With the increasing complexity of modern power systems, grid synchronization has become more challenging due to the presence of DC offsets, subharmonics, and voltage distortions. One of the recent approaches capable of fully addressing these issues single-handedly is the symmetrical second-order generalized integrator phase-locked loop (SSOGI-PLL). It uses a low-pass filter (LPF) tuned to the system frequency to make the quadrature output of the SOGI function like a band-pass filter (BPF). As a result, the system can operate effectively in the presence of subharmonics and DC-offset. Moreover, the low-pass filter (LPF), tuned to the grid frequency, facilitates accurate measurement of the total harmonic distortion (THD) in the grid voltage. Although the small-signal model of the SSOGI-PLL has been developed, certain dynamic parameters, particularly the third pole introduced by internal filtering and control dynamics, are approximated using empirical assumptions. These approximations, often expressed as multiples of the fundamental frequency, result in uncertainty in modeling accuracy and limit the reliability of the analysis.

This paper focuses on the systematic refinement of the existing small-signal model of the SSOGI-PLL by identifying the most accurate location of the third pole. Starting from the established analytical model, multiple candidate representations are formulated by assigning different values to the uncertain pole, such as 2.5, 2.8, and 3 times the fundamental angular frequency. The dynamic behavior of these models is evaluated through time-domain and frequency-domain analysis and compared with the response of the nonlinear SSOGI-PLL system.

Extensive validation is performed using MATLAB/Simulink simulations under various grid disturbance scenarios, including voltage sag and swell, harmonic and subharmonic distortion, frequency deviations, and phase-jump perturbations. The comparative results demonstrate that the proposed methodology enables accurate identification of the third pole and significantly improves the agreement between the small-signal model and the nonlinear system behavior.

The refined model provides a reliable analytical foundation for stability assessment and performance evaluation of SSOGI-PLL-based synchronization systems. By resolving the uncertainty associated with the third pole, this work enhances the credibility of small-signal analysis and supports more reliable design and optimization for this grid synchronization scheme.