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Regular Paper | Open Access

Consensus-based Optimal Control Strategy for Multi-microgrid Systems with Battery Degradation Consideration

Tonghe Wang1, Hong Liang2, Bo He3, Haochen Hua4, Yuchao Qin5, Junwei Cao6()
Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou 510640, China
Meihua Holdings Group Co., Ltd., Langfang 065001, China
Department of Astronautical Science and Technology, Space Engineering University, Beijing 101416, China
College of Energy and Electrical Engineering, Hohai University, Nanjing, 211100, China
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK
Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China
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Abstract

Consensus has been widely used in distributed control, where distributed individuals need to share their states with their neighbors through communication links to achieve a common goal. However, the objectives of existing consensus-based control strategies for energy systems seldom address battery degradation cost, which is an important performance indicator to assess the performance and sustainability of battery energy storage (BES) systems. In this paper, we propose a consensus-based optimal control strategy for multi-microgrid systems, aiming at multiple control objectives including minimizing battery degradation cost. Distributed consensus is used to synchronize the ratio of BES output power to BES state-of-charge (SoC) among all microgrids while each microgrid is trying to reach its individual optimality. In order to reduce the pressure of communication links and prevent excessive exposure of local information, this ratio is the only state variable shared between microgrids. Since our complex nonlinear problem might be difficult to solve by traditional methods, we design a compressive sensing-based gradient descent (CSGD) method to solve the control problem. Numerical simulation results show that our control strategy results in a 74.24% reduction in battery degradation cost on average compared to the control method without considering battery degradation. In addition, the compressive sensing method causes an 89.12% reduction in computation time cost compared to the traditional Monte Carlo (MC) method in solving the control problem.

Keywords

Battery degradationcompressive sensingconsensusdistributed controlmulti-microgrid

References

[1]
M. Razi and Y. Ali, “Ranking renewable energy production methods based on economic and environmental criteria using multi-criteria decision analysis,” Environment Systems and Decisions, vol. 39, no. 2, pp. 198–213, Jun. 2019.
Crossref Google Scholar
[2]
M. F. Zia, E. Elbouchikhi, and M. Benbouzid, “Microgrids energy management systems: a critical review on methods, solutions, and prospects,” Applied Energy, vol. 222, pp. 1033–1055, Jul. 2018.
Crossref Google Scholar
[3]
C. R. Reddy and K. H. Reddy, “A new passive islanding detection technique for integrated distributed generation system using rate of change of regulator voltage over reactive power at balanced islanding,” Journal of Electrical Engineering & Technology, vol. 14, no. 2, pp. 527–534, Jan. 2019.
Crossref Google Scholar
[4]
B. Van Scoy and L. Lessard, “Systematic analysis of distributed optimization algorithms over jointly-connected networks,” arXiv preprint arXiv:2003.10500, 2020.
Crossref Google Scholar
[5]
Y. S. Li, D. W. Gao, W. Gao, H. G. Zhang, and J. G. Zhou, “A distributed double-Newton descent algorithm for cooperative energy management of multiple energy bodies in energy Internet,” IEEE Transactions on Industrial Informatics, vol. 17, no. 9, pp. 5993–6003, Sept. 2021.
Crossref Google Scholar
[6]
J. G. Lai and X. Q. Lu, “Robust self-consistent control of PV-battery-based microgrids without continuous communication,” International Journal of Electrical Power & Energy Systems, vol. 119, pp. 105900, Jul. 2020.
Crossref Google Scholar
[7]
W. Y. Zheng, W. C. Wu, Z. G. Li, H. B. Sun, and Y. H. Hou, “A non-iterative decoupled solution for robust integrated electricity-heat scheduling based on network reduction,” IEEE Transactions on Sustainable Energy, vol. 12, no. 2, pp. 1473–1488, Apr. 2021.
Crossref Google Scholar
[8]
W. Y. Zheng, Y. H. Hou, and Z. G. Li, “A dynamic equivalent model for district heating networks: formulation, existence and application in distributed electricity-heat operation,” IEEE Transactions on Smart Grid, vol. 12, no. 3, pp. 2685–2695, May 2021.
Crossref Google Scholar
[9]
B. Liu, W. L. Lu, and T. P. Chen, “A new approach to the stability analysis of continuous-time distributed consensus algorithms,” Neural Networks, vol. 46, pp. 242–248, Oct. 2013.
