Energy function for a grid-tied, droop-controlled inverter

A reduced-order model is used to derive a candidate energy function for a system that includes an infinite bus connected with a single frequency-droop-controlled inverter (a `MicroSource´) whose frequency command is actuated according to its low-pass-filtered active power measurement. The analysis of the large-signal stability of such a system is important in understanding the duration that a frequency-droop-controlled inverter can withstand a particular grid transient before islanding or tripping offline becomes mandatory. It is shown that a large-signal instability for this system can occur under abnormal grid conditions. Additionally, for poor selections of droop gain and low-pass cutoff frequency, these control parameters can potentially have a significant effect on the ability of the system to maintain synchronism after a fault on the main grid is cleared. The proposed energy function is shown through simulation to provide insight on the impact of the frequency droop gain and filter time constant on this instability during and after faulted conditions, particularly for high levels of droop gain and/or measurement filter time constant.