Abstract：Lossy power flow model is an extension of the lossless linear power flow (LPF) model and has become one of the mainstream methods for approximation calculation and analysis in power systems. Mathematically, it is defined as a fixed-point iterative problem formulated jointly by the lossless LPF model and the network losses compensation model. Currently, existing network losses compensation models are only oriented to single-region, single-voltage level, and single-type of power grids, and mainly focuses on AC transmission grids. However, the operation modes of the integrated transmission and distribution grid with multi-terminal flexible interconnected are complex, and the network losses characteristics vary significantly. Obviously, existing models would weaken the applicability and effectiveness of the lossy power flow in the integrated transmission and distribution grids, also lead to further deterioration of the mismatch of the transmission and distribution boundary power flow. The reason is that conventional network losses compensation models cannot consider the significant differences of losses characteristics caused by the complexity of grids, which makes it difficult to accurately quantify the impact of the losses on power flow errors at different levels and types of grids. For this reason, a precise lossy power flow model based on two-layer fixed-point iteration is proposed in this paper. For the problem of inaccurate network losses compensation, this paper fully considers the characteristics of network structure, data attributes and physical features, and proposes precise lossy power flow models for transmission, distribution, AC and DC grids. First, the lossless LPF model is formulated for AC and DC grids. Second, differentiated network losses compensation models are proposed to modify the node power injection according to the characteristics of AC, DC, transmission, and distribution grids. Finally, the modified node power injections are re-substituted into the lossless LPF model and solved iteratively until convergence. For the mismatch problem of transmission-distribution boundary power flow, the integrated transmission and distribution lossy power flow is formulated as a two-layer fixed-point iterative problem. Among them, the outer fixed-point is the transmission-distribution boundary node, which is used to solve the mismatch problem of power flow between transmission and distribution grids, and the master-slave splitting method is used to solve the problem collaboratively. For the transmission grid power flow calculation, the distribution network is equated to the load, and the boundary node voltage information is solved. For the distribution network power flow calculation, the transmission grid is equated to the source, and the voltage information of the boundary node is utilized as the operating point for the slack node of the distribution network to solve the boundary node power injection. The inner fixed-point is node voltage information in the network to solve the AC/DC lossy power flow based on the proposed network losses compensation model. The errors and reasons for different lossy power flow models are analyzed in several test cases, and compared in terms of solution accuracy, convergence speed and computational efficiency. The results show that the proposed precise lossy power flow model achieves higher computational accuracy under both deterministic and uncertainty scenarios. In addition, the proposed model is overall better than the existing model in terms of convergence performance and has lower computational complexity. Finally, for different control strategies and optimization objectives, the optimization errors of the proposed model are smaller than those of the conventional models, implying that the proposed model can provide operators with more reasonable economic scheduling decisions.
王淏, 谢开贵, 邵常政, 胡博, 郑东. 柔性互联输配一体化电网有损潮流的精细化建模及应用[J]. 电工技术学报, 2024, 39(9): 2593-2607.
Wang Hao, Xie Kaigui, Shao Changzheng, Hu Bo, Zheng Dong. Precise Lossy Power Flow Modeling and Application of Integrated Transmission and Distribution Grids with Multi-Terminal Flexible Interconnected. Transactions of China Electrotechnical Society, 2024, 39(9): 2593-2607.
