| 引用本文: | 杨铎烔,林振福,聂智杰,等.计及低复杂度且少保守性的并联分数阶逆变器系统稳定性研究[J].电力系统保护与控制,2025,53(1):47-58. |
| YANG Duotong,LIN Zhenfu,NIE Zhijie,et al.Stability analysis of parallel fractional-order inverter systems considering low complexity and conservatism[J].Power System Protection and Control,2025,53(1):47-58 |
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| 摘要: |
| 三电平T型换流器(three-level T-type converter, 3LT2C)与LCL滤波器在可再生能源发电系统中被广泛使用。最近研究表明，由于LCL滤波器的电感和电容的分数特性，分数阶模型在描述LCL-3LT2C变换器的静态和动态行为方面比整数阶模型具有更高的准确性。为了评估并网分数LCL-3LT2C(FLCL-3LT2C)的稳定性，通常采用分数阶阻抗模型；然而，由于分数微积分的存在，特征方程的整体阶次会增加，从而导致高处理器计算负荷。此外，现有的特征值估计方法在特征值取值范围精度方面存在不足。为了解决这些问题，提出了一种基于Ostrowski定理的低复杂度和较少保守性的稳定性判据，该准则根据系统环路增益矩阵确定关键稳定点。首先，在不平衡电网下建立了单个和多并联F3LT2C的分数序列导纳模型。其次，通过Ostrowski定理确定了系统的临界稳定点。仿真和实验结果验证了所提出的分数模型的建模准确性，以及提出的低复杂度和少保守性稳定性判据的有效性。 |
| 关键词: 稳定裕度 T型并网变流器 分数阶电感和电容 Gershgorin定理 Ostrowski定理 |
| DOI：10.19783/j.cnki.pspc.240010 |
| 分类号: |
| 基金项目:广东省重点领域研发计划项目资助(2021B 0101230003) |
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| Stability analysis of parallel fractional-order inverter systems considering low complexity and conservatism |
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YANG Duotong, LIN Zhenfu, NIE Zhijie, ZHANG Zihao, ZENG Boru
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Southern Power Grid Digital Grid Research Institute Co., Ltd., Guangzhou 510700, China
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| Abstract: |
| The three-level T-type converter (3LT2C) and LCL filter have been widely used in renewable energy power generation systems. Recent studies show that, because of the fractional characteristics of the inductance and capacitance of the LCL filter, the fractional-order model has higher accuracy than the integer-order model in describing the static- and dynamic-behaviors of the physical LCL-3LT2C converter. To evaluate the stability of the grid-connected fractional LCL-3LT2C (FLCL-3LT2C), a fractional impedance model is often used. However, because of the fractional calculus, the overall order of the characteristic equation would increase, thus leading to a high computation burden. The existing eigenvalues estimation method is not sufficiently accurate. To solve these problems, a low-complexity and less-conservative stability criterion based on the Ostrowski theorem is proposed. This determines the critical stability point according to the system loop gain matrix. First, the fractional sequence admittance models for a single and multi-parallel F3LT2C are established with an unbalanced grid. Second, the critical stability points of the system are determined by the Ostrowski theorem. Simulation and experimental results verify the modeling accuracy of the proposed fractional model and the effectiveness of the proposed stability theorem with low-complexity and less-conservativeness. |
| Key words: stability margin T-type grid-connected converter fractional inductor and capacitor Gershgorin theorem Ostrowski theorem |
