Abstract
Designing an efficient distributed economic dispatch (DED) strategy for the smart grid (SG) in the presence of multiple generators plays a paramount role in obtaining various benefits of a new generation power system, such as easy implementation, low maintenance cost, high energy efficiency, and strong robustness against uncertainties. It has drawn a lot of interest from a wide variety of scientific disciplines, including power engineering, control theory, and applied mathematics. We present a state-of-the-art review of some theoretical advances toward DED in the SG, with a focus on the literature published since 2015. We systematically review the recent results on this topic and subsequently categorize them into distributed discrete- and continuous-time economic dispatches of the SG in the presence of multiple generators. After reviewing the literature, we briefly present some future research directions in DED for the SG, including the distributed security economic dispatch of the SG, distributed fast economic dispatch in the SG with practical constraints, efficient initialization-free DED in the SG, DED in the SG in the presence of smart energy storage batteries and flexible loads, and DED in the SG with artificial intelligence technologies.
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References
Bai L, Ye MJ, Sun C, et al., 2019. Distributed economic dispatch control via saddle point dynamics and consensus algorithms. IEEE Trans Contr Syst Technol, 27(2):898–905. https://doi.org/10.1109/TCST.2017.2776222
Binetti G, Abouheaf M, Lewis F, et al., 2013. Distributed solution for the economic dispatch problem. Proc 21st Mediterranean Conf on Control and Automation, p.243–250. https://doi.org/10.1109/MED.2013.6608729
Binetti G, Davoudi A, Naso D, et al., 2014a. A distributed auction-based algorithm for the nonconvex economic dispatch problem. IEEE Trans Ind Inform, 10(2):1124–1132. https://doi.org/10.1109/TII.2013.2287807
Binetti G, Davoudi A, Lewis FL, et al., 2014b. Distributed consensus-based economic dispatch with transmission losses. IEEE Trans Power Syst, 29(4):1711–1720. https://doi.org/10.1109/TPWRS.2014.2299436
Bragin MA, Luh PB, 2017. Distributed and asynchronous unit commitment and economic dispatch. IEEE Power & Energy Society General Meeting, p.1–5. https://doi.org/10.1109/PESGM.2017.8273960
Chen G, Zhao ZY, 2018. Delay effects on consensus-based distributed economic dispatch algorithm in microgrid. IEEE Trans Power Syst, 33(1):602–612. https://doi.org/10.1109/TPWRS.2017.2702179
Chen G, Zhao ZY, 2020. Distributed algorithms for resource allocation in cyber-physical energy systems with uniform/nonuniform communication delays. J Franklin Inst, 357(7):4363–4391. https://doi.org/10.1016/j.jfranklin.2020.02.056
Chen G, Ren JH, Feng EN, 2017. Distributed finite-time economic dispatch of a network of energy resources. IEEE Trans Smart Grid, 8(2):822–832. https://doi.org/10.1109/TSG.2016.2516017
Cherukuri A, Cortés J, 2015. Distributed generator coordination for initialization and anytime optimization in economic dispatch. IEEE Trans Contr Netw Syst, 2(3):226–237. https://doi.org/10.1109/TCNS.2015.2399191
Cherukuri A, Cortés J, 2016. Initialization-free distributed coordination for economic dispatch under varying loads and generator commitment. Automatica, 74:183–193. https://doi.org/10.1016/j.automatica.2016.07.003
Cortés J, 2008. Discontinuous dynamical systems. IEEE Contr Syst Mag, 28(3):36–73. https://doi.org/10.1109/MCS.2008.919306
Dai PC, Yu WW, Wen GH, et al., 2020. Distributed reinforcement learning algorithm for dynamic economic dispatch with unknown generation cost functions. IEEE Trans Ind Inform, 16(4):2258–2267. https://doi.org/10.1109/TII.2019.2933443
