Structured storage policies for energy distribution networks

ABSTRACT

We consider the problem of dynamically controlling a two-bus energy distribution network with energy storage capabilities. An operator seeks to dynamically adjust the amount of energy to charge to, or discharge from, energy storage devices in response to randomly evolving demand, renewable supply, and prices. The objective is to minimize the expected total discounted costs incurred within the network over a finite planning horizon. We formulate a Markov decision process model that prescribes the optimal amount of energy to charge or discharge and transmit between the two buses during each stage of the planning horizon. Established are the multimodularity of the value function and the monotonicity of the optimal policy in the energy storage levels. We also show that the optimal operational cost is convex and monotone in the storage capacities. Furthermore, we establish bounds on the optimal cost by analyzing comparable single-storage systems with pooled and decentralized storage configurations, respectively. These results extend to more general multi-bus network topologies. Numerical examples illustrate the main results and highlight the significance of interacting demand-side entities.

KEYWORDS:

• Energy storage
• network
• Markov decision processes

Acknowledgments

The authors are grateful to two anonymous referees and the editors for their constructive comments.

Additional information

Funding

This research was supported, in part, by grants from the Mascaro Center for Sustainable Innovation and the Center for Industry Studies (CIS) at the University of Pittsburgh.

Notes on contributors

Arnab Bhattacharya

Arnab Bhattacharya is a Ph.D. candidate in the Department of Industrial Engineering at the University of Pittsburgh. He earned B.Tech and M.Tech degrees in industrial engineering from the Indian Institute of Technology, Kharagpur. His research interests include stochastic modeling, analysis, and optimization of smart grid systems with a focus on the effective management of stored energy. Arnab is a member of the Institute for Operations Research and the Management Sciences (INFORMS) and the Institute of Industrial and Systems Engineers (IISE).

Jeffrey P. Kharoufeh

Jeffrey P. Kharoufeh is a professor in the Department of Industrial Engineering at the University of Pittsburgh. He holds a Ph.D. in industrial engineering and operations research from Penn State University. His primary research interest is the modeling, analysis, and control of stochastic systems with applications in energy, reliability, maintenance optimization, queueing, and communications systems. He is a senior member of IISE and a member of INFORMS and the Applied Probability Society.

Bo Zeng

Bo Zeng is an associate professor in the Department of Industrial Engineering at the University of Pittsburgh. He earned a Ph.D. in operations research from the Department of Industrial Engineering at Purdue University. His research interests include polyhedral theory and algorithm development for stochastic, robust, and multilevel mixed-integer programs, with applications in power, logistics and cyber-physical systems. He is a member of IISE, INFORMS, and IEEE.