  In a phase-locked loop (PLL) synchronized inverter, due to the strong
nonlinear coupling between the PLL's parame-ters and the operation power angle,
the equivalent damping coefficient will quickly deteriorate while the power
angle is close to 90{\deg} under an ultra-weak grid, which causes the
synchronous instability. To address this issue, in this letter, a pure
integral-type phase-locked loop (IPLL) with a damping branch is proposed to
replace the traditional PI-type PLL. The equivalent damping coefficient of an
IPLL-synchronized inverter is decoupled with the steady-state power angle. As a
result, the IPLL-synchronized inverter can stably operate under an ultra-weak
grid when the equilibrium point exists. Finally, time-domain simulation results
verify the effectiveness and correctness of the proposed IPLL.
