A Simplified Space Vector Pulse Width Modulation Method Based on ghγ Coordinates System for the Three-Level Four-Leg Inverter
Zhang Zhi1,2, Chen Haohui1,2, Chen Sizhe2, Zhang Zhaoyun1, Li Yiyun1
1. School of Electrical Engineering and Intelligence Dongguan University of Technology Dongguan 523808 China; 2. School of Automation Guangdong University of Technology Guangzhou 510006 China
Abstract：The topology of the three-level, four-leg neutral-point-clamped (3L4L-NPC) inverter is more complex than the traditional two-level and three-leg ones, which complicates the vector space (VS) and space vector pulse width modulation (SVPMW) algorithm. Traditional methods designate a subspace under the αβγ and abc coordinates system to simplify the VS. However, the disadvantages of excess tetrahedrons in the subspace, manually finding for redundant vectors, lots of storage space for switching sequences and poor scalability remain unsolved. This paper proposes a simplified SVPWM method based on the ghγ coordinates system. By decomposing the three-level VS into several two-level ones and designating the first small sectors as subspaces, combining the exact charge adjusting method for capacitance voltage on DC-side, duty cycles and switching sequences of the 3L4L-NPC inverter can be automatically calculated. Firstly, the decomposability of the three-level VS is discussed. Since it has the same characteristics in both horizontal and vertical dimensions as the two-level one, the three-level VS can be replaced by the two-level ones with redundant vectors as center points. Secondly, the two-level SVPWM method is simplified. Duty cycles and switching sequences can be calculated automatically through integer computation and space vector construction in the first small sector, which can be extended to the decomposed two-level VSs. Thirdly, rules for dividing the three-level VS are established. The selected two-level VS and its redundant vectors are calculated using the hexagonal layer where the reference voltage vector locates on gh plane and γ axis. Combining the improved two-level SVPWM method, tetrahedrons containing modulation information can be found without global searching. Finally, the charge that causes fluctuations in the capacitance voltage on the DC side is classified into three types: the charge difference left over from the previous modulation cycle, the initial supplementary charge in this cycle, and the adjustment charge provided by small vectors in this cycle. Charge error is caused by the first two types. The stability of capacitor voltages can be maintained by a linear calculation that makes the sum of the third type and the charge error zero. In addition, the above three-level modulation process is extended to make it applicable to multi-level inverters. Simulation of the algorithm was first performed on Matlab/Simulink platform. When the three-phase balanced reference voltage was set at different modulation ratios, the output voltage was three and five levels at smaller and larger modulation ratios, respectively, and the latter was closer to a sinusoidal waveform. Then, harmonics were injected into the reference voltage, which generated non-saddle modulation waves. The output voltages transformed their levels when the reference values crossed half of the DC source. Next, the voltages of two capacitors on the DC side were set at 250 V and 450 V with the modulation ratio of m=0.9 and DC source voltage at Vdc=700 V. After 0.025 s, the neutral-point potential reached relative equilibrium and was accompanied by three times oscillation of fundamental frequency with an amplitude of 0.63 V. Meanwhile, the neutral-point potential oscillations were less than 1 V when modulation ratios were less than or equal to 1. Furthermore, semi-physical simulations were carried out with dSPACE-SCALEXIO. The results showed that the three-level four-leg inverter could accurately output voltages with different modulation ratios and asymmetric voltages. A compared test was carried out when DC-side capacitor voltages were set at 100 V and 300 V. The conventional control method used about 30 ms to stabilize the voltage, and three times fluctuations occurred. In contrast, capacitor voltages could be balanced without 20 ms and maintained smoothly through the proposed method. In addition, a multi-level simulation with a large modulation ratio was implemented on a four-level four-leg inverter, which outputs three-phase line voltage with seven levels. The following conclusions can be drawn from the simulation and experimental analyses. (1) Compared with the traditional SVPMW method, the proposed one does not require manual decomposition of three-level VS and large storage space, and can automatically calculate duty cycles and switching sequences under different operating conditions. (2) The proposed neutral-point potential balancing method can make two capacitor voltages on the DC-side consistent more quickly by accurately calculating the capacitor charge. (3) The proposed modulation method can be extended to multi-level inverters by changing the level.
