Stability analysis of parallel fractional-order inverter systems considering low complexity and conservatism
DOI:10.19783/j.cnki.pspc.240010
Key Words:stability margin  T-type grid-connected converter  fractional inductor and capacitor  Gershgorin theorem  Ostrowski theorem
Author NameAffiliation
YANG Duotong Southern Power Grid Digital Grid Research Institute Co., Ltd., Guangzhou 510700, China 
LIN Zhenfu Southern Power Grid Digital Grid Research Institute Co., Ltd., Guangzhou 510700, China 
NIE Zhijie Southern Power Grid Digital Grid Research Institute Co., Ltd., Guangzhou 510700, China 
ZHANG Zihao Southern Power Grid Digital Grid Research Institute Co., Ltd., Guangzhou 510700, China 
ZENG Boru 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.
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