Advertisement

Economic power dispatch in smart grids: a framework for distributed optimization and consensus dynamics

  • Wenwu Yu
  • Chaojie Li
  • Xinghuo Yu
  • Guanghui Wen
  • Jinhu Lü
Research Paper
  • 225 Downloads

Abstract

By using the distributed consensus theory in multi-agent systems, the strategy of economic power dispatch is studied in a smart grid, where many generation units work cooperatively to achieve an optimal solution in a local area. The relationship between the distributed optimization solution and consensus in multi-agent systems is first revealed in this paper, which can serve as a general framework for future studies of this topic. First, without the constraints of capacity limitations, it is found that the total cost for all the generators in a smart grid can achieve the minimal value if the consensus can be reached for the incremental cost of all the generation units and the balance between the supply and demand of powers is kept. Then, by designing a distributed consensus control protocol in multi-agent systems with appropriate initial conditions, incremental cost consensus can be realized and the balance for the powers can also be satisfied. Furthermore, the difficult problem for distributed optimization of the total cost function with bounded capacity limitations is also discussed. A reformulated barrier function is proposed to simplify the analysis, under which the total cost can reach the minimal value if consensus can be achieved for the modified incremental cost with some appropriate initial values. Thus, the distributed optimization problems for the cost function of all generation units with and without bounded capacity limitations can both be solved by using the idea of consensus in multi-agent systems, whose theoretical analysis is still lacking nowadays. Finally, some simulation examples are given to verify the effectiveness of the results in this paper.

Keywords

power dispatch strategy consensus incremental cost capacity limitations distributed protocol multi-agent systems 
012204 

Notes

Acknowledgements

This work was supported by National Key Research and Development Program of China (Grant No. 2016YFB0800401), National Natural Science Foundation of China (Grant Nos. 61673107, 61673104, 61621003, 61532020), National Ten Thousand Talent Program for Young Top-notch Talents, Cheung Kong Scholars Programme of China for Young Scholars, Six Talent Peaks of Jiangsu Province of China (Grant No. 2014-DZXX-004), and Fundamental Research Funds for the Central Universities of China (Grant No. 2242016K41058).

