A Modified Park Transformation Algorithm for Phase-Locked Loop Applications in Unbalanced Three-Phase Systems

This paper proposes a novel modified Park transformation (MPT) algorithm for phase-locked loop (PLL) applications in unbalanced three-phase systems. Unlike the conventional Park transformation, the proposed MPT algorithm directly incorporates unbalanced characteristics into its transformation matrix, thereby streamlining control strategies without requiring supplementary filtering. The effectiveness of the proposed MPT is verified through rigorous mathematical derivations, comparative simulations, and practical implementations using a digital signal processor (DSP). The results demonstrate that the MPT algorithm significantly improves the stability and accuracy of PLL systems under unbalanced conditions, providing an effective solution for handling phase unbalances in various power systems. Theoretical derivations and practical results, including crucial waveform comparisons, confirm the superior performance of the MPT algorithm and establish a robust framework for future research and applications.