## 4 Performance Assessment of Branch Power Change Estimation
### Experimental Verification
From the loads assigned to \(P_{c1}\), by combining several devices, the power changes \(dP_{c}\) and the constant load \(P_{c1}\) are connected every 30 s. For example: the first groups of 5 points shown in Figure 16 correspond to \(dP_{c}\) generated by the following load combinations: group #1--a, group #2--a + b, group #3--a + b + c, group #4--c + d, group #5--a + b + c + d. When loads a and b are used as constant loads (\(P_{c1}\) in Figure 15) the last three groups of 5 points shown in Figure 16 correspond to \(dP_{c}\) generated by the following load combinations group #37--c, group #38--d, group #39--c + d.  
Figure 14: Picture of the test bed for method experimental verification. Figure 13: Test bed structural diagram. For the detection of power step and step size estimation the method presented in [37] was used. Every power event with the positive magnitude \(dP_{C}\) was repeated 5 times (Figure 16). The value of \(dP_{C}\) is measured by consumer MUT, the value of \(dP_{S}\) is measured by sum meter, and PCC in the branch is calculated as \(dP_{n}=dP_{S}-dP_{C}\) (Figure 16). The resistance \(R_{eq}\) is estimated according (18) and samples obtained are plotted in Figure 17. The mean resistance measured using the ohmmeter was 669.08 m\(\Omega\), and mean calculated resistance \(R_{eq}\) was 667.95 m\(\Omega\). Therefore, the mean absolute error \(e\big{(}\overline{R_{eq}}\big{)}\) was 0.17% and the standard deviation \(\sigma\big{(}e\big{(}R_{eq}\big{)}\big{)}\) of estimation error mean was 3.08%. All measured samples (195 samples) were split into training and testing data sets. The training data set is always kept the same, and the testing data set cases are shown in Table 8.  
In Figure 18, the partitioning of PCC samples for training and testing are displayed. The training dataset is used to train a model of PCC prediction as described in chapter 3, Equations (18) and (19). In Figure 19, the measured PCC \(dP_{n}\) and predicted PCC \(dP_{n}\) together with corresponding average values using training/testing dataset case E1 are shown and assuming absence of systematic errors because both meters were calibrated. Figure 16: Measured \(dP_{C}\) and calculated \(dP_{n}\). Figure 15: Power consumptions \(P_{C1}\), \(P_{L1}\) and \(P_{L2}\). Figure 17: The equivalent resistance \(R_{eq}\) estimates (**a**) and relative error (**b**). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Dataset Case** & **Training Data Set** & **Testing Data Set** \\ \hline E1 & \begin{tabular}{c} 98 samples/50\% (odd samples, sample numbers \\ 2n \(-\) 1, n integer number from 1 to N/2) \\ \end{tabular} & \begin{tabular}{c} 97 samples/50\% (even samples, sample numbers 2n, n integer number from 1 to N/2) \\ \end{tabular} \\ \hline E2 & \begin{tabular}{c} 98 samples/50\% (odd samples) \\ \end{tabular} & \begin{tabular}{c} 49 samples/25\% (sample numbers 4n, n integer number from 1 to N/4) \\ \end{tabular} \\ \hline E3 & \begin{tabular}{c} 98 samples/50\% (odd samples) \\ \end{tabular} & \begin{tabular}{c} 25 samples/12.5\% (sample numbers 8n, n integer number from 1 to N/8) \\ \end{tabular} \\ \hline E4 & \
\begin{tabular}{c} 98 samples/50\% (odd samples) \\ \end{tabular} &
\begin{tabular}{c} 13 samples/6.25\% (sample numbers16n, n integer number from 1 to N/16) \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 8: Cases of training and testing measured datasets (total number of samples and percentage of the full dataset). Figure 18: Measured \(dP_{n}\) samples split to 50% for training and 50% for testing datasets (E1 case). The difference between measured PCC \(dP_{n}\) and predicted PCC \(d\hat{P}_{n}\) is in the range from \(-3.5\) W to \(4.4\) W for the exercised testing data set E1 (Figure 20).