1 Probabilis c energy forecas ng for smart grids and buildings Rob J Hyndman 21 March 2017

Demand forecas ng

Demand forecas ng in the smart grid Figure: http://solutions.3m.com Energy sources (fossil fuel, wind, solar, wave, ...) Supply → Energy consumers Demand 2

Demand forecas ng in the smart grid Need demand forecasts for outage planning, energy trading, demand response, system management, ... Predictors calendar effects Time of day Day of week Time of year Holidays prevailing and recent weather condi ons demand response incen ves household characteris cs We build a nonlinear nonparametric stochas c model of demand as a func on of these predictors. 3

Probabilis c forecas ng

Probabilis c forecas ng Aim: forecast en re probability distribu on of demand, not only the average. 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Day Half−Hourly electricity demand 4

Probabilis c forecas ng Aim: forecast en re probability distribu on of demand, not only the average. 3 4 5 12 13 14 15 16 Day Point (mean) forecasts 4

Probabilis c forecas ng Aim: forecast en re probability distribu on of demand, not only the average. 3 4 5 12 13 14 15 16 Day level 50 90 Point forecasts with prediction intervals 4

Probabilis c forecas ng Aim: forecast en re probability distribu on of demand, not only the average. 3 4 5 12 13 14 15 16 Day Percentile 95% 75% 50% 25% 05% Point forecasts with percentiles 4

Probabilis c forecas ng Aim: forecast en re probability distribu on of demand, not only the average. 3 4 5 12 13 14 15 16 Day 10 20 30 40 50 60 70 80 90 level Point forecasts with prediction intervals 4

Probabilis c forecas ng Aim: forecast en re probability distribu on of demand, not only the average. 3 4 5 12 13 14 15 16 Day Percentile 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% Point forecasts with percentiles 4

Probabilis c forecas ng Aim: forecast en re probability distribu on of demand, not only the average. 3 4 5 12 13 14 15 16 Day Percentile 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% Point forecasts with percentiles 4 3 4 5 12 13 14 15 16 Day Point forecasts with percentiles

Probabilis c forecas ng Half-hourly data. Blue: 50% region. Grey: 95% region. 5 0. Time Ele q q 00:00 04:00 08:00 12:00 16:00 20:00 q q 0.0 0.2 0.4 0.6 QR−GAMBOOST Time Electricity demand (scaled) q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 00:00 04:00 08:00 12:00 16:00 20:00

Forecast accuracy measures MAE: Mean absolute error MSE: Mean squared error MAPE: Mean absolute percentage error 6

Forecast accuracy measures MAE: Mean absolute error MSE: Mean squared error MAPE: Mean absolute percentage error ¯ Good when forecas ng a typical future value (e.g., the mean or median). 6

Forecast accuracy measures MAE: Mean absolute error MSE: Mean squared error MAPE: Mean absolute percentage error ¯ Good when forecas ng a typical future value (e.g., the mean or median). ¯ Useless for evalua ng forecast percen les and forecast distribu ons. 6

Forecast accuracy measures MAE: Mean absolute error MSE: Mean squared error MAPE: Mean absolute percentage error ¯ Good when forecas ng a typical future value (e.g., the mean or median). ¯ Useless for evalua ng forecast percen les and forecast distribu ons. qt (p) = Percen le forecast of yt , to be exceeded with probability 1 − p. 6

Forecast accuracy measures MAE: Mean absolute error MSE: Mean squared error MAPE: Mean absolute percentage error ¯ Good when forecas ng a typical future value (e.g., the mean or median). ¯ Useless for evalua ng forecast percen les and forecast distribu ons. qt (p) = Percen le forecast of yt , to be exceeded with probability 1 − p. ¯ If qt (p) is accurate, then yt should be less than qt (p) about 100p% of the me. ¯ Need to penalize unlikely side more (a “pinball loss” func on) 6

Forecast scoring 7 0 20 40 60 80 100 Demand distribution Demand

Forecast scoring 7 0 20 40 60 80 100 Demand distribution Demand 50%

Forecast scoring 7 0 20 40 60 80 100 Demand distribution Demand 50% Score qt (0.5)

Forecast scoring 8 0 20 40 60 80 100 Demand distribution Demand

Forecast scoring 8 0 20 40 60 80 100 Demand distribution Demand 20%

Forecast scoring 8 0 20 40 60 80 100 Demand distribution Demand 20% Score qt (0.8)

Forecast scoring 9 0 20 40 60 80 100 Demand distribution Demand

Forecast scoring 9 0 20 40 60 80 100 Demand distribution Demand 90%

Forecast scoring 9 0 20 40 60 80 100 Demand distribution Demand 90% Score qt (0.1)

Forecast scoring Quan le Score for observa on y: For 0 < p < 1: S(yt , qt (p)) = p(yt − qt (p)) if yt ≥ qt (p) (1 − p)(qt (p) − yt ) if yt < qt (p) Scores are averaged over all observed data for each p to measure the accuracy of the forecasts for each percen le. Average score over all percen les gives the best distribu on forecast: QS = 1 99T 99 p=1 T t=1 S(qt (p), yt ) Equivalent to CRPS (Con nuous Rank Probability Score). Reduces to MAE if we are only interested in p = 0.5. 10

