Abstract：In real-world power grids with high renewable energy penetration, grid-connected inverters (GCIs) operate under increasingly complex and fluctuating conditions, which can create or even exacerbate weak grid conditions, leading to grid frequency deviations and voltage imbalances. These issues pose serious challenges to harmonic suppression and system stability. Conventional repetitive control (CRC) strategies exhibit poor adaptability to frequency variations, significantly reducing harmonic rejection performance. High-order selective harmonic repetitive control (HO-SHRC) enhances adaptability by increasing system gain at specified harmonics. However, as the control order increases, the linear increase in memory demand and system latency significantly raises implementation costs and reduces real-time performance. Therefore, this paper proposed a simplified infinite-order selective harmonic repetitive control (SIO-SHRC) strategy based on the geometric series principle. By leveraging geometric weighting, the model approximated an infinite-order controller with a compact, low-order structure, reducing memory and delay without sacrificing performance. The proposed SIO-SHRC employed only two geometric decay factors, α and β, to control the distribution of weights in the infinite series, thereby transforming complex high-order computations into an efficient recursive form. Moreover, a novel structure was introduced that enables the controller to operate on a single cycle of stored data, significantly improving the system's responsiveness and memory efficiency. In addition, the design naturally avoids redundant computation and excessive phase lag. A digital implementation of the SIO-SHRC was presented with a plug-in structure, incorporating a low-pass filter and a phase-lead compensator to enhance robustness and ensure stability under nonideal grid conditions. Stability criteria for the overall control system were derived to ensure convergence under typical scenarios. Simulation and experimental results on a three-phase grid-connected inverter system confirmed the superiority of SIO-SHRC. Compared with CRC, SHRC, and HO-SHRC controllers, the proposed method demonstrated faster convergence, lower steady-state error, and better frequency adaptability. For instance, under a grid frequency shift from 50 Hz to 50.5 Hz, SIO-SHRC achieved steady-state tracking within 0.08 seconds, with an RMS error of only 0.15 A and a total harmonic distortion (THD) of 2.56%. In contrast, HO-SHRC required 0.15 seconds and yielded 0.32 A RMS error. Even under nonideal conditions, such as step changes in the active power reference and sudden grid voltage sags, the SIO-SHRC controller demonstrated rapid dynamic response and high-precision current tracking. The following conclusions can be drawn. (1) Compared to other high-order RC variants, the SIO-SHRC achieved nearly the same or better harmonic suppression performance while dramatically reducing computational and storage demands. (2) The proposed geometric-weighted structure offered a general and compatible framework that can be easily adapted to suppress different harmonic orders. (3) The low-complexity design with minimal delay and high gain made SIO-SHRC a practical and scalable solution for modern GCIs operating in weak and unstable grids. Overall, the method bridges theoretical innovation and engineering feasibility, offering considerable potential for deployment in future large-scale renewable energy systems.
方为, 卢闻州, 刘文泽. 并网逆变器简化无限阶选择谐波重复控制策略[J]. 电工技术学报, 2026, 41(14): 4839-4851.
Fang Wei, Lu Wenzhou, Liu Wenze. Simplified Infinite Order Selective Harmonic Repetitive Control Strategy for Grid-Connected Inverters. Transactions of China Electrotechnical Society, 2026, 41(14): 4839-4851.
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2026, Vol. 41 