Crossref Google Scholar
[10]
Z. A. Zhang and M. Y. Chow, “Convergence analysis of the incremental cost consensus algorithm under different communication network topologies in a smart grid,” IEEE Transactions on Power Systems, vol. 27, no. 4, pp. 1761–1768, Nov. 2012.
Crossref Google Scholar
[11]
P. Speciale, D. P. Paudel, M. R. Oswald, T. Kroeger, L. Van Gool, and M. Pollefeys, “Consensus maximization with linear matrix inequality constraints,” in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017, pp. 5048–5056.
Crossref Google Scholar
[12]
L. Zhu, S. Shi, and X. M. Gu, “A consensus-based distributed clock synchronization for wireless sensor network,” in 2018 14th International Wireless Communications & Mobile Computing Conference (IWCMC), 2018, pp. 828–832.
Crossref Google Scholar
[13]
Q. Zhou, Z. Tian, M. Shahidehpour, X. Liu, A. Alabdulwahab, and A. Abusorrah, “Optimal consensus-based distributed control strategy for coordinated operation of networked microgrids,” IEEE Transactions on Power Systems, vol. 35, no. 3, pp. 2452–2462, May 2020.
Crossref Google Scholar
[14]
K. Utkarsh, A. Trivedi, D. Srinivasan, and T. Reindl, “A consensus-based distributed computational intelligence technique for real-time optimal control in smart distribution grids,” IEEE Transactions on Emerging Topics in Computational Intelligence, vol. 1, no. 1, pp. 51–60, Feb. 2017.
Crossref Google Scholar
[15]
M. Fattahi and A. Afshar, “Distributed consensus of multi-agent systems with input faults and time-varying delays,” Asian Journal of Control, vol. 20, no. 4, pp. 1682–1685, Jul. 2018.
Crossref Google Scholar
[16]
H. Pourbabak, J. W. Luo, T. Chen, and W. C. Su, “A novel consensus-based distributed algorithm for economic dispatch based on local estimation of power mismatch,” IEEE Transactions on Smart Grid, vol. 9, no. 6, pp. 5930–5942, Nov. 2018.
Crossref Google Scholar
[17]
J. G. Zhou, S. Kim, H. G. Zhang, Q. Y. Sun, and R. K. Han, “Consensus-based distributed control for accurate reactive, harmonic, and imbalance power sharing in microgrids,” IEEE Transactions on Smart Grid, vol. 9, no. 4, pp. 2453–2467, Jul. 2018.
Crossref Google Scholar
[18]
J. Khazaei and Z. X. Miao, “Consensus control for energy storage systems,” IEEE Transactions on Smart Grid, vol. 9, no. 4, pp. 3009–3017, Jul. 2018.
Crossref Google Scholar
[19]
M. Zeraati, M. E. H. Golshan, and J. M. Guerrero, “A consensus-based cooperative control of PEV battery and PV active power curtailment for voltage regulation in distribution networks,” IEEE Transactions on Smart Grid, vol. 10, no. 1, pp. 670–680, Jan. 2019.
Crossref Google Scholar
[20]
R. Wang, Q. Q. Li, B. Y. Zhang, and L. H. Wang, “Distributed consensus based algorithm for economic dispatch in a microgrid,” IEEE Transactions on Smart Grid, vol. 10, no. 4, pp. 3630–3640, Jul. 2019.
Crossref Google Scholar
[21]
S. Z. Tajalli, T. Niknam, and A. Kavousi-Fard, “Stochastic electricity social welfare enhancement based on consensus neighbor virtualization,” IEEE Transactions on Industrial Electronics, vol. 66, no. 12, pp. 9571–9580, Dec .2019.
Crossref Google Scholar
[22]
Y. F. Guo, Q. W. Wu, H. L. Gao, and F. F. Shen, “Distributed voltage regulation of smart distribution networks: consensus-based information synchronization and distributed model predictive control scheme,” International Journal of Electrical Power & Energy Systems, vol. 111, pp. 58–65, Oct. 2019.
Crossref Google Scholar
[23]
R. K. Han, L. X. Meng, G. F. Trecate, E. A. A. Coelho, J. C. Vasquez, and J. M. Guerrero, “Containment and consensus-based distributed coordination control for voltage bound and reactive power sharing in AC microgrid,” in 2017 IEEE Applied Power Electronics Conference and Exposition (APEC), 2017, pp. 3549–3556.
