Mitigating Practical Limitations of LQR for Optimal Control of Grid-Tied Voltage Source Inverter via LQG(MEE) Integration

Although the linear-quadratic regulator (LQR) has been adopted as an optimal control strategy for some grid-connected inverter (GCI) studies, certain critical practical challenges are not addressed for real-world applications, such as noisy measurements, background harmonic voltage, grid impedance variations under weak grid operation, partial state availability, and higher power quality. To address this gap, this article proposes the integration of linear-quadratic-Gaussian minimum energy estimator control with LQR, combining optimal state estimation and feedback control to enhance the performance, which in turn results in lower total harmonic distortion (THD) in the grid current, guaranteeing improved power quality in a three-phase GCI with an inductor–capacitor–inductor filter in the dq frame. In addition, this approach effectively decouples control performance from sensor inaccuracies and grid-side disturbances, leading to improved harmonic attenuation, enhanced disturbance rejection, and reduced dependence on additional sensors, reducing hardware costs. To reduce the computational burden of tuning controller parameters, the sensitivity analysis has been illustrated. A simple integral action is presented to guarantee the optimal set point. Then, the augmented state-space model is built by applying the separation theorem to facilitate studying stability analysis. It was validated for the linearized model and the actual nonlinear system, based on eigenvalue trajectories and Lyapunov theorem, respectively. After that, simulation and experimental results validate the performance of the suggested control scheme. A comparative analysis between the proposed method and the sliding mode control has been investigated experimentally in this article. The experimental findings emphasize that the proposed solution not only overcomes the practical limitations of LQR but also mitigates THD in the current of the grid by 30%, even under varying operating conditions.