PEAK DEMAND FORECAST

1. Probabilistic forecasting of long-term peak electricity demand Rob J Hyndman Joint work with Shu Fan Probabilistic forecasting of peak electricity demand 1

2. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Competitions and evaluation 6 MEFM package 7 References and resources Probabilistic forecasting of peak electricity demand The problem 2

3. The problem We want to forecast the peak electricity demand in a half-hour period in twenty years time. We have ﬁfteen years of half-hourly electricity data, temperature data and some economic and demographic data. The location is South Australia: home to the most volatile electricity demand in the world. Sounds impossible? Probabilistic forecasting of peak electricity demand The problem 3

4. The problem We want to forecast the peak electricity demand in a half-hour period in twenty years time. We have ﬁfteen years of half-hourly electricity data, temperature data and some economic and demographic data. The location is South Australia: home to the most volatile electricity demand in the world. Sounds impossible? Probabilistic forecasting of peak electricity demand The problem 3

5. South Australian demand data Probabilistic forecasting of peak electricity demand The problem 4

6. South Australian demand data Probabilistic forecasting of peak electricity demand The problem 4 Black Saturday →

7. South Australian demand data Probabilistic forecasting of peak electricity demand The problem 5 SA State wide demand (summer 2015) SAStatewidedemand(GW) 1.01.52.02.53.0 Oct Nov Dec Jan Feb Mar

8. South Australian demand data Probabilistic forecasting of peak electricity demand The problem 5

9. Temperature data (Sth Aust) Probabilistic forecasting of peak electricity demand The problem 6

10. Temperature data (Sth Aust) Probabilistic forecasting of peak electricity demand The problem 7 10 20 30 40 1.01.52.02.53.03.5 Time: 12 midnight Temperature (deg C) Demand(GW) Workday Non−workday

11. Demand boxplots (Sth Aust) Probabilistic forecasting of peak electricity demand The problem 8 qqqq q q q q qq qq q q q q q q qq q q q q q q q q q q q q q q qq q q q q q q q q qq qqq q qq q qqq qqq q q qq q q q q q q qq q q q q qq q q q q qq q q q qq qq q qqq q q q q q q q q q q q q qq qqq qqqq qq q qq q q qq qq q qq q q q qq q q q q q q q q q q q q q qq q q q q q qq q q Mon Tue Wed Thu Fri Sat Sun 1.01.52.02.53.03.5 Time: 12 midnight Day of week Demand(GW)

12. Demand densities (Sth Aust) Probabilistic forecasting of peak electricity demand The problem 9 1.0 1.5 2.0 2.5 3.0 3.5 01234 Density of demand: 12 midnight South Australian half−hourly demand (GW) Density

13. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Competitions and evaluation 6 MEFM package 7 References and resources Probabilistic forecasting of peak electricity demand The model 10

14. Predictors calendar effects prevailing and recent weather conditions climate changes economic and demographic changes changing technology Modelling framework Semi-parametric additive models with correlated errors. Each half-hour period modelled separately for each season. Variables selected to provide best out-of-sample predictions using cross-validation on each summer. Probabilistic forecasting of peak electricity demand The model 11

15. Predictors calendar effects prevailing and recent weather conditions climate changes economic and demographic changes changing technology Modelling framework Semi-parametric additive models with correlated errors. Each half-hour period modelled separately for each season. Variables selected to provide best out-of-sample predictions using cross-validation on each summer. Probabilistic forecasting of peak electricity demand The model 11

16. Monash Electricity Forecasting Model y∗ t = yt/¯yi yt denotes per capita demand (minus offset) at time t (measured in half-hourly intervals); ¯yi is the average demand for quarter i where t is in quarter i. y∗ t is the standardized demand for time t. log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Probabilistic forecasting of peak electricity demand The model 12

17. Monash Electricity Forecasting Model Probabilistic forecasting of peak electricity demand The model 13

18. Monash Electricity Forecasting Model Probabilistic forecasting of peak electricity demand The model 13

19. Annual model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et log(¯yi) = log(¯yi−1) + j cj(zj,i − zj,i−1) + εi First differences modelled to avoid non-stationary variables. Predictors: Per-capita GSP, Price, Summer CDD, Winter HDD. Probabilistic forecasting of peak electricity demand The model 14