Dominguez-Garcia AD, Cady ST, Hadjicostis CN, 2012. Decentralized optimal dispatch of distributed energy resources. Proc 51st IEEE Conf on Decision and Control, p.3688–3693. https://doi.org/10.1109/CDC.2012.6426665
Duan J, Chow MY, 2020. Robust consensus-based distributed energy management for microgrids with packet losses tolerance. IEEE Trans Smart Grid, 11(1):281–290. https://doi.org/10.1109/TSG.2019.2921231
Farhangi H, 2010. The path of the smart grid. IEEE Power Energy Mag, 8(1):18–28. https://doi.org/10.1109/MPE.2009.934876
Guo FH, Wen CY, Mao JF, et al., 2016. Distributed economic dispatch for smart grids with random wind power. IEEE Trans Smart Grid, 7(3):1572–1583. https://doi.org/10.1109/TSG.2015.2434831
He X, Ho DWC, Huang TW, et al., 2018. Second-order continuous-time algorithms for economic power dispatch in smart grids. IEEE Trans Syst Man Cybern Syst, 48(9):1482–1492. https://doi.org/10.1109/TSMC.2017.2672205
He X, Yu JZ, Huang TW, et al., 2019. Distributed power management for dynamic economic dispatch in the multimicrogrids environment. IEEE Trans Contr Syst Technol, 27(4):1651–1658. https://doi.org/10.1109/TCST.2018.2816902
Hu B, Guan ZH, Fu MY, 2019. Distributed event-driven control for finite-time consensus. Automatica, 103:88–95. https://doi.org/10.1016/j.automatica.2019.01.026
Hu HX, Wen GH, Yu WW, et al., 2019. Finite-time coordination behavior of multiple Euler-Lagrange systems in cooperation-competition networks. IEEE Trans Cybern, 49(8):2967–2979. https://doi.org/10.1109/TCYB.2018.2836140
Huang BN, Liu LN, Zhang HG, et al., 2019. Distributed optimal economic dispatch for microgrids considering communication delays. IEEE Trans Man Cybern Syst, 49(8):1634–1642. https://doi.org/10.1109/TSMC.2019.2900722
Kar S, Hug G, 2012. Distributed robust economic dispatch in power systems: a consensus + innovations approach. IEEE Power and Energy Society General Meeting, p.1–8. https://doi.org/10.1109/PESGM.2012.6345156
Kouveliotis-Lysikatos I, Hatziargyriou N, 2017. Distributed economic dispatch considering transmission losses. IEEE Manchester PowerTech, p.1–6. https://doi.org/10.1109/PTC.2017.7981003
Li CJ, Yu XH, Yu WW, 2014. Optimal economic dispatch by fast distributed gradient. Proc 13th Int Conf on Control Automation Robotics & Vision, p.571–576. https://doi.org/10.1109/ICARCV.2014.7064367
Li CJ, Yu XH, Yu WW, et al., 2016. Distributed event-triggered scheme for economic dispatch in smart grids. IEEE Trans Ind Inform, 12(5):1775–1785. https://doi.org/10.1109/TII.2015.2479558
Li CJ, Yu XH, Huang TW, et al., 2018. Distributed optimal consensus over resource allocation network and its application to dynamical economic dispatch. IEEE Trans Neur Netw Learn Syst, 29(6):2407–2418. https://doi.org/10.1109/TNNLS.2017.2691760
Li FY, Qin JH, Kang Y, 2019. Multi-agent system based distributed pattern search algorithm for non-convex economic load dispatch in smart grid. IEEE Trans Power Syst, 34(3):2093–2102. https://doi.org/10.1109/TPWRS.2018.2889989
Li H, Zhou YJ, Jiang GP, et al., 2019. Fixed-time distributed algorithm for economic dispatch in smart grid. Chinese Automation Congress, p.2960–2965. https://doi.org/10.1109/CAC48633.2019.8996348
Li KX, Liu QS, Yang SF, et al., 2018. Cooperative optimization of dual multiagent system for optimal resource allocation. IEEE Trans Syst Man Cybern Syst, in press. https://doi.org/10.1109/TSMC.2018.2859364
Li PK, Liu Y, Xin HH, et al., 2018. A robust distributed economic dispatch strategy of virtual power plant under cyber-attacks. IEEE Trans Ind Inform, 14(10):4343–4352. https://doi.org/10.1109/TII.2017.2788868
