Analytical modelling of three-phase four-wire grid-connected inverter under unbalanced conditions applying digital controllers

This paper presents an analytical model for a two-level three-phase four-wire grid-connected voltage source converter (TGC-VSC) controlled by digital pulse-width modulation (DPWM). This model relies on a phase-locked loop (PLL)-less approach to investigate the performance of the dead-beat (DB) and proportional-integral-resonant (PIR) controller in the presence of unbalanced conditions on the alternating current (AC) low-voltage side of the distribution system. A single-phase digital triple-loop control system has been employed for each phase of the TGC-VSC, which operates as a grid-forming inverter (voltage source) or grid-following inverter (current source) coupled to an AC power grid with three phases and neutral. The main aim of this work is to evaluate the previous single-phase approach of the three-loop control system applied in this work to a three-phase four-wire system, with the main difference being the connection to the grid without an PLL and the application of an PIR controller in the third control loop instead of an proportional-integral (PI). Alternatively, the latter can inject active power into the grid to help flatten the demand-side power curve of the industry, reducing operating costs. Therefore, the aim is to test the aforementioned digital controllers in a grid-connected inverter. The controllers are validated using MATLAB/Simulink simulations, yielding the steady-state voltage and current errors [Formula: see text] and [Formula: see text] in grid-forming, and [Formula: see text], [Formula: see text] and [Formula: see text] in grid-following inverter configurations.