  Residential end-use load shape estimation from whole-house metered data , 1988 .

[11]  M.R. Iravani,et al.  Power Management Strategies for a Microgrid With Multiple Distributed Generation Units , 2006, IEEE Transactions on Power Systems.

[12]  H. Lilliefors.  On the Kolmogorov-Smirnov Test for the Exponential Distribution with Mean Unknown , 1969 .

[13]  C. F. Walker,et al.  Residential Load Shape Modelling Based on Customer Behavior , 1985, IEEE Transactions on Power Apparatus and Systems.

[14]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[15]  Jörg Scheffler.  Operation of low voltage distribution networks with decentralised combined heat and power fuel cell systems for residential application , 2001, 2001 IEEE/PES Transmission and Distribution Conference and Exposition. Developing New Perspectives (Cat. No.01CH37294).

[16]  S. Heunis,et al.  A Probabilistic Model for Residential Consumer Loads , 2002, IEEE Power Engineering Review.

[17]  P. Postolache,et al.  Customer Characterization Options for Improving the Tariff Offer , 2002, IEEE Power Engineering Review.

[18]  D. Kirschen.  Demand-side view of electricity markets , 2003 .

[19]  H. Lilliefors.  On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown , 1967 .

[20]  Regina Lamedica,et al.  A bottom-up approach to residential load modeling , 1994 .

[21]  H. Aki,et al.  Operational strategies of networked fuel cells in residential homes , 2006, IEEE Transactions on Power Systems.

[22]  R. Herman,et al.  The statistical description of grouped domestic electrical load currents , 1993 .

[23]  Serge Lefebvre,et al.  Residential load modeling for predicting distribution transformer load behavior, feeder load and cold load pickup , 2002 .

[24]  A. K. Ghosh,et al.  Distribution circuit state estimation using a probabilistic approach , 1997 .

[25]  J. Jardini,et al.  Daily load profiles for residential, commercial and industrial low voltage consumers , 2000 .