Simplified Three-Phase Phase-Locked Loop Simulation Model Implementation

Using MATLAB's built-in components as reference, we implement a simplified three-phase phase-locked loop (PLL) simulation model. The implementation retains only essential computational steps - notably the abc-dqz transformation that calculates solely the quadrature-axis voltage component (Vq) while eliminating non-critical modules like frequency feedback loops and automatic parameter adjustment blocks. Additionally, we develop a computational model for single-phase PLL systems with simplified architecture, preserving necessary components such as PI controllers. The validation phase examines both dynamic and static performance characteristics when input signal frequencies vary between 45-65Hz. Final simulations analyze locking accuracy under three-phase input conditions containing harmonic distortions, unbalanced amplitudes, and DC offset components, with implementation focusing on MATLAB's Simulink environment using Park transformations and PI-based frequency/phase correction algorithms.