This paper presents the application and improvement of a grid synchronization scheme for a flywheel energy storage system which is operated as a grid stabilizer in a power range of multiple 100 MW. In detail, different grid anomalies such as voltage dips, frequency deviations or phase jumps need to be handled by the system in order to achieve appropriate grid support. For this purpose, the Decoupled Double Synchronous Reference Frame-Phase Locked Loop (DDSRF-PLL) is utilized for grid synchronization. As proposed in this paper, the DDSRF-PLL can be improved by adding a separated voltage phase angle estimation path based on a second order bandpass. Thereby, the aim is to reduce transient synchronization angle errors and frequency overshoots. Simulated and measured evaluations show the effectiveness of the enhanced approach to reduce transient synchronization errors due to voltage dips or phase angle jumps.