Intra-day Electricity Demand and Temperature.

• Author: McCulloch, James

1. INTRODUCTION

   This paper introduces a parsimonious model for modelling the relationship between high frequency electricity demand and intra-day temperature. Modelling frameworks developed in the literature for high frequency electricity data suggest to either use multi-equation modelling (Cottet and Smith, 2003; Cancelo et al., 2008; Soares and Medeiros, 2008) which treats each intra-day period as a different series, or univariate time series modelling (Darbellay and Slam, 2000; Smith, 2000; Taylor, 2003, 2010, 2012; Kim, 2013) that treats the entire time series as a single series. A comprehensive overview of electricity demand forecasting models is provided in Hahn et al. (2009). The major drawback of the first methodology is that it is a more complex model that can require a large number parameters to be estimated. A univariate time series model is parsimonious and, since our primary goal is to elucidate the relationship between temperature and high frequency demand, we choose a parsimonious univariate modelling approach for demand forecasting.

   We use time of the day, time of the year and outside temperature as the main driving factors when predicting electricity demand at 5-minute frequency. To our knowledge, none of the existing research papers have incorporated these three variables simultaneously for demand forecasting at such high frequency. Temperature variations are documented to play a crucial role when forecasting electricity demand. Intuitively, during cold winter months electricity demand is expected to increase due to electrical heating, whereas during hot summer months the use of air conditioners and coolers also leads to increased electricity consumption. A non-exhaustive list of papers that deal with forecasting demand using low frequency data (typically, monthly or daily) includes Pardo et al. (2002), Moral-Carcedo and Vicens-Otero (2005), Bessec and Fouquau (2008), Hekkenberg et al. (2009), Lam et al. (2009), Tung et al. (2013), Moral-Carcedo and Perez-Garca (2015). None of these research works incorporates time of the day as an explanatory variable. Other weather variables, such as sunshine hours, rainfall, wind, humidity, cloudiness etc. are shown to have a much lower impact on electricity demand, see e.g. Basta and Helman (2013) and Moral-Carcedo and Perez-Garca (2015). Furthermore, focusing exclusively on the temperature allows us to avoid potential collinearity problems when simultaneously employing several weather variables as explanatory variables in the regression modelling (1), see e.g. Lam et al. (2009) and Moral-Carcedo and Perez-Garca (2015). Studies that have analysed intra-day (hourly) patterns in electricity demand based on the hour-of-the day and have documented the existence of this effect include Darbellay and Slam (2000), Taylor (2003), Mirasgedis et al. (2006), Soares and Medeiros (2008), Taylor (2010) and Kim (2013). The paper by Taylor (2010) also incorporates an intra-year effect.

   This paper introduces a parsimonious Generalised Additive Model (GAM) forecasting model for high frequency intra-day (5-min) aggregate electricity demand. The parsimonious model allows us to focus exclusively on modelling the link between electricity demand and human activity cycle (modelled through the time of the day), the intra-day temperature variations and time of the year. High frequency data enables us to obtain interesting and novel insights into demand forecasting. Using yearly and seasonal demand models, we document a strong relationship between high frequency electricity demand and intra-day temperature. When examining intra-day demand using daylight saving time (DST), i.e. clock time and standard (astronomical) time, we show that using the DST (clock) time provides a significant improvement to the model fit. We explain how and why model fit improves even further when we introduce the time weighted temperature model, which assigns different temperature signal weighting based on the DST time. This relates the magnitude of the temperature demand signal to the human daily activity cycle. The motivation behind using the time weighted temperature model is the observation that electricity demand attributed to temperature variation away from the maximum comfort temperature (20.0 degrees Celsius (2)) is time sensitive: Electricity consumption is less sensitive to temperature variation away from the 'comfort' temperature late at night and early in the morning, which are time periods characterised by low human activity. At the same time, electricity is more sensitive to temperature variation away from the 'comfort' during periods of high human activity. We observe that the minimum morning sensitivity is at 4:00am, the morning maximum is reached at 9:00am and the night decline begins at 18:30pm. Our proposed methodology, which suggests to weight temperature demand signal depending on the DST time (daily activity cycle) is confirmed when using cross-sectional regressions estimated at each (5-minute) time interval, resulting in cross-sectional daily time dependent demand.

