## 2 Materials and Methods
### Meter Error and Resolution Modelling  
Readings of electrical quantities acquired by consumer and sum meter exhibit measurement errors, including those caused by limited resolution compared to error-free synthesized data. We assume the following model of current and voltage readings  
\[I=I_{0}\cdot\left(1+\frac{E_{I}}{100\%}\right) \tag{6}\]  
\[V=V_{0}\cdot\left(1+\frac{E_{V}}{100\%}\right), \tag{7}\]  
where \(I_{0}\) and \(V_{0}\) are error-free values of the current and voltage obtained during synthesis, \(E_{I}\) and \(E_{V}\) are the relative percentage gain errors of current and voltage, respectively. The gain error can be divided into systematic components (\(e_{I}\), \(e_{V}\)) and random components (\(r_{I}\), \(r_{V}\)), such that:  
\[E_{I}=r_{I}+e_{I};\ E_{V}=r_{V}+e_{V}. \tag{8}\]  
Figure 2: Consumer load power, DG branch power consumption, ZIP model coefficient of loads, change of DG branch power consumption after consumer power event, and power losses coefficient in the synthesized data obtained from grid configuration case no. 2 (Table 2). The systematic relative gain error is more related to the aging of the meter and the influence of environmental conditions. The random component of the gain error represents higher frequency thermal noise caused due to the electrical components in the measurement channel of the current and voltage. In a similar way, the active power readings can be modelled by  
\[P=I\cdot V\cdot\cos\varphi=I_{0}\cdot\left(1+\frac{E_{I}}{100\%}\right)\cdot V_ {0}\cdot\left(1+\frac{E_{V}}{100\%}\right)\cdot\cos\varphi. \tag{9}\]  
We do not consider phase angle measurement errors in this research. It can be derived from (6)-(8) that:  
\[P=I_{0}\cdot V_{0}\cdot(1+e_{P}+r_{P})\cdot\cos\varphi \tag{10}\]  
where systematic gain error and random gain error of active power measurement are correspondingly denoted  
\[e_{P}\approx\frac{e_{I}}{100\%}+\frac{e_{V}}{100\%}, \tag{11}\]  
\[r_{P}\approx\frac{r_{I}}{100\%}+\frac{r_{V}}{100\%}, \tag{12}\]  
when lower order terms such as \(e_{V}\cdot e_{I}/(100\%\cdot 100\%)\), \(e_{V}\cdot r_{V}/(100\%\cdot 100\%)\), \(r_{V}\cdot e_{I}/(100\%\cdot 100\%)\), and \(r_{V}\cdot r_{I}/(100\%\cdot 100\%)\) are neglected. Later, relative errors expressed in parts rather than percent will be used  
\[\gamma_{I}=\frac{e_{I}}{100\%}, \tag{13}\]  
\[\gamma_{V}=\frac{e_{V}}{100\%}, \tag{14}\]  
\[V=V_{0}\cdot\left(1+\frac{E_{V}}{100\%}\right), \tag{7}\]0  
\[V=V_{0}\cdot\left(1+\frac{E_{V}}{100\%}\right), \tag{7}\]1  
The accuracy class of an energy meter (0.2, 0.5, 1, and 2 according to the standards IEC 62053-21 and IEC 62053-22) defines the allowed range of power measurement errors. Class 1 m are subject to a maximum error of \(\pm 1\%\) of the measured active power value. The presented research focusses on identifying changes in gain error, while the random component of gain error is presumed to be constant. For example, if current and voltage systematic gain errors are equal to 0.5% and random gain errors equal to 0.5% (rectangular distribution), then the power systematic gain error will be 1% and the power gain error will not exceed the range between 0 and 2%. In a real-life application, the average of \(K\) measurement samples will be used to estimate the power, current, and voltage of the sum and consumer MUT before and after the power event (Figure 3). Therefore, the variance of random component will be reduced \(\sqrt{K}\) times due to the averaging operation. In the research that follows, \(K\) is set to 10. While active power calculations in meter metrology modules are performed with high resolution, quantity readings are presented on the meter display or transmitted through communication channels with a restricted resolution.