Short-Term Electric Load Forecasting Using Multiple Gaussian Process Models

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.





References:
[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,
http://www.tepco.co.jp/forecast/index-j.html, accessed November 22,
2012.