Enhanced Operation of a Virtual Synchronous Machine Under Unbalanced Grid Voltage Condition Based on Lyapunov Energy Function

Three-phase grid connected inverters integrated with renewable energy sources like photovoltaic systems require to provide inertia to damp out oscillations in the frequency. However, during grid voltage sag or unbalance classical virtual synchronous machines (VSMs) cannot maintain oscillation free power supplied to the grid. Therefore, the maximum power point tracking of the photovoltaic system cannot be maintained, and optimal usage of the available photovoltaic power cannot be accomplished. To cater this problem, in this article a Lyapunov energy function-based augmented controller architecture has been proposed alongside a VSM during unbalanced grid voltage to effectively suppress these double frequency oscillations in the power. Identifying the dynamics of these oscillations followed by detailed stability analyses for the proposed architecture have been presented. In comparison to classical VSMs, the augmented system provides better transient response as well as double frequency power oscillation damping during grid voltage sag or unbalance. To verify the efficacy and understand the challenges of practical implementation of the proposed architecture, experimental verification on a reduced scale laboratory prototype is performed and various important case study results are obtained and presented in this article.