Adaptive Virtual Synchronous Machine Applied to Four-Leg Three-Phase VSC

Nowadays, the power distribution grid is dominated by single-phase loads that produce unbalance currents, which cause stability problems and large frequency deviations in power systems. The Virtual Synchronous Machine (VSM) method has been proposed for renewable energy sources to reproduce the static and dynamic properties of the traditional synchronous generator, injecting/absorbing active/reactive power to/from the grid. However, the implementation and design of a VSM are not straightforward tasks, especially in an unbalanced network. Because it is necessary to compute and adjust the required inertia and damping parameters during unbalanced currents. Therefore, this paper proposes an adaptive inertia control scheme for a Four-Leg Three-Phase Voltage Source Converter (4LVSC), using the VSM approach, to improve a four-wire power system stability and compensate unbalanced currents. The proposed adaptive inertia comprises a Proportional-Integral (PI), and a Linear Quadratic Regulator (LQR) controller, which uses an optimization problem to minimize the power change and frequency droop when unbalances are presented in a power system. Time-domain simulations have been carried out on a unbalance four-wire power system considering active power variations to evaluate both the power and frequency responses using both controllers. Results show that the LQR-VSM controller presents lower frequency oscillations when compared to the VSM with constant inertia approach.