Abstract：As the main outlook of the future distribution network, it is of great research value to jointly allocate active-reactive power resources of AC-DC active distribution network. However, the access of single-phase load and the three-phase power inconsistency of distributed generation will lead to more severe three-phase unbalance situation in the distribution network. To deal with the three-phase unbalance problem in AC-DC active distribution network, a joint three-phase active and reactive power optimization method is proposed, which takes the phase-to-phase coupling relationship and the three-phase unbalance factor limitation into account. Firstly, the original three-phase power flow model considering the phase-to-phase coupling relationship is established and the model is mapped to a high-dimensional space then. Secondly, the complete symmetrical three-phase power flow model of each subsystem of AC-DC active distribution network and the symmetrical three-phase voltage unbalance factor constraints are derived using the semidefinite programming. Then, a joint three-phase active-reactive power optimization model of AC-DC active distribution network with the objective of minimizing the total network operation cost is proposed. To verify the accuracy and effectiveness of the proposed method, the maximum relaxation deviation and maximum logarithmic relaxation mismatch results are firstly demonstrated via case studies on the modified IEEE 33-bus AC-DC distribution system. Under different unbalanced circumstances, the maximum relaxation deviations of the proposed method are always lower than 10-7 with the corresponding relaxation mismatch under 10-5. Besides, the results of voltage deviation percentage of the proposed method are lower than the results of the standard three-phase SDP method. Moreover, in contrast to the traditional three-phase decoupled model, the proposed method is able to obtain a smaller operation cost results, e.g., 4.489% and 13.188% reduction on operation cost and transmission loss cost under 20%-line impedance unbalance circumstance, and more real voltage results. And it can effectively limit the three-phase unbalance of the system voltage with the voltage unbalance factor model always under the pre-set 2% threshold at the same time. To further verify the calculation performances on large scale systems, case studies are carried out on the modified IEEE 69-,141- and 1056-bus AC-DC distribution systems. Compared with the standard three-phase SDP method, the proposed method can provide more accurate optimization results while the computing time do not increase too much. Meanwhile, compared with the linearized model, the average mismatches are always smaller, which indicates the infeasibility of the linearized model. The following conclusions can be drawn from the simulation analysis: (1) Under different three-phase unbalance circumstances, the proposed method can guarantee the relaxation accuracy of the algorithm and gain better performances on accuracies compared with the standard three-phase SDP method. (2) The proposed method can obtain a smaller operation cost and more real bus voltages compared with the traditional three-phase decoupled model, which indicates its’ applicability in the actual operation states of the AC-DC distribution network. (3) The effectiveness of the three-phase voltage unbalance limitation constraint is verified which consequently proves that the proposed model satisfies the actual operation requirements of the AC-DC distribution network. (4) In large-scale AC-DC distribution test systems, the proposed method is superior on calculation accuracy, but has no evident disadvantages on calculation speed performance.
孙乾皓, 张耀, 周一丹, 王家乐, 赵英杰. 基于半正定规划的交直流主动配电网三相有功无功联合优化[J]. 电工技术学报, 2024, 39(9): 2608-2620.
Sun Qianhao, Zhang Yao, Zhou Yidan, Wang Jiale, Zhao Yingjie. Three-Phase Active-Reactive Power Optimization of AC-DC Active Distribution Network Based on Semi-Definite Programming. Transactions of China Electrotechnical Society, 2024, 39(9): 2608-2620.
