Widely available measurement equipment in electrical distribution grids, such as power-quality measurement devices, substation meters, or customer smart meters do not provide phasor measurements due to the lack of high resolution time synchronisation. Instead such measurement devices allow to obtain magnitudes of voltages and currents and the local phase angle between those. In addition, these measurements are subject to measurement errors of up to few percent of the measurand. In order to utilize such measurements for grid monitoring, this paper presents and assesses a stochastic grid calculation approach that allows to derive 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 meter models and case study results for a real Danish distribution grid are presented.

翻译：配电网络中广泛可用的测量设备，如电能质量监测装置、变电站仪表或用户智能电表，由于缺乏高分辨率时间同步而无法提供相量测量。这些测量设备仅能获取电压和电流的幅值以及二者之间的局部相位角。此外，此类测量值的误差可达被测量的百分之几。为将这些测量数据用于电网监测，本文提出并评估了一种随机电网计算方法，该方法能够推导出电流和电压相量的置信区域。文中引入了两种不同的计量模型：用于验证估计器理论特性的PMU模型，以及引入高斯近似的电能表模型。针对两种计量模型对估计结果进行了比较，并展示了实际丹麦配电网的案例研究结果。