Abstract：Second-order generalized integrator frequency-locked loop (SOGI-FLL) is a grid synchronization algorithm based on SOGI, which consists of adaptive filter (AF) and frequency-locked loop (FLL). SOGI is a widely used in current control and grid synchronization to achieve zero steady-state error when tracking sinusoidal signals, but its accuracy is affected by digital implementation. AF is a closed-loop structure of SOGI, and its accuracy is also affected by the digital implementation. Moreover, in AF digital implementation, the orthogonality of two output signals needs to be ensured to guarantee the phase stability of the grid. Discretization results are different when using different discretization methods. Common discretization methods are divided into two categories, i.e. numerical integration methods and non-integration methods. If using non-integration methods, the hierarchy of AF to be discretized can affect the discretization results as well. AF can be divided into three levels of integrator, SOGI and AF. Different discretization methods are used for the digital implementation of each hierarchy, which are compared by bode diagram, simulations and experiments. The comparisons of digital implementation focus on accuracy and orthogonality of output signals.
杨才伟, 王剑, 游小杰, 王琛琛, 詹哲军. 二阶广义积分器锁频环数字实现准确性对比[J]. 电工技术学报, 2019, 34(12): 2584-2596.
Yang Caiwei, Wang Jian, You Xiaojie, Wang Chenchen, Zhan Zhejun. Accuracy Comparison of Digital Implementation on the Second-Order Generalized Integrator Frequency-Locked Loop. Transactions of China Electrotechnical Society, 2019, 34(12): 2584-2596.
[1] M Ghoshal A, John V. High-accuracy multi-rate implementation of resonant integrator using FPGA[J]. IET Power Electronics, 2017, 10(3): 348-356. [2] Khajehoddin S A, Karimi-Ghartemani M, Jain P K, et al.A resonant controller with high structural robustness for fixed-point digital implementations[J]. IEEE Transactions on Power Electronics, 2012, 27(7): 3352-3362. [3] Yepes A G, Freijedo F D, LopezÓ, et al. High- performance digital resonant controllers implemented with two integrators[J]. IEEE Transactions on Power Electronics, 2011, 26(2): 563-576. [4] Teodorescu R, Blaabjerg F, Liserre M, et al.Proportional-resonant controllers and filters for grid- connected voltage-source converters[J]. IEE Proceedings- Electric Power Applications, 2006, 153(5): 750-762. [5] Bojoi R I, Griva G, Bostan V, et al.Current control strategy for power conditioners using sinusoidal signal integrators in synchronous reference frame[J]. IEEE Transactions on Power Electronics, 2005, 20(6): 1402-1412. [6] 冬雷, 韩劲草, 肖辅荣, 等. 一种基于自适应滤波器的新型单相锁相环技术[J]. 电工技术学报, 2016, 31(增刊1): 155-161. Dong Lei, Han Jincao, Xiao Furong, et al.A novel single-phase phase-locked loop based on adaptive filter[J]. Transactions of China Electrotechnical Society, 2016, 31(S1): 155-161. [7] 张纯江, 赵晓君, 郭忠南, 等. 二阶广义积分器的三种改进结构及其锁相环应用对比分析[J]. 电工技术学报, 2017, 32(22): 42-49. Zhang Chunjiang, Zhao Xiaojun, Guo Zhongnan, et al.Three improved second order generalized integrators and the comparative analysis in phase locked loop application[J]. Transactions of China Electro- technical Society, 2017, 32(22): 42-49. [8] 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. [9] Rodriguez P, Luna A, Ciobotaru M, et al.Advanced grid synchronization system for power converters under unbalanced and distorted operating con- ditions[C]//IECON 2006-32nd Annual Conference on IEEE Industrial Electronics, Paris, France, 2006: 5173-5178. [10] Rodríguez P, Luna A, Muñoz-Aguilar R S, 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. [11] De Brabandere K, Loix T, Engelen K, et al.Design and operation of a phase-locked loop