Extended Two-Terminal Network Model of Parallel VSMs for Analysis of Active Power–Frequency Response

The disturbance types have a significant impact on the power–frequency response of multiple virtual synchronous machines (multiple VSMs). Therefore, we established an effective model to analyze the dynamic characteristics of multiple VSMs under any disturbance. Considering that the active and reactive power loops are decoupled, the model developed for the active power and frequency control loop of VSMs is equivalent to a two-terminal network that includes the first (parallel) and second (series) "admittance." The active power and angular frequency increments were analogized as the current and voltage of the circuit network. An extended two-terminal network model of the multiple-VSM parallel system was established to comprehensively and accurately depict the response of the output active power and angular frequency under disturbances of the load and active power reference. The key active power– frequency response characteristics of the multiple-VSM parallel system were deduced. The effectiveness of the proposed extended model was verified through simulations and experiments. The results indicated the suitability of the proposed model for active power–frequency response analyses of multiple-VSM parallel systems. Furthermore, the experimental results obtained under different modes agree with the theoretical analysis results, thereby validating the key conclusions.