  As the integration of renewable energy generation increases and as
conventional generation is phased out, there is a gradual decline in the grid's
strength and resilience at the connection point of wind turbines (WTs).
Previous studies have shown that traditional grid-following controlled
converters exhibit deteriorating dynamic characteristics and may result in an
unstable system when connected to a weak grid. Due to the limitations of linear
analysis, transient stability investigations are necessary. However, existing
methods, such as standalone time-domain simulations or analytical Lyapunov
stability criteria, have drawbacks, including computational intensity or
excessive conservatism. Our prior research proposed an innovative approach to
estimate the system boundary - a time-limited region of attraction (TLRoA),
using a hybrid linearised Lyapunov function-based method and the time-reversal
technique to compensate for the known limitations. However, in that work, the
accuracy of the estimated TLRoA was not investigated, i.e. the TLRoA was not
compared against a forward simulated region of attraction, and the sensitivity
of the system parameters on the TLRoA was not explored. Moreover, the framework
did not consider nonlinear control elements such as PLL saturation. In this
paper, we not only build upon our previous work and propose directions that
address these gaps but also enhance its effectiveness by introducing optimal
sampling to improve further the speed of estimating the TLRoA. Furthermore, the
stability boundary is verified using time-domain simulation studies in PSCAD.