Crossref Google Scholar
[24]
A. T. Jiang, Y. Han, P. Yang, C. L. Wang, and J. Q. Xiong, “Enhanced consensus-based distributed control for accurate reactive power sharing of islanded microgrids without LBC lines,” in 2018 IEEE 4th Southern Power Electronics Conference (SPEC), 2018, pp. 1–8.
Crossref Google Scholar
[25]
N. Zhang, Q. Y. Sun, J. W. Wang, and L. X. Yang, “Distributed adaptive dual control via consensus algorithm in the energy Internet,” IEEE Transactions on Industrial Informatics, vol. 17, no. 7, pp. 4848–4860, Jul. 2021.
Crossref Google Scholar
[26]
L. T. Xing, Y. Mishra, Y. C. Tian, G. Ledwich, C. J. Zhou, W. L. Du, and F. Qian, “Distributed state-of-charge balance control with event-triggered signal transmissions for multiple energy storage systems in smart grid,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 8, pp. 1601–1611, Aug. 2019.
Crossref Google Scholar
[27]
H. Q. Yang, S. H. Li, Q. Li, and W. R. Chen, “Hierarchical distributed control for decentralized battery energy storage system based on consensus algorithm with pinning node,” Protection and Control of Modern Power Systems, vol. 3, no. 1, pp. 6, Feb. 2018.
Crossref Google Scholar
[28]
X. Chen, M. X. Shi, J. Y. Zhou, W. P. Zuo, Y. Chen, J. Y. Wen, and H. B. He, “Consensus-based distributed control for photovoltaic-battery units in a DC microgrid,” IEEE Transactions on Industrial Electronics, vol. 66, no. 10, pp. 7778–7787, Oct. 2019.
Crossref Google Scholar
[29]
M. F. Zia, E. Elbouchikhi, and M. Benbouzid, “Optimal operational planning of scalable DC microgrid with demand response, islanding, and battery degradation cost considerations,” Applied Energy, vol. 237, pp. 695–707, Mar. 2019.
Crossref Google Scholar
[30]
A. Hossain, H. R. Pota, S. Squartini, F. Zaman, and K. M. Muttaqi, “Energy management of community microgrids considering degradation cost of battery,” Journal of Energy Storage, vol. 22, pp. 257–269, Apr. 2019.
Crossref Google Scholar
[31]
S. Tamura, “A V2G strategy to increase the cost–benefit of primary frequency regulation considering EV battery degradation,” Electrical Engineering in Japan, vol. 212, no. 1–4, pp. 11–22, Sept. 2020.
Crossref Google Scholar
[32]
K. Antoniadou-Plytaria, D. Steen, L. A. Tuan, O. Carlson, and M. A. F. Ghazvini, “Market-based energy management model of a building microgrid considering battery degradation,” IEEE Transactions on Smart Grid, vol. 12, no. 2, pp. 1794–1804, Mar. 2021.
Crossref Google Scholar
[33]
K. Ginigeme and Z. L. Wang, “Distributed optimal vehicle-to-grid approaches with consideration of battery degradation cost under real-time pricing,” IEEE Access, vol. 8, pp. 5225–5235, Jan. 2020.
Crossref Google Scholar
[34]
A. Bera, S. Almasabi, Y. T. Tian, R. H. Byrne, B. Chalamala, T. A. Nguyen, and J. Mitra, “Maximizing the investment returns of a grid-connected battery considering degradation cost,” IET Generation, Transmission & Distribution, vol. 14, no. 21, pp. 4711–4718, Nov. 2020.
Crossref Google Scholar
[35]
Y. Iwafune and K. Ogimoto, “Economic impacts of the demand response of electric vehicles considering battery degradation,” Energies, vol. 13, no. 21, pp. 5771, Nov. 2020.
Crossref Google Scholar
[36]
Y. X. Guo and C. Y. Zhao, “Islanding-aware robust energy management for microgrids,” IEEE Transactions on Smart Grid, vol. 9, no. 2, pp. 1301–1309, Mar. 2018.