[1] 姚良忠, 吴婧, 王志冰, 等. 未来高压直流电网发展形态分析[J]. 中国电机工程学报, 2014, 34(34): 6007-6020. Yao Liangzhong, Wu Jing, Wang Zhibing, et al.Pattern analysis of future HVDC grid development[J]. Proceedings of the CSEE, 2014, 34(34): 6007-6020. [2] 束洪春, 邵宗学, 赵伟, 等. 含柔性直流的交直流混联电力系统紧急频率控制研究[J]. 电工技术学报, 2023, 38(20): 5590-5604. Shu Hongchun, Shao Zongxue, Zhao Wei, et al.Research on emergency power control of AC-DC hybrid power system with flexible DC[J]. Transactions of China Electrotechnical Society, 2023, 38(20): 5590-5604. [3] 陈一丰, 唐坤杰, 董树锋, 等. 输配一体化潮流计算收敛性分析及提升方法[J]. 中国电机工程学报, 2022, 42(20): 7524-7535. Chen Yifeng, Tang Kunjie, Dong Shufeng, et al.Convergence analysis and promotion method of power flow calculation of integrated transmission and distribution networks[J]. Proceedings of the CSEE, 2022, 42(20): 7524-7535. [4] 辛保安, 郭铭群, 王绍武, 等. 适应大规模新能源友好送出的直流输电技术与工程实践[J]. 电力系统自动化, 2021, 45(22): 1-8. Xin Baoan, Guo Mingqun, Wang Shaowu, et al.Friendly HVDC transmission technologies for large-scale renewable energy and their engineering practice[J]. Automation of Electric Power Systems, 2021, 45(22): 1-8. [5] 唐巍, 张起铭, 张璐, 等. 新型配电系统多层级交直流互联理念、关键技术与发展方向[J]. 电力系统自动化, 2023, 47(6): 2-17. Tang Wei, Zhang Qiming, Zhang Lu, et al.Concept, key technologies and development direction of multilevel AC/DC interconnection in new distribution system[J]. Automation of Electric Power Systems, 2023, 47(6): 2-17. [6] 郑宗强, 韩冰, 闪鑫, 等. 输配电网高级应用协同运行关键技术分析[J]. 电力系统自动化, 2017, 41(6): 122-128. Zheng Zongqiang, Han Bing, Shan Xin, et al.Analysis on key technologies for coordinated operation of advanced application software in transmission and distribution network[J]. Automation of Electric Power Systems, 2017, 41(6): 122-128. [7] Simpson-Porco J W. Lossy DC power flow[J]. IEEE Transactions on Power Systems, 2018, 33(3): 2477-2485. [8] Neumann F, Hagenmeyer V, Brown T.Assessments of linear power flow and transmission loss approximations in coordinated capacity expansion problems[J]. Applied Energy, 2022, 314: 118859. [9] Sood P, Tylavsky D J, Qi Y.Improved dc network model for contingency analysis[C]//2014 North American Power Symposium (NAPS), Pullman, WA, USA, 2014: 1-6. [10] Fatemi S M, Abedi S, Gharehpetian G B, et al.Introducing a novel DC power flow method with reactive power considerations[J]. IEEE Transactions on Power Systems, 2015, 30(6): 3012-3023. [11] Qi Yingying, Shi Di, Tylavsky D.Impact of assumptions on DC power flow model accuracy[C]//2012 North American Power Symposium (NAPS), Champaign, IL, USA, 2012: 1-6. [12] 马钰, 韦钢, 李扬, 等. 考虑孤岛源-荷不确定性的直流配电网可靠性评估[J]. 电工技术学报, 2021, 36(22): 4726-4738. Ma Yu, Wei Gang, Li Yang, et al.Reliability evaluation of DC distribution network considering islanding source-load uncertainty[J]. Transactions of China Electrotechnical Society, 2021, 36(22): 4726-4738. [13] Guo Libang, Ding Yi, Bao Minglei, et al.Nodal reliability evaluation for a VSC-MTDC-based hybrid AC/DC power system[J]. IEEE Transactions on Power Systems, 2020, 35(3): 2300-2312. [14] Tang Kunjie, Dong Shufeng, Zhu Chengzhi, et al.Affine arithmetic-based coordinated interval power flow of integrated transmission and distribution networks[J]. IEEE Transactions on Smart Grid, 2020, 11(5): 4116-4132. [15] 房宇轩, 胡俊杰, 马文帅. 计及用户意愿的电动汽车聚合商主从博弈优化调度策略[J/OL]. 电工技术学报, 2023: 1-13. https://doi.org/10.19595/j.cnki.1000-6753.tces.230923. Fang Yuxuan, Hu Junjie, Ma Wenshuai. Optimal dispatch strategy for electric vehicle aggregators based on stackelberg game theory considering user intention[J/OL]. Transactions of China Electrotechnical Society, 2023: 1-13. https://doi.org/10.19595/j.cnki.1000-6753.tces.230923 [16] 李振坤, 钱晋, 符杨, 等. 基于负荷聚合商优选分级的配电网多重阻塞管理[J]. 电力系统自动化, 2021, 45(19): 109-116. Li Zhenkun, Qian Jin, Fu Yang, et al.Multiple congestion management for distribution network based on optimization classification of load aggregators[J]. Automation of Electric Power Systems, 2021, 45(19): 109-116. [17] 李勇, 凌锋, 乔学博, 等. 基于网侧资源协调的自储能柔性互联配电系统日前-日内优化[J]. 