  This work presents a distributed method for control centers to monitor the
operating condition of a power network, i.e., to estimate the network state,
and to ultimately determine the occurrence of threatening situations. State
estimation has been recognized to be a fundamental task for network control
centers to ensure correct and safe functionalities of power grids. We consider
(static) state estimation problems, in which the state vector consists of the
voltage magnitude and angle at all network buses. We consider the state to be
linearly related to network measurements, which include power flows, current
injections, and voltages phasors at some buses. We admit the presence of
several cooperating control centers, and we design two distributed methods for
them to compute the minimum variance estimate of the state given the network
measurements. The two distributed methods rely on different modes of
cooperation among control centers: in the first method an incremental mode of
cooperation is used, whereas, in the second method, a diffusive interaction is
implemented. Our procedures, which require each control center to know only the
measurements and structure of a subpart of the whole network, are
computationally efficient and scalable with respect to the network dimension,
provided that the number of control centers also increases with the network
cardinality. Additionally, a finite-memory approximation of our diffusive
algorithm is proposed, and its accuracy is characterized. Finally, our
estimation methods are exploited to develop a distributed algorithm to detect
corrupted data among the network measurements.
