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Short-Term Electric Load Forecasting Using Multiple Gaussian Process Models

Authors: Hitoshi Takata, Tomohiro Hachino, Seiji Fukushima, Yasutaka Igarashi


This paper presents a Gaussian process model-based short-term electric load forecasting. The Gaussian process model is a nonparametric model and the output of the model has Gaussian distribution with mean and variance. The multiple Gaussian process models as every hour ahead predictors are used to forecast future electric load demands up to 24 hours ahead in accordance with the direct forecasting approach. The separable least-squares approach that combines the linear least-squares method and genetic algorithm is applied to train these Gaussian process models. Simulation results are shown to demonstrate the effectiveness of the proposed electric load forecasting.

Keywords: Genetic Algorithm, direct method, Gaussian process model, electric load forecasting, separable least-squares method

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[1] T. Ishida and S. Tamaru, Daily electric load forecasting using artificial neural network (in Japanese), IEEJ Trans. B, Vol. 114, No. 11, pp. 1109–1115, 1994.
[2] H. Takata, K. Sonoda and T. Hachino, Daily electric load forecasting using ANN and GA in Tanegashima (in Japanese), The Research Reports of the Faculty of Engineering Kagoshima University, No. 40, pp. 55–58, 1998.
[3] O. Ishioka, Y. Sato, T. Ishihara, Y. Ueki, T. Matsui and T. Iizaka, Development of electric load forecasting system using neural networks (in Japanese), IEEJ Trans. B, Vol. 120, No. 12, pp. 1550–1556, 2000.
[4] H. Mori and H. Kobayashi, Optimal fuzzy inference for short-term load forecasting, IEEE Trans. Power Syst., Vol. 11, No. 1, pp. 350–356, 1996.
[5] H. M. A. Hamadi and S. A. Soliman, Short-term electric load forecasting based on Kalman filtering algorithm with moving window weather and load model, Trans. on Electric Power Systems Research, No. 68, pp. 47–59, 2004.
[6] T. Namerikawa and Y. Hosoda, H∞ filter-based short-term electric load prediction considering characteristics of load curve (in Japanese), IEEJ Trans. C, Vol. 132, No. 9, pp. 1446–1453, 2012.
[7] T. Hachino and V. Kadirkamanathan, Multiple Gaussian process models for direct time series forecasting, IEEJ Trans. on Electrical and Electronic Engineering, Vol. 6, No. 3, pp. 245–252, 2011.
[8] A. O’Hagan, Curve fitting and optimal design for prediction (with discussion), Journal of the Royal Statistical Society B, Vol. 40, pp. 1–42, 1978.
[9] C. K. I. Williams, Prediction with Gaussian processes: from Linear regression to linear prediction and beyond, in Learning and Inference in Graphical Models, Kluwer Academic Press, pp. 599–621, 1998.
[10] M. Seeger, Gaussian processes for machine learning, International Journal of Neural Systems, Vol. 14, No. 2, pp. 1–38, 2004.
[11] C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning, MIT Press, 2006.
[12] J. Kocijan, A. Girard, B. Banko and R. Murray-Smith, Dynamic systems identification with Gaussian processes, Mathematical and Computer Modelling of Dynamical Systems, Vol. 11, No. 4, pp. 411–424, 2005.
[13] G. Gregorˇciˇc and G. Lightbody, Gaussian process approach for modelling of nonlinear systems, Engineering Applications of Artificial Intelligence, Vol. 22, No. 4-5, pp. 522–533, 2009.
[14] T. Hachino and H. Takata, Identification of continuous-time nonlinear systems by using a Gaussian process model, IEEJ Trans. on Electrical and Electronic Engineering, Vol. 3, No. 6, pp. 620–628, 2008.
[15] A. Girard, C. E. Rasmussen, J. Q. Candela and R. Murray-Smith, Gaussian process priors with uncertain inputs -application to mutiple-step ahead time series forecasting”, in Advances in Neural Information Processing Systems, Vol. 15, pp. 542–552, MIT Press, 2003.
[16] J. Q. Candela, A. Girard, J. Larsen and C. E. Rasmussen, Propagation of uncertainty in Bayesian kernel models -application to multiple-step ahead forecasting, Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. II-701–704, 2003.
[17] J. M. Wang, D. J. Fleet and A. Hertzmann, Gaussian process dynamical models for human motion, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 30, No. 2, pp. 283–298, 2008.
[18] B. Likar and J. Kocijan, Predictive control of a gas-liquid separation plant based on a Gaussian process model, Computers and Chemical Engineering, Vol. 31, No. 3, pp. 142–152, 2007.
[19] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, 1989.
[20] G. H. Golub and V. Pereyra, The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate, SIAM Journal of Numerical Analysis, Vol. 10, No. 2, pp. 413–432, 1973.
[21] J. Bruls, C. T. Chou, B. R. J. Haverkamp and M. Verhaegen, Linear and non-linear system identification using separable least-squares, European Journal of Control, Vol. 5, pp. 116–128, 1999.
[22] F. Previdi and M. Lovera, Identification of non-linear parametrically varying models using separable least squares, International Journal of Control, Vol. 77, No. 16, pp. 1382–1392, 2004.
[23] R. von Mises, Mathematical Theory of Probability and Statistics, Academic Press, 1964.
[24] TEPCO ELECTRICITY FORECAST, Tokyo Electric Power Company,, accessed November 22, 2012.