The smart grid vision is to build an intelligent power network with anunprecedented level of situational awareness and controllability over itsservices and infrastructure. This paper advocates statistical inference methodsto robustify power monitoring tasks against the outlier effects owing to faultyreadings and malicious attacks, as well as against missing data due to privacyconcerns and communication errors. In this context, a novel load cleansing andimputation scheme is developed leveraging the low intrinsic-dimensionality ofspatiotemporal load profiles and the sparse nature of "bad data.'' A robustestimator based on principal components pursuit (PCP) is adopted, which effectsa twofold sparsity-promoting regularization through an $\ell_1$-norm of theoutliers, and the nuclear norm of the nominal load profiles. Upon recasting thenon-separable nuclear norm into a form amenable to decentralized optimization,a distributed (D-) PCP algorithm is developed to carry out the imputation andcleansing tasks using networked devices comprising the so-termed advancedmetering infrastructure. If D-PCP converges and a qualification inequality issatisfied, the novel distributed estimator provably attains the performance ofits centralized PCP counterpart, which has access to all networkwide data.Computer simulations and tests with real load curve data corroborate theconvergence and effectiveness of the novel D-PCP algorithm.
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