peak half-hourly South Australia

Forecasting long-term peak half-hourly electricity demand for South Australia Dr Shu Fan B.S., M.S., Ph.D. Professor Rob J Hyndman B.Sc. (Hons), Ph.D., A.Stat. Business & Economic Forecasting Unit Report for The Australian Energy Market Operator (AEMO) Telephone: (03) 9905 2358 Fax: (03) 9905 5474 ABN: 12 377 614 012 16 July 2013

Contents Summary 3 1 The modelling improvements for the current round of forecasts 4 2 Modelling electricity demand of summer 5 3 Forecasting electricity demand of winter 28 References 43 Monash University: Business & Economic Forecasting Unit 2

Summary Australian Energy Market Operator (AEMO) prepares peak electricity demand and seasonal energy consumption forecasts for the South Australia (SA) region of the National Electricity Market (NEM). Peak electricity demand and seasonal energy consumption in South Australia is subject to a range of uncertainties. The electricity demand experienced each year will vary widely depending upon prevailing weather conditions (and the timing of those conditions) as well as the general randomness inherent in individual usage. This variability can be seen in the difference between the expected peak demand at the 1-in-10-year probability of exceedance (or 10% PoE) level and the peak demand level we expect to be exceeded 9 in 10 years (or 90% PoE). The electricity demand forecasts are subject to further uncertainty over time depending upon a range of factors including economic activity, population growth and changing customer behavior. Over the next decade we expect customer behavior to change in response to changing climate and electricity prices, to changes in technology and measures to reduce carbon intensity. Our model uses various drivers including recent temperatures at two locations (Adelaide and Edinburgh), calendar effects and some demographic and economic variables. The report uses a semi-parametric additive model to estimate the relationship between demand and the driver variables. The forecast distributions are obtained using a mixture of seasonal bootstrapping with variable length and random number generation. This report is part of Monash University s ongoing work with AEMO to develop better forecasting techniques. As such it should be read as part of a series of reports on modelling and forecasting half-hourly electricity demand. The focus of the forecasts presented in this report is Native Demand less industry demand plus PV generation. In this report, we firstly outline the improvements to the modelling work for the current round of forecast in 2013, and then we estimate the demand models with all information up to March 2013 for the summer and winter season respectively, finally we produce seasonal peak electricity demand forecasts for South Australia for the next 20 years. In SA, the annual peak tends to occur in summer season. The forecasting capacity of the demand model for each season has been verified by reproducing the historical probability distribution of demand. Monash University: Business & Economic Forecasting Unit 3

1 The modelling improvements for the current round of forecasts According to the action plan for the 2012/13 round of forecast, we have implemented the following improvements to the modelling and forecasting work, We have reviewed the previous price elasticity work for South Australia and extended to all the regions in the NEM, the findings were reported in Fan and Hyndman (2013b). Based on the findings that the customers sensitivities to price generally vary against both time of day and time of year, we have incorporated peak price elasticity s in maximum demand modelling that reflects these findings. We have analysed the load factor in each of the NEM region and discussed the implications for the peak demand forecasts in Fan and Hyndman (2013a). Measures to help address the load factor variations have been used, including the incorporation of peak price elasticity, the application of dynamic bias adjustment, and the use of simulated temperature in the energy model. We have incorporated the simulated temperature data (via heating and cooling degree days) into the seasonal demand model. This will give a better representation of the POE distribution and allow for temperature-related variations in the energy model. In our forecasts, we have used bias adjustment to address the saturation effects (i.e. of air conditioners at peak times) in the model fitting process. In the presence of potentially changing load factors, we realize that it may not be appropriate to apply a uniform bias adjustment over the whole historical data. We have investigated how the model bias has been changing over the past years, and have applied dynamic bias adjustment in the forecasts. The half-hourly load traces of PV were provided by AEMO for this round of models, allowing superior model fits (in explaining actual demand consumed) and ensuring consistency in the measures of PV used by AEMO and Monash at times of peak. Monash University: Business & Economic Forecasting Unit 4

