  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.