   The contributions of this paper are as follows. Firstly, our results allow us to characterise the high frequency relationship between electricity consumption and temperature. To our knowledge, none of the papers in the existing literature model demand and temperature data at such high (5-minute) frequency. Secondly, we show that the sensitivity of electricity demand to temperature is a function of time of day. Daily times of low human activity such as 04:00am have a much lower demand/temperature sensitivity than a period of higher human activity as as 18:00pm. In addition, we demonstrate that when using DST (clock time) as an independent variable for electricity demand prediction, we obtain a significant improvement compared to using standard (astronomical) time.

   We emphasise that the results on DST and time weighted temperature modelling are novel in the literature and are important innovations in high frequency electricity demand forecasting. Finally, this is the first study that predicts electricity demand in Australia using both the outside temperature and time of the day.

   The parsimonious GAM model is accurate, with a MAPE (Mean Average Predicted Error) next day forecast error of 3.20%. (3) The best publicly available electricity demand forecast is the Australian Energy Market Operator (AEMO) next day forecast with a MAPE error of 2.04%. The AEMO forecasting model is not publicly available and it is reasonable to infer the AEMO forecasting model uses multivariate prediction variables with advanced but opaque forecasting techniques such as Deep Neural Networks or Gradient Boosting. The parsimonious GAM model allows for a transparent understanding of the high frequency interaction of temperature and demand and provides a solid foundation for the development of more accurate and complex forecasting models.

   The remainder of the paper is organised as follows. Section 2 describes data used in our analysis. GAM model specification and its variations tested in the paper are introduced in Section 3. An extensive empirical analysis demonstrating the quality of fit of the proposed models to the entire data set as well as seasonal models is presented in Section 4. Section 5 deals with the prediction results for the electricity demand, and Section 6 concludes the paper.

2. DATA

   This section discusses and provides some preliminary analysis on the data used in this study, which will enable us to formulate appropriate model specifications in Section 3.

   2.1 Data Description

   We use instantaneous intra-day electricity demand in Megawatts (MW), available at 5 minute frequency for the Australian state of New South Wales (NSW) and the Australian Capital Territory (ACT) for the year 3-February-2014 to 2-February-2015. Demand is aggregate data (i.e. including households, companies, industrial and public sectors) that has been downloaded from the Australian Energy Market Operator (AEMO) website. (4) The electricity demand observations are merged with instantaneous temperature data over the same period and frequency. The temperature data was obtained from the Australian Government Bureau of Meteorology. (5)

   We have restricted our consideration to business days only, (6) which results in 250 days of data and each day of data has 12*24 = 288 five minute demand observations, from 00:00-00:05 until 23:55-24:00. Thus, a total of 72,000 five-minute demand and temperature data points will be used for the empirical analysis.

   The 5-minute temperature data is recorded in the Sydney suburb of Homebush, which is a suburb located close to the population centre of the Greater Sydney urban area. If we assume that the Homebush temperature represents the instantaneous temperature in Greater Sydney, then this temperature observation is valid for 61% of population of the NSW/ACT electricity demand area.

   However, it should be noted that the assumption that we can represent temperature related electricity demand in the NSW/ACT demand area with a single temperature is a deliberate simplification to preserve the parsimonious property of our modelling. An obvious improvement to the accuracy of modelling electricity demand as a function of temperature would be to use multiple temperature (and potentially humidity) measurements from different suburban, urban and rural areas and set up an adequate average temperature index weighted by population.

   To provide an idea of the relationship between demand and temperature data, we show in Figure 1 winter and summer patterns of demand (top panel) and temperature (bottom panel) over the five business days of a typical week. In both, summer (red line, 12-January-15 to 16-January-15) and winter (blue line, 14-July-14 to 18-July-14) graphs we observe a cyclical pattern in evolution of temperature and demand throughout the week. The winter demand graph experiences two daily peaks, which correspond to an increasing usage...