2 Modelling electricity demand of summer 2.1 Historical data 2.1.1 Demand data AEMO provided half-hourly South Australia electricity demand values from 2000 to 2013. Each day is divided into 48 periods which correspond with NEM settlement periods. Period 1 is midnight to 0:30am Eastern Standard Time. We define the period October March as summer for the purposes of this report. Only data from October March were retained for summer analysis and modelling. All data from April September for each year were omitted. Thus, each year consists of 182 days. Time plots of the half-hourly demand data are plotted in Figures 1 3. These clearly show the intra-day pattern (of length 48) and the weekly seasonality (of length 48 7 = 336); the seasonal seasonality (of length 48 182 = 8736) is less obvious. AEMO also provided half-hourly aggregated major industrial demands for summer season which is plotted in Figure 4. Although this load can vary considerably over time, it is not temperature sensitive, thus we do not include this load in the modelling. Figure 1: Half-hourly demand data for South Australia from 2000 to 2013. Only data from October March are shown. Monash University: Business & Economic Forecasting Unit 5

SA State wide demand (summer 2013) SA State wide demand (GW) 1.5 2.0 2.5 3.0 Oct Nov Dec Jan Feb Mar Figure 2: Half-hourly demand data for South Australia for last summer. Figure 3: Half-hourly demand data for South Australia, January 2013. Monash University: Business & Economic Forecasting Unit 6

Figure 4: Half-hourly demand data for major industries. 2000 2013. AEMO also provided half-hourly values of rooftop generation for South Australia from 2009 to 2013. Figure 5: Half-hourly rooftop generation data. 2009 2013. Monash University: Business & Economic Forecasting Unit 7

2.2 Semi-parametric demand model We use a semi-parametric additive model to estimate the relationship between demand and its drivers: temperature, calendar effects, demographic variables and economic variables. The model is described in detail in Hyndman (2007a). One feature of our model is that major industrial loads are subtracted and the remaining demand is modelled using temperature, calendar and economic effects. Major industrial demand is thought to be independent of these effects and is therefore modelled separately. The model for each half-hour period can be written as log(y t,p o t,p ) = h p (t) + f p (w 1,t, w 2,t ) + g(z t ) + n t (1) where y t,p denotes the demand at time t (measured in half-hourly intervals) during period p (p = 1,..., 48); o t,p denotes the major industrial demand for time t during period p; Here, major industrial loads are subtracted and will be modelled separately. h p (t) models all calendar effects; f p (w 1,t, w 2,t ) models all temperature effects where w 1,t is a vector of recent temperatures at Adelaide and w 2,t is a vector of recent temperatures at Edinburgh; z t contains current and past demographic or economic variables and degree days at time t; (these terms do not depend on the period p); AEMO estimates the term g(z t ) and provides the projections of average quarterly demand; n t denotes the model error at time t. In particular, the function of calendar effects h p (t) includes annual, weekly and daily seasonal patterns as well as public holidays: h p (t) = α t,p + β t,p + l p (t) (2) α t,p takes a different value for each day of the week (the day of the week effect); β t,p takes value zero on a non-work day, some non-zero value on the day before a non-work day and a different value on the day after a non-work day (the holiday effect); l p (t) is a smooth function that repeats each year (the time of summer effect). The smooth function l(t) is estimated using a cubic regression spline. Monash University: Business & Economic Forecasting Unit 8

The function f p (w 1,t, w 2,t ) models the effects of recent temperatures on the demand, it includes the following terms: 6 f p (w 1,t, w 2,t ) = fk,p (x t k ) + g k,p (d t k ) + k=0 6 Fj,p (x t 48j ) + G j,p (d t 48 j ) j=1 (3) + q p (x + t ) + r p(x t ) + s p( x t ), where x t is the average temperatures across the two sites; d t is the difference in temperatures between the two sites; x + t x t is the maximum of the x t values in the past 24 hours; is the minimum of the x t values in the past 24 hours; x t is the average temperature in the past seven days. Each of the functions ( f k,p, g j,p, F k,p, G j,p, q p, r p and s p ) is assumed to be smooth and is estimated using a cubic regression spline. Another feature is that the model has been split into two separate models one linear model based on the seasonal variables (demographic and economic variables, and degree days), and the other nonparametric model based on the remaining variables which are measured at half-hourly intervals. Thus, log(y t,p o t,p ) = log(y t,p ) + log(ȳ i) where ȳ i is the average non-offset demand for each year in which time period t falls, and y t,p is the standardized non-offset demand for time t and period p. Monash University: Business & Economic Forecasting Unit 9

Figure 6: Top: Half-hourly demand data for South Australia from 2000 to 2013. Bottom: Adjusted half-hourly demand where each year of demand is normalized by seasonal average demand. Only data from October March are shown. Monash University: Business & Economic Forecasting Unit 10

