Dissipativity-based Voltage Control in Distribution Grids

We consider the problem of decentralized control of reactive power provisioned by distributed energy resources for voltage support in the distribution grid. We assume that the reactance matrix of the grid is unknown and potentially time-varying. We present conditions for stability of the system when the reactive power at each inverter is set using a potentially heterogeneous droop curve. These conditions utilize energy dissipation requirements and can be naturally satisfied even when the reactance matrix is unknown by using an adaptive controller and when the reactance matrix is time-varying.