20. Annual model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et log(¯yi) = log(¯yi−1) + j cj(zj,i − zj,i−1) + εi First differences modelled to avoid non-stationary variables. Predictors: Per-capita GSP, Price, Summer CDD, Winter HDD. Probabilistic forecasting of peak electricity demand The model 14

21. Annual model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et log(¯yi) = log(¯yi−1) + j cj(zj,i − zj,i−1) + εi First differences modelled to avoid non-stationary variables. Predictors: Per-capita GSP, Price, Summer CDD, Winter HDD. zCDD = summer max(0, ¯T − 17.5) ¯T = daily mean Probabilistic forecasting of peak electricity demand The model 14

22. Annual model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et log(¯yi) = log(¯yi−1) + j cj(zj,i − zj,i−1) + εi First differences modelled to avoid non-stationary variables. Predictors: Per-capita GSP, Price, Summer CDD, Winter HDD. zHDD = winter max(0, 19.5 − ¯T) ¯T = daily mean Probabilistic forecasting of peak electricity demand The model 14

23. Annual model SA summer cooling degree days Year scdd 2002 2004 2006 2008 2010 2012 2014 300400500600700 SA winter heating degree days 800850 Probabilistic forecasting of peak electricity demand The model 15

24. Annual model Variable Coefﬁcient Std. Error t value P value ∆gsp.pc 2.02 5.05 0.38 0.711 ∆price −1.67 0.68 −2.46 0.026 ∆scdd 1.11 0.25 4.49 0.000 ∆whdd 2.07 0.33 0.63 0.537 GSP needed to stay in the model to allow scenario forecasting. All other variables led to improved AICC. Probabilistic forecasting of peak electricity demand The model 16

27. Annual model Probabilistic forecasting of peak electricity demand The model 17 Year Annualdemand 1.01.21.41.61.82.0 2002 2004 2006 2008 2010 2012 2014 Actual Fitted

28. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Calendar effects “Time of summer” effect (a regression spline) Day of week factor (7 levels) Public holiday factor (4 levels) New Year’s Eve factor (2 levels) Probabilistic forecasting of peak electricity demand The model 18

32. Fitted results (Summer 3pm) Probabilistic forecasting of peak electricity demand The model 19 0 50 100 150 −0.40.00.4 Day of summer Effectondemand Mon Tue Wed Thu Fri Sat Sun −0.40.00.4 Day of week Effectondemand Normal Day before Holiday Day after −0.40.00.4 Holiday Effectondemand Time: 3:00 pm

33. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Temperature effects Ave temp across two sites, plus lags for previous 3 hours and previous 3 days. Temp difference between two sites, plus lags for previous 3 hours and previous 3 days. Max ave temp in past 24 hours. Min ave temp in past 24 hours. Ave temp in past seven days. Each function estimated using boosted regression splines. Probabilistic forecasting of peak electricity demand The model 20

40. Monash Electricity Forecasting Model Temperature effects 6 k=0 fk,p(xt−k) + gk,p(dt−k) + qp(x+ t ) + rp(x− t ) + sp(¯xt) + 6 j=1 Fj,p(xt−48j) + Gj,p(dt−48j) xt is ave temp across two sites at time t; dt is the temp difference between two sites at time t; x+ t is max of xt values in past 24 hours; x− t is min of xt values in past 24 hours; ¯xt is ave temp in past seven days. Probabilistic forecasting of peak electricity demand The model 21

45. Fitted results (Summer 3pm) Probabilistic forecasting of peak electricity demand The model 22 10 20 30 40 −0.4−0.20.00.20.4 Temperature Effectondemand 10 20 30 40 −0.4−0.20.00.20.4 Lag 1 temperature Effectondemand 10 20 30 40 −0.4−0.20.00.20.4 Lag 2 temperature Effectondemand 10 20 30 40 −0.4−0.20.00.20.4 Lag 3 temperature Effectondemand 10 20 30 40 −0.4−0.20.00.20.4 Lag 1 day temperature Effectondemand 10 15 20 25 30 −0.4−0.20.00.20.4 Last week average temp Effectondemand 15 25 35 −0.4−0.20.00.20.4 Previous max temp Effectondemand 10 15 20 25 −0.4−0.20.00.20.4 Previous min temp Effectondemand Time: 3:00 pm