The top panel of Figure 6 shows the original demand data with the average seasonal demand values shown in red, and the bottom panel shows the half-hourly adjusted demand data. Then log(y t,p ) = h p(t) + f p (w 1,t, w 2,t ) + e t (4) and log(ȳ pc i ) = g(z t ) + ɛ i (5) where ȳ pc i is the per-capita seasonal average demand. Note that per-capita demand (demand/population) and per-capita GSP (GSP/population) are considered in the seasonal model, so as to allow for both population and economic changes in the model. For half-hourly demand, the log value is modelled, rather than the raw demand figures as we found that the logarithm resulted in the best fit to the available half-hourly data, and natural logarithms have been used in all calculations. One of our findings in the price elasticity report (Fan and Hyndman, 2013b) is that the price coefficients vary for different demand quantiles. For instance, the overall price elasticity coefficient for annual average demand was 0.12, while the median value of price elasticity coefficients estimated at the 95% demand quantile was 0.08, indicating price elasticity of peak demand is smaller than the price elasticity applying to annual average demand. In this report, therefore, we will apply this finding to adjust the price coefficient of annual when estimating the peak electricity demand. Specifically, the adjusted price coefficient is c p = c p 0.08/0.12, where c p price coefficient is the original coefficient. Monash University: Business & Economic Forecasting Unit 11

2.2.1 Temperature data and degree days AEMO provided half-hourly temperature data for Adelaide and Edinburgh, from 2000 to 2013. The relationship between demand (excluding major industrial loads) and temperature is shown in Figure 7. Figure 7: Half-hourly SA electricity demand (excluding major industrial demand) plotted against average temperature (degrees Celsius). The half-hourly temperatures are used to calculate cooling degree days in summer and heating degree days in winter, which will be considered in the seasonal demand model. For each day, the cooling degrees is defined as the difference between the mean temperature (mean value of Adelaide and Edinburgh average temperature for each day) and 17.5 C. If this difference is negative, the cooling degrees is set to zero. These values are added up for each summer to give the cooling degree-days for the summer, that is, CD = max(0, t mean 17.5 ). summer Accordingly, the heating degrees is defined as the difference between 19.5 C and the mean temperature for each day. If this difference is negative, the heating degrees is set to zero. These values are Monash University: Business & Economic Forecasting Unit 12

added up for each winter to give the heating degree-days for the winter, HD = max(0, 19.5 t mean ). winter Monash University: Business & Economic Forecasting Unit 13

2.2.2 Variable selection of half-hourly demand model We fit a separate model to the data from each half-hourly period. Specific features of the models we consider are summarized below. We model the logarithm of adjusted demand rather than raw demand values. Better forecasts were obtained this way and the model is easy to interpret as the temperature and calendar variable have a multiplicative effect on demand. Temperature effects are modelled using additive regression splines. The following temperatures & calendar variables are considered in the model 1, Temperatures from the last three hours and the same period from the last six days; The maximum temperature in the last 24 hours, the minimum temperature in the last 24 hours, and the average temperature in the last seven days; Calendar effects include the day of the week, public holidays, days just before or just after public holidays, and the time of the year. The best model that was obtained (based on the out-of-sample MSE for the afternoons of the summer 2011/2012 and 2012/2013) contained the following variables: the current temperature and temperatures in the last 3 hours; temperatures for the same time period in the last 3 days; the current temperature differential; temperatures differential for the same time period in the last 4 days; the minimum temperature in the last 24 hours; the average temperature in the last seven days; the maximum temperature in the last 24 hours; the day of the week; the holiday effect; the day of season effect. Depending on the time of day, the fitted model explains up to 93% of the variation in the half-hourly demand data. The remaining variation is due to natural randomness and variation in variables that are not in the model (and may not be measurable). Figure 8 shows the R 2 values for each half-hourly model showing the amount of variation in the demand data that is explained with each model. Because temperature is a stronger driver during working hours, the R 2 values are higher during this period, which is also the peak period of electricity demand. Monash University: Business & Economic Forecasting Unit 14

