Forecasting and Assessing Risk of Individual Electricity Peaks

Introduction The overarching aim of this open access book is to present self-contained theory and algorithms for investigation and prediction of electric demand peaks. A cross-section of popular demand forecasting algorithms from statistics, machine learning and mathematics is presented, followed by extreme value theory techniques with examples. In order to achieve carbon targets, good forecasts of peaks are essential. For instance, shifting demand or charging battery depends on correct demand predictions in time. Majority of forecasting algorithms historically were focused on average load prediction. In order to model the peaks, methods from extreme value theory are applied. This allows us to study extremes without making any assumption on the central parts of demand distribution and to predict beyond the range of available data. While applied on individual loads, the techniques described in this book can be extended naturally to substations, or to commercial settings. Extreme value theory techniques presented can be also used across other disciplines, for example for predicting heavy rainfalls, wind speed, solar radiation and extreme weather events. The book is intended for students, academics, engineers and professionals that are interested in short term load prediction, energy data analytics, battery control, demand side response and data science in general.

[1]  Rayman Preet Singh,et al.  On hourly home peak load prediction , 2012, 2012 IEEE Third International Conference on Smart Grid Communications (SmartGridComm).

[2]  Davide Ferrari,et al.  The Maximum Lq-Likelihood Method: An Application to Extreme Quantile Estimation in Finance , 2009 .

[3]  Yuan Zhang,et al.  Short-Term Residential Load Forecasting Based on LSTM Recurrent Neural Network , 2019, IEEE Transactions on Smart Grid.

[4]  A. M. Hasofer,et al.  A Test for Extreme Value Domain of Attraction , 1992 .

[5]  M. Falk Best Attainable Rate of Joint Convergence of Extremes , 1989 .

[6]  Danica Vukadinovic Greetham,et al.  Electric vehicles and low-voltage grid: impact of uncontrolled demand side response , 2017 .

[7]  M. Ivette Gomes,et al.  Statistical choice of extreme value domains of attraction — a comparative analysis , 1996 .

[8]  C. Neves,et al.  A general estimator for the right endpoint with an application to supercentenarian women’s records , 2014, 1412.3972.

[9]  Valerio Lucarini,et al.  Convergence of Extreme Value Statistics in a Two-Layer Quasi-Geostrophic Atmospheric Model , 2017, Complex..

[10]  Statistics of heteroscedastic extremes , 2016 .

[11]  Isabel Serra,et al.  Likelihood inference for generalized Pareto distribution , 2015, Comput. Stat. Data Anal..

[12]  Roberto Lacal Arántegui,et al.  Photovoltaics and wind status in the European Union after the Paris Agreement , 2018 .

[13]  Nathan Charlton,et al.  A refined parametric model for short term load forecasting , 2014 .

[14]  J. Corcoran Modelling Extremal Events for Insurance and Finance , 2002 .

[15]  Yuhong Yang,et al.  Maximum Lq-likelihood estimation. , 2010, 1002.4533.

[16]  C. Jeffree,et al.  Tilting maximum Lq-Likelihood estimation for extreme values drawing on block maxima , 2018, 1810.03319.

[17]  Anthony C. Davison,et al.  Statistics of Extremes , 2015, International Encyclopedia of Statistical Science.

[18]  Enrique Castillo,et al.  The Selection of the Domain of Attraction of an Extreme Value Distribution from a Set of Data , 1989 .

[19]  M. Ivette Gomes,et al.  Mixed moment estimator and location invariant alternatives , 2009 .

[20]  Sidney I. Resnick TAIL EQUIVALENCE AND ITS APPLICATIONS , 1971 .

[21]  E. Castillo Extreme value and related models with applications in engineering and science , 2005 .

[22]  Tao Hong,et al.  Probabilistic electric load forecasting: A tutorial review , 2016 .

[23]  B. Gnedenko Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire , 1943 .

[24]  L. Haan,et al.  On tail trend detection: modeling relative risk , 2011, 1106.4149.

[25]  L. Haan,et al.  On the block maxima method in extreme value theory: PWM estimators , 2013, 1310.3222.