[1] 赵冬梅, 王浩翔, 陶然. 计及风电-负荷不确定性的风-火-核-碳捕集多源协调优化调度[J]. 电工技术学报, 2022, 37(3): 707-718. Zhao Dongmei, Wang Haoxiang, Tao Ran.A multi-source coordinated optimal scheduling model considering wind-load uncertainty[J]. Transactions of China Electrotechnical Society, 2022, 37(3): 707-718. [2] 朱晓荣, 司羽. 考虑物理—信息—交通网耦合的配电网多时段动态供电恢复策略[J]. 电工技术学报, 2023, 38(12): 3306-3320. Zhu Xiaorong, Si Yu.Multi-period dynamic power supply restoration strategy considering physical-cyber-traffic network coupling[J]. Transactions of China Electrotechnical Society, 2023, 38(12): 3306-3320. [3] 黄伟, 熊伟鹏, 华亮亮, 等. 基于动态调度优先级的主动配电网多目标优化调度[J]. 电工技术学报, 2018, 33(15): 3486-3498. Huang Wei, Xiong Weipeng, Hua Liangliang, et al.Multi-objective optimization dispatch of active distribution network based on dynamic schedule priority[J]. Transactions of China Electrotechnical Society, 2018, 33(15): 3486-3498. [4] 虎智峰, 陈静, 张婧菲, 等. 考虑新能源不确定性边界的主动配电网优化调度[J]. 智慧电力, 2022, 50(11): 48-55. Hu Zhifeng, Chen Jing, Zhang Jingfei, et al.Optimal dispatch of active distribution network considering uncertainty boundary of renewable power generation[J]. Smart Power, 2022, 50(11): 48-55. [5] Ahmed H M A, Eltantawy A B, Salama M M A. A planning approach for the network configuration of AC-DC hybrid distribution systems[J]. IEEE Transactions on Smart Grid, 2018, 9(3): 2203-2213. [6] Zhang Lu, Liang Jun, Tang Wei, et al.Converting AC distribution lines to DC to increase transfer capacities and DG penetration[J]. IEEE Transactions on Smart Grid, 2018, 10(2): 1477-1487. [7] 张涛, 穆云飞, 贾宏杰, 等. 含电力电子变压器的交直流配电网随机运行优化[J]. 电网技术, 2022, 46(3): 860-869. Zhang Tao, Mu Yunfei, Jia Hongjie, et al.Stochastic operation optimization for AC/DC distribution network with power electronic transformer[J]. Power System Technology, 2022, 46(3): 860-869. [8] 姜涛, 李雪, 李国庆, 等. 含多端柔性直流的交直流电力系统静态电压稳定域构建方法[J]. 电工技术学报, 2022, 37(7): 1746-1759. Jiang Tao, Li Xue, Li Guoqing, et al.A predictor-corrector algorithm for forming voltage stability region of hybrid AC/DC power grid with inclusion of VSC-MTDC[J]. Transactions of China Electrotechnical Society, 2022, 37(7): 1746-1759. [9] 孙旭, 邱晓燕, 张志荣, 等. 基于数据驱动的交直流配电网分布鲁棒优化调度[J]. 电网技术, 2021, 45(12): 4768-4778. Sun Xu, Qiu Xiaoyan, Zhang Zhirong, et al.Distributed robust optimal dispatching of AC/DC distribution network based on data driven mode[J]. Power System Technology, 2021, 45(12): 4768-4778. [10] 郑重, 苗世洪, 李超, 等. 面向微型能源互联网接入的交直流配电网协同优化调度策略[J]. 电工技术学报, 2022, 37(1): 192-207. Zheng Zhong, Miao Shihong, Li Chao, et al.Coordinated optimal dispatching strategy of AC/DC distribution network for the integration of micro energy Internet[J]. Transactions of China Electrotechnical Society, 2022, 37(1): 192-207. [11] 张晓英, 张艺, 王琨, 等. 基于改进NSGA-Ⅱ算法的含分布式电源配电网无功优化[J]. 电力系统保护与控制, 2020, 48(1): 55-64. Zhang Xiaoying, Zhang Yi, Wang Kun, et al.Reactive power optimization of distribution network with distributed generations based on improved NSGA-Ⅱ algorithm[J]. Power System Protection and Control, 2020, 48(1): 55-64. [12] 乐健, 周谦, 王曹, 等. 基于分布式协同的配电网电压和功率优化控制方法研究[J]. 