Crossref Google Scholar
[37]
Z. C. Shi, H. Liang, S. J. Huang, and V. Dinavahi, “Distributionally robust chance-constrained energy management for islanded microgrids,” IEEE Transactions on Smart Grid, vol. 10, no. 2, pp. 2234–2244, Mar. 2019.
Crossref Google Scholar
[38]
Y. L. Mo and R. M. Murray, “Privacy preserving average consensus,” IEEE Transactions on Automatic Control, vol. 62, no. 2, pp. 753–765, Feb. 2017.
Crossref Google Scholar
[39]
T. J. Yin, Y. Z. Lv, and W. W. Yu, “Accurate privacy preserving average consensus,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 67, no. 4, pp. 690–694, Apr. 2020.
Crossref Google Scholar
[40]
X. S. Hu, F. C. Sun, and Y. Zou, “Comparison between two model-based algorithms for Li-ion battery SOC estimation in electric vehicles,” Simulation Modeling Practice and Theory, vol. 34, pp. 1–11, May 2013.
Crossref Google Scholar
[41]
T. Morstyn, A. V. Savkin, B. Hredzak, and V. G. Agelidis, “Multi-agent sliding mode control for state of charge balancing between battery energy storage systems distributed in a DC microgrid,” IEEE Transactions on Smart Grid, vol. 9, on. 5, pp. 4735–4743, Sept. 2018.
Crossref Google Scholar
[42]
Y. Fan, G. Q. Hu, and M. Egerstedt, “Distributed reactive power sharing control for microgrids with event-triggered communication,” IEEE Transactions on Control Systems Technology, vol. 25, no. 1, pp. 118–128, Jan. 2017.
Crossref Google Scholar
[43]
H. C. Hua, Z. Q. Wei, Y. C. Qin, T. H. Wang, L. Y. Li, and J. W. Cao, “Review of distributed control and optimization in energy internet: From traditional methods to artificial intelligence-based methods,” IET Cyber-Physical Systems: Theory & Applications, vol. 6, no. 2, pp. 63–79, Jun. 2021.
Crossref Google Scholar
[44]
F. H. Aghdam, N. T. Kalantari, and B. Mohammadi-Ivatloo, “A chance-constrained energy management in multi-microgrid systems considering degradation cost of energy storage elements,” Journal of Energy Storage, vol. 29, pp. 101416, Jun. 2020.
Crossref Google Scholar
[45]
S. Q. Wang, D. X. Guo, X. B. Han, L. G. Lu, K. Sun, W. H. Li, D. U. Sauer, and M. G. Ouyang, “Impact of battery degradation models on energy management of a grid-connected DC microgrid,” Energy, vol. 207, pp. 118228, Sept. 2020.
Crossref Google Scholar
[46]
Q. L. Wei, G. Shi, R. Z. Song, and Y. Liu, “Adaptive dynamic programming-based optimal control scheme for energy storage systems with solar renewable energy,” IEEE Transactions on Industrial Electronics, vol. 64, no. 7, pp. 5468–5478, Jul. 2017.
Crossref Google Scholar
[47]
S. Nadarajah, F. Margot, and N. Secomandi, “Comparison of least squares Monte Carlo methods with applications to energy real options,” European Journal of Operational Research, vol. 256, no. 1, pp. 196–204, Jan. 2017.
Crossref Google Scholar
[48]
E. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 21–30, Mar. 2008.
Crossref Google Scholar
[49]
L. J. Hou, Y. L. Qin, H. Zheng, Z. M. Pan, J. C. Mei, and Y. T. Hu, “Hybrid high-order and fractional-order total variation with nonlocal regularization for compressive sensing image reconstruction,” Electronics, vol. 10, no. 2, pp. 150, Jan. 2021.
Crossref Google Scholar
[50]
S. H. Fang, Z. M. Kong, P. Hu, and L. Ding, “A novel topology identification method based on compressive sensing for multidimensional networks,” International Journal of Modern Physics B, vol. 34, no. 30, pp. 2050294, Dec. 2020.
Crossref Google Scholar
[51]
D. Y. Lin, W. D. Min, J. F. Xu, J. X. Yang, and J. L. Zhang, “An energy-efficient routing method in WSNs based on compressive sensing: From the perspective of social welfare,” IEEE Embedded Systems Letters, vol. 13, no. 3, pp. 126–129, Sept. 2020.
