Direct current (DC) microgrid consists of many parallel power converters that share load currents through the inductance of DC/DC converters. Usually, the inductance parameters are dependent on the physical implementation of the system, and their values may not match their nameplates. Such disparities could lead to unequal response characteristics of the system, which can potentially reduce the performances of the DC microgrid operation. This paper proposes a robust control strategy for inductive parametric uncertainties of DC/DC converters using an optimal control method with integral action. To achieve such a goal, the system model parameters with nominal values are transformed into parametric unmatched uncertainties to form a robust control problem, which is then transformed into a linear quadratic regulator problem. The inductance uncertainties are stabilized with the uncertainty dynamic algebraic Riccati equation (UDARE) using state feedback gain under linear quadratic regulator. The closed-loop control with integral action is adopted to achieve a steady-state error of zero on the DC-link voltage at any uncertainty of the inductive parameter, which subsequently ensures the equal load current sharing. Off-line simulations and real-time validations based on OpalRT have been conducted to demonstrate the effectiveness and robustness of the proposed robust control strategy.

Using a linear Kalman filtering approach (LKFA), the finite-control-set model predictive control (FCS- MPC) proposes for DC-grid voltage estimation control in direct current microgrid systems (DCMS). The proposed control algorithm technique addresses real-time measurements needed to implement the FCS-MPC by adopting the LKFA for real-time application. The state-space model is used to produce the second DCMS predictive model, which provides access to a sample time for the performance of an efficient algorithm. The dynamic model of DCMS is transformed into a stationary linear stochastic discrete time-invariant system to standardize the state estimation design. The DC-grid voltage estimation reference is computed leveraging LKFA and a state feedback control law based on the dynamic algebraic Riccati equation with integral action. The proposed algorithm has been verified under varying load demands. Fast computations, DC-grid voltage estimation, and equally estimated power-sharing between DERs have all been realized.

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.

Using a linear Kalman filter approach(LKFA), this study proposes sensor-less finite-control-set model predictive control for stabilizing DC-grid voltage estimation in direct current microgrids (DCMs). In controlling many parallel power converters in DCMs, the proposed control method eliminates the need for an inductance current sensor. The second prediction is derived from the state-space model so that an efficient algorithm may be performed. The dynamic model of DCMs in the second prediction is converted into a stationary linear stochastic discrete time-invariant system to standardize the state estimation design. The DC-grid voltage reference is then computed adopting LKFA using a state feedback control law based on the dynamic algebraic Riccati equation with integral action to guarantee zero steady-state error during transient responses. Under load demand variation, the efficacy of the proposed approach is shown using a sensor-less control algorithm. Robustness against parametric uncertainty, DC-grid voltage estimation, and equally estimated power-sharing amongst DERs have all been achieved, as have the fast convergence.