Abstract:Under an unbalanced power grid, the circulating current of a modular multilevel converter (MMC) contains double-line frequency positive, negative and zero sequence components, and unbalanced DC components, leading to unbalanced arm currents. Consequently, asymmetrical electrical stresses and nonuniform temperature distributions exist. However, traditional circulating current control methods generally take the AC components suppression as the control objective and ignore the potential impact of unequal DC components. Therefore, this paper considers unbalanced DC circulating current and proposes a zero-sequence voltage injection method to equalize DC circulating current. In addition, the effects of this method on the arm current and sub-module (SM) capacitor voltage are discussed in detail. Firstly, the DC circulating current equalization mechanism based on zero-sequence voltage injection is analyzed from the arm power transmission perspective. The expression of the amplitude and phase of the zero-sequence voltage is obtained. Then, a zero-sequence voltage injection method is proposed to equalize DC circulating current. The phase of zero-sequence voltage is obtained from the grid current and the deviation of DC circulating current, and a proportional resonant controller is added to adjust its amplitude. After that, the effects of this method on the arm current and SM capacitor voltage are quantitatively studied. The analysis results show that when a single-phase voltage drop occurs, the arm current peak can be reduced by 10.9 % at most, and the standard deviation of the arm current root-mean-square (RMS) value can be reduced to zero. Besides, the maximum SM capacitor voltage ripple can drop by more than 8 % under the above condition. Simulation and experiment are performed on Matlab/Simulink platform and a three-phase five-level MMC prototype. In the simulation, the proposed method is first applied when single-phase voltage drops to 40 %, which shows that the DC circulating current becomes balanced, and both the arm current peak and the maximum SM capacitance voltage ripple are reduced. The simulation results are quantitatively compared with theoretical analysis results, further verifying the accuracy of the theoretical analysis. Then, for dynamic performance comparison with the existing method, the proposed method is enabled under single-phase-to-ground and two-phase-to-ground faults. The results indicate that the method proposed in this paper has better dynamic performance, such as shorter compensation time and smaller overshoot. Additionally, the SM capacitor voltage can recover to a stable state more quickly. As for the experiment, when the proposed control method is added under a-phase voltage drop condition, DC circulating current achieves equalization in barely 40ms under different power factors. The trend of the arm current peak and the SM capacitor voltage ripple is also consistent with the analysis above. The following conclusions can be drawn from this paper: (1) The proposed method can reduce the arm current peak and equalize the arm current RMS value, thereby reducing the difference in electrical and thermal stress among phase units. (2) The maximum SM capacitor voltage ripple can also be reduced, which is beneficial to expand the MMC operation range and reduce both SM capacitance volume and cost. (3) The method proposed in this paper does not require positive-negative sequence separation and is convenient to implement, which has better dynamic performance than existing methods under different grid faults.
潘子迅, 杨晓峰, 赵锐, 崔晨阳, 郑琼林. 不平衡电网下模块化多电平换流器的直流环流均衡策略[J]. 电工技术学报, 2024, 39(2): 541-553.
Pan Zixun, Yang Xiaofeng, Zhao Rui, Cui Chenyang, Zheng Trillion Q. DC Circulating Current Balancing Control of Modular Multilevel Converter under Unbalanced Power Grid. Transactions of China Electrotechnical Society, 2024, 39(2): 541-553.
[1] 茆美琴, 程德健, 袁敏, 等. 基于暂态能量流的模块化多电平高压直流电网接地优化配置[J]. 电工技术学报, 2022, 37(3): 739-749. Mao Meiqin, Cheng Dejian, Yuan Min, et al.Optimal allocation of grounding system in high voltage direct current grid with modular multi-level converters based on transient energy flow[J]. Transactions of China Electrotechnical Society, 2022, 37(3): 739-749. [2] 束洪春, 代月, 安娜, 等. 基于线性回归的柔性直流电网纵联保护方法[J]. 电工技术学报, 2022, 37(13): 3213-3226, 3288. Shu Hongchun, Dai Yue, An Na, et al.Pilot protection method of flexible DC grid based on linear regression[J]. Transactions of China Electrotechnical Society, 2022, 37(13): 3213-3226, 3288. [3] 江畅, 程启明, 马信乔, 等. 不平衡电网电压下基于模块化多电平变流器的统一电能质量调节器的微分平坦控制[J]. 电工技术学报, 2021, 36(16): 3410-3421. Jiang Chang, Cheng Qiming, Ma Xinqiao, et al.Differential flat control for unified power quality controller based on modular multilevel converter under unbalanced grid voltage[J]. Transactions of China Electrotechnical Society, 2021, 36(16): 3410-3421. [4] 梁营玉, 张涛, 刘建政, 等. 不平衡电网电压下模块化多电平换流器的环流抑制策略[J]. 