Abstract
Electricity price forecasting is an interesting problem for all the agents involved in electricity market operation. For instance, every profit maximisation strategy is based on the computation of accurate one-day-ahead forecasts, which is why electricity price forecasting has been a growing field of research in recent years. In addition, the increasing concern about environmental issues has led to a high penetration of renewable energies, particularly wind. In some European countries such as Spain, Germany and Denmark, renewable energy is having a deep impact on the local power markets. In this paper, we propose an optimal model from the perspective of forecasting accuracy, and it consists of a combination of several univariate and multivariate time series methods that account for the amount of energy produced with clean energies, particularly wind and hydro, which are the most relevant renewable energy sources in the Iberian Market. This market is used to illustrate the proposed methodology, as it is one of those markets in which wind power production is more relevant in terms of its percentage of the total demand, but of course our method can be applied to any other liberalised power market. As far as our contribution is concerned, first, the methodology proposed by García-Martos et al (2007 and 2012) is generalised twofold: we allow the incorporation of wind power production and hydro reservoirs, and we do not impose the restriction of using the same model for 24 h. A computational experiment and a Design of Experiments (DOE) are performed for this purpose. Then, for those hours in which there are two or more models without statistically significant differences in terms of their forecasting accuracy, a combination of forecasts is proposed by weighting the best models (according to the DOE) and minimising the Mean Absolute Percentage Error (MAPE). The MAPE is the most popular accuracy metric for comparing electricity price forecasting models. We construct the combination of forecasts by solving several nonlinear optimisation problems that allow computation of the optimal weights for building the combination of forecasts. The results are obtained by a large computational experiment that entails calculating out-of-sample forecasts for every hour in every day in the period from January 2007 to December 2009. In addition, to reinforce the value of our methodology, we compare our results with those that appear in recent published works in the field. This comparison shows the superiority of our methodology in terms of forecasting accuracy.
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Notes
Note that short-term forecasting is our aim in this paper, as wind power is included as an explanatory variable. The extension of the forecasting horizon would only be feasible if wind power forecasting methods were able to compute accurate forecasts in the long run. Such forecasts are not possible at the moment.
A forecasting method will be defined by a Model (UMM, DFM with two common factors or DFM with three common factors). We consider the following cases: no wind power production, hourly production or daily information on this production, and considering: no hydro reservoirs data or doing so.
As in previous works, the effect of the Day is included as a block.
Models with other interactions were also considered but they were not significant. The F-statistics were smaller than one. Hence, they could be removed from the model and considered negligible.
Note that the square root of the percentage error is analysed. First, the percentage error was considered, but the diagnostic checking was not correct because the residuals were not homoscedastic. The proposed transformation solves this problem.
These methods come from the three levels of ‘Model’ (UMM, DFM with two unobserved dynamic factors and DFM with three unobserved dynamic factors), three levels of ‘Wind’ (no wind power forecasts included, hourly forecasts of wind power production and daily forecasts) and two levels of ‘Hydro’ (not including the reservoir level as exogenous variable and including it).
We use García-Martos et al. (2007, 2012), as these are the most accurate models for short-term forecasting in the Iberian Market, and their accuracy has been demonstrated not just for a few days or weeks but for large spans of years under different circumstances. Another benchmarking model is the very recent work by Cruz et al (2011), where they use several models and take into account both the wind power production and the load forecasts.
For the month of December 2007, the MAPE2, which is more robust to the presence of spikes in forecasting errors, is 9.5%, and the apparently low-quality result for this month is due to some particular spikes on Christmas Eve. Note that forecasts are computed for every day and hour in the period considered, even in the case in which the hourly price could be considered as an outlier.
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Acknowledgements
The authors would like to thank financial support from Project DPI2011-23500, Ministerio de Ciencia e Innovación, Spain.
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Appendix
Appendix
Daily MAPE statistics
Table A1 provides the basic metrics (average and standard deviation) of the daily MAPE for methods: UMM (García-Martos et al, 2007), DFM (García-Martos et al, 2012), and the Combined Forecasts method proposed in this paper, for the months from November 2007 to December 2011.
From Table A1 it is observed that not only is the average daily MAPE smaller for the combined forecasts, but also the standard deviation. (Be aware that the results here are not in percentage as in Table 1 but expressed as a per unit basis, ie, 10% is 0.1 expressed as a per unit basis.)
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García-Martos, C., Caro, E. & Jesús Sánchez, M. Electricity price forecasting accounting for renewable energies: optimal combined forecasts. J Oper Res Soc 66, 871–884 (2015). https://doi.org/10.1057/jors.2013.177
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DOI: https://doi.org/10.1057/jors.2013.177