###### Abstract  
A photovoltaic grid-connected inverter is a strongly nonlinear system. A model predictive control method can improve control accuracy and dynamic performance. Methods to accurately model and optimize control parameters are key to ensuring the stable operation of a photovoltaic grid-connected inverter. Based on the nonlinear characteristics of photovoltaic arrays and switching devices, we established a nonlinear model of photovoltaic grid-connected inverters using the state space method and solved its model predictive controller. Then, using the phase diagram, folded diagram, and bifurcation diagram methods, we studied the nonlinear dynamic behavior under the influence of control parameters on both fast and slow scales. Finally, we investigated the methods of parameter selection based on the characteristics of nonlinear dynamic behavior. Our research shows that the predictive controller parameters are closely related to the bifurcation and chaos behaviors of the grid-connected photovoltaic inverter. The three-dimensional bifurcation diagram can be used to observe the periodic motion region of the control parameters. After selecting the optimization target, the bifurcation diagram can be used to guide the selection of control parameters for inverter design. The research results can be used to guide the modeling, stability analysis, and optimization design of photovoltaic grid-connected inverters.  
Photovoltaic grid-connected inverter; Nonlinear dynamics; Predictive control; Nonlinear model 202020  
characteristics of the system, thus providing more accurate modeling for photovoltaic grid-connected inverter [7; 8; 9].  
An inverter circuit contains power switching devices, which are strongly nonlinear systems. Establishing a piecewise smooth model can better reveal the inherent physical characteristics of the system, such as bifurcation and chaos [10; 11; 12; 13]. Since the 1980s, the nonlinear dynamic behaviors of power electronics systems have been widely studied, including the bifurcation and chaotic behaviors of DC/DC converters [14; 15; 16], DC/AC converters [11; 13; 17], and motor systems [18; 19]. Studies have shown that the bifurcation and chaotic behaviors are closely related to the control and stability of power electronic systems, the bifurcation behavior of multi-inverter microgrids has an inherent relationship with system stability [20; 21], and chaos control in power electronics systems is crucial for system stability [22; 23]. With the continuous increase of the number of distributed photovoltaic grid-connected inverters, accurate system modeling, control, and stability analysis are becoming more and more important. Only by comprehensively considering the nonlinear characteristics of photovoltaic arrays and the switching characteristics of inverter circuits can accurate models of photovoltaic grid-connected inverters be established.  
The main work of this paper is to establish a nonlinear model for photovoltaic grid-connected inverters and solve its predictive controller, study the nonlinear dynamic behavior of photovoltaic grid-connected inverters using methods including time-domain waveforms, phase diagrams, folded diagrams, and bifurcation diagrams, and finally explore how to select control parameters using nonlinear dynamic behavior characteristics such as bifurcation and chaos. The work of this paper may serve as a valuable reference in the modeling, optimization control, and stability analysis of large-scale distributed new energy grid-connected power generation systems.