Li Q, Gao DW, Zhang HG, et al., 2019. Consensus-based distributed economic dispatch control method in power systems. IEEE Trans Smart Grid, 10(1):941–954. https://doi.org/10.1109/TSG.2017.2756041
Li ZG, Wu WC, Zhang BM, et al., 2013. Dynamic economic dispatch using Lagrangian relaxation with multiplier updates based on a quasi-Newton method. IEEE Trans Power Syst, 28(4):4516–4527. https://doi.org/10.1109/TPWRS.2013.2267057
Li ZS, Guo QL, Sun HB, et al., 2016. Sufficient conditions for exact relaxation of complementarity constraints for storage-concerned economic dispatch. IEEE Trans Power Syst, 31(2):1653–1654. https://doi.org/10.1109/TPWRS.2015.2412683
Liang S, Zeng XL, Chen GP, et al., 2019. Distributed suboptimal resource allocation via a projected form of singular perturbation. https://arxiv.org/abs/1906.03628
Liu Y, Xin HH, Qu ZH, et al., 2016. An attack-resilient cooperative control strategy of multiple distributed generators in distribution networks. IEEE Trans Smart Grid, 7(6):2923–2932. https://doi.org/10.1109/TSG.2016.2542111
Mao S, Dong ZW, Schultz P, et al., 2019. A finite-time distributed optimization algorithm for economic dispatch in smart grids. IEEE Trans Syst Man Cybern Syst, in press. https://doi.org/10.1109/TSMC.2019.2931846
Martinez G, Zhang Y, Giannakis GB, 2014. An efficient primal-dual approach to chance-constrained economic dispatch. North American Power Symp, p.1–6. https://doi.org/10.1109/NAPS.2014.6965379
Mudumbai R, Dasgupta S, Cho BB, 2012. Distributed control for optimal economic dispatch of a network of heterogeneous power generators. IEEE Trans Power Syst, 27(4):1750–1760. https://doi.org/10.1109/TPWRS.2012.2188048
Park JB, Lee KS, Shin JR, et al., 2005. A particle swarm optimization for economic dispatch with nonsmooth cost functions. IEEE Trans Power Syst, 20(1):34–42. https://doi.org/10.1109/TPWRS.2004.831275
Pourbabak H, Luo JW, Chen T, et al., 2018. A novel consensus-based distributed algorithm for economic dispatch based on local estimation of power mismatch. IEEE Trans Smart Grid, 9(6):5930–5942. https://doi.org/10.1109/TSG.2017.2699084
Ren W, Beard RW, Atkins EM, 2007. Information consensus in multivehicle cooperative control. IEEE Contr Syst Mag, 27(2):71–82. https://doi.org/10.1109/MCS.2007.338264
Shi XS, Zheng RH, Lin ZY, et al., 2020. Distributed optimization for economic power dispatch with event-triggered communication. Asian J Contr, online. https://doi.org/10.1002/asjc.2140
Wang D, Wang Z, Wen CY, et al., 2019. Second-order continuous-time algorithm for optimal resource allocation in power systems. IEEE Trans Ind Inform, 15(2):626–637. https://doi.org/10.1109/TII.2018.2881974
Wang HW, Li CJ, Li JY, et al., 2019. A survey on distributed optimisation approaches and applications in smart grids. J Contr Dec, 6(1):41–60. https://doi.org/10.1080/23307706.2018.1549516
Wang R, Li QQ, Zhang BY, et al., 2019a. Distributed consensus based algorithm for economic dispatch in a microgrid. IEEE Trans Smart Grid, 10(4):3630–3640. https://doi.org/10.1109/TSG.2018.2833108
Wang R, Li QQ, Shi Y, et al., 2019b. A gossip-based asynchronous distributed algorithm for economic dispatch problem with transmission losses. IEEE Innovative Smart Grid Technologies-Asia, p.770–775. https://doi.org/10.1109/ISGT-Asia.2019.8881641
Wang YN, Lin ZY, Liang X, et al., 2016. On modeling of electrical cyber-physical systems considering cyber security. Front Inform Technol Electron Eng, 17(5):465–478. https://doi.org/10.1631/FITEE.1500446
Wen GH, Hu GQ, Hu JQ, et al., 2016. Frequency regulation of source-grid-load systems: a compound control strategy. IEEE Trans Ind Inform, 12(1):69–78. https://doi.org/10.1109/TII.2015.2496309