R squared (%) 40 50 60 70 80 90 100 R squared 12 midnight 3:00 am 6:00 am 9:00 am 12 noon 3:00 pm 6:00 pm 9:00 pm 12 midnight Time of day Figure 8: The R 2 values for each half-hourly model showing the amount of variation in the demand data that is explained with each model. Some of the fitted terms of the model at 3pm are plotted in Figure 9 and Figure 10. These show the marginal effect of each variable on the log demand after accounting for all the other variables in the model. The dashed lines show 95% confidence intervals around each line. Monash University: Business & Economic Forecasting Unit 15

Time: 3:00 pm Effect on demand 0.4 0.2 0.0 0.2 0.4 Effect on demand 0.4 0.2 0.0 0.2 0.4 0 50 100 150 Day of season Mon Tue Wed Thu Fri Sat Sun Day of week Effect on demand 0.4 0.2 0.0 0.2 0.4 Normal Holiday Day after Holiday Figure 9: Calendar terms in the fitted model at 3pm. Monash University: Business & Economic Forecasting Unit 16

Time: 3:00 pm Effect on demand 0.4 0.2 0.0 0.2 0.4 Effect on demand 0.4 0.2 0.0 0.2 0.4 10 15 20 25 30 35 40 45 15 10 5 0 5 Temperature Temperature differential Effect on demand 0.4 0.2 0.0 0.2 0.4 10 15 20 25 30 35 Last week average temp Figure 10: Temperature terms in the fitted model at 3pm. Monash University: Business & Economic Forecasting Unit 17

2.3 Model predictive capacity We investigate the predictive capacity of the model by looking at the fitted values. Figure 11 shows the actual historical demand (top) and the fitted (or predicted) demands. Figure 12 illustrates the model prediction for January 2013. It can be seen that the fitted values follow the actual demand remarkable well, indicating that the vast majority of the variation in the data has been accounted for through the driver variables. Both fitted and actual values shown here are after the major industrial load has been subtracted from the data. Actual demand (summer) 1.0 1.5 2.0 2.5 3.0 3.5 2000 2002 2004 2006 2008 2010 2012 Time Predicted demand (summer) 1.0 1.5 2.0 2.5 3.0 3.5 2000 2002 2004 2006 2008 2010 2012 Time Figure 11: Time plots of actual and predicted demand before adjustment. Note that these predicted values are not true forecasts as the demand values from these periods were used in constructing the statistical model. Consequently, they tend to be more accurate than what is possible using true forecasts. Monash University: Business & Economic Forecasting Unit 18

Demand (January 2013) SA demand (GW) 0 1 2 3 4 5 Actual Predicted 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Temperature (deg C) 10 20 30 40 50 Adelaide Edinburgh Date in January Temperatures (January 2013) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Date in January Figure 12: Actual and predicted demand before adjustment for January 2013. Monash University: Business & Economic Forecasting Unit 19

2.4 Half-hourly model residuals The time plot of the half-hourly residuals from the demand model is shown in Figure 13. Figure 13: Half-hourly residuals (actual predicted) from the demand model before adjustment. Next we plot the half-hourly residuals against the predicted adjusted log demand in Figure 14. That is, we plot e t against log(y t,p ) where these variables are defined in Model (4). In the presence of potentially changing load factors, we have investigated how the model bias has been changing over the past years, that is, we plot the half-hourly residuals against the predicted adjusted log demand for different periods separately, and the results are shown in Figure 14. Here we observe a negative bias for the largest demand predictions (where the predicted log adjusted demand is greater than 0.3) for the early years (from 2000 to 2005). This is evident by the blue line a loess curve (Cleveland and Devlin, 1988) estimating the average of the residuals as a function of the predicted adjusted log-demand. Similarity, we observe a negative bias for the largest demand predictions for the recent years (from 2006 to 2012). The negative bias for large demand predictions means that the model tends to overestimate the peak demand. When we simulate the residuals by re-sampling in the forecasting procedure, therefore, we will adjust the residuals according to the relationship between the model residuals and fitted demands as shown in Figure 14, in particular, we will make the bias adjustment following the blue loess curve. Monash University: Business & Economic Forecasting Unit 20

Figure 14: Residuals vs predicted log adjusted demand from model (4). The blue line is an estimate of the bias in the model. We found that the majority of the extreme negative biases for the recent years came from summer 2009, during which there were extreme weather conditions. Specifically, the model appears to have predicted that demand would keep on climbing as temperatures rose higher and higher, but this did not occur in reality. After discussion with AEMO, we think that the record breaking temperatures experienced in late January 2009 may have resulted in "saturation of demand" that is, air conditioners and other cooling appliances throughout the entire State were working as hard as they could, meaning that further increases in temperature did not elicit higher levels of demand. As this phenomenon has never been seen before, and the temperature data underlying model has not been this high before, the model was not equipped to capture the apparent plateauing of demand. Monash University: Business & Economic Forecasting Unit 21