46. Half-hourly models log(y∗ t ) = f(calendar effects, temperatures) + et Data split into working/non-working days, and into night/day/evening (6 subsets). Separate model for each half-hour period within each subset (96 models). Same predictors used for all models in a subset. Predictors chosen by cross-validation on last two summers. Each model is ﬁtted to the data twice, ﬁrst excluding the last summer and then excluding the previous summer. Average out-of-sample MSE calculated from omitted data. Probabilistic forecasting of peak electricity demand The model 23

51. Half-hourly models x x1 x2 x3 x4 x5 x6 x48 x96 x144 x192 x240 x288 d d1 d2 d3 d4 d5 d6 d48 d96 d144 d192 d240 d288 x+ x− ¯x dow hol dos MSE 1 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.037 2 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.034 3 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.031 4 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.027 5 • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.025 6 • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.020 7 • • • • • • • • • • • • • • • • • • • • • • • • • • 1.025 8 • • • • • • • • • • • • • • • • • • • • • • • • • • 1.026 9 • • • • • • • • • • • • • • • • • • • • • • • • • 1.035 10 • • • • • • • • • • • • • • • • • • • • • • • • 1.044 11 • • • • • • • • • • • • • • • • • • • • • • • 1.057 12 • • • • • • • • • • • • • • • • • • • • • • 1.076 13 • • • • • • • • • • • • • • • • • • • • • 1.102 14 • • • • • • • • • • • • • • • • • • • • • • • • • • 1.018 15 • • • • • • • • • • • • • • • • • • • • • • • • • 1.021 16 • • • • • • • • • • • • • • • • • • • • • • • • 1.037 17 • • • • • • • • • • • • • • • • • • • • • • • 1.074 18 • • • • • • • • • • • • • • • • • • • • • • 1.152 19 • • • • • • • • • • • • • • • • • • • • • 1.180 20 • • • • • • • • • • • • • • • • • • • • • • • • • 1.021 21 • • • • • • • • • • • • • • • • • • • • • • • • 1.027 22 • • • • • • • • • • • • • • • • • • • • • • • 1.038 23 • • • • • • • • • • • • • • • • • • • • • • 1.056 24 • • • • • • • • • • • • • • • • • • • • • 1.086 25 • • • • • • • • • • • • • • • • • • • • 1.135 26 • • • • • • • • • • • • • • • • • • • • • • • • • 1.009 27 • • • • • • • • • • • • • • • • • • • • • • • • • 1.063 28 • • • • • • • • • • • • • • • • • • • • • • • • • 1.028 29 • • • • • • • • • • • • • • • • • • • • • • • • • 3.523 30 • • • • • • • • • • • • • • • • • • • • • • • • • 2.143 31 • • • • • • • • • • • • • • • • • • • • • • • • • 1.523 Probabilistic forecasting of peak electricity demand The model 24

52. Half-hourly models Probabilistic forecasting of peak electricity demand The model 25 60708090 R−squared Time of day R−squared(%) 12 midnight 6:00 am 9:00 am 12 noon 3:00 pm 6:00 pm 9:00 pm3:00 am 12 midnight

53. Half-hourly models Probabilistic forecasting of peak electricity demand The model 25 Demand (January 2015) Date in January SAdemand(GW) 012345 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Actual Predicted Temperatures (January 2015) ) 40 temp_23090 temp_23083

54. Half-hourly models Probabilistic forecasting of peak electricity demand The model 25

55. Half-hourly models Probabilistic forecasting of peak electricity demand The model 25

56. Half-hourly models Probabilistic forecasting of peak electricity demand The model 25 Predictions adjusted for saturated usage.

57. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Competitions and evaluation 6 MEFM package 7 References and resources Probabilistic forecasting of peak electricity demand Forecasts 26

58. Peak demand forecasting log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Multiple alternative futures created: Calendar effects known; Future temperatures simulated (taking account of climate change); Assumed values for GSP, population and price; Residuals simulated Probabilistic forecasting of peak electricity demand Forecasts 27

59. Seasonal block bootstrapping Conventional seasonal block bootstrap Same as block bootstrap but with whole years as the blocks to preserve seasonality. But we only have about 10–15 years of data, so there is a limited number of possible bootstrap samples. Double seasonal block bootstrap Suitable when there are two seasonal periods (here we have years of 151 days and days of 48 half-hours). Divide each year into blocks of length 48m. Block 1 consists of the ﬁrst m days of the year, block 2 consists of the next m days, and so on. Bootstrap sample consists of a sample of blocks where each block may come from a different randomly selected year but must be at the correct time of year. Probabilistic forecasting of peak electricity demand Forecasts 28

66. Seasonal block bootstrapping Probabilistic forecasting of peak electricity demand Forecasts 29 Actual temperatures Days degreesC 0 10 20 30 40 50 60 10152025303540 Bootstrap temperatures (fixed blocks) Days degreesC 0 10 20 30 40 50 60 10152025303540 Bootstrap temperatures (variable blocks) 40

67. Seasonal block bootstrapping Problems with the double seasonal bootstrap Boundaries between blocks can introduce large jumps. However, only at midnight. Number of values that any given time in year is still limited to the number of years in the data set. Probabilistic forecasting of peak electricity demand Forecasts 30

68. Seasonal block bootstrapping Problems with the double seasonal bootstrap Boundaries between blocks can introduce large jumps. However, only at midnight. Number of values that any given time in year is still limited to the number of years in the data set. Probabilistic forecasting of peak electricity demand Forecasts 30

69. Seasonal block bootstrapping Variable length double seasonal block bootstrap Blocks allowed to vary in length between m − ∆ and m + ∆ days where 0 ≤ ∆ < m. Blocks allowed to move up to ∆ days from their original position. Has little effect on the overall time series patterns provided ∆ is relatively small. Use uniform distribution on (m − ∆, m + ∆) to select block length, and independent uniform distribution on (−∆, ∆) to select variation on starting position for each block. Probabilistic forecasting of peak electricity demand Forecasts 31

73. Seasonal block bootstrapping Probabilistic forecasting of peak electricity demand Forecasts 32 Actual temperatures Days degreesC 0 10 20 30 40 50 60 10152025303540 Bootstrap temperatures (fixed blocks) Days degreesC 0 10 20 30 40 50 60 10152025303540 Bootstrap temperatures (variable blocks) Days degreesC 0 10 20 30 40 50 60 10152025303540

74. Seasonal block bootstrapping Probabilistic forecasting of peak electricity demand Forecasts 32

75. Peak demand forecasting Climate change adjustments CSIRO estimates for 2030: 0.3◦ C for 10th percentile 0.9◦ C for 50th percentile 1.5◦ C for 90th percentile We implement these shifts linearly from 2010. No change in the variation in temperature. Thousands of “futures” generated using a seasonal bootstrap. Probabilistic forecasting of peak electricity demand Forecasts 33

83. Peak demand backcasting log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Multiple alternative pasts created: Calendar effects known; Past temperatures simulated; Actual values for GSP, population and price; Residuals simulated Probabilistic forecasting of peak electricity demand Forecasts 34

84. Peak demand backcasting Probabilistic forecasting of peak electricity demand Forecasts 35 PoE (seasonal interpretation, summer) Year PoEDemand(total) 2.42.62.83.03.23.43.63.8 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 10 % 50 % 90 % q q q q q q q q q q q q q q

85. Peak demand backcasting log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Multiple alternative pasts created: Calendar effects known; Past temperatures simulated; Actual values for GSP, population and price; Residuals simulated Probabilistic forecasting of peak electricity demand Forecasts 36

87. Peak demand forecasting Probabilistic forecasting of peak electricity demand Forecasts 37 Population Year 000'spersons 2000 2005 2010 2015 2020 2025 2030 2035 16002000 base low high GSP Year $million 2000 2005 2010 2015 2020 2025 2030 2035 2000035000 base low high Price Year c/kWh 2000 2005 2010 2015 2020 2025 2030 2035 1520253035 base low high

88. Peak demand distribution Probabilistic forecasting of peak electricity demand Forecasts 38 Seasonal POE levels (summer) Year PoEDemand 2.02.53.03.54.04.5 2002 2005 2008 2011 2014 2017 2020 2023 2026 2029 2032 2035 q q q q q q q q q q q q q 10 % POE 50 % POE 90 % POE Actual annual maximum

89. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Competitions and evaluation 6 MEFM package 7 References and resources Probabilistic forecasting of peak electricity demand Challenges and extensions 39

90. Challenges Some judgmental adjustments are done to account for demand response activity. We have a separate model for PV generation based on solar radiation and temperatures. But limited PV data available, so PV adjustments are probably inaccurate. Difﬁcult to account for new technology such as local storage intended to ﬂatten demand. Climate change effect is assumed additive at all temperature levels — probably simplistic. Probabilistic forecasting of peak electricity demand Challenges and extensions 40

94. Implementation Probabilistic forecasting of peak electricity demand Challenges and extensions 41 Our model is used for long-term forecasting in: Victoria’s Vision 2030 energy plan; all regions of the National Energy Market; South Western Interconnected System (WA); some local distributors.

95. Implementation Probabilistic forecasting of peak electricity demand Challenges and extensions 41 Our model is used for long-term forecasting in: Victoria’s Vision 2030 energy plan; all regions of the National Energy Market; South Western Interconnected System (WA); some local distributors. It is also used for short-term forecasting comparisons in: all regions of the National Energy Market.

96. Short-term forecasts log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Simulating temperatures and residuals is ok for long-term forecasts because short-term dynamics wash out after a few weeks. But short-term forecasts need to take account of recent temperatures and recent residuals due to serial correlation. Short-term temperature forecasts are available. Probabilistic forecasting of peak electricity demand Challenges and extensions 42

99. Short-term forecasting model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures, lagged demand) + et Lagged demand inputs Demand in last 3 hours and last 3 days; Maximum demand in past 24 hours; Minimum demand in past 24 hours; Average demand in past 7 days Each function is estimated using boosted regression splines. Probabilistic forecasting of peak electricity demand Challenges and extensions 43

100. Short-term forecasting model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures, lagged demand) + et Lagged demand inputs Demand in last 3 hours and last 3 days; Maximum demand in past 24 hours; Minimum demand in past 24 hours; Average demand in past 7 days Each function is estimated using boosted regression splines. Probabilistic forecasting of peak electricity demand Challenges and extensions 43

101. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Competitions and evaluation 6 MEFM package 7 References and resources Probabilistic forecasting of peak electricity demand Competitions and evaluation 44

102. GEFCom2012 Probabilistic forecasting of peak electricity demand Competitions and evaluation 45

103. GEFCom2012 Probabilistic forecasting of peak electricity demand Competitions and evaluation 45 Methods published in IJF, April 2014.

104. Forecast accuracy measures MAE: Mean absolute error MSE: Mean squared error MAPE: Mean absolute percentage error ¯ Good when forecasting a typical future value (e.g., the mean or median). Probabilistic forecasting of peak electricity demand Competitions and evaluation 46

108. Forecast accuracy measures MAE: Mean absolute error MSE: Mean squared error MAPE: Mean absolute percentage error ¯ Good when forecasting a typical future value (e.g., the mean or median). ¯ Useless for evaluating forecast percentiles (probability of exceedance values) and forecast distributions. Probabilistic forecasting of peak electricity demand Competitions and evaluation 46

109. Evaluating forecast distributions Probabilistic forecasting of peak electricity demand Competitions and evaluation 47 PoE (seasonal interpretation, summer) Year PoEDemand(total) 2.42.62.83.03.23.43.63.8 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 10 % 50 % 90 % q q q q q q q q q q q q q q

110. Evaluating forecast distributions Probabilistic forecasting of peak electricity demand Competitions and evaluation 47 PoE (seasonal interpretation, summer) Year PoEDemand(total) 2.42.62.83.03.23.43.63.8 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 10 % 50 % 90 % q q q q q q q q q q q q q q 12 out of 13 above 90% PoE 6 out of 13 above 50% PoE 2 out of 13 above 10% PoE

111. Forecast scoring Probabilistic forecasting of peak electricity demand Competitions and evaluation 48 0 1 2 3 4 5 6 Demand distribution Demand (GWh)

