Distributed state estimation with lossy measurement compression in smart grid

State estimation in smart grid highly relies on the availability of measurements. Due to the interconnected nature of the power grid, the measurements at different substations are not totally independent and thus contain some redundancy. Among the various environments the power grid work in, there are certain circumstances the system communication capability is limited such that transmitting a lot of measurements within a small time interval is expensive and sometimes even impossible, and thus the measurements need to be compressed before transmitted to remove the redundancy. While it is possible to design lossless compression methods in some cases, in this paper, we focus on the problem of lossy compression of the measurements to adapt to more severe conditions. An algorithm is proposed to jointly design the pre-processors that compressing the measurements subject to the communication constraints and the subsequent estimator that using only the compressed measurements for state estimation. The effectiveness of the proposed algorithm is illustrated by numerical results.