Small-signal modelling and analysis of microgrids with synchronous and virtual synchronous generators

In autonomous alternating current microgrids, the grid-forming virtual synchronous generators can cooperate with the conventional synchronous generators to improve system inertia and frequency regulation capability. However, undesired active power oscillations between the synchronous generators and grid-forming virtual synchronous generators may trigger their overcurrent protection and even result in a blackout. To explicitly reveal the oscillatory modes over all frequency bands, a high-fidelity full-order state-space model is first developed. A potentially destabilising sub-synchronous oscillation mode resulting from the interaction between grid-forming virtual synchronous generators voltage controller and synchronous generators q-axis damper winding is identified. Other modes reflecting the low-frequency oscillation and frequency restoration dynamics are also assessed. Subsequently, to make a reasonable trade-off between the accuracy and simplicity of system modelling, an enhanced quasi-stationary model dedicated to low-frequency oscillation evaluation is simplified from the full-order type. The enhanced quasi-stationary model features simplicity and low-order benefits, which makes it more practical for multi-generator system analysis. Moreover, by considering the dynamics of synchronous generators field winding and excitation system, the enhanced quasi-stationary model significantly improves the low-frequency oscillation characterisation accuracy compared with the existing quasi-stationary model. The two developed models are comprehensively compared with the existing small-signal models. Real-time simulations based on RT-LAB are conducted to verify the correctness of the theoretical analysis and the accuracy of the proposed small-signal models.