Hierarchical forecas ng

Hierarchical electricity demand data yt yA,t yAA,t yAB,t yAC,t yB,t yBA,t yBB,t yC,t yCA,t yCB,t yCC,t yt = yA,t + yB,t + yC,t yA,t = yAA,t + yAB,t + yAC,t yB,t = yBA,t + yBB,t yC,t = yCA,t + yCB,t + yCC,t Aggrega ons may be based on: Geography (suburbs, regions, states) Demography (number of people in household, age distribu ons) Appliances (air condi oning, electric hea ng) 11

Hierarchical electricity demand data 12 5701 791 366 42 9 1

Hierarchical forecas ng yt yA,t yAA,t yAB,t yAC,t yB,t yBA,t yBB,t yC,t yCA,t yCB,t yCC,t Easier to forecast at more aggregated levels. We forecast at every level and reconcile the forecasts. Op mal reconcila on algorithm: Hyndman et al (2011, 2016, 2017) Forecast means should add up, but percen les are more complicated Current research topic: How to reconcile percen les at all levels? 13

Building-level energy forecas ng

Managing commercial buildings Commercial buildings require energy forecas ng to help: Manage peak demand. Quan fy the impacts of building management changes. Assess performance and energy efficiency. Buildings Alive works with 150+ commercial buildings which include supermarkets, hospitals and office blocks. Each require daily forecasts to inform facili es managers. 14

Building Level Data 15 BID1012 BID1002 Jan 17 Jan 19 Jan 21 500 1000 1500 2000 500 1000 1500 2000 Date Power (kW)

Building Level Data Natural cubic splines for each period of the day (df = 2). 16 BID1002 BID1012 20 30 40 20 30 40 500 1000 1500 Temperature (degrees Celsius) Power (kW) 25 50 75 Period

Quan le Regression Probabilis c forecasts can be produced using quan le regression. Use the pinball loss func on: Sp (y, qp ) = p(y − qp ) for y ≥ qp , (1 − p)(qp − y) for qp > y. 0.00 0.25 0.50 0.75 1.00 −1.0 −0.5 0.0 0.5 1.0 Squared error OLS loss function 0.0 0.2 0.4 0.6 0.8 −1.0 −0.5 0.0 0.5 1.0 Sτ (y, qτ ) Pinball loss function 17

Quan le Regression Forecas ng 18 BID1012 BID1002 Jan 17 Jan 19 Jan 21 500 1000 1500 2000 500 1000 1500 2000 Power (kW) 0.25 0.50 0.75 Quantile

Assessing performance Forecas ng a full distribu on allows facili es managers to be er assess risks and take appropriate ac ons. Allows facili es managers to know the severity and probability of demand peaks. Can immediately assess if a building’s performance was good compared to historical performance under similar condi ons. 19

Compe ons, conferences and resources

GEFCom Global Energy Forecas ng Compe ons Organized by Professor Tao Hong (UNC) GEFCom 2012: Load, Wind Forecas ng GEFCom 2014: Load, Price, Wind, Solar Forecas ng GEFCom 2017: Hierarchical probabilis c forecasts, real- me, rolling origin. gefcom.org Winning entries published in Interna onal Journal of Forecas ng. Huge improvements in forecast accuracy over previously published methods. 20

Interna onal Symposium on Energy Analy cs 2017 Predic ve Energy Analy cs in the Big Data World Proudly sponsored by Interna onal Ins tute of Forecasters June 22–23, 2017 Cairns, Australia Featured speakers Yannig Goude, Electricite de France, France Rob J Hyndman, Monash University, Australia Pierre Pinson, Technical University of Denmark, Denmark Richard Povinelli, Marque e University, USA Rafal Weron, Wroclaw University of Technology, Poland Hamidreza Zareipour, University of Calgary, Canada Xun Zhang, Chinese Academy of Sciences, China 21

Interna onal Symposium on Forecas ng 2017 22

Some resources Blogs robjhyndman.com/hyndsight/ blog.drhongtao.com/ 23

Some resources Blogs robjhyndman.com/hyndsight/ blog.drhongtao.com/ Organiza ons Interna onal Ins tute of Forecasters: forecasters.org IEEE Working Group on Energy Forecas ng: linkedin.com/groups/ IEEE-Working-Group-on-Energy-4148276 23

References

References Rob J Hyndman and Shu Fan (2010). “Density forecas ng for long-term peak electricity demand”. IEEE Transac ons on Power Systems 25(2), 1142–1153. Shu Fan and Rob J Hyndman (2012). “Short-term load forecas ng based on a semi-parametric addi ve model”. IEEE Transac ons on Power Systems 27(1), 134–141. Souhaib Ben Taieb and Rob J Hyndman (2014). “A gradient boos ng approach to the Kaggle load forecas ng compe on”. Interna onal Journal of Forecas ng 30(2), 382–394 Souhaib Ben Taieb, Raphael Huser, Rob J Hyndman, and Marc G Genton (2015). Probabilis c me series forecas ng with boosted addi ve models: an applica on to smart meter data. Working paper 15/12. Monash University Souhaib Ben Taieb, Raphael Huser, Rob J Hyndman, and Marc G Genton (2016). “Forecas ng uncertainty in electricity smart meter data by boos ng addi ve quan le regression”. IEEE Transac ons on Smart Grid 7 (5), 2448–2455 Rob J Hyndman, Alan J Lee, and Earo Wang (2016). “Fast computa on of reconciled forecasts for hierarchical and grouped me series”. Computa onal Sta s cs & Data Analysis 97, 16–32. Souhaib Ben Taieb, James W Taylor, and Rob J Hyndman (2017). Coherent Probabilis c Forecasts for Hierarchical Time Series. Working paper 17/03. Monash University 24