Based on the above observation, we realize that it is not appropriate to apply a uniform bias adjustment over the whole historical data, instead, we will apply piecewise bias adjustments for different historical time periods. In the forecasting procedure, we will apply the bias adjustment to the forecasts following the blue loess curve of the most recent years. This procedure (investigate the changing pattern of the model residuals incorporating the newest data) will be reviewed in each new round of forecast so that dynamic bias adjustments can be achieved to reflect the newest changes in demand. Monash University: Business & Economic Forecasting Unit 22

2.5 Demand forecasting Forecasts of the distribution of demand are computed by simulation from the fitted model as described in (Hyndman, 2007b). The temperatures at Adelaide and Edinburgh are simulated from historical values observed in 2000 2013 using a double seasonal bootstrap with variable length as described in (Hyndman and Fan, 2008). The temperature bootstrap is designed to capture the serial correlation that is present in the data due to weather systems moving across South Australia. We also add a small amount of noise to the simulated temperature data to allow temperatures to be as high as any observed since 1900. A total of more than 1000 years of temperature profiles were generated in this way for each year to be forecast. In this report, some simple climate change adjustments are made to allow for the possible effects of global warming. Estimates were taken from CSIRO modelling (Climate Change in Australia). The shifts in temperature till 2030 are predicted to be 0.3 C, 0.9 C and 1.5 C for the 10th percentile, 50th percentile and 90th percentile respectively (CSIRO, 2009). The temperature projections are given relative to the period 1980 1999 (referred to as the 1990 baseline for convenience). These shifts are implemented linearly from 2013 to 2033. CSIRO predicts that the change in the standard deviation of temperature will be minimal in Australia. This matches work by (Räisänen, 2002). Three different scenarios for population, GSP, major industrial loads and average price are considered. The simulated temperatures, known calendar effects, assumed values of GSP, electricity price and major industrial demand and simulated residuals are all combined using the fitted statistical model to give simulated electricity demand for every half-hourly period in the years to be forecast. Thus, we are predicting what could happen in the years 2013/14 2032/33 under these fixed economic and demographic conditions, but allowing for random variation in temperature events and other conditions. Monash University: Business & Economic Forecasting Unit 23

2.5.1 Probability distributions In this report, we calculate the forecast distributions of the half-hourly demand for the seasonal non-industrial maximum half-hourly demand. Figure 15 shows the simulated seasonal maximum demand densities for 2013/2014 2032/2033, and Figure 16 shows quantiles of prediction of seasonal maximum demand. Monash University: Business & Economic Forecasting Unit 24

Low Base Density 0.0 0.5 1.0 1.5 2.0 Density 0.0 0.5 1.0 1.5 2.0 2 3 4 5 6 Demand (GW) High 2 3 4 5 6 Demand (GW) Density 0.0 0.5 1.0 1.5 2.0 2013/2014 2014/2015 2015/2016 2016/2017 2017/2018 2018/2019 2019/2020 2020/2021 2021/2022 2022/2023 2023/2024 2024/2025 2025/2026 2026/2027 2027/2028 2028/2029 2029/2030 2030/2031 2031/2032 2032/2033 2 3 4 5 6 Demand (GW) Figure 15: Distribution of simulated seasonal maximum demand for 2013/2014 2032/2033. Monash University: Business & Economic Forecasting Unit 25

Percentage 0 20 40 60 80 100 Low Percentage 0 20 40 60 80 100 Base 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Percentage 0 20 40 60 80 100 Quantile High Quantile 2013/2014 2014/2015 2015/2016 2016/2017 2017/2018 2018/2019 2019/2020 2020/2021 2021/2022 2022/2023 2023/2024 2024/2025 2025/2026 2026/2027 2027/2028 2028/2029 2029/2030 2030/2031 2031/2032 2032/2033 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Quantile Figure 16: Quantiles of prediction of seasonal maximum demand for 2013/2014 2032/2033. Monash University: Business & Economic Forecasting Unit 26

