Analysis on Node Voltage Security of Distribution Network with Wind Power Considering Time Delay
Cui Qingxue1, Li Xialin1, Ge Leijiao1, Li Tianchu2, Li Xian2
1. Key Laboratory of Smart Grid of Ministry of Education Tianjin University Tianjin 300072 China; 2. Power Research Institute of Hainan Power Grid Co. Ltd Haikou 570311 China
Abstract：The superposition effect of time-delay phenomenon leads to the failure of preset parameters for the safe operation control of distribution network voltage, and the system operation condition is further deteriorated. However, the previous analysis models of distribution network security operation control seldom consider the time-delay or execute according to the time-delay of a fixed constant, which is difficult to meet the actual demand. At the same time, there is still a lack of relevant literature that considers the time-delay factor in the node voltage security analysis of distribution network. In order to address these issues, this paper has carried out in-depth research on node voltage security analysis of wind power distribution network with time-delay. By solving the time-delay stability margin, a numerical reference is provided for the accurate regulation of the safe operation of the node voltage of the distribution network with wind power. Firstly, construct a mathematical model of partial derivative differential transcendental equation for node voltage safety analysis of time-delay distribution networks with wind power. Then, propose a Lyapunov-Krasovskii generalized function construction method, and apply Wirtinger's inequality technique to deal with the integral term in the generalized derivative to solve the constructed partial derivative differential transcendental equation and obtain the stability criterion to know its time-delay stability margin. Finally, the simulation is verified with the help of the typical case and IEEE 33 examples. Simulation results of typical second-order systems show that the proposed method can significantly reduce the conservatism of stability criteria. Simulation results of distribution network with a single wind turbine generator unit show that when the upper limit of time-delay is 5.1 s, the system voltage is critical stable; when it is greater than 5.1 s, that is, it exceeds the upper limit of stability, and the distribution system gradually loses stability. Simulation results of distribution network with two wind turbine generators show that the system voltage is critical stable when the upper limit of time-delay is 5.9s; when it is greater than 5.9s, that is, it exceeds the upper limit of stability, and the system gradually loses stability. The regulated system without considering the effect of time-delay can not adapt to the operation of fluctuating power supply, and can not accurately reflect the dynamic response with wind turbines. After adjusting according to the time-delay stability margin, the node voltage of the distribution network can adapt to the operation of fluctuating power sources, accurately reflect the dynamic response with the distribution network system, and change within the safe operation range. The following conclusions can be drawn from the simulation analysis: (1) Time-delay has a significant impact on the dynamic response of the system, and multiple time-delay links caused by intermittent wind power need to be considered in the distribution network system model. (2) The method presented in this paper can be used to analyze the upper bound of time-delay for safe operation of systems under the influence of random time delays. When the control communication time is less than the upper bound of the delay, the system can maintain stability. When the control communication time exceeds the upper limit of time-delay, the system voltage will gradually lose stability. Under the same delay parameter value, the system stability margin obtained in this paper is larger, which shows that this paper effectively reduces the conservatism of the criterion.
崔庆雪, 李霞林, 葛磊蛟, 李天楚, 李献. 计及时滞的含风电配电网节点电压安全分析[J]. 电工技术学报, 2023, 38(5): 1299-1311.
Cui Qingxue, Li Xialin, Ge Leijiao, Li Tianchu, Li Xian. Analysis on Node Voltage Security of Distribution Network with Wind Power Considering Time Delay. Transactions of China Electrotechnical Society, 2023, 38(5): 1299-1311.
