Phase-locked loop (PLL) and the grid voltage feedforward (GVF) are commonly adopted in grid-connected inverters. However, both of these two links may have impact on the stability of the system in weak grid. From the perspective of impedance, considering PLL and the GVF is equivalent to two additional admittances YPLL(s) and Yff(s) in parallel on top of the original output admittance. The output admittance Bode plots considering the PLL and grid voltage feed-forward are given in Fig.A1, which shows that the output characteristics in the middle and low frequency bands are influenced by the two factors, resulting in a joint-action frequency band.
Fig.A1 Bode plots of output admittance of inverter considering dual factors
As the grid impedance increases, the admittance intersection frequency point enters the GVF-dominant frequency range of firstly. Accordingly, the primary consideration is to improve the GVF by introducing weighting coefficient to ensure the stability of the inverter as well as maintain a certain level of harmonic suppression capability of the system. With the increasing of the grid impedance, the bandwidth of the current loop decreases rapidly, approaching the frequency range influenced by the PLL bandwidth. This results in coupling between the current loop and the PLL. The introduction of the weighting coefficient into the GVF can enhance the bandwidth of the current loop, thereby improving the poor robustness induced by PLL.
However, for weaker grids with smaller SCR, the presence of the PLL would bring about a less or even negative phase margin, leading to the system unstable. Consequently, the improving effect of the weighting-coefficient-based GVF is limited in this case. Therefore, as shown in Fig.A2, a voltage feedforward path is added to improve the phase introduced by the phase-locked loop, allowing the system to adapt to a wider range of varying grid impedance. Specifically, an all-pass filter (APF) is added in this path, and then phase compensation is applied to it, which is followed by the design of its parameters at last.
Fig.A2 Control block diagram with an improved feedforward path
Finally, a prototype was constructed, and experimental waveforms verified the theoretical analysis mentioned above. The results indicate that, with the addition of the improved voltage feedforward path to the grid-connected inverter, the system can maintain a certain level of robustness even when the grid impedance varies significantly. The contribution of this article lies in following aspects: (1) The frequency-band division considering dual unstable factors is carried out. Then, the three regions including the PLL-dominant region, joint-action region and GVF-dominant region are acquired. (2) It is found that, the GVF with weighted coefficient has the merit of enhancing the robustness issue caused by the PLL to a certain extent. While, the role of improvement is somewhat limited since the phase margin is not big enough. (3) In joint-action frequency region, on the basis of the weighted coefficient, the improved feedforward path is ultimately introduced to ensure a good stability of the system in weak grid.
刘昊, 方天治, 张惠丽, 朱延涛. 弱电网下应对复杂稳定性问题的并网逆变器改进电压前馈通路研究[J]. 电工技术学报, 2024, 39(16): 4955-4967.
Liu Hao, Fang Tianzhi, Zhang Huili, Zhu Yantao. Research on an Improved Voltage Feedforward Path of Grid-Connected Inverter Coping with Complex Stability Issues in Weak Grid. Transactions of China Electrotechnical Society, 2024, 39(16): 4955-4967.
[1] Lin Zhiheng, Ruan Xinbo, Wu Liguo, et al.Multi resonant component-based grid-voltage-weighted feedforward scheme for grid-connected inverter to suppress the injected grid current harmonics under weak grid[J]. IEEE Transactions on Power Electronics, 2020, 35(9): 9784-9793.
[2] 涂春鸣, 高家元, 赵晋斌, 等. 弱电网下具有定稳定裕度的并网逆变器阻抗重塑分析与设计[J]. 电工技术学报, 2020, 35(6): 1327-1335.
Tu Chunming, Gao Jiayuan, Zhao Jinbin, et al.Analysis and design of grid-connected inverter impedance remodeling with fixed stability margin in weak grid[J]. Transactions of China Electrotechnical Society, 2020, 35(6): 1327-1335.
[3] 李佳琪, 陈健, 张文, 等. 高渗透率光伏配电网中电池储能系统综合运行控制策略[J]. 电工技术学报, 2019, 34(2): 437-446.
