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Analysis of a Distributed Consensus Based Economic Dispatch Algorithm

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

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.

Keywords

Consensus Smart grid Microgrids Optimal dispatch Constrains 

References

  1. 1.
    B. Chowdhury and S. Rahman, “A review of recent advances in economic dispatch,” Power Systems, IEEE Transactions on, pp. 1248–1259, 1990.MathSciNetCrossRefGoogle Scholar
  2. 2.
    R. Mudumbai, S. Dasgupta and B. Cho, “Distributed control for optimal economic dispatch of power generators: the heterogenous case,” in Proc. of the IEEE CDC, 2011.Google Scholar
  3. 3.
    R. Mudumbai, S. Dasgupta and B. Cho, “Distributed control for optimal economic dispatch of a network of heterogeneous power generators,” IEEE Trans. on Power Systems pp 1750–1760, 2012.CrossRefGoogle Scholar
  4. 4.
    S. Marvin, H. Chappells, and S. Guy, “Pathways of smart metering development: shaping environmental innovation,” Computers, Environment and Urban Systems, pp. 109–126, 1999.CrossRefGoogle Scholar
  5. 5.
    D. Milborrow, “Penalties for intermittent sources of energy,” Cabinet Office, London, p. 17, 2001.Google Scholar
  6. 6.
    R. Dugan and T. McDermott, “Distributed generation,” IEEE Industry Applications Magazine, vol. 8, pp. 19–25, Mar/Apr 2002.CrossRefGoogle Scholar
  7. 7.
    Y. G. Rebours, D. S. Kirschen, M. Trotignon, and S. Rossignol, “A survey of frequency and voltage control ancillary services part i: Technical features,” IEEE Transactions on Power Systems, vol. 22, pp. 350–357, Feb. 2007.Google Scholar
  8. 8.
    F. Wu, K. Moslehi, and A. Bose, “Power system control centers: past, present, and future,” Proceedings of the IEEE, vol. 93, no. 11, pp. 1890–1908, 2005.CrossRefGoogle Scholar
  9. 9.
    U. S. D. of Energy, “Economic dispatch of electric generation capacity,” A REPORT TO CONGRESS AND THE STATES, 2007.Google Scholar
  10. 10.
    L. Vargas, V. Quintana, and A. Vannelli, “A tutorial description of an interior point method and its applications to security-constrained economic dispatch,” Power Systems, IEEE Transactions on, vol. 8, no. 3, pp. 1315–1324, 2002.CrossRefGoogle Scholar
  11. 11.
    J. Lopes, C. Moreira, A. Madureira, F. Resende, X. Wu, N. Jayawarna, Y. Zhang, N. Jenkins, F. Kanellos, and N. Hatziargyriou, “Control strategies for microgrids emergency operation,” in International Conference on Future Power Systems, Amsterdam, Netherlands, 2005.Google Scholar
  12. 12.
    M. Amin and B. Wollenberg, “Toward a smart grid: power delivery for the 21st century,” IEEE Power and Energy Magazine, vol. 3, no. 5, pp. 34–41, 2005.CrossRefGoogle Scholar
  13. 13.
    S. Kar and G. Hug, “Distributed robust economic dispatch in power systems: A consensus and innovations approach,” in Power and Energy Society General Meeting, 2012 IEEE, 2012.Google Scholar
  14. 14.
    Z. Zhang and M.-Y. Chow, “Convergence analysis of the incremental cost consensus algorithm under different communication network topologies in a smart grid,” Power Systems, IEEE Transactions on, vol. 27, no. 4, pp. 1761–1768, 2012.CrossRefGoogle Scholar
  15. 15.
    S. Yang, S. Tan, and J.-X. Xu, “Consensus based approach for economic dispatch problem in a smart grid,” Power Systems, IEEE Transactions on, 2013.CrossRefGoogle Scholar
  16. 16.
    A. Bidram, A. Davoudi, F. Lewis, and Z. Qu, “Secondary control of microgrids based on distributed cooperative control of multi-agent systems,” Generation, Transmission Distribution, IET, vol. 7, no. 8, pp. –, 2013.CrossRefGoogle Scholar
  17. 17.
    M. Fathi and H. Bevrani, “Adaptive energy consumption scheduling for connected microgrids under demand uncertainty,” Power Delivery, IEEE Transactions on, pp. 1576–1583, 2013.CrossRefGoogle Scholar
  18. 18.
    E. Dall’Anese, H. Zhu, and G. Giannakis, “Distributed optimal power flow for smart microgrids,” Smart Grid, IEEE Transactions on, vol. 4, no. 3, pp. 1464–1475, 2013.CrossRefGoogle Scholar