[1] 曾博, 徐富强, 刘一贤, 等. 综合考虑经济-环境-社会因素的多能耦合系统高维多目标规划[J]. 电工技术学报, 2021, 36(7): 1434-1445. Zeng Bo, Xu Fuqiang, Liu Yixian, et al.High-dimensional multiobjective optimization for multi-energy coupled system planning with consideration of economic, environmental and social factors[J]. Transactions of China Electrotechnical Society, 2021, 36(7): 1434-1445. [2] 周博, 艾小猛, 方家琨, 等. 计及超分辨率风电出力不确定性的连续时间鲁棒机组组合[J]. 电工技术学报, 2021, 36(7): 1456-1467. Zhou Bo, Ai Xiaomeng, Fang Jiakun, et al.Continuous-time modeling based robust unit commitment considering beyond-the-resolution wind power uncertainty[J]. Transactions of China Electrotechnical Society, 2021, 36(7): 1456-1467. [3] 朱泽安, 周修宁, 王旭, 等. 基于稳暂态联合仿真模拟的区域多可再生能源系统评估决策[J]. 电工技术学报, 2020, 35(13): 2780-2791. Zhu Zean, Zhou Xiuning, Wang Xu, et al.Evaluation and decision-making of regional multi-renewable energy system based on steady-transient integrated simulation[J]. Transactions of China Electrotechnical Society, 2020, 35(13): 2780-2791. [4] 卓振宇, 张宁, 谢小荣, 等. 高比例可再生能源电力系统关键技术及发展挑战[J]. 电力系统自动化, 2021, 45(9): 171-191. Zhuo Zhenyu, Zhang Ning, Xie Xiaorong, et al.Key technologies and developing challenges of power system with high proportion of renewable energy[J]. Automation of Electric Power Systems, 2021, 45(9): 171-191. [5] 李保杰, 李进波, 李洪杰, 等. 土耳其“3.31”大停电事故的分析及对我国电网安全运行的启示[J]. 中国电机工程学报, 2016, 36(21): 5788-5795, 6021. Li Baojie, Li Jinbo, Li Hongjie, et al.Analysis of Turkish blackout on March 31, 2015 and lessons on China power grid[J]. Proceedings of the CSEE, 2016, 36(21): 5788-5795, 6021. [6] 张沛, 田佳鑫, 谢桦. 计及多个风场预测误差的电力系统风险快速计算方法[J]. 电工技术学报, 2021, 36(9): 1876-1887. Zhang Pei, Tian Jiaxin, Xie Hua.A fast risk assessment method with consideration of forecasting errors of multiple wind farms[J]. Transactions of China Electrotechnical Society, 2021, 36(9): 1876-1887. [7] Dong Chaoyu, Jia Hongjie, Xu Qianwen, et al.Time-delay stability analysis for hybrid energy storage system with hierarchical control in DC microgrids[J]. IEEE Transactions on Smart Grid, 2018, 9(6): 6633-6645. [8] 乐健, 赵联港, 廖小兵, 等. 考虑控制时滞和参数不确定的虚拟同步电机并网系统稳定性分析[J]. 中国电机工程学报, 2021, 41(12): 4275-4286. Le Jian, Zhao Liangang, Liao Xiaobing, et al.Stability analysis of grid-connected inverter system containing virtual synchronous generator under time delay and parameter uncertainty[J]. Proceedings of the CSEE, 2021, 41(12): 4275-4286. [9] Cao Yulei, Li Chongtao, He Tingyi, et al.A novel rekasius substitution based exact method for delay margin analysis of multi-area load frequency control systems[J]. IEEE Transactions on Power Systems, 2021, 36(6): 5222-5234. [10] 郭春义, 彭意, 徐李清, 等. 考虑延时影响的MMC-HVDC系统高频振荡机理分析[J]. 电力系统自动化, 2020, 44(22): 119-126. Guo Chunyi, Peng Yi, Xu Liqing, et al.Analysis on high-frequency oscillation mechanism for MMC-HVDC system considering influence of time delay[J]. Automation of Electric Power Systems, 2020, 44(22): 119-126. [11] 马燕峰, 霍亚欣, 李鑫, 等. 考虑时滞影响的双馈风电场广域附加阻尼控制器设计[J]. 电工技术学报, 2020, 35(1): 158-166. Ma Yanfeng, Huo Yaxin, Li Xin, et al.Design of wide area additional damping controller for doubly fed wind farms considering time delays[J]. Transactions of China Electrotechnical Society, 2020, 35(1): 158-166. [12] 古丽扎提·海拉提, 王杰. 多时滞广域测量电力系统稳定分析与协调控制器设计[J]. 电工技术学报, 2014, 29(2): 279-289. Gulizhati Hailati, Wang Jie.Multiple time delays analysis and coordinated stability control for power system wide area measurement[J]. Transactions of China Electrotechnical Society, 2014, 29(2): 279-289. [13] Zhang Chuanke, He Yong, Jiang Lin, et al.Notes on stability of time-delay systems: bounding inequalities and augmented Lyapunov-Krasovskii functionals[J]. IEEE Transactions on Automatic Control, 2017, 62(10): 5331-5336. [14] 肖伸平, 张天, 唐军, 等. 基于PI控制的时滞电力系统稳定性分析[J]. 电网技术, 2020, 44(10): 3949-3954. Xiao Shenping, Zhang Tian, Tang Jun, et al.Stability analysis for power systems with time-delay based on PI control[J]. Power System Technology, 2020, 44(10): 3949-3954. [15] Zhang Chuanke, He Yong, Jiang L, et al.Delay-variation-dependent stability of delayed discrete-time systems[J]. IEEE Transactions on Automatic Control, 2016, 61(9): 2663-2669. [16] 钱伟, 王晨晨, 费树岷. 