Synchronising DER inverters to weak grid using Kalman filter and LQR current controller

Grid-following (GFL) inverters are commonly used for integrating renewable energy sources into power grids. However, the dynamic performance of GFL models can be significantly impacted by the Phase-Locked Loop (PLL) in a weak grid, leading to instability due to inaccuracies in grid source phase angle estimation. The proposed method in this manuscript replaces the PLL with an Advanced Angle Estimation based Kalman Filter including a Linear Quadratic Regulator (LQR) controller of the GFL. This method is robust in incorporating grid impedance terms as part of state space models in the Kalman Filter approach to estimate instantaneous phase angle using {\alpha}-\b{eta} Synchronous Reference Frame equations. The stability performance of the proposed approach is validated through eigenvalue analysis in a two-source case. Additionally, an LQR controller is employed to regulate capacitor voltage, inverter current, and the current at the Point of Common Coupling (PCC). The proposed controller surpasses existing approaches in terms of accuracy and distortion reduction under abrupt grid impedance increases. Moreover, drop compensation is integrated into the Kalman Filter to enhance robustness of the inverter against external oscillation disturbances from a synchronous machine connected to the GFL via the PCC. The results in this paper demonstrate substantial improvement in oscillation damping across a range of frequencies compared with published research works.