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

Considering that the traditional linearization method can not accurately analyze the grid-tied inverter (GTI) system with nonlinear nature. In the single-phase case, a novel nonlinear model for GTI system considering nonlinear factors including synchronous reference frame phase-locked loop (SRF-PLL) and duty cycle saturation in pulsewidth modulation (PWM) is proposed, and the corresponding global asymptotic stability condition is given. Specifically, some system nonlinear factors, e.g. duty cycle saturation phenomenon, and Park (dq-) transformation and cosine operation in second-order generalized integrator-based PLL (SOGI-PLL), are investigated respectively, and their sector-bounded conditions are derived. In order to seek less conservative results, the system state of SOGI-PLL is restructured such that the linear part of 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 derivation of Lyapunov function by using S-procedure lemma, and the global asymptotic stability condition of inverter system is thus obtained. The system stability regions (SRs) under different grid impedance, current reference, and control parameters are further analyzed. Finally, the effectiveness of proposed theories is fully supported by transient experimental results.