Deep Learning for Energy Markets

Deep Learning is applied to energy markets to predict extreme loads observed in energy grids. Forecasting energy loads and prices is challenging due to sharp peaks and troughs that arise due to supply and demand fluctuations from intraday system constraints. We propose deep spatio-temporal models and extreme value theory (EVT) to capture theses effects and in particular the tail behavior of load spikes. Deep LSTM architectures with ReLU and $\tanh$ activation functions can model trends and temporal dependencies while EVT captures highly volatile load spikes above a pre-specified threshold. To illustrate our methodology, we use hourly price and demand data from 4719 nodes of the PJM interconnection, and we construct a deep predictor. We show that DL-EVT outperforms traditional Fourier time series methods, both in-and out-of-sample, by capturing the observed nonlinearities in prices. Finally, we conclude with directions for future research.

[1]  Dmitry Yarotsky,et al.  Error bounds for approximations with deep ReLU networks , 2016, Neural Networks.

[2]  Nicholas G. Polson,et al.  Deep learning for spatio‐temporal modeling: Dynamic traffic flows and high frequency trading , 2017, Applied Stochastic Models in Business and Industry.

[3]  Hassan Soltan,et al.  A methodology for Electric Power Load Forecasting , 2011 .

[4]  Richard L. Smith Risk Management: Measuring Risk with Extreme Value Theory , 2002 .

[5]  Zijun Zhang,et al.  Short-Term Electricity Price Forecasting With Stacked Denoising Autoencoders , 2017, IEEE Transactions on Power Systems.

[6]  Kenneth A. Lindsay,et al.  Forecasting spikes in electricity prices , 2012 .

[7]  Johannes Schmidt-Hieber,et al.  Nonparametric regression using deep neural networks with ReLU activation function , 2017, The Annals of Statistics.

[8]  Nitish Srivastava,et al.  Dropout: a simple way to prevent neural networks from overfitting , 2014, J. Mach. Learn. Res..

[9]  Nicole A. Lazar,et al.  Statistics of Extremes: Theory and Applications , 2005, Technometrics.

[10]  Ohad Shamir,et al.  The Power of Depth for Feedforward Neural Networks , 2015, COLT.

[11]  P. McSharry,et al.  Short-Term Load Forecasting Methods: An Evaluation Based on European Data , 2007, IEEE Transactions on Power Systems.

[12]  F. Benth,et al.  Pricing Futures and Options in Electricity Markets , 2014 .

[13]  Lorenzo Rosasco,et al.  Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review , 2016, International Journal of Automation and Computing.

[14]  J. Tawn,et al.  Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications , 2004 .

[15]  T. Senjyu,et al.  A Novel Approach to Forecast Electricity Price for PJM Using Neural Network and Similar Days Method , 2007, IEEE Transactions on Power Systems.

[16]  S. Coles,et al.  An Introduction to Statistical Modeling of Extreme Values , 2001 .

[17]  Ser-Huang Poon,et al.  Hedging the Black Swan: Conditional Heteroskedasticity and Tail Dependence in S&P500 and Vix , 2009 .

[18]  Stuart A. Klugman,et al.  On the estimation of long tailed skewed distributions with actuarial applications , 1983 .

[19]  Nicholas G. Polson,et al.  Deep learning for short-term traffic flow prediction , 2016, 1604.04527.

[20]  Y.-y. Hong,et al.  Locational marginal price forecasting in deregulated electricity markets using artificial intelligence , 2002 .

[21]  Pravin Varaiya,et al.  Smart Operation of Smart Grid: Risk-Limiting Dispatch , 2011, Proceedings of the IEEE.

[22]  Marco van Akkeren,et al.  A GARCH forecasting model to predict day-ahead electricity prices , 2005, IEEE Transactions on Power Systems.

[23]  Wojciech Czarnecki,et al.  On Loss Functions for Deep Neural Networks in Classification , 2017, ArXiv.

[24]  Thorsten Rheinländer Risk Management: Value at Risk and Beyond , 2003 .

[25]  Caston Sigauke,et al.  Extreme daily increases in peak electricity demand: Tail-quantile estimation , 2013 .