张志, 陈浩辉, 陈思哲, 张兆云, 李义云. 一种基于ghγ 坐标系的三电平四桥臂逆变器简化空间矢量脉宽调制方法[J]. 电工技术学报, 2023, 38(16): 4324-4338.
Zhang Zhi, Chen Haohui, Chen Sizhe, Zhang Zhaoyun, Li Yiyun. A Simplified Space Vector Pulse Width Modulation Method Based on ghγ Coordinates System for the Three-Level Four-Leg Inverter. Transactions of China Electrotechnical Society, 2023, 38(16): 4324-4338.
[1] 游建章, 郭谋发. 含四桥臂H桥变流器的不对称配电网综合补偿方法[J]. 电工技术学报, 2022, 37(11): 2849-2858. You Jianzhang, Guo Moufa.Comprehensive com- pensation method for asymmetric distribution network with four-arm H-bridge converter[J]. Transactions of China Electrotechnical Society, 2022, 37(11): 2849-2858. [2] 陈轶涵, 郭鸿浩, 陈杰, 等. 中频三相四桥臂逆变器控制策略不平衡负载状态相量模型分析[J]. 电工技术学报, 2019, 34(9): 1912-1923. Chen Yihan, Guo Honghao, Chen Jie, et al.Analysis on control strategies for unsymmetrical state of medium frequency three phase four leg inverter based on vector model[J]. Transactions of China Electro- technical Society, 2019, 34(9): 1912-1923. [3] 付永升, 李静, 胡文婷, 等. 不平衡负载下车载三相四线双向充电器中线桥臂控制与软启动设计[J]. 电工技术学报, 2019, 34(24): 5176-5188. Fu Yongsheng, Li Jing, Hu Wenting, et al.Neutral leg control and soft-start design of 3-phase 4-wire on-board bidirectional charger under imbalance load condition[J]. Transactions of China Electrotechnical Society, 2019, 34(24): 5176-5188. [4] 徐永海, 张蒙蒙, 杨依睿, 等. 不平衡负载下四桥臂逆变器双重准比例复数积分控制策略[J]. 电力系统保护与控制, 2020, 48(7): 141-150. Xu Yonghai, Zhang Mengmeng, Yang Yirui, et al.Dual quasi-proportional complex integral control strategy of the four-leg inverter with unbalanced load[J]. Power System Protection and Control, 2020, 48(7): 141-150. [5] 周娟, 秦静, 王子绩, 等. 内置重复控制器无差拍控制在有源滤波器中的应用[J]. 电工技术学报, 2013, 28(2): 233-238. Zhou Juan, Qin Jing, Wang Ziji, et al.Application of deadbeat control with plug-in repetitive controller in active power filter[J]. Transactions of China Electro- technical Society, 2013, 28(2): 233-238. [6] 李勇, 刘宏, 刘乾易, 等. 四桥臂SVG改进电流检测方法及控制策略[J]. 电力系统及其自动化学报, 2019, 31(4): 123-131. Li Yong, Liu Hong, Liu Qianyi, et al.Improved current detection method and control strategy for four-leg SVG[J]. Proceedings of the CSU-EPSA, 2019, 31(4): 123-131. [7] 谭翠兰, 邢彦一, 陈启宏, 等. 三相四桥臂并网逆变器重复控制积分抗饱和策略[J]. 电工技术学报, 2019, 34(17): 3631-3639. Tan Cuilan, Xing Yanyi, Chen Qihong, et al.Anti- windup strategy of repetitive controller for three- phase four-leg grid-tied inverter[J]. Transactions of China Electrotechnical Society, 2019, 34(17): 3631-3639. [8] 倪梦涵, 杨晓峰, 王淼, 等. 多电平均压型直流变换器输入电流纹波抑制策略[J]. 电工技术学报, 2021, 36(16): 3354-3364. Ni Menghan, Yang Xiaofeng, Wang Miao, et al.Input current ripple suppression strategy of multilevel voltage-balancing DC-DC converter[J]. Transactions of China Electrotechnical Society, 2021, 36(16): 3354-3364. [9] 王要强, 张亨泰, 赖锦木, 等. 低应力高电平开关电容逆变器及其调制策略[J]. 