## 4 Performance Assessment of Branch Power Change Estimation
### Network Power Consumption Change After the Consumer Power Event  
The prediction of change in power losses of DG branch denoted as \(d\hat{P}_{w}\) is estimated using (26) (see Figure 6), whereas the actual \(dP_{w}\) can be obtained from testing data readings according to definition (see quantities notation in Figure 1)  
\[dP_{w}=\sum_{i=1}^{N}dP_{wi}+\ dP_{Rs}=\sum_{i=1}^{N}dl_{wi}^{2}R_{wi}+\ dI_{s}^{2}R_{s}. \tag{28}\]  
The prediction of change in grid loads power consumption \(d\hat{P}_{nL}\) is estimated using (22) (see Figure 7), whereas the actual \(dP_{nL}\) can be obtained from testing data readings according to definition (see quantities notation in Figure 1)  
\[dP_{nL}=\sum_{i=1}^{N}\Big{(}P_{L(2)i}-P_{L(1)i}\Big{)}=\sum_{i=1}^{N}dP_{Li} \tag{29}\]  
where \(P_{L(1)i}\) and \(P_{L(2)i}\) are power consumption of the \(i\)th consumer before and after the power event respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Grid Case** & \(\mathbf{R_{usum}}\)**, **m\(\mathbf{\Omega}\)** & \(e(\overline{R_{eq}})\)**, \%** & \(\sigma(e(\overline{R_{eq}}))\)**, \%** \\ \hline
1 & 210 & 0.64 & 0.56 \\
2 & 165 & 1.66 & 0.76 \\
3 & 165 & 1.37 & 0.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Equivalent resistance estimation. Meter class and random power error case M1 from Table 4 and training data T1 from Table 5.  
Figure 5: \(R_{eq}\) (a) and relative error of its estimate (b) vs. grid loads configuration case (see Table 3 and Figure 2). Grid case no. 1 from Table 2.  
The overall predicted PCC in the DG branch \(d\hat{P}_{n}\) is estimated using (26), whereas it's the actual \(dP_{nL}\) is calculated from testing data set  
\[dP_{n}=dP_{w}+dP_{nL} \tag{30}\]  
The absolute error of prediction of \(d\hat{P}_{n}\) is  
\[\Delta\big{(}d\hat{P}_{n}\big{)}=dP_{n}-d\hat{P}_{n} \tag{31}\]  
The predicted PCC \(d\hat{P}_{n}\) and its prediction error \(\Delta\big{(}d\hat{P}_{n}\big{)}\) are shown in Figure 8.  
The average \(\overline{dP_{n}}\) calculated from all estimated samples of \(d\hat{P}_{n}\) which are obtained using testing dataset are shown in Table 7 along with relative error average,  
\[\mathrm{e}\Big{(}\overline{dP_{n}}\Big{)}=\overline{\frac{d\hat{P}_{n}- \overline{dP_{n}}}{dP_{n}}}\cdot 100\%, \tag{32}\]  
the standard deviation \(\sigma\big{(}\Delta\big{(}d\hat{P}_{n}\big{)}\big{)}\) of absolute error \(\Delta\big{(}\hat{P}_{n}\big{)}\) values, and the relative errors of \(\overline{dP_{n}}\)  
\[\mathrm{e}\big{(}\sigma\big{(}\Delta\big{(}d\hat{P}_{n}\big{)}\big{)}\big{)}= \frac{\sigma\big{(}\Delta\big{(}d\hat{P}_{n}\big{)}\big{)}}{\overline{dP_{n}} }\cdot 100\%, \tag{33}\]  
where \(\overline{dP_{n}}\) denotes average of actual \(dP_{n}\) values in the testing dataset. Figure 6: Predicted DG branch power loss change \(d\hat{P}_{n}\). Grid case no. 1 from Table 5.0 Meter class and random power error case M1 from Table 4 and training/testing data set case T1 (Table 5). Table 5.1 Predicted network loads change \(d\hat{P}_{nL}\). Grid case no. 1 from Table 5.2 Meter class and random power error case M1 from Table 4 and testing data (50% (even) of data). The results in Table 7 were obtained in the case where systematic errors were absent in the readings of the consumer MUT. It can be seen that the ratio between training data set size and testing data set size does not significantly influence the standard deviation of prediction error of \(\overline{dP_{n}}\). Also, no strong correlation was observed between random error influenced by meter accuracy class of power measurement and error of prediction of \(\overline{dP_{n}}\). By analyzing relative error of \(\overline{dP_{n}}\) and its standard deviation in Table 7, it cannot be confirmed that higher accuracy class of consumer meter (compare M2 and M3 cases) yields higher accuracy of PCC prediction. Moreover, we have observed that less random noise level due to better meter accuracy class may cause higher PCC estimation error (compare case T2/M2 to T2/M3).