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

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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.

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References

  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: 398–405

    Article  Google Scholar 

  2. Bakirtzis A, Petridis V, Kazarlis S. Genetic algorithm solution to the economic dispatch problem. Proc Gener Trans Distrib, 1994, 141: 377–382

    Article  Google Scholar 

  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: 411–416

    Article  Google Scholar 

  4. Gaing Z L. Particle swarm optimization to solving the economic dispatch considering the generator constraints. IEEE Trans Power Syst, 2003, 18: 1187–1195

    Article  Google Scholar 

  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: 34–42

    Article  Google Scholar 

  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: 49–63

    Article  Google Scholar 

  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: 102–114

    Article  Google Scholar 

  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: 427–438

    Article  Google Scholar 

  9. Ren W, Beard R W. Distributed Consensus in Multi-vehicle Cooperative Control. Berlin: Springer, 2008

    Book  MATH  Google Scholar 

  10. Yu W, Wen G, Chen G, et al. Distributed Cooperative Control of Multi-agent Systems. Newark: Wiley, 2016

    Book  Google Scholar 

  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: 575–600

    Article  MathSciNet  MATH  Google Scholar 

  12. Chen Y, Lü J, Lin Z. Consensus of discrete-time multi-agent systems with transmission nonlinearity. Automatica, 2013, 49: 1768–1775

    Article  MathSciNet  MATH  Google Scholar 

  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: 1520–1533

    Article  MathSciNet  MATH  Google Scholar 

  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: 986–994

    Article  Google Scholar 

  15. Ren W, Beard R W. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Auto Control, 2005, 50: 655–661

    Article  MathSciNet  MATH  Google Scholar 

  16. Yu W, Chen G, Cao M. Consensus in directed networks of agents with nonlinear dynamics. IEEE Trans Auto Control, 2011, 56: 1436–1441

    Article  MathSciNet  MATH  Google Scholar 

  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: 881–891

    Article  Google Scholar 

  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: 2137–2146

    Article  Google Scholar 

  19. Nedić A, Ozdaglar A. Distributed subgradient methods for multiagent optimization. IEEE Trans Auto Control, 2009, 54: 48–61

    Article  MATH  Google Scholar 

  20. Yuan D, Ho D W C, Xu S. Regularized primal-dual subgradient method for distributed constrained optimization. IEEE Trans Cybern, 2016, 46: 2109–2118

    Article  Google Scholar 

  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: 698–707

    Article  MathSciNet  Google Scholar 

  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. 1–7

    Google Scholar 

  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: 1761–1768

    Article  Google Scholar 

  24. Zhang Z, Chow M Y. The Influence of Time Delays on Decentralized Economic Dispatch by Using Incremental Cost Consensus Algorithm. Berlin: Springer, 2012. 313–326

    Google Scholar 

  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. 3688–3693

    Google Scholar 

  26. Kar S, Hug G. Distributed robust economic dispatch in power systems: a consensus+innovation approach. Power Energy Soc Gen Meet, 2012

    Google Scholar 

  27. Yang S, Tan S, Xu J. Consensus based approach for economic dispatch problem in a smart grid. IEEE Trans Power Syst, 2013, 28: 4416–4426

    Article  Google Scholar 

  28. Cherukuri A, Cortes J. Distributed generator coordination for initialization and anytime optimization in economic dispatch. IEEE Trans Control Netw Syst, 2015, 2: 226–237

    Article  MathSciNet  Google Scholar 

  29. Horn R A, Johnson C R. Matrix Analysis. Cambridge: Cambridge University Press, 1985

    Book  MATH  Google Scholar 

  30. Chen G, Wang X, Li X. Introduction to Complex Networks: Models, Structures and Dynamics. Bei**g: High Education Press, 2012

    Google Scholar 

  31. Godsil C, Royle G. Algebraic Graph Theory. Berlin: Springer, 2001

    Book  MATH  Google Scholar 

  32. Hale J, Lunel S V. Introduction to Functional Differential Equations. Berlin: Springer, 1993

    Book  MATH  Google Scholar 

  33. Barabási A L, Albert R. Emergence of scaling in random networks. Science, 1999, 286: 509–512

    Article  MathSciNet  MATH  Google Scholar 

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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).

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Authors and Affiliations

  1. School of Mathematics, Southeast University, Nan**g, 210096, China

    Wenwu Yu & Guanghui Wen

  2. School of Engineering, RMIT University, Melbourne, VIC, 3001, Australia

    Chaojie Li & **nghuo Yu

  3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Bei**g, 100190, China

    **hu Lü

  4. University of Chinese Academy of Sciences, Bei**g, 100049, China

    **hu Lü

  5. NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Wenwu Yu

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  1. Wenwu Yu
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  2. Chaojie Li
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  3. **nghuo Yu
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  4. Guanghui Wen
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  5. **hu Lü
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Correspondence to Wenwu Yu.

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Conflict of interest The authors declare that they have no conflict of interest.

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Yu, W., Li, C., Yu, X. et al. Economic power dispatch in smart grids: a framework for distributed optimization and consensus dynamics. Sci. China Inf. Sci. 61, 012204 (2018). https://doi.org/10.1007/s11432-016-9114-y

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