Li Jiaqi, Chen Jian, Zhang Wen, et al.Integrated control strategy for battery energy storage systems in distribution networks with high photovoltaic penetration[J]. Transactions of China Electrotechnical Society, 2019, 34(2): 437-446.
[4] 许津铭, 卞申一阳, 钱浩, 等. 弱电网下单相并网逆变器延时锁相环的鲁棒控制及优化方法[J]. 中国电机工程学报, 2020, 40(7): 2062-2070, 2386.
Xu Jinming, Bian Shenyiyang, Qian Hao, et al.Robust control and optimization of delay-based phase-locked loop of single-phase grid-connected inverters under weak grid conditions[J]. Proceedings of the CSEE, 2020, 40(7): 2062-2070, 2386.
[5] Li Ming, Zhang Xing, Guo Zixuan, et al.The control strategy for the grid-connected inverter through impedance reshaping in q-axis and its stability analysis under a weak grid[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2021, 9(3): 3229-3242.
[6] Wen Bo, Dong Dong, Boroyevich D, et al.Impedance-based analysis of grid-synchronization stability for three-phase paralleled converters[J]. IEEE Transactions on Power Electronics, 2016, 31(1): 26-38.
[7] 李光辉, 王伟胜, 刘纯, 等. 直驱风电场接入弱电网宽频带振荡机理与抑制方法(一):宽频带阻抗特性与振荡机理分析[J]. 中国电机工程学报, 2019, 39(22): 6547-6562.
Li Guanghui, Wang Weisheng, Liu Chun, et al.Mechanism analysis and suppression method of wideband oscillation of PMSG wind farms connected to weak grid (partⅠ): analysis of wideband impedance characteristics and oscillation mechanism[J]. Proceedings of the CSEE, 2019, 39(22): 6547-6562.
[8] 李光辉, 王伟胜, 刘纯, 等. 直驱风电场接入弱电网宽频带振荡机理与抑制方法(二):基于阻抗重塑的宽频带振荡抑制方法[J]. 中国电机工程学报, 2019, 39(23): 6908-6920, 7104.
Li Guanghui, Wang Weisheng, Liu Chun, et al.Mechanism analysis and suppression method of wideband oscillation of PMSG wind farms connected to weak grid (part Ⅱ): suppression method of wideband oscillation based on impedance reshaping[J]. Proceedings of the CSEE, 2019, 39(23): 6908-6920, 7104.
[9] 涂春鸣, 高家元, 李庆, 等. 具有复数滤波器结构锁相环的并网逆变器对弱电网的适应性研究[J]. 电工技术学报, 2020, 35(12): 2632-2642.
Tu Chunming, Gao Jiayuan, Li Qing, et al.Research on adaptability of grid-connected inverter with complex coefficient-filter structure phase locked loop to weak grid[J]. Transactions of China Electrotechnical Society, 2020, 35(12): 2632-2642.
[10] 郭磊, 王丹, 刁亮, 等. 针对电网不平衡与谐波的锁相环改进设计[J]. 电工技术学报, 2018, 33(6): 1390-1399.
Guo Lei, Wang Dan, Diao Liang, et al.A modified design of phase-locked loop for unbalanced and distorted grid voltage conditions[J]. Transactions of China Electrotechnical Society, 2018, 33(6): 1390-1399.
[11] Xu Jinming, Qian Qiang, Zhang Binfeng, et al.Harmonics and stability analysis of single-phase grid-connected inverters in distributed power generation systems considering phase-locked loop impact[J]. IEEE Transactions on Sustainable Energy, 2019, 10(3): 1470-1480.
[12] 许津铭, 卞申一阳, 钱强, 等. 弱电网下基于电网电流前馈的单相逆变器锁相环[J]. 中国电机工程学报, 2020, 40(8): 2647-2657.
Xu Jinming, Bian Shenyiyang, Qian Qiang, et al.Grid current feedforward based phase-locked loop for single-phase-inverters in weak grid case[J]. Proceedings of the CSEE, 2020, 40(8): 2647-2657.
[13] 冯伟, 孙凯, 关雅娟, 等. 孤立微电网中基于输出电压复合控制的电压源型并网逆变器谐波电流抑制策略[J]. 电工技术学报, 2016, 31(7): 72-80.