电工技术学报, 2021, 36(20): 4237-4248. Wang Yaoqiang, Zhang Hengtai, Lai Jinmu, et al.Topology and modulation strategy for switched capacitor inverter with low voltage stress and high level[J]. Transactions of China Electrotechnical Society, 2021, 36(20): 4237-4248. [10] 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. [11] Chee S J, Kim H S, Sul S K, et al.Common-mode voltage reduction of three-level four-leg PWM con- verter[J]. IEEE Transactions on Industry Applications, 2015, 51(5): 4006-4016. [12] 王宝诚, 郭小强, 杨勇, 等. 三电平四桥臂光伏逆变器漏电流抑制研究[J]. 中国电机工程学报, 2018, 38(14): 4194-4201, 4325. Wang Baocheng, Guo Xiaoqiang, Yang Yong, et al.Research on leakage current suppression for three- level four-leg PV inverter[J]. Proceedings of the CSEE, 2018, 38(14): 4194-4201, 4325. [13] 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. [14] Tabart Q, Vechiu I, Etxeberria A, et al.Hybrid energy storage system microgrids integration for power quality improvement using four-leg three-level NPC inverter and second-order sliding mode control[J]. IEEE Transactions on Industrial Electronics, 2018, 65(1): 424-435. [15] Tsai M J, Chen H C, Cheng Potai.Eliminating the neutral-point oscillation of the four-wire NPC active power filter[J]. IEEE Transactions on Power Elec- tronics, 2019, 34(7): 6233-6240. [16] Golwala H, Chudamani R.New three-dimensional space vector-based switching signal generation technique without null vectors and with reduced switching losses for a grid-connected four-leg inverter[J]. IEEE Transactions on Power Electronics, 2016, 31(2): 1026-1035. [17] Roh C, Kwak S, Choi S.Three-phase three-level four-leg NPC converters with advanced model predictive control[J]. Journal of Power Electronics, 2021, 21(10): 1574-1584. [18] Rojas F, Kennel R, Cardenas R, et al.A new space-vector-modulation algorithm for a three-level four-leg NPC inverter[J]. IEEE Transactions on Energy Conversion, 2017, 32(1): 23-35. [19] Bouzidi M, Benaissa A, Barkat S.Hybrid direct power/current control using feedback linearization of three-level four-leg voltage source shunt active power filter[J]. International Journal of Electrical Power & Energy Systems, 2014, 61: 629-646. [20] Franquelo L G, Prats M A M, Portillo R C, et al. Three-dimensional space-vector modulation algorithm for four-leg multilevel converters using abc coor- dinates[J]. IEEE Transactions on Industrial Elec- tronics, 2006, 53(2): 458-466. [21] Rojas F, Cárdenas R, Kennel R, et al.A simplified space-vector modulation algorithm for four-leg NPC converters[J]. IEEE Transactions on Power Elec- tronics, 2017, 32(11): 8371-8380. [22] 杨智彭, 何晋伟, 王成山. 面向独立供电系统的四桥臂电流源变流器3D-SVPWM方法[J]. 电力系统自动化, 2020, 44(16): 145-153. Yang Zhipeng, He Jinwei, Wang Chengshan.Three- dimensional space vector pulse width modulation method of four-leg current-source converter for independent power supply system[J]. Automation of Electric Power Systems, 2020, 44(16): 145-153.
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