###### Abstract  
The smart electricity meter (SEM) is an important part of smart power grid, and the accuracy of SEMs is the basis for power grid operation control and trade settlement between power supply and electricity consumption, but the evolution behaviors of metering error of SEMs under field operation conditions have not yet been identified. The SEMs were installed and operated on site, metering error data were collected under various temperature and current conditions. The influences of current, power coefficient, and temperature on metering error and consistency were analyzed separately with the help of quadratic polynomials, and then an integrated model elaborating the joint effects of multi-stress was developed based on a binary quadratic polynomial. We find that a lower temperature and a larger current result in a higher metering error of SEMs; however, the effects of current on metering error are determined by power coefficients. The results have reference value for remote metrological verification, error monitoring, and the optimization of the operation and maintenance scheme of SEMs. s 2021 11 11457 110.11.11457.11.11457.11.11457.11.11457.111.11457.111457.111.11457.111457.111457.  
effects of temperature on metering error of SEMs [12]. [PERSON] et al. studied the influences of environmental factors and current stress on the basic error of single-phase electricity meters, but only provided a polynomial model to fit the effects of temperature and did not model the effects of current [13]. In terms of the effects of multi-stress on metering error, previous studies analyzed the influences of temperature, humidity, pressure, and wind speed on measurement precision, identified that temperature was the most important factor to affect metering error, and did not provide a model to describe the integrated influences of the multi-stress on metering accuracy [14]. Although [PERSON] et al. presented an online evaluation method to compute the metering error of operating SEMs using the power acquisition data, they did not pay attention to environmental and electrical conditions [15]. Therefore, our study will identify the joint effects of temperature and current on metering error, and will develop a binary-nonlinear-regression-based method to analyze the evolution behaviors of metering precision. Metering error consistency represents the accuracy of a batch of SEMs and can be estimated by the standard deviation. Existing research has analyzed the function, principle, and structure composition of SEMs to find out the causes of metering error and has proposed potential methods and theories to control the metering error consistency of SEMs [16]. [PERSON] analyzed and optimized the effects of temperature on the metering accuracy consistency of SEMs using computer simulation methods [17]. [PERSON] et al. identified the key components that may affect metering accuracy first, and then estimated the metering error consistency of SEMs using the component parameters [18]. A huge number of SEMs are installed every year; for instance, 4 million SEMs are replaced every year [19]. There is a lack of research on the evolution behaviors of metering error consistency for a batch of SEMs--our study is trying to answer this question. Metrological characterization decreases over time due to the influences of the thermal, electromagnetic, and aging phenomena of internal electronic components [4; 20; 21]. Metrological supervision of electricity energy meters seeking to ensure the trustworthiness of measurement data is an important challenge due to (i) the complexity of the electrical energy measurement task, both the impossibility to carry out direct measurements and the difficulty of granting a proper metrological traceability of measurement instruments; and (ii) the high costs of electrical energy meter calibration due to both the reference instruments to be used and the need for expert human operators [22; 23].