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Analysis of a Distributed Consensus Based Economic Dispatch Algorithm

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Uncertainty in Complex Networked Systems

Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

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Abstract

We present a consensus-based approach to the optimal economic dispatch of power generators in a smart microgrid. Under the proposed approach, generators independently make adjustments to their power frequency primary controller set points using three pieces of information: (a) their own marginal cost of generation, (b) the measured frequency deviation, and (c) marginal generation cost of a subset of other generators obtained using local message exchanges. We show that in the absence of power losses, these independent adjustments can be designed in such a way that frequency deviations are reduced to zero, and additionally, the overall cost of generation is minimized; that a slight modification to enforce harp power constraints on power generation achieves the same as long as the global optimum is within those bounds. When power losses are taken into account, our algorithm still reduces the frequency deviations to zero; however, in this case, the total cost of generation is only approximately minimized, though the resulting suboptimality can be shown to be negligible for typical levels of power losses. The proposed approach can be thought of as a gradient search of a carefully chosen objective function, whose minimization only requires the frequency deviation and message exchanges between neighboring generators. We prove that the algorithm uniformly converges to the global optimum and illustrate its performance using numerical simulations.

Rahman is with This work was partly supported by US NSF grants CAREER award ECCS-1150801, and CCF-1302456.

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, 52242, USA

    Raghuraman Mudumbai & Soura Dasgupta

  2. Shandong Computer Science Center, Shandong Provincial Key Laboratory of Computer Networks, Jinan, China

    Soura Dasgupta

  3. Department of Electrical Engineering, Information Technology University, Lahore, Pakistan

    M. Muhammad Mahboob Ur Rahman

Authors
  1. Raghuraman Mudumbai
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  2. Soura Dasgupta
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  3. M. Muhammad Mahboob Ur Rahman
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Corresponding author

Correspondence to Soura Dasgupta .

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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Tamer BaĹźar

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Mudumbai, R., Dasgupta, S., Muhammad Mahboob Ur Rahman, M. (2018). Analysis of a Distributed Consensus Based Economic Dispatch Algorithm. In: Başar, T. (eds) Uncertainty in Complex Networked Systems. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-04630-9_14

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