Recovering missing data via matrix completion in electricity distribution systems

The performance of matrix completion based recovery of missing data in electricity distribution systems is analyzed. Under the assumption that the state variables follow a multi-variate Gaussian distribution the matrix completion recovery is compared to estimation and information theoretic limits. The assumption about the distribution of the state variables is validated by the data shared by Electricity North West Limited. That being the case, the achievable distortion using minimum mean square error (MMSE) estimation is assessed for both random sampling and optimal linear encoding acquisition schemes. Within this setting, the impact of imperfect second order source statistics is numerically evaluated. The fundamental limit of the recovery process is characterized using Rate-Distortion theory to obtain the optimal performance theoretically attainable. Interestingly, numerical results show that matrix completion based recovery outperforms MMSE estimator when the number of available observations is low and access to perfect source statistics is not available.