[26]  Mario Nicodemi,et al.  Extreme Value Statistics , 2009, Encyclopedia of Complexity and Systems Science.

[27]  J. Munkres ALGORITHMS FOR THE ASSIGNMENT AND TRANSIORTATION tROBLEMS* , 1957 .

[28]  Hesham K. Alfares,et al.  Electric load forecasting: Literature survey and classification of methods , 2002, Int. J. Syst. Sci..

[29]  Hartmut Schmeck,et al.  Designing K-nearest neighbors model for low voltage load forecasting , 2017, 2017 IEEE Power & Energy Society General Meeting.

[30]  Saifur Rahman,et al.  Analysis and Evaluation of Five Short-Term Load Forecasting Techniques , 1989, IEEE Power Engineering Review.

[31]  Matthew Rowe,et al.  The Real-Time Optimisation of DNO Owned Storage Devices on the LV Network for Peak Reduction , 2014 .

[32]  W. Patterson,et al.  Energy forecasting , 1977, Nature.

[33]  M. Meerschaert Regular Variation in R k , 1988 .

[34]  P. McSharry,et al.  Short-Term Load Forecasting Methods: An Evaluation Based on European Data , 2007, IEEE Transactions on Power Systems.

[35]  A. Jenkinson The frequency distribution of the annual maximum (or minimum) values of meteorological elements , 1955 .

[36]  Jonathan A. Tawn,et al.  Modelling non‐stationary extremes with application to surface level ozone , 2009 .

[37]  M. Fréchet Sur la loi de probabilité de l'écart maximum , 1928 .

[38]  Siddharth Arora,et al.  Forecasting electricity smart meter data using conditional kernel density estimation , 2014, 1409.2856.

[39]  Lambros Ekonomou,et al.  Greek long-term energy consumption prediction using artificial neural networks , 2010 .

[40]  Eric P. Smith,et al.  An Introduction to Statistical Modeling of Extreme Values , 2002, Technometrics.

[41]  Alexander Schrijver,et al.  Combinatorial optimization. Polyhedra and efficiency. , 2003 .

[42]  Haimonti Dutta,et al.  Machine Learning for the New York City Power Grid , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[43]  L. Haan,et al.  Extreme value theory : an introduction , 2006 .

[44]  M. Gilli,et al.  An Application of Extreme Value Theory for Measuring Financial Risk , 2006 .

[45]  Georgios Giasemidis,et al.  Short term load forecasting and the effect of temperature at the low voltage level , 2019, International Journal of Forecasting.

[46]  R. Fisher,et al.  Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[47]  Johan Segers,et al.  Testing the Gumbel hypothesis by Galton's ratio , 2000 .

[48]  Dana Abi Ghanem,et al.  “I think we need to get a better generator”: Household resilience to disruption to power supply during storm events , 2016 .

[49]  L. Haan,et al.  A moment estimator for the index of an extreme-value distribution , 1989 .

[50]  Chao Huang,et al.  Modified maximum spacings method for generalized extreme value distribution and applications in real data analysis , 2013, Metrika.

[51]  Peter Grindrod,et al.  A new error measure for forecasts of household-level, high resolution electrical energy consumption , 2014 .

[52]  James W. Taylor,et al.  Triple seasonal methods for short-term electricity demand forecasting , 2010, Eur. J. Oper. Res..

[53]  Magnus Ekström,et al.  Consistency of Generalized Maximum Spacing Estimates , 2001 .

[54]  Industrial Strategy National Energy Efficiency Data-Framework (NEED) , 2020 .

[55]  Siddharth Arora,et al.  Short-Term Forecasting of Anomalous Load Using Rule-Based Triple Seasonal Methods , 2013, IEEE Transactions on Power Systems.

[56]  Cláudia Neves,et al.  Semi-parametric approach to the Hasofer–Wang and Greenwood statistics in extremes , 2007 .

[57]  D. Farnsworth A First Course in Order Statistics , 1993 .

