Stability bounds of droop-controlled inverters in power grid networks

The energy mix of future power systems will include high shares of wind power and solar PV. These generation facilities are generally connected via power-electronic inverters. While conventional generation responds dynamically to the state of the electric power system, inverters are power electronic hardware and need to be programmed to react to the state of the system. Choosing an appropriate control scheme and the corresponding parameters is necessary to guarantee that the system operates safely. A prominent control scheme for inverters is droop control, which mimics the response of conventional generation. In this work, we investigate the stability of coupled systems of droop-controlled inverters in arbitrary network topologies. Employing linear stability analysis, we derive effective local stability criteria that consider both the overall network topology as well as its interplay with the inverters' intrinsic parameters. First, we explore the stability of an inverter coupled to an infinite grid in an analytic fashion and uncover stability and instability regions. Secondly, we extend the analysis to a generic topology of inverters and provide mathematical criteria for stability and instability of the system. Last, we showcase the usefulness of the criteria by examining two model systems using numerical simulations. The developed criteria show which parameters might lead to an unstable operating state.