Analysis of a Distributed Consensus Based Economic Dispatch Algorithm

  • Raghuraman Mudumbai
  • Soura DasguptaEmail author
  • M. Muhammad Mahboob Ur Rahman
Part of the Systems & Control: Foundations & Applications book series (SCFA)


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.


Consensus Smart grid Microgrids Optimal dispatch Constrains 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Raghuraman Mudumbai
    • 1
  • Soura Dasgupta
    • 1
    • 2
    Email author
  • M. Muhammad Mahboob Ur Rahman
    • 3
  1. 1.Department of Electrical and Computer EngineeringUniversity of IowaIowa CityUSA
  2. 2.Shandong Computer Science CenterShandong Provincial Key Laboratory of Computer NetworksJinanChina
  3. 3.Department of Electrical EngineeringInformation Technology UniversityLahorePakistan

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