Various faults can cause voltage sag in the power grid at different voltage levels across the network. Balanced or unbalanced voltage sags lead to grid instability by tripping off a large number of wind or solar power plants from the electric power network. This is particularly problematic to maintain the stability of renewable energy-rich converter-dominated modern power systems. To mitigate the adverse effects of voltage sag, grid-connected converters (GCCs) need to be capable of operating in self-healing and fault-tolerant mode by embedding low voltage ride-through (LVRT) capability into the control system of GCCs. In order to facilitate the implementation of LVRT capabilities for unbalanced faults, fast and accurate frequency-adaptive sequence extraction of grid voltages and currents is essential. This motivated the present work of making a systematic comparison of adaptive observer-based sequence extraction techniques to provide LVRT capabilities into the control system of GCCs. In order to show the effectiveness of each observer, various comparative analyses were performed through Matlab-based numerical simulation. Different observers were benchmarked by the dynamic performance improvement during the low-voltage fault period. Experimental results using a laboratory-scale prototype GCC show that adaptive observers are a suitable choice of sequence extractors for LVRT operation of grid-connected converters in unbalanced and distorted grids. The results obtained in this work will contribute to enhancing the stability of modern power systems that are getting more and more converter-dominated.