Price forecasting is at the center of decision making in electricity markets. Much research has been done in forecasting energy prices for a single market while little research has been reported on forecasting price difference between markets, which presents higher volatility and yet plays a critical role in applications such as virtual trading. To this end, this paper takes the first attempt at it and employs novel deep learning architecture with Bidirectional Long-Short Term Memory (LSTM) units and Sequence-to-Sequence (Seq2Seq) architecture to forecast nodal price difference between day-ahead and real-time markets. In addition to value prediction, these deep learning architectures are also used to develop classification models to predict the price difference bands/ranges. The proposed methods are tested using historical PJM market data, and evaluated using Root Mean Squared Error (RMSE) and other customized performance metrics. Case studies show that both deep learning methods outperform common methods including ARIMA, XGBoost and Support Vector Regression (SVR) methods. More importantly, the deep learning methods can capture the magnitude and timing of price difference spikes. Numerical results show the Seq2Seq model performs particularly well and demonstrates generalization capability to extended forecasting lead time.


Electrical and Computer Engineering

Research Center/Lab(s)

Intelligent Systems Center


This work was supported in part by DARPA under Grant D18AP00054, in part by the U.S. Department of Energy's Office of Energy Efficiency and Renewable Energy (EERE) under the Water Power Technologies Office Award DE-EE0008781, in part by the National Science Foundation under Grant OAC-1919789, in part by the Missouri University of Science and Technology Intelligent Systems Center, in part by the Mary K. Finley Missouri Endowment, in part by the National Science Foundation, in part by the Lifelong Learning Machines Program from DARPA/Microsystems Technology Office, in part by the Army Research Laboratory (ARL), and in part by the Army Night Vision Laboratory under Grant W911NF-18-2-0260 and Grant W911NF-14-2-0034.

Keywords and Phrases

Convergence; Deep learning; Electricity supply industry; Forecasting; Predictive models; Time series analysis; Timing

International Standard Serial Number (ISSN)


Document Type

Article - Journal

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Final Version

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Publication Date

01 Jan 2022