Adaptive Virtual Inertia and Voltage Estimation: Enabled Model Predictive Control for Improved Performance in Islanded DC Microgrids

The low inertia of voltage estimation degrades system performance in islanded DC microgrids (DC MGs). To mitigate this issue, we propose an Adaptive Virtual Inertia and Voltage Estimation with Model Predictive Control (AVIE-MPC) approach, which enhances DC MGs performance while ensuring input-to-state stability (ISS). First, the voltage-source converter generates a stochastic state-space model of the DC MG. The virtual DC grid voltage is estimated using covariance adaptation in a standard Kalman filter algorithm. State estimation via feedback control stabilizes the voltage. The feedback gain is derived from the dynamic algebraic Riccati equation (DARE). Integral action eliminates estimation errors through DARE-based operations. Second, references to the expected cost function, which plays a crucial role in MPC performance, are determined by virtual DC grid voltage estimation and the integral of the virtual voltage estimation error. During each sample period, measurements of the virtual DC grid voltage and the current at each power converter output are fed into the expected cost function. The cost function ensures equal current sharing among converters. The DC MG state estimation is compared with the switching control input, and the optimal control signals are iteratively sent to converters. Finally, the proposed AVIE-MPC approach is validated through co-simulation in Simulink and real-time testing on an Opal-RT platform. The ISS property bounds the DC grid voltage estimation error via Lyapunov stability analysis.