基于Minkowski Sum的热泵负荷调度灵活性聚合方法
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摘要
随着"煤改电"工程的实施,配电网中的热泵负荷显著增加。站在热泵用户的角度,采用合作博弈模式联盟热泵的调度灵活性参与配电网日前调度。为准确刻画该热泵负荷集群的聚合灵活性,采用基于Minkowski Sum的约束空间叠加方法,并通过寻找其最大内接正方体或直角棱锥简化约束而将热泵集群刻画为"虚拟同步机"或"虚拟储能"模型。进一步地,提出基于近似Shapley Value的用户间收益分配方法。基于IEEE 33节点系统的算例证明了本方法的有效性。
With the implementation of the "coal to electricity" project, the heat pump load in the distribution network increases significantly. Standing in the point of heat pump users, cooperative game mode is used for heat pumps joining in day-ahead dispatching of distribution network. In order to accurately describe the polymerization flexibility of the heat pump load cluster, this paper uses the constraint space superposition method based on Minkowski Sum, and describes the heat pump cluster as a "virtual synchronous machine" or "virtual energy storage" model by looking for its maximal inner cube or rectangular pyramid simplification constraint. Furthermore, a method of income distribution among users based on approximated Shapley Value is proposed. The validity of the proposed method is verified by the case based on IEEE 33 mode system.
With the implementation of the "coal to electricity" project, the heat pump load in the distribution network increases significantly. Standing in the point of heat pump users, cooperative game mode is used for heat pumps joining in day-ahead dispatching of distribution network. In order to accurately describe the polymerization flexibility of the heat pump load cluster, this paper uses the constraint space superposition method based on Minkowski Sum, and describes the heat pump cluster as a "virtual synchronous machine" or "virtual energy storage" model by looking for its maximal inner cube or rectangular pyramid simplification constraint. Furthermore, a method of income distribution among users based on approximated Shapley Value is proposed. The validity of the proposed method is verified by the case based on IEEE 33 mode system.
引文
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[9] 严旭,吴锴,周孟戈,等.基于不同可调度热源的风电出力平滑模型[J].电力系统保护与控制,2013,41(21):122-128.YAN Xu, WU Kai, ZHOU Mengge, et al. Model of smoothing wind power based on various dispatchable heat sources[J]. Power System Protection and Control, 2013, 41(21): 122-128.
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[11] 栗子豪,吴文传,朱洁,等.基于机会约束的主动配电网热泵日前调度模型及可解性转换[J].电力系统自动化,2018,42(11):24-31.DOI:10.7500/AEPS20170825007.LI Zihao, WU Wenchuan, ZHU Jie, et al. Chance-constrained model for day-ahead heat pump scheduling in active distribution network and its tractability transformation[J]. Automation of Electric Power Systems, 2018, 42(11): 24-31. DOI: 10.7500/AEPS20170825007.
[12] LI Zihao, WU Wenchuan, ZHANG Boming. Kullback-Leibler divergence-based distributionally robust optimisation model for heat pump day-ahead operational schedule to improve PV integration[J]. IET Generation, Transmission & Distribution, 2018, 12(13): 3136-3144.
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[16] ZHAO L, ZHANG W, HAO H, et al. A geometric approach to aggregate flexibility modeling of thermostatically controlled loads[J]. IEEE Transactions on Power Systems, 2017, 32(6): 4721-4731.
[17] SONG M, GAO C, YAN H, et al. Thermal battery modeling of inverter air conditioning for demand response[J]. IEEE Transactions on Smart Grid, 2018, 9(6): 5522-5534.
[18] LIU W, GU W, SHENG W, et al. Decentralized multi-agent system-based cooperative frequency control for autonomous microgrids with communication constraints[J]. IEEE Transactions on Sustainable Energy, 2017, 5(2): 446-456.
[19] MA K, HU G, SPANOS C J. A cooperative demand response scheme using punishment mechanism and application to industrial refrigerated warehouses[J]. IEEE Transactions on Industrial Informatics, 2017, 11(6): 1520-1531.
[20] MOSTAFA H A, EL SHATSHAT R, SALAMA M M A. A correlated equilibrium game-theoretic approach for multiple participants electric distribution systems operation[J]. IEEE Transactions on Smart Grid, 2016, 7(1): 32-42.
[21] CHAI B, CHEN J, YANG Z, et al. Demand response management with multiple utility companies: a two-level game approach[J]. IEEE Transactions on Smart Grid, 2014, 5(2): 722-731.
