Abstract：Voltage drop and the abrupt change of phase will occur when a fault occurs in the power system integrated with renewable energy sources (RESs). Factors, such as imbalanced load and asymmetric faults, will further cause the imbalanced amplitude and phase of three-phase voltage, leading to the phase-locked deviation of the double second-order generalized integrator phase-locked loop (DSOGI-PLL), which are commonly used in the real project. This deviation affects the output characteristics of the RESs, and some recent studies have analyzed the impact of the dynamic response of the PLL on the output characteristics of the grid-connected inverter. However, most of the above studies focus on the symmetrical faults and few studies quantitatively analyze the impact of the imbalanced amplitude of the grid voltage and the large abrupt change of phase of the voltage at the point of common coupling (PCC) on the phase-locked deviation under asymmetrical faults. The compensation method for the phase-locked deviation is also lacked. Therefore, a phase compensation method based on the dynamic analytical formula of phase-locked deviation is proposed in this paper, which realizes the fast and synchronous tracking of the DSOGI-PLL on the PCC voltage phase. Firstly, the abrupt change mechanism of positive sequence voltage phase under imbalanced three-phase voltage amplitude and phase is comprehensively analyzed. Considering the influence of the dynamic response of the DSOGI-PLL, the analytical phase-locked deviation equation applicable to small disturbances is obtained using the small-signal model. Besides, the analytical equation applicable to large disturbances is obtained based on the waveform fitting. Secondly, a phase compensation scheme is proposed by analyzing the impact of the DSOGI-PLL dynamic response on the output characteristics of photovoltaic (PV), reducing the influence of PLL phase-locked deviation. The phase-locked deviation of the DSOGI-PLL under faults is compensated in real time by adding a compensation link in the DSOGI-PLL control, realizing the fast and synchronous tracking of the PCC voltage phase during the dynamic tracking process. Finally, a large number of simulations are carried out in the PV grid-connected system and simulation results show that the phase compensation scheme proposed in this paper can effectively reduce the phase-locked deviation, whether the abrupt change of PCC voltage phase after faults is small or large in the PV grid-connected system, benefiting the safe and stable operation of the system. The following conclusions can be drawn from theoretical analysis and simulation verification: (1) The abrupt change of positive-sequence voltage phase is affected by the imbalanced amplitude and phase of three-phase voltage. (2) A phase compensation scheme is proposed based on the analysis of phase-locked deviation during the dynamic response of DSOGI-PLL to reduce the negative impact. The phase-locked deviation of the DSOGI-PLL after a fault is compensated in real time by adding a phase compensation link in the DSOGI-PLL control. (3) The phase compensation scheme proposed in this paper realizes the fast and synchronous tracking of PCC voltage phase by the DSOGI-PLL in the dynamic tracking process, effectively reducing the phase-locked deviation of DSOGI-PLL after grid-connected system faults and facilitating the safe and stable operation of the system.
郑涛, 刘昱彤, 章若竹, 艾静雯. 计及双二阶锁相环动态过程影响的锁相偏差检测及相位补偿[J]. 电工技术学报, 2025, 40(15): 4818-4834.
Zheng Tao, Liu Yutong, Zhang Ruozhu, Ai Jingwen. Phase-Locked Deviation Detection and Phase Angle Compensation Scheme Considering the Influence of Dynamic Process of DSOGI-PLL. Transactions of China Electrotechnical Society, 2025, 40(15): 4818-4834.
