Load curve data cleansing and imputation via sparsity and low rank

TL;DR

This paper introduces a robust, distributed load data cleansing and imputation method for smart grids using sparsity and low-rank techniques, enhancing data accuracy and privacy.

Contribution

It develops a novel decentralized principal components pursuit algorithm for load data cleansing and imputation, leveraging sparsity and low-rank structures.

Findings

The D-PCP algorithm effectively cleanses and imputes load data.

The distributed method matches the centralized PCP performance under certain conditions.

Simulations confirm convergence and robustness of the proposed approach.

Abstract

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.