Wen GH, Yu XH, Liu ZW, et al., 2018. Adaptive consensus-based robust strategy for economic dispatch of smart grids subject to communication uncertainties. IEEE Trans Ind Inform, 14(6):2484–2496. https://doi.org/10.1109/TII.2017.2772088
Wu J, Yang T, Wu D, et al., 2017. Distributed optimal dispatch of distributed energy resources over lossy communication networks. IEEE Trans Smart Grid, 8(6):3125–3137. https://doi.org/10.1109/TSG.2017.2720761
Xie J, Yu QY, Cao C, 2018. A distributed randomized gradient-free algorithm for the non-convex economic dispatch problem. Energies, 11(1):244. https://doi.org/10.3390/en11010244
Xing H, Mou YT, Fu MY, et al., 2015a. Distributed algorithm for economic power dispatch including transmission losses. European Control Conf, p.1076–1081. https://doi.org/10.1109/ECC.2015.7330683
Xing H, Mou YT, Fu MY, et al., 2015b. Distributed bisection method for economic power dispatch in smart grid. IEEE Trans Power Syst, 30(6):3024–3035. https://doi.org/10.1109/TPWRS.2014.2376935
Xu YL, Zhang W, Liu WX, 2015. Distributed dynamic programming-based approach for economic dispatch in smart grids. IEEE Trans Ind Inform, 11(1):166–175. https://doi.org/10.1109/TII.2014.2378691
Yan X, Quintana VH, 1997. An efficient predictor-corrector interior point algorithm for security-constrained economic dispatch. IEEE Trans Power Syst, 12(2):803–810. https://doi.org/10.1109/59.589693
Yang SP, Tan SC, Xu JX, 2013. Consensus based approach for economic dispatch problem in a smart grid. IEEE Trans Power Syst, 28(4):4416–4426. https://doi.org/10.1109/TPWRS.2013.2271640
Yang T, Wu D, Sun YN, et al., 2015. Impacts of time delays on distributed algorithms for economic dispatch. IEEE Power & Energy Society General Meeting, p.1–5. https://doi.org/10.1109/PESGM.2015.7286216
Yang T, Wu D, Sun YN, et al., 2016. Minimum-time consensus-based approach for power system applications. IEEE Trans Ind Electron, 63(2):1318–1328. https://doi.org/10.1109/TIE.2015.2504050
Yang T, Lu J, Wu D, et al., 2017. A distributed algorithm for economic dispatch over time-varying directed networks with delays. IEEE Trans Ind Electron, 64(6):5095–5106. https://doi.org/10.1109/TIE.2016.2617832
Yang T, Yi XL, Wu JF, et al., 2019. A survey of distributed optimization. Ann Rev Contr, 47:278–305. https://doi.org/10.1016/j.arcontrol.2019.05.006
Yang ZQ, Xiang J, Li YJ, 2017. Distributed consensus based supply-demand balance algorithm for economic dispatch problem in a smart grid with switching graph. IEEE Trans Ind Electron, 64(2):1600–1610. https://doi.org/10.1109/TIE.2016.2615037
Yi P, Hong YG, Liu F, 2016. Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems. Automatica, 74:259–269. https://doi.org/10.1016/j.automatica.2016.08.007
Yu M, Song C, Feng SX, et al., 2020. A consensus approach for economic dispatch problem in a microgrid with random delay effects. Int J Electr Power Energy Syst, 118:105794. https://doi.org/10.1016/j.ijepes.2019.105794
Yu WW, Li CJ, Yu XH, et al., 2018. Economic power dispatch in smart grids: a framework for distributed optimization and consensus dynamics. Sci China Inform Sci, 61(1):012204. https://doi.org/10.1007/s11432-016-9114-y
Yu XH, Cecati C, Dillon T, et al., 2011. The new frontier of smart grids. IEEE Ind Electron Mag, 5(3):49–63. https://doi.org/10.1109/MIE.2011.942176
Yuan Y, Li HQ, Hu JH, et al., 2019. Stochastic gradient-push for economic dispatch on time-varying directed networks with delays. Int J Electr Power Energy Syst, 113:564–572. https://doi.org/10.1016/j.ijepes.2019.05.051
Zeng WT, Zhang Y, Chow MY, 2017. Resilient distributed energy management subject to unexpected misbehaving generation units. IEEE Trans Ind Inform, 13(1):208–216. https://doi.org/10.1109/TII.2015.2496228
