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. I. INTRODUCTION The electricity network is changing towards a locally controlled smart grid which incorporates an advanced sensing and management infrastructure. Energy sources such as solar or wind power are envisioned as integral elements of the network at the end-user level. As a result, the number of nonlinear loads is expected to increase, which results in larger perturbations in the electricity grid [1]. The complexity of the control strategies in the smart grid is expected to increase guided by the challenges posed by new and distributed energy sources. The implementation of advanced control strategies demands access to accurate and low latency data describing the state of the grid, which increases the performance requirements for the sensing infrastructure. The state estimation problem when data injection attacks are present is studied in [2], [3], [4], and [5]. Sensor failures, errors during data collection, unreliable transmission, and storage issues are just some of the causes of the operator having an incomplete set of observations of the state variables describing the grid. Given the size and complexity of the sensing infrastructure, tracking all these events is not feasible. It is therefore necessary to estimate the missing state variables using the available observations.