Advanced Single-Phase PLL-Based Transfer Delay Operators: A Comprehensive Review and Optimal Loop Filter Design

In recent years, several research works have addressed and developed the phase-locked loop (PLL) in single-phase grid-connected converters with different structures and properties. Each has merits and demerits, such as a complex structure, high computational burden, and slow transient response. This paper aims to comprehensively review advanced single-phase PLLs based on transport delay operators to realize signal orthogonality. A deep insight into the PLLs' small-signal modeling, main characteristics, stability analysis, and loop filter design are provided in this paper. The main advantages and drawbacks are explained for each type of PLL in terms of different performance indexes, such as settling time, estimation error, and ripples in the estimated grid information. This paper also aims to provide optimal tuning and design of the loop filter gains from the large-signal model point of view, including all the nonlinearities, adopting the stochastic optimization method. All simulations are implemented using the MATLAB/Simulink 2018b environment to validate all theoretical analyses of this paper. The sampling and nominal frequencies are set to be 100 kHz and 50 Hz throughout all the simulation studies.