Strategic bidding for a price-maker hydroelectric producer: Stochastic dual dynamic programming and Lagrangian relaxation

ABSTRACT

In bid-based markets, energy producers seek bidding strategies that maximize their revenue. In this article, we seek the maximum-revenue bidding schedule for a single price-maker hydroelectric producer. We assume the producer sells energy in the day-ahead electricity market and has the ability to impact the market-clearing price with its bids. To obtain the price-maker hydroelectric producer’s bidding schedule, we use a combination of Stochastic Dual Dynamic Programming and Lagrangian relaxation. In this framework, we dualize the water balance equations, allowing an exact representation of the non-concave immediate revenue function, while preserving the concave shape of the future revenue function. We model inflow uncertainty and its stagewise dependence by a periodic autoregressive model. To demonstrate our approaches’ utility, we model Honduras’ electricity market assuming that the thermal producers act as price-takers and that one price-maker hydro producer operates all of the hydroelectric plants.

KEYWORDS:

• Bidding problem
• Lagrangian relaxation
• price-maker
• stochastic dual dynamic programming
• periodic autoregressive model

Additional information

Notes on contributors

Gregory Steeger

Gregory Steeger is an assistant professor at the United Stated Air Force Academy. He obtained his Ph.D. in quantitative economics in 2014, from the Colorado School of Mines. His research interests include optimization, stochastic processes, reliability, queueing, and mathematical economics. He serves as an analyst in the United States Air Force and enjoys applying his research to real-world problems in the military and Department of Defense.

Timo Lohmann

Timo Lohmann is a senior gas market analyst at Uniper Global Commodities SE. He obtained his Ph.D. in operations research in 2014, from the Colorado School of Mines. His research interests include energy system modeling, stochastic programming, and decomposition algorithms. He has applied operations research methods to real-world problems at different energy consultancies and utilities. At his current position, he works on global natural gas and LNG modeling approaches.

Steffen Rebennack

Steffen Rebennack is a chaired professor at the Institute of Operations Research at the Karlsruhe Institute of Technology (KIT). He obtained his Ph.D. in 2010 from the University of Florida. In 2015, he received the ENRE Young Researcher Prize. His research interests are in stochastic and large-scale optimization. He applies his research to real-world optimization problems with a focus on power systems applications. He serves as a co-editor for the European Journal of Operational Research.