Zhang W, Liu WX, Wang X, et al., 2015. Online optimal generation control based on constrained distributed gradient algorithm. IEEE Trans Power Syst, 30(1):35–45. https://doi.org/10.1109/TPWRS.2014.2319315
Zhang X, Li N, Papachristodoulou A, 2015. Achieving realtime economic dispatch in power networks via a saddle point design approach. IEEE Power & Energy Society General Meeting, p.1–5. https://doi.org/10.1109/PESGM.2015.7286222
Zhang Y, Chow MY, 2015. Distributed optimal generation dispatch considering transmission losses. North American Power Symp, p.1–6. https://doi.org/10.1109/NAPS.2015.7335143
Zhang Y, Rahbari-Asr N, Chow MY, 2016. A robust distributed system incremental cost estimation algorithm for smart grid economic dispatch with communications information losses. J Netw Comput Appl, 59:315–324. https://doi.org/10.1016/j.jnca.2015.05.014
Zhang Z, Chow MY, 2011. Incremental cost consensus algorithm in a smart grid environment. IEEE Power and Energy Society General Meeting, p.1–6. https://doi.org/10.1109/PES.2011.6039422
Zhang Z, Chow MY, 2012. Convergence analysis of the incremental cost consensus algorithm under different communication network topologies in a smart grid. IEEE Trans Power Syst, 27(4):1761–1768. https://doi.org/10.1109/TPWRS.2012.2188912
Zhao CC, He JP, Cheng P, et al., 2017a. Analysis of consensus-based distributed economic dispatch under stealthy attacks. IEEE Trans Ind Electron, 64(6):5107–5117. https://doi.org/10.1109/TIE.2016.2638400
Zhao CC, He JP, Cheng P, et al., 2017b. Consensus-based energy management in smart grid with transmission losses and directed communication. IEEE Trans Smart Grid, 8(5):2049–2061. https://doi.org/10.1109/TSG.2015.2513772
Zhao ZY, Chen G, 2018. Distributed event-based algorithm for economic dispatch problem over digraph with time delays. Proc 15th Int Conf on Control, Automation, Robotics and Vision, p.77–82. https://doi.org/10.1109/ICARCV.2018.8581366
Zhou XQ, Ai Q, Wang H, 2018. Consensus-based distributed economic dispatch incorporating storage optimization and generator ramp-rate constraints in microgrids. J Renew Sustain Energy, 10(4):045501. https://doi.org/10.1063/1.5043187
Zhu YN, Yu WW, Wen GH, 2016. Distributed consensus strategy for economic power dispatch in a smart grid with communication time delays. IEEE Int Conf on Industrial Technology, p.1384–1389. https://doi.org/10.1109/ICIT.2016.7474960
Zhu YN, Ren W, Yu WW, et al., 2019. Distributed resource allocation over directed graphs via continuous-time algorithms. IEEE Trans Syst Man Cybern Syst, in press. https://doi.org/10.1109/TSMC.2019.2894862
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Project supported by the National Natural Science Foundation of China (Nos. 61722303, 61673104, and 61973133), the Six Talent Peaks Project of Jiangsu Province, China (No. 2019-DZXX-006), and the Australian Research Council (No. DP200101199)
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Guanghui WEN drafted the manuscript. Xinghuo YU and Zhiwei LIU helped organize the manuscript. Guanghui WEN revised and finalized the paper.
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Guanghui WEN, Xinghuo YU, and Zhiwei LIU declare that they have no conflict of interest.
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Wen, G., Yu, X. & Liu, Z. Recent progress on the study of distributed economic dispatch in smart grid: an overview. Front Inform Technol Electron Eng 22, 25–39 (2021). https://doi.org/10.1631/FITEE.2000205
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DOI: https://doi.org/10.1631/FITEE.2000205
Key words
- Distributed economic dispatch
- Distributed optimization
- Smart grid
- Continuous-time optimization algorithm
- Discrete-time optimization algorithm