电工技术学报, 2016, 31(9): 120-128. Liang Yingyu, Zhang Tao, Liu Jianzheng, et al.A circulating current suppressing method for modular multilevel converter under unbalanced grid voltage[J]. Transactions of China Electrotechnical Society, 2016, 31(9): 120-128. [5] Shi Xiaojie, Wang Zhiqiang, Liu Bo, et al.Steady-state modeling of modular multilevel converter under unbalanced grid conditions[J]. IEEE Transactions on Power Electronics, 2017, 32(9): 7306-7324. [6] Hahn F, Andresen M, Buticchi G, et al.Thermal analysis and balancing for modular multilevel con-verters in HVDC applications[J]. IEEE Transactions on Power Electronics, 2018, 33(3): 1985-1996. [7] Bakhshizadeh M K, Ma Ke, Loh P C, et al.Indirect thermal control for improved reliability of modular multilevel converter by utilizing circulating current[C]// 2015 IEEE Applied Power Electronics Conference and Exposition (APEC), 2015, Charlotte, NC, USA, 2015: 2167-2173. [8] 卓谷颖, 江道灼, 连霄壤. 模块化多电平换流器不平衡环流抑制研究[J]. 电力系统保护与控制, 2012, 40(24): 118-124. Zhuo Guying, Jiang Daozhuo, Lian Xiaorang.Study of unbalanced circular current suppressing for modular multilevel converter[J]. Power System Protection and Control, 2012, 40(24): 118-124. [9] Zhou Yuebin, Jiang Daozhuo, Guo Jie, et al.Analysis and control of modular multilevel converters under unbalanced conditions[J]. IEEE Transactions on Power Delivery, 2013, 28(4): 1986-1995. [10] 李金科, 金新民, 吴学智, 等. 不平衡交流电网模块化多电平变流器特性分析及环流抑制方法[J]. 中国电机工程学报, 2017, 37(12): 3535-3544, 3682. Li Jinke, Jin Xinmin, Wu Xuezhi, et al.Characteristic analysis and a circulating current control method in modular multilevel converters under unbalanced grid conditions[J]. Proceedings of the CSEE, 2017, 37(12): 3535-3544, 3682. [11] 张臣, 叶华, 韦凌霄, 等. 不平衡状态下MMC双回路环流抑制策略[J]. 电工技术学报, 2019, 34(9): 1924-1933. Zhang Chen, Ye Hua, Wei Lingxiao, et al.Double-loop circulating current suppressing strategy for modular multilevel converter under unbalanced con-ditions[J]. Transactions of China Electrotechnical Society, 2019, 34(9): 1924-1933. [12] Liang Yingyu, Liu Jianzheng, Zhang Tao, et al.Arm current control strategy for MMC-HVDC under unbalanced conditions[J]. IEEE Transactions on Power Delivery, 2017, 32(1): 125-134. [13] 赖锦木, 尹项根, 王要强, 等. 基于桥臂电流控制的MMC改进电容电压均衡控制策略研究[J]. 高电压技术, 2022, 48(8): 3132-3145. Lai Jinmu, Yin Xianggen, Wang Yaoqiang, et al.Improved capacitor voltage balancing control strategy for modular multilevel converter with arm current control[J]. High Voltage Engineering, 2022, 48(8): 3132-3145. [14] Wang Jinyu, Tang Yi, Liu Xiong.Arm current balancing control for modular multilevel converters under unbalanced grid conditions[J]. IEEE Transa-ctions on Power Electronics, 2020, 35(3): 2467-2479. [15] Xu Jianzhong, Yu Yongjie, Zhao Chengyong.The predictive closed-loop averaging control of MMC phase-unit losses under unbalanced conditions[J]. IEEE Transactions on Power Delivery, 2019, 34(1): 198-207. [16] 孟沛彧, 向往, 潘尔生, 等. 分址建设直流输电系统拓扑方案与运行特性研究[J]. 电工技术学报, 2022, 37(19): 4808-4822. Meng Peiyu, Xiang Wang, Pan Ersheng, et al.Research on topology and operation characteristics of HVDC transmission system based on site-division construction[J]. Transactions of China Electro-technical Society, 2022, 37(19): 4808-4822. [17] Rodriguez P, Timbus A V, Teodorescu R, et al.Flexible active power control of distributed power generation systems during grid faults[J]. IEEE Transactions on Industrial Electronics, 2007, 54(5): 2583-2592. [18] Hao Quanrui, Li Bowei, Sun Yifan, et al.Operating region and boundary control of modular multilevel converter station under unbalanced grid conditions[J]. IEEE Transactions on Power Delivery, 2020, 35(3): 1146-1157. [19] 薛花, 田广平, 扈曾辉, 等. 电网不平衡下模块化多电平变换器无源一致性控制方法[J]. 电力系统自动化, 2022, 46(3): 85-95. Xue Hua, Tian Guangping, Hu Zenghui, et al.Passivity-consensus based control method for modu-lar multilevel converter in unbalanced power grid[J]. Automation of Electric Power Systems, 2022, 46(3): 85-95. [20] 施恩泽, 吴学智, 荆龙, 等. 网压不平衡下环流注入对模块化多电平换流器的影响分析[J]. 电工技术学报, 2018, 33(16): 3719-3731. Shi Enze, Wu Xuezhi, Jing Long, et al.Analysis of the impact on modular multilevel converter with circulating current injection under unbalanced grid voltage[J]. Transactions of China Electrotechnical Society, 2018, 33(16): 3719-3731. [21] Zhao Cong, Luan Kedong, Zhang Hang, et al.Enhancement of ZSVI by circulating current injection for full-bridge MMC with low energy storage require-ments[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2020, 8(4): 4075-4085. [22] 杨晓峰, 李泽杰, 郑琼林. 基于虚拟阻抗滑模控制的MMC环流抑制策略[J]. 中国电机工程学报, 2018, 38(23): 6893-6904, 7123. Yang Xiaofeng, Li Zejie, Zheng Trillion Q.A novel MMC circulating current suppressing strategy based on virtual impedance sliding mode control[J]. Pro-ceedings of the CSEE, 2018, 38(23): 6893-6904, 7123. [23] 王逸超, 欧名勇, 陈燕东, 等. 不平衡电压下并网逆变器的功率波动抑制与电流平衡协调控制方法[J]. 中国电机工程学报, 2017, 37(23): 6981-6987, 7089. Wang Yichao, Ou Mingyong, Chen Yandong, et al.Coordinate control of power fluctuation suppression and current balance under unbalanced voltage conditions[J]. Proceedings of the CSEE, 2017, 37(23): 6981-6987, 7089.