Comparative Analysis of Lattice-based All-Pass Filter and Second Order Generalized Integrator as Orthogonal System Generator of a PLL

Abstract

This paper presents a steady-state comparison of two methods that generate an orthogonal voltage system for a single-phase Phase-Locked Loop (PLL) structure: a widely accepted one based on a Second Order Generalized Integrator (SOGI) and a new one based on a All-Pass Filter (APF) with Lattice structure. Both methods are very attractive because of their simple digital implementation, low computational load and good performance under harmonically distorted grid conditions and variable frequency, so they are a good alternative to other known methods. The paper derives and analyzes the full state space models of the two methods.It is shown that these two methods are equivalent in the most common operation conditions of distributed energy resources, although the APF structure is clearly better than the SOGI one because it maintains its orthogonal generation ability for any higher notch frequencies and any lower sampling frequencies. The comparative analysis were validated by simulation with MATLAB/Simulink and experimental results using a fixed-point DSP.