Nonlinear Modeling and Global Stability Condition of Single-Phase Grid-Tied Inverter Considering SRF-PLL and Duty-Cycle Saturation

Abstract

Considering that the traditional linearization method cannot accurately analyze the grid-tied inverter (GTI) system with nonlinear nature, in the single-phase case, a novel nonlinear model for the GTI system considering nonlinear factors, including synchronous reference frame phase-locked loop (PLL) and duty-cycle saturation in pulsewidth modulation, is proposed, and the corresponding global asymptotic stability condition is given. Specifically, some system nonlinear factors, e.g., duty-cycle saturation phenomenon and Park ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> ) transformation and cosine operation in second-order generalized integrator-based PLL (SOGI-PLL), are investigated, and their sector-bounded conditions are derived. In order to seek less conservative results, the system state of the SOGI-PLL is restructured such that the linear part of the PLL system can be stabilized. Then, the nonlinear state-space model with sector bounded for the whole GTI system is formulated. Furthermore, the deduced sector conditions are introduced into the derivation of the Lyapunov function by using the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S-procedure</i> lemma, and the global asymptotic stability condition of the inverter system is, thus, obtained. The system stability regions under different grid impedances, current references, and control parameters are further analyzed. Finally, the effectiveness of the proposed theories is fully supported by transient experimental results.