  19. 19.
    M. Kraning, E. Chu, J. Lavaei, and S. Boyd, “Dynamic network energy management via proximal message passing,” Optimization, vol. 1, no. 2, pp. 1–54, 2013.Google Scholar
  20. 20.
    M. Aganagic and S. Mokhtari, “Security constrained economic dispatch using nonlinear dantzig-wolfe decomposition,” Power Systems, IEEE Transactions on, pp. 105–112, 1997.CrossRefGoogle Scholar
  21. 21.
    L. Moreau, “Stability of multi-agent systems with time-dependent communication links”, IEEE Trans. Autom. Control, pp. 169–182, 2005.MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays”, IEEE Trans. Autom. Control, pp. 1520–1533, 2004.MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    S. Guler, B. Fidan, S. Dasgupta, B. D. O. Anderson and I. Shames “Adaptive Source Localization Based Station Keeping of Autonomous Vehicles”, IEEE Transactions on Automatic Control, pp. 3122–3135, 2017.MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    B. Fidan, S. Dasgupta and B. D. O. Anderson, “Adaptive rangemeasurementbased target pursuit”, International Journal of Adaptive Control and Signal Processing, pp. 66–81, 2013.Google Scholar
  25. 25.
    M. Cao, C. Yu, A. S. Morse, B. D. O. Anderson and S. Dasgupta, “Generalized controller for directed triangle formations”, in Proceedings of the IFAC World Congress, vol. 41, pp. 6590–6595, 2008.Google Scholar
  26. 26.
    M. Fu, S. Dasgupta and Y. C. Soh, “Integral quadratic constraint approach vs. multiplier approach”, Automatica, pp. 281–287, 2005.MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    M. Fu and S. Dasgupta, “Parametric Lyapunov functions for uncertain systems: The multiplier approach”, Advances in linear matrix inequality methods in control, pp. 95–108, 2000.CrossRefGoogle Scholar
  28. 28.
    Christie, R.D., and Bose, A., “Load frequency control issues in power system operations after deregulation”, IEEE Transactions on Power Systems, pp. 1191–1200, 1996.CrossRefGoogle Scholar
  29. 29.
    M. Basu, R. Mudumbai and S. Dasgupta, “Intelligent Distributed Economic Dispatch in Smart Grids”, Intelligent Systems Technologies and Applications, pp. 285–295, S. Berretti, S. M. Thampi and S. Dasgupta Eds, Springer 2015.Google Scholar
  30. 30.
    R. Mudumbai, S. Dasgupta, and R. Mahboob, “A distributed consensus based algorithm for optimal dispatch in smart power grids,” Proceedings of the 32nd IASTED International Conference on Modeling, Identification and Control (MIC), Feb 2013.Google Scholar
  31. 31.
    C. Chen, “Economic dispatch using simplified personal best oriented particle swarm optimizer,” in Electric Utility Deregulation and Restructuring and Power Technologies, 2008. DRPT 2008. Third International Conference on. IEEE, 2008, pp. 572–576.Google Scholar
  32. 32.
    N. Jaleeli, L. VanSlyck, D. Ewart, L. Fink, and A. Hoffmann, “Understanding automatic generation control,” Power Systems, IEEE Transactions on, vol. 7, no. 3, pp. 1106–1122, Aug 1992.CrossRefGoogle Scholar
  33. 33.
    F. Clough, “Stability of large power systems,” Journal of the Institution of Electrical Engineers, vol. 65, no. 367, pp. 653–659, 1927.CrossRefGoogle Scholar
  34. 34.
    A. Dobakhshari, S. Azizi, and A. Ranjbar, “Control of microgrids: Aspects and prospects,” in IEEE International Conference on Networking, Sensing and Control (ICNSC), april 2011, pp. 38–43.Google Scholar
  35. 35.
    R. C. Buck, Advanced Calculus, 3rd Ed, McGraw Hill, 1978.Google Scholar
  36. 36.
  37. 37.
    Sundarapandian, V., “An invariance principle of discrete-time nonlinear systems”, Applied Mathematics Letters, pp. 85–91, 2003.MathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    A. Mohammadi, M. Varahram, and I. Kheirizad, “Online solving of economic dispatch problem using neural network approach and comparing it with classical method,” in Emerging Technologies, 2006. ICET’06. International Conference on. IEEE, 2007, pp. 581–586.Google Scholar

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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