[22] 陈丽霞,孙弢,周云,等.电力系统发电侧和负荷侧共同碳责任分摊方法[J].电力系统自动化,2018,42(19):106-111.DOI:10.7500/AEPS20171113004.CHEN Lixia, SUN Tao, ZHOU Yun, et al. Method of carbon obligation allocation between generation side and demand side in power system[J]. Automation of Electric Power Systems, 2018, 42(19): 106-111. DOI: 10.7500/AEPS20171113004.
[23] 郭俊杰.空气源热泵热水装置优化分析与运行策略研究[D].上海:上海交通大学,2013.GUO Junjie. Research on optimization and operation strategy of air source heat pump water heater[D]. Shanghai: Shanghai Jiao Tong University, 2013.
[24] SANANDAJI B M, VINCENT T L, POOLLA K. Ramping rate flexibility of residential HVAC loads[J]. IEEE Transactions on Sustainable Energy, 2017, 7(2): 865-874.
[25] WEIBEL C. Minkowski sums of polytopes: combinatorics and computation[EB/OL]. [2016-04-23]. http://www.docin.com/P-1545153463.html.Similar Records, 2007.
[26] EAVES B C, FREUND R M. Optimal scaling of balls and polyhedra[J]. Mathematical Programming, 1982, 23(1): 138-147.
[27] TIWARY H R. On the hardness of computing intersection, union and Minkowski Sum of polytopes[J]. Discrete & Computational Geometry, 2008, 40(3): 469-479.
[28] 王刚,董亦华,王珂,等.计及网络约束的发用电一体化综合优化调度模型[J].电力系统自动化,2017,41(14):105-111.DOI:10.7500/AEPS20161228006.WANG Gang, DONG Yihua, WANG Ke, et al. Comprehensive optimal scheduling model for integration of power generation and consumption considering network constraints[J]. Automation of Electric Power Systems, 2017, 41(14): 105-111. DOI: 10.7500/AEPS20161228006.
[2] 马荣江,张了,付宇,等.热风型低环境温度空气源热泵:一种适用于北京地区农宅的清洁高效采暖技术[J].建设科技,2016(14):76-81.MA Rongjiang, ZHANG Le, FU Yu, et al. Hot air low ambient temperature air source heat pump: a clean and efficient heating technology suitable for farm houses in Beijing area[J]. Construction Science and Technology, 2016(14): 76-81.
[3] 乐慧,李好玥,江亿.用空气源热泵实现农村采暖的“煤改电”同时为电力削峰填谷[J].中国能源,2016,38(11):9-15.LE Hui, LI Haoyue, JIANG Yi. Using the air source heat pump to realize the “coal to electricity” in rural heating, and to power the peak and fill the valley[J]. Energy of China, 2016, 38(11): 9-15.
[4] 刘艳茹,杨卫红,王基,等.“煤改电”工程实施前后农网负荷特性分析[J].电气技术,2017,18(4):110-115.LIU Yanru, YANG Weihong, WANG Ji, et al. Load characteristic analysis of rural network before and after the coal-to-electricity project[J]. Electrical Engineering, 2017, 18(4): 110-115.
[5] 于汀,刘广一,蒲天骄,等.计及柔性负荷的主动配电网多源协调优化控制[J].电力系统自动化,2015,39(9):95-100.YU Ting, LIU Guangyi, PU Tianjiao, et al. Multiple coordinated optimization control of active distribution network considering flexible load[J]. Automation of Electric Power Systems, 2015, 39(9): 95-100.
[6] MENDAZA I D D C, SZCZESNY I G, PILLAI J R, et al. Demand response control in low voltage grids for technical and commercial aggregation services[J]. IEEE Transactions on Smart Grid, 2016, 7(6): 2771-2780.
[7] VANHOUDT D, GEYSEN D, CLAESSENS B, et al. An actively controlled residential heat pump: potential on peak shaving and maximization of self-consumption of renewable energy[J]. Renewable Energy, 2014, 63: 531-543.
[8] SCHIBUOLA L, SCARPA M, TAMBANI C. Demand response management by means of heat pumps controlled via real time pricing[J]. Energy and Buildings, 2015, 90: 15-28.
[9] 严旭,吴锴,周孟戈,等.基于不同可调度热源的风电出力平滑模型[J].电力系统保护与控制,2013,41(21):122-128.YAN Xu, WU Kai, ZHOU Mengge, et al. Model of smoothing wind power based on various dispatchable heat sources[J]. Power System Protection and Control, 2013, 41(21): 122-128.
[10] YE H, GE Y, SHAHIDEHPOUR M, et al. Uncertainty marginal price, transmission reserve, and day-ahead market clearing with robust unit commitment[J]. IEEE Transactions on Power Systems, 2016, 32(3): 1782-1795.
