State estimation in power distribution networks with poorly synchronized measurements

We consider the problem of designing a state estimation architecture for the power distribution grid, capable of filtering raw measurements from low-end phasor measurement units (PMUs) and presenting the state estimate to the control and monitoring applications that need it. Specifically, two algorithms to solve the estimation problem, which perfectly fit with the designed architecture, are proposed. Then, the contribution of this paper is threefold: i) the proposed approach is leaderless, scalable, and consists in the distributed solution of a least square problem which takes into explicit consideration the inexact time synchronization of inexpensive PMUs. ii) The first algorithm is a provably convergent scalable specialization of the alternating directions method of multipliers (ADMM). iii) The second algorithm is an extremely lightweight Jacobi-like algorithm which can be powerfully exploited in setup where the computational burden represent a major issue. Both algorithms can be implemented locally, even in a peer-to-peer fashion. The proposed approach is validated via simulations on the IEEE 123 test feeder, considering the IEEE standard C37.118-2005 for PMUs.