## 5 Discussion  
The conducted analysis substantiates that PCC in a distributed grid (DG) branch, attributable to consumer load power event, is significantly influenced not only by the magnitude of the consumer power demand change but also by the characteristics of the other network loads--such as their ZIP model parameters--along with their sizes and location distribution across the grid. The lack of measurement data due to incomplete deployment of smart meters hinders accurate PCC estimation based solely on available readings. As a result, developing a predictive model to estimate PCC in response to power events becomes the only viable alternative. The accuracy and robustness of such a model will depend strongly on the quality and quantity of data--including readings from sum and consumer meters--collected under controlled reference conditions and utilized for model training. A tradeoff is often sought between model complexity and the volume of training data to be collected and used during in-service grid and meter monitoring. This tradeoff is influenced by considerations such as anomaly or meter error detection speed (i.e., convergence rate) and the reliability of estimates (including meter error and PCC). In case of a boundary option, one may rely on extended observation period during reference conditions and employ averaging techniques to derive model parameters that reflect the aggregate behavior of user loads, grid losses, and consumer activity. However, such a model does not capture the underlying physical phenomena of an electrical grid and require a large number of data samples to ensure reliable estimates of meter errors or PCC in the monitored distribution branch. In the extreme opposite case, it is feasible to construct data-driven models of higher complexity, capable of predicting the attributes of interest using less input (testing) data. Machine learning algorithms represent the most likely methodological choice and will be explored further in our subsequent research publications. Nonetheless, integrating fundamental principles of electrical grid physics into these models  
Figure 22: Absolute error of \(e_{P}\) (**a**), \(e_{V}\) (**b**), \(e_{I}\) (**c**) estimation for different testing dataset. Results of datasets \(E1\), \(E2\) and \(E3\) are overlapped. may help overcome some of the inherent limitations of machine learning, which, being purely data-driven, necessitate extensive datasets encompassing diverse conditions and ranges of independent variables--a requirement that is not easily satisfied in real-world operational environments. Although exploring advanced modeling techniques, including machine learning, for predicting \(d\hat{P}_{n}\) is a promising direction, this task remains challenging due to the scarcity of voltage, current, and power data during consumer power event monitoring phases. Averaging \(d\hat{P}_{n}\) might initially seem inappropriate given the variability in network configurations across different events, it remains valuable because the power balance Equation (1) retains validity when applied to averaged quantities. By averaging \(d\hat{P}_{n}\) various grid and load setups are accounted for, thereby mitigating the impact of a single prediction error under some rear conditions, notwithstanding the loss of direct physical meaning. Future scholarly work should focus on techniques for recognition of conditions for acquiring test data (including load setup, types, and locations) as compared to those during the data training phase. Additionally, aligning the consumer power steps recorded during monitoring with those from the model's training phase could enhance the repeatability of \(R_{eq}\) and \(dP_{n}\) estimates. Since the mean value of \(R_{eq}\) is used in monitoring phase, it is indeed important to acquire sufficient number of its samples (like 195 in Figure 17).