Abstract：Phase-locked loop (PLL) is one of the key elements of grid-connected inverter for renewable energy integration. Its performance and stability are important to guarantee the increasing penetration of renewable energy resources in utility. In this paper, the mathematical fundament of PLL is indicated by using nonlinear dynamic model. Meanwhile, the physical fundament of PLL is displayed by using the synchronous generator model. Lyapunov energy function is utilized to identify the stability of PLL. Based on the proposed model, the affecting mechanisms of low-frequency harmonic, unbalanced, and dc-bias voltage on PLL are achieved. Besides, taking an implicit proportional-integral based PLL into account, this paper also studies how the nonlinear mathematical model can be used to explore new PLL structure. Finally, experimental results are presented to study the PLLs in frequency variation, phase stepping, unbalanced, and distorted utility voltage conditions.
曾正, 邵伟华, 刘清阳, 马青, 冉立. 并网逆变器数字锁相环的数学物理本质分析[J]. 电工技术学报, 2018, 33(4): 808-816.
Zeng Zheng, Shao Weihua, Liu Qingyang, Ma Qing, Ran Li. Mathematical and Physical Fundaments of Digital Phase-Locked Loop for Grid-Connected Inverters. Transactions of China Electrotechnical Society, 2018, 33(4): 808-816.
[1] 黄媛, 罗安, 王逸超. 一种无谐波检测的三相并网逆变器谐波灵活控制方法[J]. 电工技术学报, 2016, 31(24): 213-222. Huang Yuan, Luo An, Wang Yichao.A flexible harmonic control method for three-phase grid- connected inverter without harmonic detection[J]. Transactions of China Electrotechnical Society, 2016, 31(24): 213-222. [2] Blaabjerg F, Chen Z, Kjaer S B.Power electronics as efficient interface in dispersed power generation systems[J]. IEEE Transactions on Power Electronics, 2004, 19(5): 1184-1194. [3] Blaabjerg F, Teodorescu R, Liserre M, et al.Overview of control and grid synchronization for distributed power generation systems[J]. IEEE Transactions on Industrial Electronics, 2006, 53(5): 1398-1409. [4] Teodorescu R, Liserre M, Rodriguez P.Grid con- verters for photovoltaic and wind power systems[M]. West Sussex, UK: John Wiley & Sons, Ltd, 2011. [5] 熊凌飞, 韩民晓, 姚蜀军. 锁相环对多端柔性直流稳定性作用分析及参数选择研究[J]. 电工技术学报, 2015, 30(16): 203-212. Xiong Lingfei, Han Minxiao, Yao Shujun.Influence of PLL on the stability analysis of VSC-MTDC and parameter selection[J]. Transactions of China Electrotechnical Society, 2015, 30(16): 203-212. [6] 吴恒, 杨东升, 阮新波. 基于串联信号延迟对消法的三相非理想电网锁相控制策略[J]. 电工技术学报, 2014, 29(8): 255-264. Wu Heng, Yang Dongsheng, Ruan Xinbo.Phase- locked loop based on cascaded delayed signal cancellation for distorted grid[J]. Transactions of China Electrotechnical Society, 2014, 29(8): 255-264. [7] 曾正, 赵荣祥, 汤胜清, 等. 可再生能源分散接入用先进并网逆变器研究综述[J]. 中国电机工程学报, 2013, 33(24): 1-12. Zeng Zheng, Zhao Rongxiang, Tang Shengqing, et al.An overview on advanced grid-connected inverters used for decentralized renewable energy resources[J]. Proceedings of the CSEE, 2013, 33(24): 1-12. [8] Carugati I, Maestri S, Donato P G, et al.Variable sampling period filter PLL for distorted three-phase systems[J]. IEEE Transactions on Power Electronics, 2012, 27(1): 321-330. [9] 何宇, 漆汉宏, 邓超, 等. 一种嵌入重复控制内模的三相锁相环的设计与实现[J]. 电工技术学报, 2016, 31(22): 83-91. He Yu, Qi Hanhong, Deng Chao, et al.A novel three-phase phase-locked loop method based on internal model of repetitive control[J]. Transactions of China Electrotechnical Society, 2016, 31(22): 83-91. [10] 王宝诚, 伞国成, 郭小强, 等. 分布式发电系统电网同步锁相技术[J]. 中国电机工程学报, 2013, 33(1): 50-55. Wang Baocheng, San Guocheng, Guo Xiaoqiang, et al.Grid synchronization and PLL for distributed power generation systems[J]. Proceedings of the CSEE, 2013, 33(1): 50-55. [11] 杜雄, 刘延东, 王国宁, 等. 