Differentially Private State Estimation in Distribution Networks with Smart Meters

State estimation is routinely being performed in high-voltage power transmission grids in order to assist in operation and to detect faulty equipment. In low- and medium-voltage power distribution grids, on the other hand, few real-time measurements are traditionally available, and operation is often conducted based on predicted and historical data. Today, in many parts of the world, smart meters have been deployed at many customers, and their measurements could in principle be shared with the operators in real time to enable improved state estimation. However, customers may feel reluctance in doing so due to privacy concerns. We therefore propose state estimation schemes for a distribution grid model, which ensure differential privacy to the customers. In particular, the state estimation schemes optimize different performance criteria, and a trade-off between a lower bound on the estimation performance versus the customers' differential privacy is derived. The proposed framework is general enough to be applicable also to other distribution networks, such as water and gas networks.