A stochastic approach to estimate distribution grid state with confidence regions

Measurement equipment located in electrical distribution grids, as power-quality measurement devices, substation meters, or customer smart meters do not provide phasor measurements due to the lack of high resolution time synchronization. Instead such measurement devices only measure magnitudes of voltages and currents and the local phase angle between these. In addition, these measurements are subject to measurement errors of up to few percent of the measurand. In order to utilize measurements for grid monitoring, this paper presents and assesses a stochastic grid calculation approach that derives confidence regions for the resulting current and voltage phasors. Two different metering models are introduced: a PMU model, which is used to validate theoretical properties of the estimator, and an Electric Meter model for which a Gaussian approximation is introduced. The estimator results are compared for the two metering models and case study results for a real Danish distribution grid are presented. • Stochastic modeling and analysis of state estimates in power grids. • Analytic derivation of confidence regions of system state estimates. • Impact analysis of measurement errors on state estimates from different metering types. • Analysis of model accuracy.