(737g) Bayesian Statistical Learning and Stochastic Programming for Energy Market Participation

Gao, X., University of Notre Dame
Dowling, A., University of Notre Dame
In this presentation, we explore the deep connection between data-driven Bayesian statistical inference and stochastic programming paradigms for decision-making under uncertainty. As a motivating example, we consider optimal strategies into multi-scale electricity markets.

We use Gaussian Process (GP) regression to develop probabilistic models for multi-scale energy prices [1]. An ensemble of timeseries forecasts is then constructed by sampling from the GP predictive distribution in a rolling horizon framework. These forecasts enable two modes of optimal market participation. For self-scheduling, the resource determines when to buy/sell energy and takes the market price [2]. We formulate this as a multistage stochastic program [3,4]. Alternately, a resource can submit bidding curves, which are time-varying piece-wise constant price and energy pairs. These bidding curves communicate to the market the resources flexibility and marginal costs. Calculation of bidding curves for the day-ahead and real-time market are also formulated as stochastic programs [5,6,7]. We compare these two modes of market participation using an entire year of day-ahead market and (real-time) fifteen-minute market data from CAISO [8] for two systems: stand-alone energy storage [2] and a thermal generator [5].We show that the self-schedule mode is less robust to market uncertainty but allows a resource to insure feasible operation. In contrast, bidding into the market is more robust to uncertainty (i.e., the resource submits several contingencies in their bid) but does not guarantee feasible operation. In other words, the amount of stored energy may prevent a resource from satisfying the cleared market schedule, incurring a penalty.

This example highlights the opportunities for data-driven optimization under uncertainty for energy systems. Bayesian inference allows for construction of probability distributions (analytic or samples) to describe random model parameters. We argue this is well-suited for stochastic programming, which seeks to optimize an expected value or other risk metric defined over of the probability space.


[1] Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.

[2] Dowling, A. W., Kumar, R., & Zavala, V. M. (2017). A multi-scale optimization framework for electricity market participation. Applied Energy, 190, 147-164.

[3] Ierapetritou, M. G., Wu, D., Vin, J., Sweeney, P., & Chigirinskiy, M. (2002). Cost minimization in an energy-intensive plant using mathematical programming approaches. Industrial & Engineering Chemistry Research, 41(21), 5262-5277.

[4] Kumar, R., Wenzel, M. J., Ellis, M. J., ElBsat, M. N., Drees, K. H., & Zavala, V. M. (2018). A stochastic model predictive control framework for stationary battery systems. IEEE Transactions on Power Systems, 33(4), 4397-4406.

[5] Plazas, M. A., Conejo, A. J., & Prieto, F. J. (2005). Multimarket optimal bidding for a power producer. IEEE Transactions on Power Systems, 20(4), 2041-2050.

[6] Dominguez, R., Baringo, L., & Conejo, A. J. (2012). Optimal offering strategy for a concentrating solar power plant. Applied Energy, 98, 316-325.

[7] Zhang, X., & Hug, G. (2015, February). Bidding strategy in energy and spinning reserve markets for aluminum smelters' demand response. In 2015 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT) (pp. 1-5). IEEE.

[8] Dowling, A. W., & Zavala, V. M. (2018). Economic opportunities for industrial systems from frequency regulation markets. Computers & Chemical Engineering, 114, 254-264.