ℋ2 performance bounds for voltage regulation on a spatially-invariant DC power grid

Despite the importance of voltage regulation to operational reliability and safety of power grids, little is understood about how the topology of the physical layer, and the architecture of the communication and control layer impact the ability of the system to regulate the voltages. In this paper, we apply spatial-invariance analysis to develop analytical upper and lower bounds for the Hi gain of a DC power grid with respect to voltage regulation. These bounds establish a relation between network architecture and performance, and reveal fundamental limits to performance that cannot be overcome using feedback control.