Load curve data cleansing and imputation via sparsity and low rank

The smart grid vision is to build an intelligent power network with an unprecedented level of situational awareness and controllability over its services and infrastructure. This paper advocates statistical inference methods to robustify power monitoring tasks against the outlier effects owing to faulty readings and malicious attacks, as well as against missing data due to privacy concerns and communication errors. In this context, a novel load cleansing and imputation scheme is developed leveraging the low intrinsic-dimensionality of spatiotemporal load profiles and the sparse nature of "bad data.'' A robust estimator based on principal components pursuit (PCP) is adopted, which effects a twofold sparsity-promoting regularization through an $\ell_1$-norm of the outliers, and the nuclear norm of the nominal load profiles. Upon recasting the non-separable nuclear norm into a form amenable to decentralized optimization, a distributed (D-) PCP algorithm is developed to carry out the imputation and cleansing tasks using networked devices comprising the so-termed advanced metering infrastructure. If D-PCP converges and a qualification inequality is satisfied, the novel distributed estimator provably attains the performance of its centralized PCP counterpart, which has access to all networkwide data. Computer simulations and tests with real load curve data corroborate the convergence and effectiveness of the novel D-PCP algorithm.Comment: 8 figures, submitted to IEEE Transactions on Smart Grid - Special issue on "Optimization methods and algorithms applied to smart grid

Distributed Stochastic Market Clearing with High-Penetration Wind Power

Integrating renewable energy into the modern power grid requires risk-cognizant dispatch of resources to account for the stochastic availability of renewables. Toward this goal, day-ahead stochastic market clearing with high-penetration wind energy is pursued in this paper based on the DC optimal power flow (OPF). The objective is to minimize the social cost which consists of conventional generation costs, end-user disutility, as well as a risk measure of the system re-dispatching cost. Capitalizing on the conditional value-at-risk (CVaR), the novel model is able to mitigate the potentially high risk of the recourse actions to compensate wind forecast errors. The resulting convex optimization task is tackled via a distribution-free sample average based approximation to bypass the prohibitively complex high-dimensional integration. Furthermore, to cope with possibly large-scale dispatchable loads, a fast distributed solver is developed with guaranteed convergence using the alternating direction method of multipliers (ADMM). Numerical results tested on a modified benchmark system are reported to corroborate the merits of the novel framework and proposed approaches.Comment: To appear in IEEE Transactions on Power Systems; 12 pages and 9 figure