Feng Wei, Sun Kai, Guan Yajuan, et al.A harmonic current suppression strategy for voltage source grid-connected inverters based on output voltage hybrid control in islanded microgrids[J]. Transactions of China Electrotechnical Society, 2016, 31(7): 72-80.
[14] Timbus A, Liserre M, Teodorescu R, et al.Evaluation of current controllers for distributed power generation systems[J]. IEEE Transactions on Power Electronics, 2009, 24(3): 654-664.
[15] Li Weiwei, Ruan Xinbo, Pan Donghua, et al.Full-feedforward schemes of grid voltages for a three-phase LCL-type grid-connected inverter[J]. IEEE Transactions on Industrial Electronics, 2013, 60(6): 2237-2250.
[16] Yang Dongsheng, Ruan Xinbo, Wu Heng.Impedance shaping of the grid-connected inverter with LCL filter to improve its adaptability to the weak grid condition[J]. IEEE Transactions on Power Electronics, 2014, 29(11): 5795-5805.
[17] Wang Jiangfeng, Yao Jianhui, Hu Haibing, et al.Impedance-based stability analysis of single-phase inverter connected to weak grid with voltage feed-forward control[C]//2016 IEEE Applied Power Electronics Conference and Exposition (APEC), Long Beach, CA, USA, 2016: 2182-2186.
[18] 钱强, 谢少军, 季林, 等. 一种提升逆变器对电网适应能力的电流控制策略[J]. 中国电机工程学报, 2016, 36(22): 6193-6201.
Qian Qiang, Xie Shaojun, Ji Lin, et al.A current control strategy to improve the adaptability to utility for inverters[J]. Proceedings of the CSEE, 2016, 36(22): 6193-6201.
[19] 苗丽芳, 王乐媛, 曹斌, 等. 弱电网下电网电压前馈控制分布式逆变系统的谐振阻尼特性分析[J]. 高电压技术, 2020, 46(10): 3521-3532.
Miao Lifang, Wang Yueyuan, Cao Bin, et al.Resonance damping characteristic analysis of distributed inverter-based system with grid voltage feed-forward control in weak grid[J]. High Voltage Engineering, 2020, 46(10): 3521-3532.
[20] Li Ming, Zhang Xing, Guo Zixuan, et al.The control strategy for the grid-connected inverter through impedance reshaping in q-axis and its stability analysis under a weak grid[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2021, 9(3): 3229-3242.
[21] 杜燕, 张梦梦, 杨向真, 等. 基于自适应复合导纳校正的并网逆变器稳定方法[J]. 高电压技术, 2022, 48(6): 2088-2097.
Du Yan, Zhang Mengmeng, Yang Xiangzhen, et al.Grid-connected inverter stabilization method based on adaptive composite admittance correction[J]. High Voltage Engineering, 2022, 48(6): 2088-2097.
[22] Xu Jinming, Hu Yuan, Qian Hao, et al.Delay-based phase-locked loop parameters design based on stability region of grid-connected single-phase inverter under grid voltage sags[J]. IEEE Transactions on Industrial Electronics, 2022, 69(11): 11324-11334.
[23] Xu Jinming, Bian S, Qian Qiang, et al.Robustness improvement of single-phase inverters under weak grid cases by adding grid current feedforward in delay-based phase-locked loop[J]. IEEE Access, 2020, 8: 124275-124287.
[24] Sun Jian.Impedance-based stability criterion for grid-connected inverters[J]. IEEE Transactions on Power Electronics, 2011, 26(11): 3075-3078.
[25] Qin Kuang, Wang Wentao, Wang Xuehua, et al.An adaptive proportional feedforward scheme for LCL-type grid-connected inverter[C]//2020 IEEE Applied Power Electronics Conference and Exposition (APEC), New Orleans, LA, USA, 2020: 3287-3292.
[26] 周青峰. 适用于弱电网下LCL型并网逆变器的电网电压前馈策略研究[D]. 武汉: 华中科技大学, 2018.
Zhou Qingfeng.Feedforward scheme of grid voltage for LCL-type grid-connected inverters under weak grid conditions[D]. Wuhan: Huazhong University of Science and Technology, 2018.