African Journal of Business Management Vol. 6 (9), pp. 3246-3252, 7 March, 2012 Available online at http://www.academicjournals.org/AJBM DOI: 10.5897/AJBM11.1752 ISSN 1993-8233 ©2012 Academic Journals
Full Length Research Paper
Daily electricity demand forecasting in South Africa N. A. Makukule, C. Sigauke* and M. Lesaoana Department of Statistics and Operations Research, School of Mathematical and Computer Sciences, University of Limpopo, Turfloop Campus, P. Bag X1106, Sovenga, 0727. South Africa. Accepted 9 December, 2011
The paper investigates the impact of day of the week, holidays and other seasonal effects on daily electricity demand in South Africa using regression, seasonal autoregressive integrated moving average (SARIMA) and regression model with SARIMA (RegSARIMA) models for the period 2001 to 2009. The results from this study show that the SARIMA model produces better forecast accuracy with a mean absolute percent error (MAPE) of 1.36%. The RegSARIMA model had a MAPE of 1.75%. From these model results, we can conclude that, holidays play a major role in determining the demand of electricity. Key words: SARIMA, RegSARIMA, regression, seasonality, short-term forecasting. INTRODUCTION South Africa is a nation with diverse origins, languages, beliefs and cultures. It has a population estimation of 50 million people within its nine provinces, all dependent on Eskom for electricity supply. The efficient use of electricity has become a national priority, a necessity for the future development of the South African economy and effective provision of electricity. Forecasting electricity demand constitutes a vital part of energy policy of a country, especially for a developing country like South Africa whose electricity demand has grown rapidly over the past decade. There are various factors that influence the daily energy demand and among these are calendar effects, economic factors, interest rates and inflation and meteorological factors. In this paper, the seasonal autoregressive integrated moving average (SARIMA) and regression model with SARIMA errors commonly known as RegSARIMA models are developed. RegSARIMA models are models in which the mean function of the time series is described by a linear combination of the regressors and the covariance structure of the series is that of the SARIMA process. The RegSARIMA modeling approach captures important factors such as day of the week, holidays, daily and
*Corresponding author. E-mail:
[email protected]. Tel: +27 15 268 2188.
monthly seasonality effects, including weather effects such as temperature. These factors are known to influence daily electricity demand. Electricity demand forecasting has been studied extensively over the years using classical time series (Harvey and Kooppman, 1993; Ramanathan et al., 1997; Granger and Jeon, 2007; Tsekouras et al., 2007; Aguirre et al., 2008; Amaral et al., 2008; Amarawickrama and Hunt, 2008; Amusa et al., 2009; Gaunt, 2008; Ghosh, 2008; Soares and Medeiros, 2008; Taylor, 2008; Truong et al., 2008; Ismail et al., 2009; Sumer et al., 2009; Zhang et al., 2009; Ziramba, 2008; Goia et al., 2010) and using artificial and computational intelligence (Hongxiao et al., 2004; Azadeh et al., 2007; Amin-Naseri and Soroush, 2008; Gonzlez-Romera et al., 2008; Neto and Fiorelli, 2008; Wang et al., 2009). Updated review of different methods can be found in Feinberg and Genethliou (2005), and Hahn et al. (2009). DATA The data considered in this study is the daily electricity demand (DED) from distribution in response to some demand of electrical power. Electrical demand is bounded by the power plants available to provide supply at any time of the day including the need for reserve capacity. This DED includes the demand from people, industries etc, who are willing and able to pay for
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Figure 1. Time series plot of daily electricity demand for the period 01-01-01 to 14-12-09.
electricity but currently do not have access to electrical power. We concentrate on DED from 01 January 2001 to 14 December 2009 recorded in South Africa. Figure 1 shows a graphical plot of the daily electricity demand with a positive linear trend that is not stationary and some strong seasonality. We stationarise through differencing.
MODELS In this section we use classical time series methods in forecasting daily demand of electricity in South Africa. The methods are regression, SARIMA and RegSARIMA models. The developed models are used for predictions of out of sample forecasts. We concentrate on DED recorded in South Africa from 01 January to 14 December 2009.
Regression model The estimated model can be written as: y = β + β t + ∑ α D + ∑ γ M + ωH + δH + λH + Z (1) where β ; β ; α ,d = 2, 3, … ,7; γ, m = 2,3, … ,12 ; ω; δ and λ are constants; t is the trend component; D is a day of the week, and d = Tue, . . . , Sun; M is a month of the year, where m = Feb, . . . ,Dec; H is a day before holiday; H is a holiday; H is a day after holiday; Z is a random error term; y is the daily energy sent out. In order to capture day of the week effect, quantitative variable day of the week has been introduced into the model through the specification of six dummy variables (D ) representing all days in a week (Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday), where we take Monday as the base. That is; D =
1 0
if d = Tue, Wed, … , Sun Otherwise
,
(2)
In order to capture holiday effects, three additional dummy variables were introduced, representing holiday, day before holiday
and day after holiday. First dummy variable H , which measures the effect of the holiday, is also added in the model. H =
1 0
if day is a holiday Otherwise
,
(3)
Second dummy variable H , which measures the effects of a day before holiday, is also added to the model. H =
1 0
if day before holiday Otherwise
H =
1 0
if day after holiday Otherwise
,
(4)
Another variable introduced is H that takes a value of 1 when the observation corresponds to a day after holiday and 0 otherwise. ,
(5)
These two variables, H and H are introduced to measure the impact of the proximity of holidays to daily electricity demand. If a holiday falls on a weekend the following Monday is declared a public holiday. We do not consider school holidays in this study. To account for the monthly seasonality, eleven dummy variables (M ) are introduced, each representing one of the months in a year and January as the base month. Thus, m refers to month of February, March until December. M equals 1 if the month m is found in observation t and 0 otherwise. That is M = 1 0
if m is not January Otherwise
, for t = 1,2, … , n
(6)
where t = 1, 2, 3,…,3270 and t = 1 represents 01/01/2001 and t = 3270 represents 14/12/2009.
SARIMA model Seasonal autoregressive integrated moving average (SARIMA) model can be expressed in factored form by the notation SARIMA (p, d, q) × (P, D, Q)s. The general SARIMA model can be presented analytically as: 5 2(Β)Φ(Β5 )∇7 ∇ 8 5 9: = ;(Β)Θ(Β )