[1] 赵旭东, 王艺博, 王博闻, 等. 考虑差异化工业高载能负荷灵活性挖掘的市场实施及调度模型研究综述[J]. 电工技术学报, 2025, 40(7): 2043-2062, 2161. Zhao Xudong, Wang Yibo, Wang Bowen, etc. Review of market implementation and scheduling models considering the flexibility extraction of differentiated industrial energy-intensive loads[J] Transactions of China Electrotechnical Society, 2025, 40(7): 2043-2062, 2161. [2] 罗远翔, 王云龙, 冯扬, 等. 高比例新能源并网含抽蓄的联合系统变时段日前调度[J]. 电力系统及其自动化学报, 2024, 36(8): 115-121, 132. Luo Yuanxiang, Wang Yunlong, Feng Yang, et al.Variable-time day-ahead dispatching of high-proportion new energy grid-connected joint system with pumped storage[J]. Proceedings of the CSU-EPSA, 2024, 36(8): 115-121, 132. [3] 马秀达, 文继锋, 严伟, 等. 张北柔性直流工程电压单环控制策略应用分析[J]. 电力系统自动化, 2025, 49(2): 198-207. Ma Xiuda, Wen Jifeng, Yan Wei, et al.Application analysis of single-loop voltage control strategy in Zhangbei flexible DC project of China[J]. Automation of Electric Power Systems, 2025, 49(2): 198-207. [4] 余墨多, 黄文焘, 邰能灵, 等. 逆变型分布式电源并网运行暂态稳定机理与评估方法[J]. 电工技术学报, 2022, 37(10): 2596-2610. Yu Moduo, Huang Wentao, Tai Nengling, et al.Transient stability mechanism and judgment for inverter interfaced distributed generators connected with public grids[J]. Transactions of China Electrotechnical Society, 2022, 37(10): 2596-2610. [5] 郑宇婷, 肖凡, 谢伟杰, 等. 基于并网变流器电流稳定运行域的锁相环参数设计方法[J]. 电工技术学报, 2025, 40(10): 3181-3194. Zheng Yuting, Xiao Fan, Xie Weijie, et al.A phase-locked loop parameter design method based on current stable operation domain of grid-connected converter[J]. Transactions of China Electrotechnical Society, 2025, 40(10): 3181-3194. [6] Rodríguez P, Teodorescu R, Candela I, et al.New positive-sequence voltage detector for grid synchronization of power converters under faulty grid conditions[C]//2006 37th IEEE Power Electronics Specialists Conference, Jeju, Korea (South), 2006: 1-7. [7] 涂娟, 汤宁平. 基于改进型DSOGI-PLL的电网电压同步信号检测[J]. 中国电机工程学报, 2016, 36(9): 2350-2356. Tu Juan, Tang Ningping.Synchronizing signal detection for grid voltage based on modified DSOGI-PLL[J]. Proceedings of the CSEE, 2016, 36(9): 2350-2356. [8] 杨明, 杨倬, 李玉龙, 等. 高渗透率下基于并网逆变器阻抗重塑的锁相环设计方法[J]. 电工技术学报, 2024, 39(2): 554-566. Yang Ming, Yang Zhuo, Li Yulong, et al.A phase-locked loop design method based on impedance remodeling of grid-connected inverter under high permeability[J]. Transactions of China Electrotechnical Society, 2024, 39(2): 554-566. [9] 葛豪宇, 杨明, 方聪, 等. 弱电网下计及并网逆变器耦合效应的新型锁相环设计方法及其稳定性分析[J]. 电网技术, 2024, 48(12): 5108-5117. Ge Haoyu, Yang Ming, Fang Cong, et al.A new phase-locked loop design method and stability analysis considering the coupling effect of grid-connected inverter under weak grid[J]. Power System Techno-logy, 2024, 48(12): 5108-5117. [10] 郑涛, 黄予园, 宗伟, 等. 光伏并网系统故障二次谐波产生机理及其对变压器保护的影响[J]. 电力系统保护与控制, 2020, 48(12): 13-22. Zheng Tao, Huang Yuyuan, Zong Wei, et al.Second harmonic generation mechanism of a photovoltaic grid-connected system fault and its influence on transformer protection[J]. Power System Protection and Control, 2020, 48(12): 13-22. [11] 郑涛, 邹芃蓥, 王子鸣. 计及锁相环动态响应特性的光伏并网系统故障电流解析计算[J]. 电网技术, 2022, 46(12): 4656-4667. Zheng Tao, Zou Pengying, Wang Ziming.Fault current analysis of photovoltaic grid-connected system considering dynamic response characteristics of PLL[J]. Power System Technology, 2022, 46(12): 4656-4667. [12] Zheng T, Zhang R, Chen Y, et al.Improved scheme based on memory voltage for transformer differential protection considering the effects of PLL[J]. IET Generation Transmission Distribution, 2024, 18: 214-225. [13] 陈晓龙, 朱雨葭, 张浩, 等. 光伏电站主变压器比率差动保护对单相接地短路故障的适应性分析[J]. 电力自动化设备, 2023, 43(10): 217-224. Chen Xiaolong, Zhu Yujia, Zhang Hao, et al.Adaptability analysis of photovoltaic power station main transformer ratio differential protection to single-phase grounding short circuit fault[J]. Electric Power Automation Equipment, 2023, 43(10): 217-224. [14] 刘素梅, 毕天姝, 王晓阳, 等. 具有不对称故障穿越能力逆变型新能源电源故障电流特性[J]. 电力系统自动化, 2016, 40(3): 66-73. Liu Sumei, Bi Tianshu, Wang Xiaoyang, et al.Fault current characteristics of inverter interfaced renewable energy generators with asymmetrical fault ride-through capability[J]. Automation of Electric Power Systems, 2016, 40(3): 66-73. [15] 毕天姝, 刘素梅, 薛安成, 等. 逆变型新能源电源故障暂态特性分析[J]. 中国电机工程学报, 2013, 33(13): 165-171. Bi Tianshu, Liu Sumei, Xue Ancheng, et al.Fault characteristics of inverter-interfaced renewable energy sources[J]. Proceedings of the CSEE, 2013, 33(13): 165-171. [16] 贾科, 刘浅, 杨彬, 等. 计及锁相环动态特性的逆变电源故障暂态电流解析[J]. 