# Smart Internet of Things Power Meter for Industrial and Domestic Applications
## 4 Results
### Discussion on Uncertainty Measurement Errors  
In contemporary digital Data Acquisition Systems (DASs), the conversion of analog signals (such as voltage and current in this context) to digital values is achieved using specialized circuits known as analog-to-digital converters (ADCs). When the input range required in a DAS exceeds the input range of the ADC, an ideally linear voltage divider (a voltage reduction circuit with a predictable attenuation ratio) is necessary. Conversely, when the input voltage is significantly lower than the ADC's input range, the voltage must be amplified using either an external operational amplifier or an integrated Programmable Gain Amplifier (PGA). It is important to consider the errors that these components can introduce, both at static and dynamic levels (in both DC and AC conditions):  
* Resistors in the voltage divider: These components can introduce initial errors, temperature drift, and value drift due to aging; \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **Phoenix EEM-MA400 [VAr]** & **Janitza UMG-96 RM [VAr]** & **Siemens PAC4200 [VAr]** & **Power Meter [VAr]** \\ \hline
1 & 30 & 33.308 & 32.236 & 32.480 \\
2 & 30 & 33.433 & 32.338 & 32.526 \\
3 & 30 & 33.900 & 32.680 & 32.932 \\
4 & 30 & 33.950 & 32.792 & 33.113 \\
5 & 87 & 88.890 & 91.590 & 88.740 \\
6 & 78 & 87.702 & 90.455 & 86.994 \\
7 & 76 & 88.294 & 91.017 & 87.719 \\
8 & 82 & 88.643 & 91.314 & 87.692 \\
9 & 82 & 89.831 & 92.350 & 88.681 \\
10 & 80 & 90.879 & 93.385 & 89.763 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Reactive power samples comparison. * Operational amplifiers and PGAs: These may exhibit gain errors, offset errors, temperature drift in both gain and offset, and distortions due to the non-linearity of semiconductor components, which are influenced by the proprietary architecture and manufacturing processes. These factors typically result in gain errors, offset errors, and distortion errors;
* Errors in internal input amplifiers and buffers (gain, offset, and distortion),
- Quantization error (an intrinsic error that cannot be eliminated),
- Non-linearity errors, such as Integral Non-Linearity (INL) and Differential Non-Linearity (DNL). * Semiconductor-based components: These components often exhibit leakage currents, input capacitance variability with voltage, and errors due to power supply noise. Combined with input resistors, these factors contribute to initial errors, temperature drifts, and dynamic errors. Detailed examples of static errors, along with numerical, graphical, and other explanations, can be found in specialized studies, application notes, and articles, such as [38; 39; 40]. While static errors can generally be mitigated through calibration, dynamic uncertainty errors in AC power measurement systems and smart meters present more complex challenges, making their elimination during calibration less straightforward. From a research perspective, the authors in [41] provide a comprehensive literature review, covering relevant metrology, electrical engineering, and other related fields. They assess the impact of measurement inaccuracies and propose various technical solutions to mitigate these issues, concluding with recommendations for further research. As highlighted in [42], standards such as IEC62053-11:2003 [43], IEC62053-21:2003 [44], and EN50470-3:2006 [45] define accuracy classes for distortion factors below 3% or 2%. However, in another study [46], the calibration challenges posed by electronic energy meters in modern grids--where waveforms deviate from the near-perfect sinusoidal shapes assumed during the establishment of these standards--are addressed. With the increasing presence of switch-mode power supplies and inverters in the grid, voltage and current waveforms are becoming more distorted, leading to higher measurement errors. Further, research [47] demonstrates that measurement errors in commercial-grade energy meters can increase by up to 7% when the total harmonic distortion (THD) exceeds 3%.