Advanced control scheme and dynamic phasor modelling of grid‐tied droop‐controlled inverters

This paper develops an advanced scheme, modelling, and analysis of power flow control intended for grid-connected droop-controlled VSIs within a single-phase microgrid (MG). The proposed control scheme includes a power calculation method based on an enhanced second-order generalized integrator frequency-locked loop (ESOGI-FLL). Contrary to the existing power calculation methods that use low-pass filter (LPF) with a low cutoff frequency to reject the grid voltage distortion and achieve average power, which may result in reducing the power calculation speed, the involved ESOGI-FLL can offer a fast transient response and benefits from high filtering capability of sub- and low-order harmonics. In addition, the ESOGI-FLL provides total rejection of the DC offset, which is another issue that may adversely affect the accuracy of the traditional methods. Thus, this proposal can contribute to improving the speed and accuracy of the power computation and make the power calculation scheme immune to DC disturbance, thereby enhancing the performance of the power control. On the other hand, a dynamic phasor modelling approach is adopted considering the dynamics of the ESOGI-based power calculation, instead of the LPF transfer function used to describe the power computation dynamic in the related works. The small-signal model of the grid-connected VSI power flow considering the line impedance R/X ratio as well as that describing the dynamics of the ESOGI-based power calculation are derived. Using these models, the closed-loop model of the grid-interactive inverter including the power controller dynamics is obtained. The system stability is assessed, which helps to determine properly the controller's gains. A simulation study of a grid-connected VSI is carried out in MATLAB/Simulink™ and PSIM's processor in the loop (PIL) platforms to assess the effectiveness of the proposed control approach. The results confirm the effectiveness of the proposed control to regulate real and reactive powers with good transient performances when the grid is subject to several working conditions.