Bayesian linear state estimation using smart meters and PMUs measurements in distribution grids

In this work we address the problem of static state estimation (SE) in distribution grids by leveraging historical meter data (pseudo-measurements) with real-time measurements from synchrophasors (PMU data). We present a Bayesian linear estimator based on a linear approximation of the power flow equations for distribution networks, which is computationally more efficient than standard nonlinear weighted least squares (WLS) estimators. We show via numerical simulations that the proposed strategy performs similarly to the standard WLS estimator on a small distribution network. A key advantage of the proposed approach is that it provides explicit off-line computation of the estimation error confidence intervals, which we use to explore the tradeoffs between number of PMUs, PMU placement and measurement uncertainty. Since the estimation error in distribution systems tends to be dominated by uncertainty in loads and scarcity of instrumented nodes, the linearized method along with the use of high-precision PMUs may be a suitable way to facilitate on-line state estimation where it was previously impractical.