Crossref Google Scholar
[52]
H. C. Hua, Y. C. Qin, H. X. Xu, C. T. Hao, and J. W. Cao, “Robust control method for DC microgrids and energy routers to improve voltage stability in energy internet,” Energies, vol. 12, no. 9, pp. 1622, Apr. 2019.
Crossref Google Scholar
[53]
H. C. Hua, J. W. Cao, G. Yang, and G. Ren, “Voltage control for uncertain stochastic nonlinear system with application to energy internet: Non-fragile robust H∞ approach,” Journal of Mathematical Analysis and Applications, vol. 463, no. 1, pp. 93–110, Jul. 2018.
Crossref Google Scholar
[54]
H. C. Hua, Y. C. Qin, C. T. Hao, and J. W. Cao, “Stochastic optimal control for energy internet: a bottom-up energy management approach,” IEEE Transactions on Industrial Informatics, vol. 15, no. 3, pp. 1788–1797, Mar. 2019.
Crossref Google Scholar
[55]
R. Billinton and P. R. S. Kuruganty, “Probabilistic assessment of transient stability in a practical multimachine system,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-100, no. 7, pp. 3634–3641, Jul. 1981.
Crossref Google Scholar
[56]
M. B. D. C. Filho, A. M. L. Da Silva, V. L. Arienti, and S. M. P. Ribeiro, “Probabilistic load modeling for power system expansion planning,” in 1991 Third International Conference on Probabilistic Methods Applied to Electric Power Systems, 1991, pp. 203–207.
Google Scholar
[57]
H. C. Hua, Y. C. Qin, Z. C. He, L. Y. Li, and J. W. Cao, “Energy sharing and frequency regulation in energy network via mixed H2/H∞ control with Markovian jump,” CSEE Journal of Power and Energy Systems, vol. 7, no. 6, pp. 1302–1311, Nov. 2021.
Google Scholar
[58]
T. Odun-Ayo and M. L. Crow, “Structure-preserved power system transient stability using stochastic energy functions,” IEEE Transactions on Power Systems, vol. 27, no. 3, pp. 1450–1458, Aug. 2012.
Crossref Google Scholar
[59]
H. C. Hua, Y. C. Qin, C. T. Hao, and J. W. Cao, “Optimal energy management strategies for energy internet via deep reinforcement learning approach,” Applied Energy, vol. 239, pp. 598–609, Apr. 2019.
Crossref Google Scholar
[60]
M. U. B. Niazi, A. B. Özgüler, and A. Yildiz, “Consensus as a nash equilibrium of a dynamic game,” in 2016 12th International Conference on Signal-Image Technology & Internet-Based Systems (SITIS), 2016, pp. 365–372.
Crossref Google Scholar
[61]
G. T. Buzzard, S. H. Chan, S. Sreehari, and C. A. Bouman, “Plug-and-play unplugged: Optimization-free reconstruction using consensus equilibrium,” SIAM Journal on Imaging Sciences, vol. 11, no. 3, pp. 2001–2020, 2018.
Crossref Google Scholar
[62]
F. Xiao and L. Wang, “Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays,” IEEE Transactions on Automatic Control, vol. 53, no. 8, pp. 1804–1816, Sept. 2008.
Crossref Google Scholar
[63]
F. Ye, W. D. Zhang, and L. L. Ou, “H2 consensus control of time-delayed multi-agent systems: a frequency-domain method,” ISA Transactions, vol. 66, pp. 437–447, Jan. 2017.
Crossref Google Scholar
[64]
J. Y. Wang, G. H. Wen, Z. S. Duan, and J. H. Lü, “Stochastic consensus control integrated with performance improvement: A consensus region-based approach,” IEEE Transactions on Industrial Electronics, vol. 67, no. 4, pp. 3000–3012, Apr. 2020.
Crossref Google Scholar
[65]
J. Peng, J. Hampton, and A. Doostan, “A weighted ℓ1-minimization approach for sparse polynomial chaos expansions,” Journal of Computational Physics, vol. 267, pp. 92–111, Jun. 2014.
Crossref Google Scholar
[66]
J. D. Jakeman, M. S. Eldred, and K. Sargsyan, “Enhancing ℓ1-minimization estimates of polynomial chaos expansions using basis selection,” Journal of Computational Physics, vol. 289, pp. 18–34, May 2015.
