Stability analysis of droop controlled inverters via dynamic phasors and contraction theory

Droop techniques are widely used in distributed generation systems for the control of parallel inverters operating in grid-connected and islanded modes. Droop controllers without communication among the units are based on local measurements of active and reactive powers and usually allow the synchronization of the inverters to the common bus. On the other hand, instabilities can also occur. This paper investigates the stability of grid-connected droop controlled inverters by tackling the problem with a large signal perspective. A dynamic phasor model represented in a reference frame synchronous with the inverter voltage is proposed. The contraction theory applied to the model allows to determine an estimate of the domain of attraction of the stable equilibrium point. Simulation results demonstrate the effectiveness of the proposed analysis.