Forecasting medium-term electricity demand in a South African electric power supply system

Caston Sigauke

Abstract


The paper discusses an application of generalised additive models (GAMs) in predicting medium-term hourly electricity demand using South African data for 2009 to 2013. Variable selection was done using least absolute shrinkage and selection operator (Lasso) via hierarchical interactions, resulting in a model called GAM-Lasso. The GAM-Lasso model was then extended by including tensor product interactions to yield a second model, called GAM- -Lasso. Comparative analyses of these two models were done with a gradient-boosting model to act as a benchmark model and the third model. The forecasts from the three models were combined using a forecast combination algorithm where the average loss suffered by the models was based on the pinball loss function. The results showed significantly improved accuracy of forecasts, making this study a useful tool for decision-makers and system operators in power utility companies, particularly in maintenance planning including medium-term risk assessment. A major contribution of this paper is the inclusion of a nonlinear trend. Another contribution is the inclusion of temperature based on two thermal regions of South Africa.


Keywords


Elastic net, electricity demand, generalized additive models, LASSO

Full Text:

PDF

References


Bates, J.M. and Granger, C.W.J. The combination of forecasts. Operational Research, 1969, 20(4): 451– 468.

Bien, J., Taylor, J. and Tibshirani, R. A Lasso for hierarchical interactions. Annals of Statistics, 2013, 41(3): 1111–1141.

Chikobvu, D. and Sigauke, C. Modelling influence of temperature on daily peak electricity demand in South Africa. Journal of Energy in Southern Africa, 2013, 24(4): 63–70.

Clemen, R.T. Combining forecasts: A review and annotated bibliography. International Journal of Forecasting, 1989, 5: 559–583.

Debba, P., Koen, R., Holloway, J.P., Magadla, T., Rasuba, M., Khuluse, S. and Elphinstone, C.D. 2010.

Forecasts for electricity demand in South Africa (2010–2035) using the CSIR sectoral regression model. Available online at http://www.energy.gov.za/IRP/ irp%20files/CSIR_model_IRP%20forecasts% 202010_final_v2.pdf

Devaine, M., Gaillard, P., Goude, Y. and Stoltz, G. Forecasting the electricity consumption by aggregating specialized experts: A review of sequential aggregation of specialized experts, with an application to Slovakian and French country-wide one-day-ahead (half-) hourly predictions. Machine Learning, 2012, 90: 231–260.

Fan, S. and Hyndman, R.J. Short-term load forecasting based on a semi-parametric additive model. IEEE Transactions on Power Systems, 2012, 27(1): 134–141.

Fasiolo, M., Goude, Y., Nedellec, R. and Wood, S. N. Fast calibrated additive quantile regression, 2017. Available online at https://arxiv.org/abs/1707.03307 (accessed 10 November 2017).

Friedman, J.H. Multivariate adaptive regression splines. The Annals of Statistics, 1991, 19(1): 1–141.

Friedman, J., Hastie, T., Simon, N. and Tibshirani, R. Lasso and elastic-net regularized generalized linear models: glmnet r package version 2.0-10, 2017. Available online at https://cran.r-project.org/web/ packages/glmnet/glmnet.pdf (Accessed on 7 May March 2017).

Gaillard, P. Contributions to online robust aggregation: Work on the approximation error and on probabilistic forecasting. PhD Thesis, 2015, University Paris-Sud, France.

Gaillard, P., Goude, Y. and Nedellec, R. Additive models and robust aggregation for GEFcom2014 probabilistic electric load and electricity price forecasting. International Journal of forecasting, 2016, 32: 1038-1050.

Goude, Y., Nedellec, R. and Kong, N. Local short and middle term electricity load forecasting with semi-parametric additive models. IEEE Transactions on Smart Grid, 2014, 5(1):440- 446.

Hastie T. and Tibshirani, R. Generalized additive models (with discussion). Statistical Science, 1986, 1: 297–318.

Hastie, T. and Tibshirani, R. Generalized additive models, 1990, Chapman & Hall.

Hong T. and Fan S. Probabilistic electric load forecasting: A tutorial review. International Journal of

Forecasting, 2016, 32: 914–938.

Hong, T., Pinson, P., Fan, S., Zareipour, H., Troccoli, A. and Hyndman, R.J. Probabilistic energy forecasting: Global Energy Forecasting Competition 2014 and beyond. International Journal of Forecasting, 2016; 32(3): 896–913.