中国电机工程学报, 2020, 40(4): 1249-1257, 1415. Le Jian, Zhou Qian, Wang Cao, et al.Research on voltage and power optimal control strategy of distribution network based on distributed collaborative principle[J]. Proceedings of the CSEE, 2020, 40(4): 1249-1257, 1415. [13] Zarrilli D, Giannitrapani A, Paoletti S, et al.Energy storage operation for voltage control in distribution networks: a receding horizon approach[J]. IEEE Transactions on Control Systems Technology, 2018, 26(2): 599-609. [14] 胡丹尔, 彭勇刚, 韦巍, 等. 多时间尺度的配电网深度强化学习无功优化策略[J]. 中国电机工程学报, 2022, 42(14): 3, 5034-5044. Hu Daner, Peng Yonggang, Wei Wei, et al. Multi-timescale deep reinforcement learning for reactive power optimization of distribution network[J]. Proceedings of the CSEE, 2022, 42(14): 3, 5034-5044. [15] 姜涛, 张东辉, 李雪, 等. 含分布式光伏的主动配电网电压分布式优化控制[J]. 电力自动化设备, 2021, 41(9): 102-109, 125. Jiang Tao, Zhang Donghui, Li Xue, et al.Distributed optimal control of voltage in active distribution network with distributed photovoltaic[J]. Electric Power Automation Equipment, 2021, 41(9): 102-109, 125. [16] 张沈习, 李珂, 程浩忠, 等. 间歇性分布式电源在主动配电网中的优化配置[J]. 电力自动化设备, 2015, 35(11): 45-51. Zhang Shenxi, Li Ke, Cheng Haozhong, et al.Optimal allocation of intermittent distributed generator in active distribution network[J]. Electric Power Automation Equipment, 2015, 35(11): 45-51. [17] 刘一兵, 吴文传, 张伯明, 等. 基于有功-无功协调优化的主动配电网过电压预防控制方法[J]. 电力系统自动化, 2014, 38(9): 184-191. Liu Yibing, Wu Wenchuan, Zhang Boming, et al.Overvoltage preventive control method based on active and reactive power coordinated optimization in active distribution network[J]. Automation of Electric Power Systems, 2014, 38(9): 184-191. [18] Gao Hongjun, Liu Junyong, Wang Lingfeng.Robust coordinated optimization of active and reactive power in active distribution systems[J]. IEEE Transactions on Smart Grid, 2018, 9(5): 4436-4447. [19] 刘洪, 徐正阳, 葛少云, 等. 考虑储能调节的主动配电网有功—无功协调运行与电压控制[J]. 电力系统自动化, 2019, 43(11): 51-58. Liu Hong, Xu Zhengyang, Ge Shaoyun, et al.Coordinated operation of active-reactive power and voltage control for active distribution network considering regulation of energy storage[J]. Automation of Electric Power Systems, 2019, 43(11): 51-58. [20] 寇凌峰, 吴鸣, 李洋, 等. 主动配电网分布式有功无功优化调控方法[J]. 中国电机工程学报, 2020, 40(6): 1856-1865. Kou Lingfeng, Wu Ming, Li Yang, et al.Optimization and control method of distributed active and reactive power in active distribution network[J]. Proceedings of the CSEE, 2020, 40(6): 1856-1865. [21] 赵晋泉, 刘绪, 林昌年, 等. 单相光伏大量接入的三相不平衡配电网无功优化[J]. 电力系统自动化, 2016, 40(13): 13-18, 70. Zhao Jinquan, Liu Xu, Lin Changnian, et al.Three-phase unbalanced reactive power optimization for distribution systems with a large number of single phase solar generators[J]. Automation of Electric Power Systems, 2016, 40(13): 13-18, 70. [22] 唐冬来, 郝建维, 刘荣刚, 等. 基于动态规划的配电台区三相负荷不平衡治理方法[J]. 电力系统保护与控制, 2020, 48(21): 58-66. Tang Donglai, Hao Jianwei, Liu Ronggang, et al.Control method of three phase load imbalance in a distribution station area based on dynamic programming[J]. Power System Protection and Control, 2020, 48(21): 58-66. [23] Liu Shengyuan, Jin Renyun, Qiu Haifeng, et al.Practical method for mitigating three-phase unbalance based on data-driven user phase identification[J]. IEEE Transactions on Power Systems, 2020, 35(2): 1653-1656. [24] 程湘, 田昊, 周群, 等. 考虑相位不平衡的智能换相开关控制策略[J]. 电力系统保护与控制, 2021, 49(6): 48-55. Cheng Xiang, Tian Hao, Zhou Qun, et al.Control strategy of intelligent commutation switch considering phase imbalance[J]. Power System Protection and Control, 2021, 49(6): 48-55. [25] 伍鸿兵, 罗勇, 王嵩, 等. 