[58]  Carola Gerwig Short Term Load Forecasting for Residential Buildings - An Extensive Literature Review , 2015, KES-IDT.

[59]  J. Pickands Statistical Inference Using Extreme Order Statistics , 1975 .

[60]  Laurens de Haan,et al.  On maximum likelihood estimation of the extreme value index , 2004, math/0407062.

[61]  Nathaniel Charlton,et al.  Graph-based algorithms for comparison and prediction of household-level energy use profiles , 2013, 2013 IEEE International Workshop on Inteligent Energy Systems (IWIES).

[62]  L. Peng,et al.  Maximum likelihood estimation of extreme value index for irregular cases , 2009 .

[63]  U. Stadtmüller,et al.  Generalized regular variation of second order , 1996, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[64]  Chen Zhou,et al.  The extent of the maximum likelihood estimator for the extreme value index , 2010, J. Multivar. Anal..

[65]  J. Z. Wang,et al.  DETERMINATION OF DOMAINS OF ATTRACTION BASED ON A SEQUENCE OF MAXIMA , 1996 .

[66]  E. Dodd The greatest and the least variate under general laws of error , 1923 .

[67]  J. D. Castillo,et al.  Estimation of the generalized Pareto distribution , 2009 .

[68]  Hawoong Jeong,et al.  Modeling the Internet's large-scale topology , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[69]  Jan Picek,et al.  The contribution of the maximum to the sum of excesses for testing max-domains of attraction , 2006 .

[70]  Karl Aberer,et al.  Electricity load forecasting for residential customers: Exploiting aggregation and correlation between households , 2013, 2013 Sustainable Internet and ICT for Sustainability (SustainIT).

[71]  Frank Marohn,et al.  Testing the Gumbel Hypothesis Via the Pot-Method , 1998 .

[72]  Richard L. Smith Estimating tails of probability distributions , 1987 .

[73]  Siobhán Clarke,et al.  Evaluation of Forecasting Methods for Very Small-Scale Networks , 2015, DARE.

[74]  Isabel Fraga Alves,et al.  ESTIMATION OF THE FINITE RIGHT ENDPOINT IN THE GUMBEL DOMAIN , 2013, 1306.1452.

[75]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[76]  J. Holmes,et al.  Application of the generalized Pareto distribution to extreme value analysis in wind engineering , 1999 .

[77]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[78]  Sahin Albayrak,et al.  Adjusted Feature-Aware k-Nearest Neighbors: Utilizing Local Permutation-Based Error for Short-Term Residential Building Load Forecasting , 2018, 2018 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm).

[79]  Richard J. Campbell,et al.  Weather-Related Power Outages and Electric System Resiliency , 2012 .

[80]  L. Haan Convergence of heteroscedastic extremes , 2015 .

[81]  Georgios Giasemidis,et al.  A hybrid model of kernel density estimation and quantile regression for GEFCom2014 probabilistic load forecasting , 2016, 1610.05183.

[82]  Russell C. H. Cheng,et al.  Estimating Parameters in Continuous Univariate Distributions with a Shifted Origin , 1983 .

[83]  L. Haan On regular variation and its application to the weak convergence of sample extremes , 1973 .

[84]  L. Haan,et al.  Residual Life Time at Great Age , 1974 .

[85]  J. W. Taylor,et al.  Short-term electricity demand forecasting using double seasonal exponential smoothing , 2003, J. Oper. Res. Soc..

[86]  S. Hubbert Extreme Value Theory , 2019, Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management.

[87]  Nicole A. Lazar,et al.  Statistics of Extremes: Theory and Applications , 2005, Technometrics.

[88]  Bo Ranneby,et al.  The Maximum Spacing Method. An Estimation Method Related to the Maximum Likelihood Method , 2016 .

[89]  Gaël Varoquaux,et al.  Scikit-learn: Machine Learning in Python , 2011, J. Mach. Learn. Res..

[90]  António B. Pereira,et al.  Detecting finiteness in the right endpoint of light-tailed distributions , 2010 .

[91]  G. Gross,et al.  Short-term load forecasting , 1987, Proceedings of the IEEE.