Enhancing stability control of Phase-Locked loop in weak power grids

•Using large signal analysis, examine the stability of the PLL in the presence of power mutation or power grid frequency disturbance in a weak grid.•The PLL bandwidth frequency will be too high, causing PLL output oscillation and making the VSC converter unstable.•The Variable transient virtual inductance (VTVL) control is proposed to increase the PLL damping ratio and improve the overall stability of VSC without generating VSC output power coupling.•Adaptive adjustment coefficient control is proposed to improve the overall VSC stability by increasing the PLL adjustment time without increasing the PLL damping ratio. This paper analyzes the factors affecting the stability of phase-locked loops (PLLs) in weak power grids. By establishing a PLL model in weak power grids, it is found that line impedance, grid frequency disturbances, and output power all have an impact on PLL stability. The influence of line impedance, grid frequency disturbances, and output power on PLL is analyzed using the phase plane method. Additionally, it is observed that increasing the PLL damping ratio can enhance PLL stability, but when the damping ratio exceeds the critical damping ratio, PLL instability may occur. Therefore, this paper divides the controllable range of PLL into two cases: damping ratio greater than the critical damping ratio and damping ratio less than the critical damping ratio. For the case where the damping ratio is less than the critical damping ratio, a transient virtual inductance control method is proposed to enhance the PLL damping ratio and improve PLL stability without introducing power coupling. For the case where the damping ratio is greater than the critical damping ratio, PLL adaptive parameter adjustment control is proposed to ensure that the PLL trajectory does not diverge by increasing the PLL adjustment time without increasing the damping ratio, thus improving VSC stability. Finally, a comparison with conventional methods is conducted, and the feasibility and correctness are analyzed through time-domain simulations, followed by presenting the result analysis.