Stability Analysis of a Grid-Forming Inverter by Complex Vector Theory

This paper proposes a stability analysis method for a grid-forming inverter with a droop control in the stationary domain. The control method is based on the complex vector theory which can utilize a simple SISO optimal controller design, and the stability analysis is based on the impedance method. First, a system operating point is determined and linearized around the point to calculate the output impedance of the inverter. Then output responses of the inverter are analyzed for a small-signal excitation in the frequency domain. The feedback control is processed only in the stationary domain. However, the complex conjugate operation in the droop control is found to transform variables equivalently into the synchronous domain. The frequency analysis method in the stationary/synchronous mixed domain is proposed and described.