A Regularized State Estimation Scheme for a Robust Monitoring of the Distribution Grid

In this paper, we propose a regularized state estimation (SE) scheme for the distribution grid. The ultimate goal is to track accurately the system state at a faster time scale according to the requirements of the new operational environment. The SE algorithm operates at two different time scales in which the set of available measurements are different. At the main time instants (every 15 minutes) the set of observations comprises SCADA measurements, pseudomeasurements and micro Phasor Measurement Units (PMUs). In this case, we resort to a Regularized version of the Normal Equations based SE (R-NESE). In the intermediate time instants, only a reduced number of PMU measurements is available. To circumvent observability issues, we exploit the fact that the voltage drop in adjacent buses is limited and, on that basis, a regularized weighted total variation estimation (WTVSE) problem is formulated. Then, the impact of in-line voltage regulators (IVLRs) is explicitly taken into consideration and that, forces us to decompose and solve the original SE problem for a number of smaller regions (D-WTVSE). The latter can be iteratively solved by resorting to the Alternating Direction Method of Multipliers (ADMM). Complementarily, we also present a PMU placement method (PP) in order to improve the conditioning of the R-NESE problem. This problem can be posed as a mixed integer semidefinite programming model (MISDP) and, thus, can be efficiently solved. The performance of the proposed scheme is numerically assessed on (mostly) a 95-bus distribution system for a number of realistic conditions of noise, load and photovoltaic generation profiles. A number of benchmarks are provided, as well