Advertisement

A Hierarchical Approach Based on the Frank–Wolfe Algorithm and Dantzig–Wolfe Decomposition for Solving Large Economic Dispatch Problems in Smart Grids

  • Jianyi Zhang
  • M. Hadi Amini
  • Paul WengEmail author
Chapter

Abstract

A microgrid is an integrated energy system consisting of distributed energy resources and multiple electrical loads operating as a single, autonomous grid either in parallel to or “islanded” from the existing utility power grid, often referred to as a microgrid. The operations of a microgrid are different from those of traditional microgrids. In this paper, we present a decomposition method to solve the economic dispatch problem for a cluster of microgrids. The economic dispatch problem aims at determining both the power generation and demand levels of each microgrid under boundary and power flow constraints in order to minimize a non-linear convex economic cost, which is expressed as the combination of generation costs and demand utilities. Directly solving large economic dispatch problems is difficult because of the non-linearity of the objective function, memory limitations and privacy issues. We therefore propose a decomposition method based on a combination of the Frank–Wolfe algorithm to tackle the non-linearity and the Dantzig–Wolfe decomposition to solve the later two issues. Networks of microgrids both randomly generated and from real cases are used as test cases. The experimental results shows that the computation time increases slowly with the increasing complexity of the microgrid.

Notes

Acknowledgements

We thank Jie Gong and Ashley Ng for assistance with the revision and Figs. 3, 4.