计及分布式电源接入的三相不平衡配电网无功优化研究[J]. 计算技术与自动化, 2020, 39(3): 17-21, 36. Wu Hongbing, Luo Yong, Wang Song, et al.Research on reactive power optimization of three-phase unbalanced distribution network with access of distributed power supply[J]. Computing Technology and Automation, 2020, 39(3): 17-21, 36. [26] Robbins B A, Dominguez-Garcia A D. Optimal reactive power dispatch for voltage regulation in unbalanced distribution systems[J]. IEEE Transactions on Power Systems, 2016, 31(4): 2903-2913. [27] Chowdhury M M U T, Biswas B D, Kamalasadan S. Second-order cone programming (SOCP) model for three phase optimal power flow (OPF) in active distribution networks[J]. IEEE Transactions on Smart Grid, 2023, 14(5): 3732-3743. [28] Dall'Anese E, Zhu Hao, Giannakis G B. Distributed optimal power flow for smart microgrids[J]. IEEE Transactions on Smart Grid, 2013, 4(3): 1464-1475. [29] Gan Lingwen, Low S H.Convex relaxations and linear approximation for optimal power flow in multiphase radial networks[C]//2014 Power Systems Computation Conference, Wrocław, Poland, 2014: 1-9. [30] 徐添锐, 丁涛, 李立, 等. 适应三相不平衡主动配电网无功优化的二阶锥松弛模型[J]. 电力系统自动化, 2021, 45(24): 81-88. Xu Tianrui, Ding Tao, Li Li, et al.Second-order cone relaxation model adapting to reactive power optimization for three-phase unbalanced active distribution network[J]. Automation of Electric Power Systems, 2021, 45(24): 81-88. [31] 巨云涛, 黄炎, 张若思. 基于二阶锥规划凸松弛的三相交直流混合主动配电网最优潮流[J]. 电工技术学报, 2021, 36(9): 1866-1875. Ju Yuntao, Huang Yan, Zhang Ruosi.Optimal power flow of three-phase hybrid AC-DC in active distribution network based on second order cone programming[J]. Transactions of China Electrotechnical Society, 2021, 36(9): 1866-1875. [32] Rahul R, Adedoyin I, Biswajit D, et al.Distribution grid optimal power flow (D-OPF): Modeling, analysis, and benchmarking[J]. IEEE Transactions on Power Systems. 2023, 38(4): 3654-3668. [33] Chen Xin, Wu Wenchuan, Zhang Boming.Robust capacity assessment of distributed generation in unbalanced distribution networks incorporating ANM techniques[J]. IEEE Transactions on Sustainable Energy, 2018, 9(2): 651-663. [34] Wang Zeyu, Kirschen D S, Zhang Baosen. Accurate semidefinite programming models for optimal power flow in distribution systems[EB/OL]. arXiv, 2017 1711.07853. https://arxiv.org/abs/1711.07853.pdf. [35] Wang Zeyu, Wang Jianhui, Chen Chen.A three-phase microgrid restoration model considering unbalanced operation of distributed generation[J]. IEEE Transactions on Smart Grid, 2018, 9(4): 3594-3604. [36] Opathella C, Venkatesh B.Three-phase unbalanced power flow using a π model of controllable AC-DC converters[J]. IEEE Transactions on Power Systems, 2016, 31(6): 4286-4296. [37] Girigoudar K, Roald L A.On the impact of different voltage unbalance metrics in distribution system optimization[J]. Electric Power Systems Research, 2020, 189: 106656. [38] Wang Wei, Yu Nanpeng.Chordal conversion based convex iteration algorithm for three-phase optimal power flow problems[J]. IEEE Transactions on Power Systems, 2018, 33(2): 1603-1613. [39] Alsaleh I, Fan Lingling, Bazrafshan M.Extended radial distribution ACOPF model: retrieving exactness via convex iteration[J]. IEEE Transactions on Power Systems, 2021, 36(6): 4967-4978.
2024, Vol. 39 