2.5.2 Probability of exceedance AEMO also requires calculation of probability of exceedance levels. These can now be obtained from the simulated data. Suppose we are interested in the level x such that the probability of demand exceeding x over a 1-year period is p. There are several ways of interpreting this depending on what is intended. First, we can find x such that q = 1 p/(182 48) is the probability of any randomly chosen half-hour period having demand less than x. We simulate half-hourly demand values for each year, then we can estimate x as the qth quantile of the distribution of the simulated demand values using the approach recommended by (Hyndman and Fan, 1996). Note that even if p = 100%, the value of q is very large. A value of p = 100% means that in 100 years of simulations, we would expect the PoE to be exceeded 100 times. Because of the serial correlation in the demand data, this is still a very infrequent event. In fact, in the 11 years of observed data, the 100% PoE has not been exceeded. This apparent paradox is due to the serial correlation in the data. If the demand in a given half-hour period exceeds 2.8 GW (for example), then it is highly likely that nearby periods will also exceed 2.8 GW. Thus the true probability of such an event is much less than the stated PoE implies. In other words, when the 100% PoE is eventually exceeded, it is likely to be exceeded several times during the same temperature event. An alternative and more natural interpretation looks at the probability of the seasonal maximum exceeding x. If Y 1,..., Y m denote m simulated seasonal maxima from a given year, then we can estimate x as the qth quantile of the distribution of {Y 1,..., Y m } where q = 1 p. The PoE values based on the seasonal maxima are not subject to the same problem of serial correlation because demand values one-year apart should be independent. It should be noted that all of the PoE values given in the tables in this report are conditional on the economic and demographic driver variables observed in those years. They are also conditional on the fitted model. However, they are not conditional on the observed temperatures. They take into account the possibility of different temperature patterns from those observed. Monash University: Business & Economic Forecasting Unit 27

3 Forecasting electricity demand of winter 3.1 Historical data We define the period April September as winter for the purposes of this report. Only data from April September were retained for analysis and modelling winter demand. Thus, each year consists of 183 days. Time plots of the half-hourly demand data are plotted in Figures 17 19. These clearly show the intra-day pattern (of length 48) and the weekly seasonality (of length 48 7 = 336); the seasonal seasonality (of length 48 183 = 8784) is less obvious. The half-hourly aggregated major industrial demand is given in Figure 20. AEMO also provided half-hourly values of rooftop generation for South Australia from 2009 to 2013. The relationship between demand (excluding major industrial loads) and temperature is shown in Figure 22. To fit the model to the demand excluding major industrial loads, we normalize the half-hourly demand against seasonal average demand of each year. The top panel of Figure 23 shows the original Figure 17: Half-hourly demand data for South Australia from 2000 to 2013. Only data from April September are shown. Monash University: Business & Economic Forecasting Unit 28

SA State wide demand (winter 2012) SA State wide demand (GW) 1.2 1.4 1.6 1.8 2.0 2.2 2.4 Apr May Jun Jul Aug Sept Figure 18: Half-hourly demand data for South Australia for last winter. Figure 19: Half-hourly demand data for South Australia, July 2012. Monash University: Business & Economic Forecasting Unit 29

Figure 20: Half-hourly demand data for aggregated major industries from 2000 to 2013. Figure 21: Half-hourly rooftop generation data. 2009 2013. Monash University: Business & Economic Forecasting Unit 30

Figure 22: Half-hourly SA electricity demand (excluding major industrial demand) plotted against average temperature (degrees Celsius). demand data with the average seasonal demand values shown in red, and the bottom panel shows the half-hourly adjusted demand data. Monash University: Business & Economic Forecasting Unit 31

Figure 23: Top: Half-hourly demand data for South Australia from 2000 to 2013. Bottom: Adjusted half-hourly demand where each year of demand is normalized against seasonal average demand. Only data from April September are shown. Monash University: Business & Economic Forecasting Unit 32

3.2 Variable selection of half-hourly model We apply the same variable selection procedure for estimating the half hourly demand model for winter season. The best temperature/calendar model that was obtained (based on the out-of-sample MSE for the afternoons of the 2011 and 2012 winter) contained the following variables: the current temperature and temperatures from the last 2.5 hours; temperatures from the same time period for the last 4 days; the current temperature differential and temperature differentials from the last 2 hours; the maximum temperature in the last 24 hours; the minimum temperature in the last 24 hours; the average temperature in the last 24 hours; the day of the week; the holiday effect; the day of season effect. Depending on the time of day, the fitted model explains up to 96% of the variation in the half-hourly demand data. The remaining variation is due to natural randomness and variation in variables that are not in the model (and may not be measurable). Figure 24 shows the R 2 values for each half-hourly model showing the amount of variation in the demand data that is explained with each model. Because temperature is a stronger driver during working hours, the R 2 values are higher during this period. Monash University: Business & Economic Forecasting Unit 33