Hyndman, R.J. and Fan, S. Density forecasting for long-term peak electricity demand, IEEE Transactions on Power Systems, 2010, 25(2): 1142–1153.

Hyndman, R.J. and Athanasopoulos, G. Forecasting: principles and practice, 2013. Available online at https://www.otexts.org/fpp/9/1 (accessed 26 March 2017).

Hyndman, R.J. forecast: Forecasting functions for time series and linear models. R package version 8.1, 2017. Available online at http://github.com/robjhyndman/forecast.

Laurinec P. Doing magic and analyzing seasonal time series with GAM (Generalized Additive Model) in R, 2017. Available online at https://petolau.github.io/ Analyzing-double-seasonal-time-series-with-GAM-in-R/ (accessed 23 February 2017).

Meier, L., van de Geer, S. and Bu ̈hlman, P. The group lasso for logistic regression. Journal of the Royal Statistical Society B, 2008, 70(1): 53–71.

Munoz, A., Sanchez-Ubeda, E.F., Cruz, A. and Marin, J. Short-term forecasting in power systems: a guided tour. Energy Systems, 2010, 2: 129–160.

Pierrot, A. and Goude, Y. Short-term electricity load forecasting with generalized additive models. Proceedings of ISAP Power, 2011: 593–600.

Sigauke, C. and Chikobvu, D. Short-term peak electricity demand in South Africa. African Journal of Business Management. 2012, 6(32): 9243–9249.

Sigauke, C., Verster, A. and Chikobvu, D. Extreme daily increases in peak electricity demand: Tail-quantile estimation. Energy Policy, 2013, 53: 90–96.

Shaub, D. and Ellis, P. Convenient functions for ensemble time series forecasts. R package version 1.1.9, 2017. Available online at https://cran.r-project.org/ web/packages/forecastHybrid/forecastHybrid.pdf.

Simpson, G. Modelling seasonal data with GAMs, 2014. Available online at http://www.fromthebottomoftheheap.net/2014/05/09/modelling-seasonal-data-with-gam/ (accessed 26 February 2017).

Takeda, H., Tamura, Y. and Sato, S. Using the ensemble Kalman filter for electricity load forecasting and analysis. Energy, 2016, 104: 184–198.

Tibshirani, R. Regression shrinkage and selection via lasso. Journal of the Royal Statistical Society. Series B (methodology), 1996, 58(1): 267–288.

Van Buuren, S. and Groothuis-Oudshoorn, K. MICE: Multivariate imputation by chained equations in R. Journal of Statistical Software, 2011, 45(3): 1–67.

Wheeler M.W. Bayesian additive adaptive basis tensor product models for modelling high dimensional

surfaces: An application to high-throughput toxicity testing, 2017. Available online at https://arxiv.org/abs/ 1702.04775 (accessed 4 April 2017).

Wood, S. Generalized additive models: An introduction with R, 2006, London: Chapman and Hall.

Wood, S. MGCV r package, version 1.8-17, 2017. Available online at https://cran.r-project.org/web/packages/mgcv/index.html (accessed 15 February 2017).

Wood, S. P-splines with derivative based penalties and tensor product smoothing of unevenly distributed data. Statistics and Computing, 2017, 27: 985–989.

Xie, J., Hong, T. and Kang, C. From high-resolution data to high-resolution probabilistic load forecasts. Transmission and Distribution Conference and Exposition, IEEE/PES, 2016 DOI: 10.1109/TDC.2016.7520073.

Yuan, M. and Lin, Y. Model selection and estimation in regression with grouped variables. Journal of Royal Statistical Society Series B, 2006, 68: 49–67.

Ziel, A. Modelling and forecasting electricity load using Lasso methods. Modern Electric Power Systems, 2016. DOI: 10.1109/MEPS.2015.7477217.

Ziel, F. and Liu B. Lasso estimation for GEFCom2014 probabilistic electric load forecasting. International Journal of Forecasting, 2016, 32: 1029-1037.

Zou, H. and Hastie, T. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society. Series B (methodology), 2005, 67(2): 301–320.




DOI: http://dx.doi.org/10.17159/2413-3051/2017/v28i4a2428

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Caston Sigauke

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.