An Online Convex Optimization Approach to Real-Time Energy Pricing for Demand Response

Seung Jun Kim, Geogios B. Giannakis

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


Real-time price setting strategies are investigated for use by demand response programs in future power grids. The major challenge is that consumers have varying degrees of responsiveness to price adjustments at different time instants, which must be learned and accounted for by demand response initiatives. To this end, an online learning approach is developed here offering strong performance guarantees with minimal assumptions on the dynamics of load levels and consumer elasticity, even when consumers are adversarial and take actions strategically. The developed algorithms can determine electricity prices sequentially so as to elicit desirable usage behavior and flatten load curves, while implicitly learning individual consumers' price elasticity based on available feedback information. Two feedback structures are considered: 1) a full information setup, where aggregate load levels as well as individual price elasticity parameters are directly available, and 2) a partial information (bandit) case, where only the aggregate load levels are revealed. Fairness and sparsity constraints are also incorporated via appropriate regularizers. Numerical tests verify the effectiveness of the proposed approach.

Original languageEnglish (US)
Article number7438918
Pages (from-to)2784-2793
Number of pages10
JournalIEEE Transactions on Smart Grid
Issue number6
StatePublished - Nov 2017

Bibliographical note

Funding Information:
Manuscript received September 15, 2015; revised January 5, 2016 and March 2, 2016; accepted March 6, 2016. Date of publication March 22, 2016; date of current version October 19, 2017. This work was supported in part by the National Science Foundation under Grant 1423316, Grant 1442686, and Grant 1547347, and in part by the Institute of Renewable Energy and the Environment at the University of Minnesota under Grant RL-0010-13. Part of this work was presented at the IEEE PES Conference on Innovative Smart Grid Technologies, Washington, DC, USA, Feb. 19–22, 2014. Paper no. TSG-01143-2015.


  • Demand response
  • online learning
  • real-time pricing

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