112. Forecast scoring Probabilistic forecasting of peak electricity demand Competitions and evaluation 48 0 1 2 3 4 5 6 Demand distribution Demand (GWh) 50% 50% PoE

113. Forecast scoring Probabilistic forecasting of peak electricity demand Competitions and evaluation 48 0 1 2 3 4 5 6 Demand distribution Demand (GWh) 50% 50% PoE Score for 50% PoE

114. Forecast scoring Probabilistic forecasting of peak electricity demand Competitions and evaluation 48 0 1 2 3 4 5 6 Demand distribution Demand (GWh) 50% 50% PoE Score for 50% PoE Equivalent to absolute error

121. Forecast scoring Let Qt(1), . . . , Qt(99) be the PoEs of the forecast distribution for probabilities 1%,. . . ,99%. Then the score for observation y is S(Qt(i), yt) = 1 100 i(Qt(i) − yt) if yt < Qt(i) 1 100 (100 − i)(yt − Qt(i)) if yt ≥ Qt(i) Scores are averaged over all observed data for each i to measure the accuracy of the forecasts for each percentile. Average score over all percentiles gives the best distribution forecast. Takes account of how far PoEs are exceeded. Probabilistic forecasting of peak electricity demand Competitions and evaluation 51

124. GEFCom2014 Probabilistic forecasting of demand, price, wind, and solar. Rolling forecasts with incremental data update on a weekly basis. Forecasts submitted in the form of percentiles of future distributions. Evaluation based on quantile scoring. Prizes for student teams, and for best methods. Winning methods to be published in the IJF. Probabilistic forecasting of peak electricity demand Competitions and evaluation 52

130. GEFCom2014 Load forecasting provisional leaderboard Probabilistic forecasting of peak electricity demand Competitions and evaluation 53

131. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Competitions and evaluation 6 MEFM package 7 References and resources Probabilistic forecasting of peak electricity demand MEFM package 54

132. MEFM package for R Available on github: install.packages("devtools") library(devtools) install_github("robjhyndman/MEFM-package") Package contents: seasondays The number of days in a season sa.econ Historical demographic & economic data for South Australia sa Historical data for model estimation maketemps Create lagged temperature variables demand_model Estimate the electricity demand models simulate_ddemand Temperature and demand simulation simulate_demand Simulate the electricity demand for the next season Probabilistic forecasting of peak electricity demand MEFM package 55

133. MEFM package for R Available on github: install.packages("devtools") library(devtools) install_github("robjhyndman/MEFM-package") Package contents: seasondays The number of days in a season sa.econ Historical demographic & economic data for South Australia sa Historical data for model estimation maketemps Create lagged temperature variables demand_model Estimate the electricity demand models simulate_ddemand Temperature and demand simulation simulate_demand Simulate the electricity demand for the next season Probabilistic forecasting of peak electricity demand MEFM package 55

134. MEFM package for R Usage library(MEFM) # Number of days in each "season" seasondays # Historical economic data sa.econ # Historical temperature and calendar data head(sa) tail(sa) dim(sa) # create lagged temperature variables salags <- maketemps(sa,2,48) dim(salags) head(salags) Probabilistic forecasting of peak electricity demand MEFM package 56

135. MEFM package for R # formula for annual model formula.a <- as.formula(anndemand ~ gsp + ddays + resiprice) # formulas for half-hourly model # These can be different for each half-hour formula.hh <- list() for(i in 1:48) { formula.hh[[i]] <- as.formula(log(ddemand) ~ ns(temp, df=2) + day + holiday + ns(timeofyear, df=9) + ns(avetemp, df=3) + ns(dtemp, df=3) + ns(lastmin, df=3) + ns(prevtemp1, df=2) + ns(prevtemp2, df=2) + ns(prevtemp3, df=2) + ns(prevtemp4, df=2) + ns(day1temp, df=2) + ns(day2temp, df=2) + ns(day3temp, df=2) + ns(prevdtemp1, df=3) + ns(prevdtemp2, df=3) + ns(prevdtemp3, df=3) + ns(day1dtemp, df=3)) } Probabilistic forecasting of peak electricity demand MEFM package 57

