## 4 Performance Assessment of Branch Power Change Estimation
### Experimental Verification
Statistical parameters of \(\overline{dP_{n}}\) are shown in Table 9 and include the difference between the average PCC obtained from measured PCC samples and the average of PCC estimates denoted as \(\Delta\Big{(}\overline{dP_{n}}\Big{)}=\overline{dP_{n}}-\overline{d\hat{P}_{ n}}\), the relative error of average PCC denoted as \(e\Big{(}\overline{dP_{n}}\Big{)}=\Delta\Big{(}\overline{dP_{n}}\Big{)}/ \overline{dP_{n}}\cdot\)100%, and the standard deviation of all \(\Delta(dP_{n})\) samples (see Figure 20) denoted as \(\sigma(\Delta(dP_{n}))\). The average values mentioned are always obtained from PCC samples measured of predicted using testing data set indicated in Table 9. Considering the power balance Equation (1), which can be averaged for multiple power events, parameters \(\Delta\Big{(}\overline{dP_{n}}\Big{)}\) and \(\sigma(\Delta(dP_{n}))\) indicate how precisely the equality could be reached and how precisely meter gain errors estimated or other anomalies detected. The relationship between the measured \(dP_{n}\) and the predicted \(d\hat{P}_{n}\) is shown in Figure 21, indicating the quality of the built prediction model (26). Figure 19: Measured PCC \(dP_{n}\) and prediction PCC \(d\hat{P}_{n}\) (E1 case). Figure 20: Prediction absolute error \(\Delta(d\hat{P}_{n})\) for dataset case E1. The influence of consumer MUT systematic error was examined by injecting \((\hat{e}_{V},\hat{e}_{P})=[(-2.5\%,\,-5\%),\,(-1.5\%,\,-3\%),\,(0\%,\,0 \%),\,(1.5\%,\,3\%),\,(2.5\%,\,5\%)]\) systematic errors to the testing data set samples and applying (24) to acquire estimates of these injected errors \((\hat{e}_{V},\hat{e}_{P})\) as shown in Figure 22. The absolute error of estimation for testing datasets E1, E2, E3 is virtually equal to zero. This ideal situation can be justified by: (1) a very simple distribution grid branch equivalent schematics, which in opposite to real electrical grids, matches the assumed equivalent model for method equations development (Figure 4), (2) the limited search resolution when solving (24) using exhaustive search (0.1% for both \(e_{V}\) and \(e_{P}\)), and (3) the size and distribution of training data represented the full dataset very well, which enabled to build a data-driven model capable of high precision prediction (this could also be the case in real-life conditions when a consumer owns limited set of loads and operates them daily causing very similar power steps both at the period of model training and testing). It has to be emphasized, that the estimation error of power and voltage gain errors that are achievable in the range of 0.1% is quite sufficient for practical needs, for example, to decide about out-of-tolerance status of MUT. Yet another reason of very small error of estimation of gain error is probably lower level of random noise component in the readings of real smart meter utilized in the testbed compared to the random noise injected to the synthesized datasets used to estimate the performance of the PCC estimation method. Despite the promising results of method performance using in-laboratory build test bed, the next step of testing in larger scale distribution network will be mandatory. For the setup upscaling a remote acquisition of electrical quantities readings has to be implemented maintaining a sufficient synchronization between sum meter and consumer MUT. The synchronization is expected to achieve using 1 s time stamps transmitted by smart meters over the external interface (P1 or Modbus). Data storage in the centralized database designed for experimental needs has to be created because utilities or external organizations  
Figure 21: Scatterplot of \(dP_{n}\) prediction (dataset case E1, no systematic errors).