Low-Complexity and Less-Conservativeness Ostrowski Stability Criterion for Parallel Fractional Grid-Connected Converters Under Unbalanced Grid

Three-level T-type converter (3LT
²
C) with
LCL
filter have been widely used in renewable energy power generation system. Recent articles have shown that, due to the fractional characteristics of the inductance and capacitance of the
LCL
filter, the fractional-order model has higher accuracy than integer-order model in describing the static- and dynamic-behaviors of the physical
LCL
-3LT
²
C converter. To evaluate the stability of the grid-connected fractional
LCL
-3LT
²
C, fractional impedance model is often used. However, due to the fractional calculus, the overall order of the characteristic equation would increase, thus leading to high computation burden. Existing eigenvalues estimation method is not accurate enough for excessive estimation range. To solve these problems, a low-complexity and less-conservative stability criteria based on Ostrowski theorem is proposed, which determines the critical stability point according to the system loop gain matrix. First, the fractional sequence admittance models for a single and multiparallel F3LT
²
C are established under unbalanced grid. Second, the critical stability points of the system are determined by Ostrowski theorem. Simulation and experimental results verify the modeling accuracy of the proposed fractional model and the effectiveness of the proposed stability theorem in low-complexity and less-conservativeness.