with Kalman estimator-based filter for single-phase appli- cations[C]//IECON 2006-32nd Annual Conference on IEEE Industrial Electronics, Paris, France, 2006: 525-530. [12] Patil K R, Patel H H.Modified dual second-order generalised integrator FLL for synchronization of a distributed generator to a weak grid[C]//2016 IEEE 16th International Conference on Environment and Electrical Engineering (EEEIC), Florence, Italy, 2016: 1-5. [13] Ciobotaru M, Teodorescu R, Agelidis V G.Offset rejection for PLL based synchronization in grid- connected converters[C]//2008 Twenty-Third Annual IEEE Applied Power Electronics Conference and Exposition, Austin, TX, USA, 2008: 1611-1617. [14] Ciobotaru M, Teodorescu R, Blaabjerg F.A new single-phase PLL structure based on second order generalized integrator[C]//2006 37th IEEE Power Electronics Specialists Conference, Jeju, South Korea, 2006: 1-6. [15] Rodriguez F J, Bueno E, Aredes M, et al.Discrete- time implementation of second order generalized integrators for grid converters[C]//2008 34th Annual Conference of IEEE Industrial Electronics, Orlando, FL, USA, 2008: 176-181. [16] Guan Q, Zhang Y, Kang Y, et al.Single-phase phase-locked loop based on derivative elements[J]. IEEE Transactions on Power Electronics, 2017, 32(6): 4411-4420. [17] Możdżyński K.Simple digital integration algorithm with saturation and drift elimination based second- order generalized integrator[C]//9th International Conference on Compatibility and Power Electronics (CPE), Costa da Caparica, Portugal, 2015: 312-316. [18] Rodriguez P, Luna A, Candela I, et al.Grid synchronization of power converters using multiple second order generalized integrators[C]//34th Annual Conference of IEEE Industrial Electronics, Orlando, FL, USA, 2008: 755-760. [19] 周臻, 李长磊, 王永. 基于复合二阶广义积分器的永磁同步电机转子位置与转速估计[J]. 电工技术学报, 2017, 32(7): 59-66. Zhou Zhen, Li Changlei, Wang Yong.Position and speed estimation for a permanent magnet synchronous motor rotor using composite second order generalized integrator[J]. Transactions of China Electrotechnical Society, 2017, 32(7): 59-66. [20] Yepes A G, Freijedo F D, Doval-Gandoy J, et al.Effects of discretization methods on the performance of resonant controllers[J]. IEEE Transactions on Power Electronics, 2010, 25(7): 1692-1712. [21] Teodorescu R, Blaabjerg F, Borup U, et al.A new control structure for grid-connected LCL PV inverters with zero steady-state error and selective harmonic compensation[C]//APEC'04, Nineteenth Annual IEEE Applied Power Electronics Conference and Exposition, Anaheim, CA, USA, 2004: 580-586. [22] Yuan Xiaoming, Merk W, Stemmler H, et al.Stationary-frame generalized integrators for current control of active power filters with zero steady-state error for current harmonics of concern under unbalanced and distorted operating conditions[J]. IEEE Transactions on Industry Applications, 2002, 38(2): 523-532. [23] Franklin G F, Powell J D, Workman. Digital control of dynamic systems[M]. Menlo Park, CA: Addison- wesley, 1998. [24] Freijedo F D, Yepes A G, Malvar J, et al.Frequency tracking of digital resonant filters for control of power converters connected to public distribution systems[J]. IET Power Electronics, 2011,4(4): 454-462. [25] Harnefors L.Implementation of resonant controllers and filters in fixed-point arithmetic[J]. IEEE Transactions on Industrial Electronics, 2009, 56(4): 1273-1281. [26] Vidal A, Freijedo F D, Yepes A G, et al.Transient response evaluation of stationary-frame resonant current controllers for grid-connected applications[J]. IET Power Electronics, 2014,7(7): 1714-1724. [27] Ogata K.Discrete-time control systems[M]. Engle- wood Cliffs, NJ: Prentice Hall, 1995.
2019, Vol. 34 