References

  1. 1.
    Abdollahi, A., Moghaddam, M. P., Rashidinejad, M., and Sheikh-El-Eslami, M. K. (2012). Investigation of economic and environmental-driven demand response measures incorporating UC. IEEE Transactions on Smart Grid, 3(1):12–25.CrossRefGoogle Scholar
  2. 2.
    Amini, M. H., Boroojeni, K. G., Dragičević, T., Nejadpak, A., Iyengar, S., and Blaabjerg, F. (2017). A comprehensive cloud-based real-time simulation framework for oblivious power routing in clusters of dc microgrids. In DC Microgrids (ICDCM), 2017 IEEE Second International Conference on, pages 270–273. IEEE.Google Scholar
  3. 3.
    Amini, M. H., McNamara, P., Weng, P., Karabasoglu, O., and Xu, Y. (2017). Hierarchical electric vehicle charging aggregator strategy using Dantzig-Wolfe decomposition. IEEE Design & Test.Google Scholar
  4. 4.
    Bertsimas, D. and Tsitsiklis, J. N. (1997). Introduction to linear optimization, volume 6. Athena Scientific Belmont, MA.Google Scholar
  5. 5.
    Clarkson, K. L. (2010). Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm. ACM Transactions on Algorithms (TALG), 6(4):63.MathSciNetzbMATHGoogle Scholar
  6. 6.
    Dantzig, G. B. and Thapa, M. N. (2006). Linear programming 2: theory and extensions. Springer Science & Business Media.Google Scholar
  7. 7.
    Dantzig, G. B. and Wolfe, P. (1960). Decomposition principle for linear programs. Operations research, 8(1):101–111.CrossRefGoogle Scholar
  8. 8.
    Farhangi, H. (2010). The path of the smart grid. IEEE power and energy magazine, 8(1).MathSciNetCrossRefGoogle Scholar
  9. 9.
    Frank, M. and Wolfe, P. (1956). An algorithm for quadratic programming. Naval Research Logistics (NRL), 3(1-2):95–110.MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hatziargyriou, N. (2014). Microgrids: architectures and control. John Wiley & Sons.Google Scholar
  11. 11.
    Hug, G., Kar, S., and Wu, C. (2015). Consensus+ innovations approach for distributed multiagent coordination in a microgrid. IEEE Transactions on Smart Grid, 6(4):1893–1903.CrossRefGoogle Scholar
  12. 12.
    Jaggi, M. (2013). Revisiting Frank-Wolfe: Projection-free sparse convex optimization. In ICML (1), pages 427–435.Google Scholar
  13. 13.
    Kalvelagen, E. (2003). Dantzig-Wolfe decomposition with GAMS.Google Scholar
  14. 14.
    Katiraei, F., Iravani, R., Hatziargyriou, N., and Dimeas, A. (2008). Microgrids management. IEEE power and energy magazine, 6(3).CrossRefGoogle Scholar
  15. 15.
    Khodaei, A. (2017). Provisional microgrid planning. IEEE Transactions on Smart Grid, 8(3):1096–1104.CrossRefGoogle Scholar
  16. 16.
    Khodaei, A., Bahramirad, S., and Shahidehpour, M. (2015). Microgrid planning under uncertainty. IEEE Transactions on Power Systems, 30(5):2417–2425.CrossRefGoogle Scholar
  17. 17.
    Lacoste-Julien, S. and Jaggi, M. (2015). On the global linear convergence of Frank-Wolfe optimization variants. In Advances in Neural Information Processing Systems, pages 496–504.Google Scholar
  18. 18.
    Lasseter, R. H. and Paigi, P. (2004). Microgrid: A conceptual solution. In Power Electronics Specialists Conference, 2004. PESC 04. 2004 IEEE 35th Annual, volume 6, pages 4285–4290. IEEE.Google Scholar
  19. 19.
    Lotfi, H. and Khodaei, A. (2017). AC versus DC microgrid planning. IEEE Transactions on Smart Grid, 8(1):296–304.CrossRefGoogle Scholar
  20. 20.
    Mohamed, F. A. and Koivo, H. N. (2010). System modelling and online optimal management of microgrid using mesh adaptive direct search. International Journal of Electrical Power & Energy Systems, 32(5):398–407.CrossRefGoogle Scholar
  21. 21.
    Nikkhajoei, H. and Lasseter, R. H. (2007). Microgrid protection. In Power Engineering Society General Meeting, 2007. IEEE, pages 1–6. IEEE.Google Scholar
  22. 22.
    Parhizi, S., Lotfi, H., Khodaei, A., and Bahramirad, S. (2015). State of the art in research on microgrids: A review. Ieee Access, 3:890–925.CrossRefGoogle Scholar
  23. 23.
    Parisio, A., Rikos, E., and Glielmo, L. (2014). A model predictive control approach to microgrid operation optimization. IEEE Transactions on Control Systems Technology, 22(5):1813–1827.CrossRefGoogle Scholar
  24. 24.
    Shafiee, Q., Dragičević, T., Vasquez, J. C., and Guerrero, J. M. (2014). Hierarchical control for multiple DC-microgrids clusters. IEEE Transactions on Energy Conversion, 29(4):922–933.CrossRefGoogle Scholar
  25. 25.
    Ton, D. T. and Smith, M. A. (2012). The US department of energy’s microgrid initiative. The Electricity Journal, 25(8):84–94.CrossRefGoogle Scholar
  26. 26.
    Tsikalakis, A. G. and Hatziargyriou, N. D. (2011). Centralized control for optimizing microgrids operation. In Power and Energy Society General Meeting, 2011 IEEE, pages 1–8. IEEE.Google Scholar
  27. 27.
    Unamuno, E. and Barrena, J. A. (2015). Hybrid AC/DC microgrids—part i: Review and classification of topologies. Renewable and Sustainable Energy Reviews, 52:1251–1259.CrossRefGoogle Scholar
  28. 28.
    Yang, Q., An, D., Yu, W., Tan, Z., and Yang, X. (2016). Towards stochastic optimization-based electric vehicle penetration in a novel archipelago microgrid. Sensors, 16(6):907.CrossRefGoogle Scholar
  29. 29.
    Zimmerman, R. D., Murillo-Sánchez, C. E., and Thomas, R. J. (2011). MATPOWER: Steady-state operations, planning, and analysis tools for power systems research and education. IEEE Transactions on power systems, 26(1):12–19.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Shanghai Jiao Tong UniversityShanghaiChina
  2. 2.Department of Electrical and Computer EngineeringCarnegie Mellon UniversityPittsburghUSA

Personalised recommendations