采用正弦幅值积分器的单同步参考坐标系同步信号检测方法[J]. 电工技术学报, 2015, 30(8): 167-175. Du Xiong, Liu Yandong, Wang Guoning, et al.Synchronization signal detection method in synchronous reference frame through sinusoidal amplitude integrators[J]. Transactions of China Electrotechnical Society, 2015, 30(8): 167-175. [12] Kyoung-Jun L, Jong-Pil L, Dongsul S, et al.A novel grid synchronization PLL method based on adaptive low-pass Notch filter for grid-connected PCS[J]. IEEE Transactions on Industrial Electronics, 2014, 61(1): 292-301. [13] Vazquez S, Sanchez J A, Reyes M R, et al.Adaptive vectorial filter for grid synchronization of power converters under unbalanced and/or distorted grid conditions[J]. IEEE Transactions on Industrial Electronics, 2014, 61(3): 1355-1367. [14] Golestan S, Freijedo F D, Guerrero J M.A systematic approach to design high-order phase-locked loops[J]. IEEE Transactions on Power Electronics, 2015, 30(6): 2885-2890. [15] Golestan S, Freijedo F D, Vidal A, et al.A quasi-type-1 phase-locked loop structure[J]. IEEE Transactions on Power Electronics, 2014, 29(12): 6264-6270. [16] Rodriguez P, Pou J, Bergas J, et al.Decoupled double synchronous reference frame PLL for power con- verters control[J]. IEEE Transactions on Power Electronics, 2007, 22(2): 584-592. [17] 李珊瑚, 杜雄, 王莉萍, 等. 解耦多同步参考坐标系电网电压同步信号检测方法[J]. 电工技术学报, 2011, 26(12): 183-189. Li Shanhu, Du Xiong, Wang Liping, et al.A grid voltage synchronization method based on decoupled multiple synchronous reference frame[J]. Transa- ctions of China Electrotechnical Society, 2011, 26(12): 183-189. [18] 王颢雄, 马伟明, 肖飞, 等. 双dq变换软件锁相环的数学模型研究[J]. 电工技术学报, 2011, 27(7): 237-241. Wang Haoxiong, Ma Weiming, Xiao Fei, et al.Study of model of software phase locked-loop based on dual-dq synchronous transform[J]. Transactions of China Electrotechnical Society, 2011, 27(7): 237-241. [19] Rodri X, Guez P, Luna A, et al.A stationary reference frame grid synchronization system for three-phase grid-connected power converters under adverse grid conditions[J]. IEEE Transactions on Power Electronics, 2012, 27(1): 99-112. [20] Guo X, Wu W, Chen Z.Multiple-complex coefficient-filter-based phase-locked loop and synchronization technique for three-phase grid- interfaced converters in distributed utility networks[J]. IEEE Transactions on Industrial Electronics, 2011, 58(4): 1194-1204. [21] Li W W, Ruan X B, Bao C L, et al.Grid synchronization systems of three-phase grid- connected power converters: a complex-vector-filter perspective[J]. IEEE Transactions on Industrial Electronics, 2014, 61(4): 1855-1870. [22] 裴喜平, 郝晓弘, 陈伟. 基于模型参考自适应算法的三相锁相环系统[J]. 电工技术学报, 2014, 29(4): 196-204. Pei Xiping, Hao Xiaohong, Chen Wei.A novel three-phase phase-locked-loop system based on model reference adaptive algorithm[J]. Transactions of China Electrotechnical Society, 2014, 29(4): 196-204. [23] Zhong Q C, Hornik T.Control of power inverters in renewable energy and smart grid integration[M]. New York: Wiley-IEEE Press, 2012. [24] Endo T, Chua L O.Chaos from phase-locked loops[J]. IEEE Transactions on Circuits and Systems, 1988, 35(8): 987-1003. [25] 龚锦霞, 解大, 张延迟. 三相数字锁相环的原理及性能[J]. 电工技术学报, 2009, 24(10): 94-99. Gong Jinxia, Xie Da, Zhang Yanchi.Principle and performance of the three-phase digital phase-locked loop[J]. Transactions of China Electrotechnical Society, 2009, 24(10): 94-99. [26] Zhong Q, Boroyevich D.A droop controller is intrinsically a phase-locked loop[C]//Annual Con- ference of the IEEE Industrial Electronics Society, Vienna, Austria, 2013: 5916-5921. [27] 孙元章,焦晓红,申铁龙. 电力系统非线性鲁棒控制[M]. 北京: 清华大学出版社, 2007.
2018, Vol. 33 