R squared (%) 40 50 60 70 80 90 100 R squared 12 midnight 3:00 am 6:00 am 9:00 am 12 noon 3:00 pm 6:00 pm 9:00 pm 12 midnight Time of day Figure 24: The R 2 values for each half-hourly model showing the amount of variation in the demand data that is explained with each model. Monash University: Business & Economic Forecasting Unit 34

3.3 Model predictive capacity We investigate the predictive capacity of the model by looking at the fitted values. As the adjustments to the half-hourly residuals are small for winter model, we only plot the model fitting performance without the adjustments here. Figure 25 shows the actual historical demand (top) and the fitted (or predicted) demands for the entire winter season. Figure 26 illustrates the model prediction for July 2012. It can be seen that the actual and fitted values are almost indistinguishable, indicating that the vast majority of the variation in the data has been accounted for through the driver variables. Both fitted and actual values shown here are after the major industrial load has been subtracted from the data. Actual demand (winter) 1.0 1.5 2.0 2000 2002 2004 2006 2008 2010 2012 Time Predicted demand (winter) 1.0 1.5 2.0 2000 2002 2004 2006 2008 2010 2012 Time Figure 25: Time plots of actual and predicted demand before adjustment. Monash University: Business & Economic Forecasting Unit 35

SA demand (GW) 0 1 2 3 4 Actual Predicted Demand (July 2012) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Temperature (deg C) 0 5 10 15 20 Adelaide Edinburgh Date in July Temperatures (July 2012) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Date in July Figure 26: Actual and predicted demand before adjustment for July 2012. Monash University: Business & Economic Forecasting Unit 36

Note that these predicted values are not true forecasts as the demand values from these periods were used in constructing the statistical model. Consequently, they tend to be more accurate than what is possible using true forecasts. Monash University: Business & Economic Forecasting Unit 37

3.4 Half-hourly model residuals The time plot of the half-hourly residuals from the demand model is shown in Figure 27. Figure 27: Half-hourly residuals (actual predicted) from the demand model before adjustment. Next we plot the half-hourly residuals against the predicted adjusted log demand in Figure 28. That is, we plot e t against log(y t,p ) where these variables are defined in Model (4). The results are shown in Figure 28. Here we observe a small positive bias for the largest demand predictions (where the predicted log adjusted demand is greater than 0.3) for the early years (from 2000 to 2005). This is evident by the blue line a loess curve (Cleveland and Devlin, 1988) estimating the average of the residuals as a function of the predicted adjusted log-demand. On the other hand, the bias for the largest demand predictions for the recent years (from 2006 to 2012) is trivial. We will apply the bias adjustment to the forecasts according to the results of the most recent years. Monash University: Business & Economic Forecasting Unit 38

Figure 28: Residuals vs predicted log adjusted demand from model (4). The blue line is an estimate of the bias in the model. Monash University: Business & Economic Forecasting Unit 39

3.5 Demand forecasting 3.5.1 Probability distributions In this report, we calculate the forecast distributions of the half-hourly demand for the seasonal non-industrial maximum half-hourly demand. Figure 29 shows the simulated seasonal maximum demand densities for 2013 2032, and Figure 30 shows quantiles of prediction of seasonal maximum demand. Monash University: Business & Economic Forecasting Unit 40

Low Base Density 0 1 2 3 4 5 Density 0 1 2 3 4 5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Demand (GW) High Demand (GW) Density 0 1 2 3 4 5 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Demand (GW) Figure 29: Distribution of simulated seasonal maximum demand for 2013 2032. Monash University: Business & Economic Forecasting Unit 41

Percentage 0 20 40 60 80 100 Low Percentage 0 20 40 60 80 100 Base 2.0 2.5 3.0 3.5 4.0 2.0 2.5 3.0 3.5 4.0 Percentage 0 20 40 60 80 100 Quantile High Quantile 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2.0 2.5 3.0 3.5 4.0 Quantile Figure 30: Quantiles of prediction of seasonal maximum demand for 2013 2032. Monash University: Business & Economic Forecasting Unit 42

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