区间变时滞广域电力系统稳定性分析与控制器设计[J]. 电工技术学报, 2019, 34(17): 3640-3650. Qian Wei, Wang Chenchen, Fei Shumin.Stability analysis and controller design of wide-area power system with interval time-varying delay[J]. Transactions of China Electrotechnical Society, 2019, 34(17): 3640-3650. [17] Seuret A, Gouaisbaut F.Wirtinger-based integral inequality: application to time-delay systems[J]. Automatica, 2013, 49(9): 2860-2866. [18] Zhang Xianming, Han Qinglong, Seuret A, et al.An improved reciprocally convex inequality and an augmented Lyapunov-Krasovskii functional for stability of linear systems with time-varying delay[J]. Automatica, 2017, 84: 221-226. [19] 窦晓波, 葛浦东, 全相军, 等. 计及不确定时滞的有源配电网无功电压鲁棒控制[J]. 中国电机工程学报, 2019, 39(5): 1290-1301. Dou Xiaobo, Ge Pudong, Quan Xiangjun, et al.Reactive power and voltage robust control for active distribution network considering uncertain delay[J]. Proceedings of the CSEE, 2019, 39(5): 1290-1301. [20] 周明, 元博, 张小平, 等. 基于SDE的含风电电力系统随机小干扰稳定分析[J]. 中国电机工程学报, 2014, 34(10): 1575-1582. Zhou Ming, Yuan Bo, Zhang Xiaoping, et al.Stochastic small signal stability analysis of wind power integrated power systems based on stochastic differential equations[J]. Proceedings of the CSEE, 2014, 34(10): 1575-1582. [21] Lee T H, Park J H.Improved stability conditions of time-varying delay systems based on new Lyapunov functionals[J]. Journal of the Franklin Institute, 2018, 355(3): 1176-1191. [22] 钱伟, 蒋鹏冲. 时滞电力系统带记忆反馈控制方法[J]. 电网技术, 2017, 41(11): 3605-3611. Qian Wei, Jiang Pengchong.A method of memory feedback control for power system with time-delay[J]. Power System Technology, 2017, 41(11): 3605-3611. [23] Sun Jian, Liu G P, Chen Jie, et al.Improved delay-range-dependent stability criteria for linear systems with time-varying delays[J]. Automatica, 2010, 46(2): 466-470. [24] Wu Min, Peng Chen, Zhang Jin, et al.Further results on delay-dependent stability criteria of discrete systems with an interval time-varying delay[J]. Journal of the Franklin Institute, 2017, 354(12): 4955-4965. [25] Zhang Xianming, Han Qinglong.New Lyapunov-Krasovskii functionals for global asymptotic stability of delayed neural networks[J]. IEEE Transactions on Neural Networks, 2009, 20(3): 533-539. [26] 李宁, 孙永辉, 卫志农, 等. 基于Wirtinger不等式的电力系统延时依赖稳定判据[J]. 电力系统自动化, 2017, 41(2): 108-113. Li Ning, Sun Yonghui, Wei Zhinong, et al.Delay-dependent stability criteria for power system based on Wirtinger integral inequality[J]. Automation of Electric Power Systems, 2017, 41(2): 108-113. [27] 汪豪, 钱伟, 郭建峰, 等. 变时滞影响下广域电力系统的H∞控制[J]. 电力系统保护与控制, 2021, 49(18): 70-80. Wang Hao, Qian Wei, Guo Jianfeng, et al.H∞ control for a wide-area power system with time-varying delay[J]. Power System Protection and Control, 2021, 49(18): 70-80. [28] 孟庭如, 邹贵彬, 许春华, 等. 一种分区协调控制的有源配电网调压方法[J]. 中国电机工程学报, 2017, 37(10): 2852-2860. Meng Tingru, Zou Guibin, Xu Chunhua, et al.A voltage regulation method based on district-dividing coordinated control for active distribution network[J]. Proceedings of the CSEE, 2017, 37(10): 2852-2860. [29] Pidre J C, Carrillo C J, Lorenzo A E F. Probabilistic model for mechanical power fluctuations in asynchronous wind parks[J]. IEEE Transactions on Power Systems, 2003, 18(2): 761-768. [30] 刘华志, 李永刚, 王优胤, 等. 无功电压优化对新能源消纳的影响[J]. 电工技术学报, 2019, 34(增刊2): 646-653. Liu Huazhi, Li Yonggang, Wang Youyin, et al.Influence about reactive power voltage optimization on the dissipation of new energy[J]. Transactions of China Electrotechnical Society, 2019, 34(S2): 646-653. [31] 张子泳, 胡志坚, 刘宇凯. 计及广域信号时变时滞影响的大型双馈风力发电系统附加鲁棒阻尼控制[J]. 电工技术学报, 2014, 29(4): 246-255. Zhang Ziyong, Hu Zhijian, Liu Yukai.Additional robust damping control of large scale DFIG-based wind power generation system with wide-area signals' time-varying delay influence[J]. Transactions of China Electrotechnical Society, 2014, 29(4): 246-255.
2023, Vol. 38 