Crossref Google Scholar
[67]
A. Doostan and H. Owhadi, “A non-adapted sparse approximation of PDEs with stochastic inputs,” Journal of Computational Physics, vol. 230, no. 8, pp. 3015–3034, Apr. 2011.
Crossref Google Scholar
[68]
D. B. Xiu and G. E. Karniadakis, “The Wiener–Askey polynomial chaos for stochastic differential equations,” SIAM Journal on Scientific Computing, vol. 24, no. 2, pp. 619–644, Oct. 2002.
Crossref Google Scholar
[69]
H. Rauhut and R. Ward, “Sparse Legendre expansions via ℓ1-minimization,” Journal of Approximation Theory, vol. 164, no. 5, pp. 517–533, May 2012.
Crossref Google Scholar
[70]
L. Yan, L. Guo, and D. B. Xiu, “Stochastic collocation algorithms using ℓ1-minimization,” International Journal for Uncertainty Quantification, vol. 2, no. 3, pp. 279–293, Jan. 2012.
Crossref Google Scholar
[71]
X. Yang, H. Lei, N. A. Baker, and G. Lin, “Enhancing sparsity of Hermite polynomial expansions by iterative rotations,” Journal of Computational Physics, vol. 307, pp. 94–109, Feb. 2016.
Crossref Google Scholar
[72]
C. C. Remsing, “Optimal control and Hamilton-Poisson formalism,” International Journal of Pure and Applied Mathematics, vol. 59, no. 1, pp. 11–17, Jan. 2010.
Google Scholar
[73]
M. Zeraati, M. E. H. Golshan, and J. M. Guerrero, “Distributed control of battery energy storage systems for voltage regulation in distribution networks with high PV penetration,” IEEE Transactions on Smart Grid, vol. 9, no. 4, pp. 3582–3593, Jul. 2018.
Crossref Google Scholar
[74]
H. C. Hua, C. T. Hao, Y. C. Qin, and J. W. Cao, “Stochastic robust H∞ control strategy for coordinated frequency regulation in energy internet considering time delay and uncertainty,” in 2018 13th World Congress on Intelligent Control and Automation (WCICA), 2018, pp. 111–118.
Crossref Google Scholar
[75]
J. Giraldo, A. Cardenas, E. Mojica-Nava, N. Quijano, and R. Dong, “Delay and sampling independence of a consensus algorithm and its application to smart grid privacy,” in 53rd IEEE Conference on Decision and Control, 2014, pp. 1389–1394.
Crossref Google Scholar
[76]
W. Y. Zheng and D. J. Hill, “Distributed real-time dispatch of integrated electricity and heat systems with guaranteed feasibility,” IEEE Transactions on Industrial Informatics, vol. 18, no. 2, pp. 1175–1185, Feb. 2022.
Crossref Google Scholar
[77]
W. Y. Zheng and D. J. Hill, “Incentive-based coordination mechanism for distributed operation of integrated electricity and heat systems,” Applied Energy, vol. 285, pp. 116373, Mar. 2021.
Crossref Google Scholar
[78]
X. Y. Chen, “Energy-use internet and friendly interaction with power grid: A perspective,” in 2020 IEEE International Conference on Energy Internet (ICEI), 2020, pp. 50–55.
Crossref Google Scholar
[79]
M. J. Ye and G. Q. Hu, “Game design and analysis for price-based demand response: An aggregate game approach,” IEEE Transactions on Cybernetics, vol. 47, no. 3, pp. 720–730, Mar. 2017.
Crossref Google Scholar
[80]
M. J. Ye, “Distributed Nash equilibrium seeking for games in systems with bounded control inputs,” IEEE Transactions on Automatic Control, vol. 66, no. 8, pp. 3833–3839, Aug. 2021.
Crossref Google Scholar
CSEE Journal of Power and Energy Systems
Volume 10 Issue 5,
September 2024
Pages 1911-1924
DOI: 10.17775/CSEEJPES.2021.03180
Cite this article:
Wang T, Liang H, He B, et al. Consensus-based Optimal Control Strategy for Multi-microgrid Systems with Battery Degradation Consideration. CSEE Journal of Power and Energy Systems, 2024, 10(5): 1911-1924. https://doi.org/10.17775/CSEEJPES.2021.03180
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