[11] 栗子豪,吴文传,朱洁,等.基于机会约束的主动配电网热泵日前调度模型及可解性转换[J].电力系统自动化,2018,42(11):24-31.DOI:10.7500/AEPS20170825007.LI Zihao, WU Wenchuan, ZHU Jie, et al. Chance-constrained model for day-ahead heat pump scheduling in active distribution network and its tractability transformation[J]. Automation of Electric Power Systems, 2018, 42(11): 24-31. DOI: 10.7500/AEPS20170825007.
[12] LI Zihao, WU Wenchuan, ZHANG Boming. Kullback-Leibler divergence-based distributionally robust optimisation model for heat pump day-ahead operational schedule to improve PV integration[J]. IET Generation, Transmission & Distribution, 2018, 12(13): 3136-3144.
[13] MATHIEU J L, KAMGARPOUR M, LYGEROS J, et al. Arbitraging intraday wholesale energy market prices with aggregations of thermostatic loads[J]. IEEE Transactions on Power Systems, 2014, 30(2): 763-772.
[14] SHAFIE-KHAH M, CATAL?O J P S. A stochastic multi-layer agent-based model to study electricity market participants behavior[J]. IEEE Transactions on Power Systems, 2015, 30(2): 867-881.
[15] HE H, SANANDAJI B M, POOLLA K, et al. Aggregate flexibility of thermostatically controlled loads[J]. IEEE Transactions on Power Systems, 2015, 30(1): 189-198.
[16] ZHAO L, ZHANG W, HAO H, et al. A geometric approach to aggregate flexibility modeling of thermostatically controlled loads[J]. IEEE Transactions on Power Systems, 2017, 32(6): 4721-4731.
[17] SONG M, GAO C, YAN H, et al. Thermal battery modeling of inverter air conditioning for demand response[J]. IEEE Transactions on Smart Grid, 2018, 9(6): 5522-5534.
[18] LIU W, GU W, SHENG W, et al. Decentralized multi-agent system-based cooperative frequency control for autonomous microgrids with communication constraints[J]. IEEE Transactions on Sustainable Energy, 2017, 5(2): 446-456.
[19] MA K, HU G, SPANOS C J. A cooperative demand response scheme using punishment mechanism and application to industrial refrigerated warehouses[J]. IEEE Transactions on Industrial Informatics, 2017, 11(6): 1520-1531.
[20] MOSTAFA H A, EL SHATSHAT R, SALAMA M M A. A correlated equilibrium game-theoretic approach for multiple participants electric distribution systems operation[J]. IEEE Transactions on Smart Grid, 2016, 7(1): 32-42.
[21] CHAI B, CHEN J, YANG Z, et al. Demand response management with multiple utility companies: a two-level game approach[J]. IEEE Transactions on Smart Grid, 2014, 5(2): 722-731.
[22] 陈丽霞,孙弢,周云,等.电力系统发电侧和负荷侧共同碳责任分摊方法[J].电力系统自动化,2018,42(19):106-111.DOI:10.7500/AEPS20171113004.CHEN Lixia, SUN Tao, ZHOU Yun, et al. Method of carbon obligation allocation between generation side and demand side in power system[J]. Automation of Electric Power Systems, 2018, 42(19): 106-111. DOI: 10.7500/AEPS20171113004.
[23] 郭俊杰.空气源热泵热水装置优化分析与运行策略研究[D].上海:上海交通大学,2013.GUO Junjie. Research on optimization and operation strategy of air source heat pump water heater[D]. Shanghai: Shanghai Jiao Tong University, 2013.
[24] SANANDAJI B M, VINCENT T L, POOLLA K. Ramping rate flexibility of residential HVAC loads[J]. IEEE Transactions on Sustainable Energy, 2017, 7(2): 865-874.
[25] WEIBEL C. Minkowski sums of polytopes: combinatorics and computation[EB/OL]. [2016-04-23]. http://www.docin.com/P-1545153463.html.Similar Records, 2007.
[26] EAVES B C, FREUND R M. Optimal scaling of balls and polyhedra[J]. Mathematical Programming, 1982, 23(1): 138-147.
[27] TIWARY H R. On the hardness of computing intersection, union and Minkowski Sum of polytopes[J]. Discrete & Computational Geometry, 2008, 40(3): 469-479.
[28] 王刚,董亦华,王珂,等.计及网络约束的发用电一体化综合优化调度模型[J].电力系统自动化,2017,41(14):105-111.DOI:10.7500/AEPS20161228006.WANG Gang, DONG Yihua, WANG Ke, et al. Comprehensive optimal scheduling model for integration of power generation and consumption considering network constraints[J]. Automation of Electric Power Systems, 2017, 41(14): 105-111. DOI: 10.7500/AEPS20161228006.