In this document, the supervisory control and data acquisition (SCADA) and phasor measurement unit (PMU) measurement chain modeling will be studied, where the measurement error sources of each component in the SCADA and PMU measurement chains and the reasons leading to measurement errors exhibiting non-zero-mean, non-Gaussian, and time-varying statistical characteristic are summarized and analyzed. This document provides a few equations, figures, and discussions about the details of the SCADA and PMU measurement error chain modeling, which are intended to facilitate the understanding of how the measurement errors are designed for each component in the SCADA and PMU measurement chains. The measurement chain models described here are also used for synthesizing measurement errors with realistic characteristics in simulation cases to test the developed algorithms or methodologies.