Minimal Output Impedance Required for Stability of Grid-Supporting Inverters

In the field of power system dynamics, a main challenge is to properly tune the inverter control parameters, where one important parameter is the inverter's output impedance, physical or virtual. In this work, we provide a proof showing that a minimal output impedance must be used in order to keep the system stable. Although this result is well-known among practicing engineers, our proof reveals a fundamental property which causes instabililty, namely the pole excess of the inverter dynamic model. To prove this claim we model the system as a signal flow diagram, where the output impedances of the inverters are described using static gain feedback. Based on this model, we show that the typical dynamic model of grid supporting inverters has a pole excess larger than 2, which causes instability when high feedback gain is used. This result may be used to design a numerical method for estimating the minimal impedance. The theorem is validated based on an array of photovoltaic plants in the Ramat Negev region, which is part of the Israeli power grid.