A Linear Optimization-Based Framework for Unbalanced Three-Phase State Estimation in LV Grids

This paper proposes a state estimation method for three-phase unbalanced low-voltage (LV) distribution grids. The method is developed within a project context and is therefore designed to address several practical limitations, including: (i) lack of access to real-time energy consumption data, (ii) availability of only hourly aggregated historical data instead of per-second per-phase measurements, (iii) limited access to per-second real-time voltage measurements at a small number of nodes, and (iv) the need for low computational complexity and short runtime. To address these constraints, the state estimation process is structured into three main steps: first, real-time active and reactive power injections at the nodes are estimated using historical data; second, the estimated power values are disaggregated among the three phases and finally, state estimation is performed using a combination of real-time measurements and estimated data. The proposed state estimator employs a linear optimization approach that adjusts the estimated values to minimize the mismatch between power flow outputs and available real-time measurements. The method is applied to a real LV distribution grid in Denmark. Validation using dedicated evaluation meters shows a mean absolute error of 1.01 V and a standard deviation of 1.27 V, and a maximum error of 4.11 V.