电网技术, 2021, 45(11): 4242-4251. Jia Ke, Liu Qian, Yang Bin, et al.Transient fault current analysis of the inverter-interfaced renewable energy sources considering the dynamic characteristics of the phase-locked loop[J]. Power System Technology, 2021, 45(11): 4242-4251. [17] 程成, 谢少军, 张晴晴, 等. 计及锁相环动态的单相并网逆变器建模及稳定性研究综述[J]. 中国电机工程学报, 2024, 44(1): 255-269. Cheng Cheng, Xie Shaojun, Zhang Qingqing, et al.Overview of modeling and stability analysis for single-phase grid-connected inverters considering phase-locked loop dynamics[J]. Proceedings of the CSEE, 2024, 44(1): 255-269. [18] 祁永胜, 李凯, 高畅毓, 等. 三相电压不平衡下DDSRF-PLL与DSOGI-PLL的锁相误差检测与补偿方法[J]. 电工技术学报, 2024, 39(2): 567-579. Qi Yongsheng, Li Kai, Gao Changyu, et al.Phase estimation error detection and compensation method of DDSRF-PLL and DSOGI-PLL under three-phase voltage unbalance[J]. Transactions of China Electrotechnical Society, 2024, 39(2): 567-579. [19] 岑扬, 黄萌, 査晓明. 电网电压不平衡跌落下同步参考坐标系锁相环瞬态响应分析[J]. 电工技术学报, 2016, 31(增刊2): 28-38. Cen Yang, Huang Meng, Cha Xiaoming.The Transient Response Analysis of SRF-PLL under the Unbalance Grid Voltage Sag[J]. Transactions of China Electrotechnical Society, 2016, 31(S2): 28-38. [20] Lee C R, Chun T W, Lee H H.A second-order generalized differentiator method for eliminating DC component in the three-phase PLL for grid-connected inverters[C]//2017 20th International Conference on Electrical Machines and Systems (ICEMS), Sydney, NSW, Australia, 2017: 1-5. [21] 李红, 梁军杨, 王振民, 等. 跟网型变换器的小扰动同步稳定机理分析与致稳控制[J]. 电工技术学报, 2024, 39(12): 3802-3815. Li Hong, Liang Junyang, Wang Zhenmin, et al.Small signal synchronization stability analysis and improved control strategy for grid following converter[J]. Transactions of China Electrotechnical Society, 2024, 39(12): 3802-3815. [22] 闫培雷, 葛兴来, 王惠民, 等. 弱电网下新能源并网逆变器锁相环参数优化设计方法[J]. 电网技术, 2022, 46(6): 2210-2221. Yan Peilei, Ge Xinglai, Wang Huimin, et al.PLL parameter optimization design for renewable energy grid-connected inverters in weak grid[J]. Power System Technology, 2022, 46(6): 2210-2221. [23] Golestan S, Monfared M, Freijedo F D.Design-oriented study of advanced synchronous reference frame phase-locked loops[J]. IEEE Transactions on Power Electronics, 2013, 28(2): 765-778. [24] Lei Jiaxing, Quan Xiangjun, Feng Shuang, et al.Accurate modeling of PLL with frequency-adaptive prefilter: on the positive feedback effect[J]. IEEE Transactions on Power Electronics, 2022, 37(4): 3747-3752. [25] 王铭灏. 计及电压扰动的光伏输出特性及其对保护的影响研究[D]. 北京: 华北电力大学, 2021. Wang Minghao.Research on characteristics of photovoltaic output and its impact on the protection considering voltage disturbance[D]. Beijing: North China Electric Power University, 2021. [26] 孙雷强, 王冲, 王丽艳, 等. Buck-Boost变换电路DCM动态建模分析[J]. 电机与控制应用, 2019, 46(11): 88-93. Sun Leiqiang, Wang Chong, Wang Liyan, et al.Modeling and simulation analysis of buck-boost converter circuit in DCM[J]. Electric Machines & Control Application, 2019, 46(11): 88-93. [27] 李济山, 刘清平, 乔进军, 等. 应用最小二乘法对电网电压拟合波形函数[J]. 价值工程, 2018, 37(22): 182-186. Li Jishan, Liu Qingping, Qiao Jinjun, et al.Application of least square method to power grid voltage fitting waveform function[J]. Value Engineering, 2018, 37(22): 182-186. [28] 陆秋贤, 马刚, 涂孟夫. 基于IEWT-FE-BO-LSTM模型的超短期风功率预测[J]. 水电能源科学, 2023, 41(1): 217-220. Lu Qiuxian, Ma Gang, Tu Mengfu.Ultra-short-term wind power prediction based on IEWT-FE-BO-LSTM model[J]. Water Resources and Power, 2023, 41(1): 217-220. [29] 周颖, 乔婧, 陈宋宋, 等. 基于麻雀搜寻优化算法的代理购电用户用电量多维度协同校核[J]. 电网技术, 2025, 49(2): 604-612. Zhou Ying, Qiao Jing, Chen Songsong, et al.Multi-dimensional collaborative checking of power consumption of purchasing agent users based on ISSA optimization algorithm[J]. Power System Technology, 2025, 49(2): 604-612. [30] Li Jishan, Liu Qingping, Qiao Jinjun, et al.Application of least squares method for fitting waveform functions to grid voltage[J]. Value Engineering, 2018, 37(22): 182-186. [31] 冯翔. 复杂环网后备保护在线整定方法研究[D]. 成都: 电子科技大学, 2022. Feng Xiang.Research on online setting method of backup protection in complex ring network[D]. Chengdu: University of Electronic Science and Technology of China, 2022.
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