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Control and Optimization Methods for Electric Smart Grids pp 63–85Cite as

Optimal Demand Response: Problem Formulation and Deterministic Case

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Part of the book series: Power Electronics and Power Systems ((PEPS,volume 3))

Abstract

We consider a set of users served by a single load-serving entity (LSE). The LSE procures capacity a day ahead. When random renewable energy is realized at delivery time, it manages user load through real-time demand response and purchases balancing power on the spot market to meet the aggregate demand. Hence, optimal supply procurement by the LSE and the consumption decisions by the users must be coordinated over two timescales, a day ahead and in real time, in the presence of supply uncertainty. Moreover, they must be computed jointly by the LSE and the users since the necessary information is distributed among them. In this chapter, we present a simple yet versatile user model and formulate the problem as a dynamic program that maximizes expected social welfare. When random renewable generation is absent, optimal demand response reduces to joint scheduling of the procurement and consumption decisions. In this case, we show that optimal prices exist that coordinate individual user decisions to maximize social welfare, and present a decentralized algorithm to optimally schedule a day in advance the LSE’s procurement and the users’ consumptions. The case with uncertain supply is reported in a companion paper.

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Notes

  1. 1.

    See, however, [19] for a discussion on some implementation issues of real-time pricing for retail markets and a proposal for the Italian market.

  2. 2.

    We abuse notation to use U ia to denote both a function of vector q ia and that of a scalar q ia (t); the meaning should be clear from the context.

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Authors and Affiliations

  1. Engineering and Applied Science, California Institute of Technology, Pasadena, CA, USA

    Lijun Chen, Na Li, Libin Jiang & Steven H. Low

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  1. Lijun Chen
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  2. Na Li
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  3. Libin Jiang
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  4. Steven H. Low
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Correspondence to Lijun Chen .

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Editors and Affiliations

  1. , Electrical and Computer Engineering, North Carolina State University, Keystone Bldg 100-26, Raleigh, 27695, North Carolina, USA

    Aranya Chakrabortty

  2. , Electrical & Computer Engineering, Carnegie Mellon University, Forbes Ave. 5000, Pittsburgh, 15213-3890, Pennsylvania, USA

    Marija D. Ilić

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Chen, L., Li, N., Jiang, L., Low, S.H. (2012). Optimal Demand Response: Problem Formulation and Deterministic Case. In: Chakrabortty, A., Ilić, M. (eds) Control and Optimization Methods for Electric Smart Grids. Power Electronics and Power Systems, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1605-0_3

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  • DOI: https://doi.org/10.1007/978-1-4614-1605-0_3

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