Small-Signal Stability of Photovoltaic Systems Connected to Weak Grids Based on Linear Time-Periodic Theory: Phase-Locked Loop Analysis and Virtual Inductance Control

Large-scale photovoltaic (PV) plants connected to weak grids may experience oscillations caused by interactions between converter controls and grid impedance. This paper develops a linear time-periodic (LTP) small-signal model by linearizing nonlinear electromagnetic-transient (EMT) equations along the periodic steady-state trajectory, explicitly incorporating second-order generalized integrator (SOGI)-based positive-/negative-sequence separation and negative-sequence current control. Model accuracy is validated through time-domain response comparisons with the nonlinear model under DC-link voltage reference, grid frequency, and grid voltage disturbances. Floquet characteristic exponent trajectories reveal critical-mode migration as the phase-locked loop (PLL) proportional and integral gains vary. Three-dimensional stability surfaces and their projections characterize changes in the PLL proportional–integral (PI) parameter stability region as the short-circuit ratio (SCR) decreases from 2.63 to 1.47. Participation factor analysis identifies PLL states as the dominant contributors to the critical oscillatory modes. Accordingly, virtual inductance control is adopted to construct a virtual point of common coupling (PCC) voltage for PLL synchronization. Under the weak grid condition with SCR = 1.47, the range of the virtual inductance control coefficient that maintains small-signal stability extends from just above approximately 0.25 to 1. With a representative coefficient of 0.4, nonlinear EMT simulations and parameter scans demonstrate that the control suppresses oscillations and enlarges the PLL PI parameter stability region.