电工技术学报, 2024, 39(3): 758-773. Li Yong, Ling Feng, Qiao Boxue.Day-ahead and intra-day optimization of flexible interconnected distribution system with self-energy storage based on the grid-side resource coordination[J]. Transactions of China Electrotechnical Society, 2024, 39(3): 758-773. [18] 胡珺如, 窦晓波, 李晨, 等. 面向中低压配电网的分布式协同无功优化策略[J]. 电力系统自动化, 2021, 45(22): 47-54. Hu Junru, Dou Xiaobo, Li Chen, et al.Distributed cooperative reactive power optimization strategy for medium-and low-voltage distribution network[J]. Automation of Electric Power Systems, 2021, 45(22): 47-54. [19] Lin Chenhui, Wu Wenchuan, Zhang Boming, et al.Decentralized reactive power optimization method for transmission and distribution networks accommodating large-scale DG integration[J]. IEEE Transactions on Sustainable Energy, 2017, 8(1): 363-373. [20] 蔡瑶, 卢志刚, 潘尧, 等. 计及多重差异的交直流混合多能微网多时间尺度优化调度[J/OL]. 电工技术学报, 2023: 1-19. https://doi.org/10.19595/j.cnki.1000-6753.tces.230645. Cai Yao, Lu Zhigang, Pan Yao. Multi-time-scale optimal scheduling of AC-DC hybrid multi-energy microgrid considering multiple differences[J/OL]. Transactions of China Electrotechnical Society, 2023: 1-19. https://doi.org/10.19595/j.cnki.1000-6753.tces.230645. [21] Zhong Haiwang, Zhang Guanglun, Tan Zhenfei, et al.Hierarchical collaborative expansion planning for transmission and distribution networks considering transmission cost allocation[J]. Applied Energy, 2022, 307: 118147. [22] Stott B, Jardim J, Alsac O.DC power flow revisited[J]. IEEE Transactions on Power Systems, 2009, 24(3): 1290-1300. [23] 王虹富, 王毅, 高崇, 等. 基于网损等值负荷模型的直流潮流迭代算法[J]. 电力系统自动化, 2015, 39(1): 99-103. Wang Hongfu, Wang Yi, Gao Chong, et al.Iterative algorithm of DC power flow based on network loss equivalent load model[J]. Automation of Electric Power Systems, 2015, 39(1): 99-103. [24] 何天雨, 卫志农, 孙国强, 等. 基于网损等值负荷模型的改进直流最优潮流算法[J]. 电力系统自动化, 2016, 40(6): 58-64. He Tianyu, Wei Zhinong, Sun Guoqiang, et al.Modified direct current optimal power flow algorithm based on net loss equivalent load model[J]. Automation of Electric Power Systems, 2016, 40(6): 58-64. [25] 卫志农, 朱梓荣, 赵静波, 等. 电力系统半线性与全线性最优潮流模型[J]. 电力系统自动化, 2018, 42(14): 107-114. Wei Zhinong, Zhu Zirong, Zhao Jingbo, et al.Semi-linearized model and full-linearized model of optimal power flow in power system[J]. Automation of Electric Power Systems, 2018, 42(14): 107-114. [26] 卫志农, 张清松, 赵静波, 等. 电力系统线性化模型研究综述与改进[J]. 电网技术, 2017, 41(9): 2919-2927. Wei Zhinong, Zhang Qingsong, Zhao Jingbo, et al.Review and improvement of power system linearization models[J]. Power System Technology, 2017, 41(9): 2919-2927. [27] 赵静波, 卫志农, 刘建坤, 等. 电力系统线性化动态最优潮流模型[J]. 电力系统自动化, 2018, 42(20): 86-92. Zhao Jingbo, Wei Zhinong, Liu Jiankun, et al.Linearized dynamic optimal power flow model for power system[J]. Automation of Electric Power Systems, 2018, 42(20): 86-92. [28] 李少岩, 张友好, 顾雪平. 基于梯级流水法与裕度线性化交流潮流的目标骨干网架优化方法[J]. 电网技术, 2023, 47(7): 2788-2799. Li Shaoyan, Zhang Youhao, Gu Xueping.Skeleton network optimization method based on cascade flow method and margin linearization AC power flow model[J]. Power System Technology, 2023, 47(7): 2788-2799. [29] Schweitzer E, Saha S, Scaglione A, et al.Lossy DistFlow formulation for single and multiphase radial feeders[J]. IEEE Transactions on Power Systems, 2020, 35(3): 1758-1768. [30] Schweitzer E, Scaglione A, Monti A, et al.Automated generation algorithm for synthetic medium voltage radial distribution systems[J]. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2017, 7(2): 271-284. [31] Fernández-Pérez J C, Echavarren Cerezo F M, Rouco Rodríguez L. Linear power flow algorithm with losses for multi-terminal VSC AC/DC power systems[J]. IEEE Transactions on Power Systems, 2022, 37(3): 1739-1749. [32] Yang Jingwei, Zhang Ning, Kang Chongqing, et al.A state-independent linear power flow model with accurate estimation of voltage magnitude[J]. IEEE Transactions on Power Systems, 2017, 32(5): 3607-3617. [33] Beerten J, Cole S, Belmans R.A sequential AC/DC power flow algorithm for networks containing Multi-terminal VSC HVDC systems[C]//IEEE PES General Meeting, Minneapolis, MN, USA, 2010: 1-7.
2024, Vol. 39 