References

  1. 1.
    Ahn S J, Nam S R, Choi J H, et al. Power scheduling of distributed generators for economic and stable operation of a microgrid. IEEE Trans Smart Grid, 2013, 4: 398–405CrossRefGoogle Scholar
  2. 2.
    Bakirtzis A, Petridis V, Kazarlis S. Genetic algorithm solution to the economic dispatch problem. Proc Gener Trans Distrib, 1994, 141: 377–382CrossRefGoogle Scholar
  3. 3.
    Attaviriyanupap P, Kita H, Tanaka E, et al. A hybrid EP and SQP for dynamic economic dispatch with nonsmooth fuel cost function. IEEE Trans Power Syst, 2002, 17: 411–416CrossRefGoogle Scholar
  4. 4.
    Gaing Z L. Particle swarm optimization to solving the economic dispatch considering the generator constraints. IEEE Trans Power Syst, 2003, 18: 1187–1195CrossRefGoogle Scholar
  5. 5.
    Park J, Lee K, Shin J, et al. A particle swarm optimization for economic dispatch with nonsmooth cost functions. IEEE Trans Power Syst, 2005, 20: 34–42CrossRefGoogle Scholar
  6. 6.
    Yu X, Cecati C, Dillon T, et al. The new frontier of smart grids: an industrial electronics perspective. IEEE Ind Electron Mag, 2011, 5: 49–63CrossRefGoogle Scholar
  7. 7.
    Yu W W, Wen G H, Yu X H, et al. Bridging the gap between complex networks and smart grids. J Control Decis, 2014, 1: 102–114CrossRefGoogle Scholar
  8. 8.
    Cao Y, Yu W, Ren W, et al. An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans Ind Inf, 2013, 9: 427–438CrossRefGoogle Scholar
  9. 9.
    Ren W, Beard R W. Distributed Consensus in Multi-vehicle Cooperative Control. Berlin: Springer, 2008CrossRefzbMATHGoogle Scholar
  10. 10.
    Yu W, Wen G, Chen G, et al. Distributed Cooperative Control of Multi-agent Systems. Newark: Wiley, 2016CrossRefGoogle Scholar
  11. 11.
    Cao M, Morse A S, Anderson B D O. Reaching a consensus in a dynamically changing environment: a graphical approach. SIAM J Control Optimiz, 2008, 47: 575–600MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Chen Y, Lü J, Lin Z. Consensus of discrete-time multi-agent systems with transmission nonlinearity. Automatica, 2013, 49: 1768–1775MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Saber R O, Murray R M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Auto Control, 2004, 49: 1520–1533MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Qin J H, Yu C B, Hirche S. Stationary consensus of asynchronous discrete-time second-order multi-agent systems under switching topology. IEEE Trans Ind Inf, 2012, 8: 986–994CrossRefGoogle Scholar
  15. 15.
    Ren W, Beard R W. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Auto Control, 2005, 50: 655–661MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Yu W, Chen G, Cao M. Consensus in directed networks of agents with nonlinear dynamics. IEEE Trans Auto Control, 2011, 56: 1436–1441MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Yu W, Chen G, Cao M, et al. Second-order consensus for multi-agent systems with directed topologies and nonlinear dynamics. IEEE Trans Syst Man Cybern, 2010, 40: 881–891CrossRefGoogle Scholar
  18. 18.
    Yu W, Zhou L, Yu X, et al. Consensus in multi-agent systems with second-order dynamics and sampled data. IEEE Trans Ind Inf, 2013, 9: 2137–2146CrossRefGoogle Scholar
  19. 19.
    Nedić A, Ozdaglar A. Distributed subgradient methods for multiagent optimization. IEEE Trans Auto Control, 2009, 54: 48–61CrossRefzbMATHGoogle Scholar
  20. 20.
    Yuan D, Ho D W C, Xu S. Regularized primal-dual subgradient method for distributed constrained optimization. IEEE Trans Cybern, 2016, 46: 2109–2118CrossRefGoogle Scholar
  21. 21.
    Liu Q, Wang J. L1-minimization algorithms for sparse signal reconstruction based on a projection neural network. IEEE Trans Neural Netw Learn Syst, 2016, 27: 698–707MathSciNetCrossRefGoogle Scholar
  22. 22.
    Zhang Z, Ying X C, Chow M Y. Decentralizing the economic dispatch problem using a two-level incremental cost consensus algorithm in a smart grid environment. In: Proceedings of North American Power Symposium, Boston, 2011. 1–7Google Scholar
  23. 23.
    Zhang Z, Chow M Y. Convergence analysis of the incremental cost consensus algorithm under different communication network topologies in a smart grid. IEEE Trans Power Syst, 2012, 27: 1761–1768CrossRefGoogle Scholar
  24. 24.
    Zhang Z, Chow M Y. The Influence of Time Delays on Decentralized Economic Dispatch by Using Incremental Cost Consensus Algorithm. Berlin: Springer, 2012. 313–326Google Scholar
  25. 25.
    Dominguez-Garcia A D, Cady S T, Hadjicostis C N. Decentralized optimal dispatch of distributed energy resources. In: Proceedings of IEEE 51st Annual Conference on Decision and Control, Maui Hawaii, 2012. 3688–3693Google Scholar
  26. 26.
    Kar S, Hug G. Distributed robust economic dispatch in power systems: a consensus+innovation approach. Power Energy Soc Gen Meet, 2012Google Scholar
  27. 27.
    Yang S, Tan S, Xu J. Consensus based approach for economic dispatch problem in a smart grid. IEEE Trans Power Syst, 2013, 28: 4416–4426CrossRefGoogle Scholar
  28. 28.
    Cherukuri A, Cortes J. Distributed generator coordination for initialization and anytime optimization in economic dispatch. IEEE Trans Control Netw Syst, 2015, 2: 226–237MathSciNetCrossRefGoogle Scholar
  29. 29.
    Horn R A, Johnson C R. Matrix Analysis. Cambridge: Cambridge University Press, 1985CrossRefzbMATHGoogle Scholar
  30. 30.
    Chen G, Wang X, Li X. Introduction to Complex Networks: Models, Structures and Dynamics. Beijing: High Education Press, 2012Google Scholar
  31. 31.
    Godsil C, Royle G. Algebraic Graph Theory. Berlin: Springer, 2001CrossRefzbMATHGoogle Scholar
  32. 32.
    Hale J, Lunel S V. Introduction to Functional Differential Equations. Berlin: Springer, 1993CrossRefzbMATHGoogle Scholar
  33. 33.
    Barabási A L, Albert R. Emergence of scaling in random networks. Science, 1999, 286: 509–512MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Wenwu Yu
    • 1
    • 5
  • Chaojie Li
    • 2
  • Xinghuo Yu
    • 2
  • Guanghui Wen
    • 1
  • Jinhu Lü
    • 3
    • 4
  1. 1.School of MathematicsSoutheast UniversityNanjingChina
  2. 2.School of EngineeringRMIT UniversityMelbourneAustralia
  3. 3.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  4. 4.University of Chinese Academy of SciencesBeijingChina
  5. 5.NAAM Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

Personalised recommendations