136. MEFM package for R # Fit all models sa.model <- demand_model(salags, sa.econ, formula.hh, formula.a) # Summary of annual model summary(sa.model$a) # Summary of half-hourly model at 4pm summary(sa.model$hh[[33]]) # Simulate future normalized half-hourly data simdemand <- simulate_ddemand(sa.model, sa, simyears=50) # economic forecasts, to be given by user afcast <- data.frame(pop=1694, gsp=22573, resiprice=34.65, ddays=642) # Simulate half-hourly data demand <- simulate_demand(simdemand, afcast) Probabilistic forecasting of peak electricity demand MEFM package 58

137. MEFM package for R plot(ts(demand$demand[,sample(1:100, 4)], freq=48, start=0), xlab="Days", main="Simulated demand futures") Probabilistic forecasting of peak electricity demand MEFM package 59

138. MEFM package for R plot(ts(demand$demand[,sample(1:100, 4)], freq=48, start=0), xlab="Days", main="Simulated demand futures")0.61.01.4 Series52 0.51.52.5 Series49 0.51.52.5 Series88 0.61.21.8 0 50 100 150 Series53 Days Simulated demand futures Probabilistic forecasting of peak electricity demand MEFM package 59

139. MEFM package for R plot(demand$annmax, main="Simulated seasonal maximums", ylab="GW") Probabilistic forecasting of peak electricity demand MEFM package 60

140. MEFM package for R plot(demand$annmax, main="Simulated seasonal maximums", ylab="GW") 0 20 40 60 80 100 1.52.02.53.0 Simulated seasonal maximums Index GW Probabilistic forecasting of peak electricity demand MEFM package 60

141. MEFM package for R boxplot(demand$annmax, main="Simulated seasonal maximums", xlab="GW", horizontal=TRUE) rug(demand$annmax) Probabilistic forecasting of peak electricity demand MEFM package 61

142. MEFM package for R boxplot(demand$annmax, main="Simulated seasonal maximums", xlab="GW", horizontal=TRUE) rug(demand$annmax) 1.5 2.0 2.5 3.0 Simulated seasonal maximums GW Probabilistic forecasting of peak electricity demand MEFM package 61

143. MEFM package for R plot(density(demand$annmax, bw="SJ"), xlab="Demand (GW)", main="Density of seasonal maximum demand") rug(demand$annmax) Probabilistic forecasting of peak electricity demand MEFM package 62

144. MEFM package for R plot(density(demand$annmax, bw="SJ"), xlab="Demand (GW)", main="Density of seasonal maximum demand") rug(demand$annmax) 1.5 2.0 2.5 3.0 3.5 0.00.40.81.2 Density of seasonal maximum demand Demand (GW) Density Probabilistic forecasting of peak electricity demand MEFM package 62

145. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Competitions and evaluation 6 MEFM package 7 References and resources Probabilistic forecasting of peak electricity demand References and resources 63

146. References ¯ Hyndman, R.J. & Fan, S. (2010) “Density forecasting for long-term peak electricity demand”, IEEE Transactions on Power Systems, 25(2), 1142–1153. ¯ Fan, S. & Hyndman, R.J. (2012) “Short-term load forecasting based on a semi-parametric additive model”. IEEE Transactions on Power Systems, 27(1), 134–141. ¯ Ben Taieb, S. & Hyndman, R.J. (2013) “A gradient boosting approach to the Kaggle load forecasting competition”, International Journal of Forecasting, 29(4). ¯ Hyndman, R.J., & Fan, S. (2014). “Monash Electricity Forecasting Model”. Technical paper. robjhyndman.com/working-papers/mefm/ ¯ Fan, S., & Hyndman, R.J. (2014). “MEFM: An R package imple- menting the Monash Electricity Forecasting Model.” github.com/robjhyndman/MEFM-package Probabilistic forecasting of peak electricity demand References and resources 64

147. Some resources Blogs robjhyndman.com/hyndsight/ blog.drhongtao.com/ Organizations International Institute of Forecasters: forecasters.org IEEE Working Group on Energy Forecasting: linkedin.com/groups/ IEEE-Working-Group-on-Energy-4148276 Books Dickey and Hong (2014) Electric load forecasting: fundamentals and best practices, OTexts. www.otexts.org/book/elf Probabilistic forecasting of peak electricity demand References and resources 65

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