[26]  M. Genton,et al.  Powering Up With Space-Time Wind Forecasting , 2010 .

[27]  V. Mendes,et al.  Short-term electricity prices forecasting in a competitive market: A neural network approach , 2007 .

[28]  Derek W. Bunn Short-Term Forecasting: A Review of Procedures in the Electricity Supply Industry , 1982 .

[29]  Philippe Naveau,et al.  Modeling jointly low, moderate, and heavy rainfall intensities without a threshold selection , 2016 .

[30]  Matus Telgarsky,et al.  Neural Networks and Rational Functions , 2017, ICML.

[31]  Jürgen Schmidhuber,et al.  LSTM can Solve Hard Long Time Lag Problems , 1996, NIPS.

[32]  Jürgen Schmidhuber,et al.  Long Short-Term Memory , 1997, Neural Computation.

[33]  C. Hsiao,et al.  Locational marginal price forecasting in deregulated electric markets using a recurrent neural network , 2001, 2001 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.01CH37194).

[34]  D. Kirschen,et al.  Forecasting system imbalance volumes in competitive electricity markets , 2004, IEEE Transactions on Power Systems.

[35]  Francis R. Bach,et al.  Breaking the Curse of Dimensionality with Convex Neural Networks , 2014, J. Mach. Learn. Res..

[36]  Yuan Yu,et al.  TensorFlow: A system for large-scale machine learning , 2016, OSDI.

[37]  Paul Embrechts,et al.  Infinite-mean models and the LDA for operational risk , 2006 .

[38]  D. Dupuis Electricity price dependence in New York State zones: A robust detrended correlation approach , 2017 .

[39]  Geoffrey E. Hinton,et al.  Reducing the Dimensionality of Data with Neural Networks , 2006, Science.

[40]  Saahil Shenoy,et al.  Risk adjusted forecasting of electric power load , 2014, 2014 American Control Conference.

[41]  Mun-Kyeom Kim,et al.  A New Approach to Short-term Price Forecast Strategy with an Artificial Neural Network Approach: Application to the Nord Pool , 2015 .

[42]  Francis R. Bach,et al.  Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression , 2016, J. Mach. Learn. Res..

[43]  Pedro Emanuel Almeida Cardoso,et al.  Deep Learning Applied to PMU Data in Power Systems , 2017 .

[44]  Michael Goldstein,et al.  Quantifying uncertainty in wholesale electricity price projections using Bayesian emulation of a generation investment model , 2018 .

[45]  Remy Cottet,et al.  Bayesian Modeling and Forecasting of Intraday Electricity Load , 2003 .

[46]  B. Gnedenko Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire , 1943 .

[47]  Vadim Sokolov,et al.  Deep Learning: A Bayesian Perspective , 2017, ArXiv.

[48]  Dominik Liebl,et al.  Modeling and forecasting electricity spot prices: A functional data perspective , 2013, 1310.1628.

[49]  Wei-Peng Chen,et al.  Model selection criteria for short-term microgrid-scale electricity load forecasts , 2013, 2013 IEEE PES Innovative Smart Grid Technologies Conference (ISGT).

[50]  Eric P. Smith,et al.  An Introduction to Statistical Modeling of Extreme Values , 2002, Technometrics.

[51]  A. Davison,et al.  Statistical Modeling of Spatial Extremes , 2012, 1208.3378.

[52]  Richard L. Smith Extreme Value Analysis of Environmental Time Series: An Application to Trend Detection in Ground-Level Ozone , 1989 .

[53]  Chen-Ching Liu,et al.  Day-Ahead Electricity Price Forecasting in a Grid Environment , 2007, IEEE Transactions on Power Systems.

[54]  M. Makarov Extreme value theory and high quantile convergence , 2006 .

[55]  Richard L. Smith,et al.  Models for exceedances over high thresholds , 1990 .

[56]  H. Madsen,et al.  Forecasting Electricity Spot Prices Accounting for Wind Power Predictions , 2013, IEEE Transactions on Sustainable Energy.

[57]  Nicholas G. Polson,et al.  Bayesian analysis of traffic flow on interstate I-55: The LWR model , 2014, 1409.6034.