Modeling and Stability Analysis of a PV–Energy Storage AC/DC Integrated Three-Port Grid-Connected Power Electronic Device

Modeling and stability analysis of a PV–energy storage AC/DC integrated three-port grid-connected power electronic device is investigated in this paper for low-voltage single-phase renewable energy applications. The device consists of a PV Boost converter port, a battery-side bidirectional DC-DC converter port, and a single-phase full-bridge grid-connected inverter. To analyze the coupling-induced stability characteristics of this multi-converter system, mathematical models of the PV array, battery, and AC/DC integrated device are established. Considering the periodic time-varying nature introduced by the single-phase grid voltage, a phase-angle-based simplified discrete model is developed to transform the system into a discrete model evaluated at a fixed grid-voltage phase angle. Based on this model, eigenvalue sensitivity, eigenvalue trajectories, and bifurcation diagrams are used to identify the influence of key control parameters on system stability. The results show that excessive proportional gains in the inverter current loop and energy storage control loop reduce the stability margin and may lead to period-doubling bifurcation, Hopf bifurcation, or unstable grid current operation. The period-doubling and Hopf stability boundaries are identified at kp4 ≈ 1.40 and kp2 ≈ 1.75, respectively. In simulation, the grid-current THD increases from 2.07% to 3.60% as kp4 rises from 1.3 to 1.6 and from 2.07% to 2.27% as kp2 rises from 1.7 to 1.8. MATLAB/Simulink simulations and hardware-in-the-loop experiments further verify that the identified stability boundaries are consistent with the degradation of grid current quality and the increase in total harmonic distortion. The proposed modeling and analysis method provides a reference for parameter tuning and stable operation of single-phase PV–energy storage three-port grid-connected devices.