Closed-Form Expressions to Estimate the Mean and Variance of the Total Vector Error

The need for accurate measurements and for estimating the uncertainties associated with measures are two pillars for researchers and metrologists. This is particularly true in distribution networks due to a mass deployment of new intelligent electronic devices. Among such devices, phasor measurement units are key enablers for obtaining the full observability of the grid. The phasor measurement unit performance is mostly evaluated by means of the total vector error, which combines the error on amplitude, phase, and time. However, the total vector error is typically provided merely as a number, that could vary within an unknown interval. This may result into the phasor measurement unit incompliance with the final user expectancies. To this purpose, and with the aim of answering practical needs from the industrial world, this paper presents a closed-form expression that allows us to quantify, in a simple way, the confidence interval associated with the total vector error. The input required by the expression is the set of errors that typically affects the analog to digital converter of a phasor measurement unit. The obtained expression has been validated by means of the Monte Carlo method in a variety of realistic conditions. The results confirm the applicability and effectiveness of the proposed expression. It can be then easily implemented in all monitoring device algorithms, or directly by the manufacturer to characterize their devices, to solve the lack of knowledge that affects the total vector error computation.