Adaptive Virtual Synchronous Machine Based on MPC Applied to a Four-Leg Three-Phase VSC for Unbalanced Current Compensation

The four-leg three-phase voltage source converter has been a solution to integrate renewable energy sources in the distribution grid considering single/three-phase loads. Its operation helps reduce voltage and current unbalances caused by circulating currents flowing through the neutral conductor. However, the high penetration levels of renewables significantly impact the grid’s stability due to the reduced inertia. The virtual synchronous machine (VSM) provides the system’s inertia by injecting/absorbing active/reactive power to/from the grid. However, its design and implementation are not straightforward since the VSM adaptive parameters selection is complex, especially in unbalanced systems. An incorrect selection of the inertia produces undesired frequency oscillations that may cause the tripping of protecting devices. This paper proposes an adaptive inertial control scheme using a model-based predictive controller (MPC-VSM) acting on a VSM to improve the stability of a four-wire power system. This approach determines an optimal trajectory for the inertia and damping factor –with a minimum cost of the VSM inputs– to minimize power oscillations and frequency drop in the power grid. To show the performance of the MPC-VSM, time-domain simulations will be carried out on an unbalance four-wire power system considering active power variations. Results show that the MPC-VSM controller provides a better dynamic response when compared to the classical VSM approach.