The accuracy of the smart electricity meters was affected by operation conditions, this study focused on the measurement error and consistency of smart electricity meters. The mean and standard deviation of power error were calculated based on the normal distribution, and three times of standard deviation was employed to elaborate the consistency of measurement errors. The evolution model of the measurement error of electricity meters with calendar time was constructed based on a sinusoidal function, and then Eyring model was employed to describe the effects of temperature and current stresses on the evolution behavior of the power error mean value for electricity meters. In terms of the effects of temperature, the mean value of metering power error declines with the increase of temperature and the decrease of the current. The results have reference value for power metering error compensation, optimization of operation and maintenance scheme, and design optimization to improve the consistency and reliability of electricity meters.