Statistical Modeling of the Relationship Between Installed Capacity and Exported Power: A Case Study From the Banat Region

This paper extends previous research on the statistical analysis of prosumers connected to the low-voltage distribution network in the Banat region of Romania by evaluating the performance of regression models used to analyze the relationship between installed capacity and exported power. The analysis was conducted using a real-world dataset comprising 21,426 prosumers and included linear, polynomial, and logarithmic regression models. The results indicate that the second-order polynomial regression provides the best balance between estimation accuracy and model complexity, whereas the third-order polynomial regression yields only a marginal improvement in the coefficient of determination. A subsequent segmentation of prosumers according to installed capacity showed that, for installations exceeding 50 kW, the second-order polynomial model achieves superior performance. Finally, two complementary analyses were performed: a residual analysis, which confirmed that the global model adequately describes most observations but exhibits limitations for large-capacity installations, and a one-way analysis of variance (Welch's ANOVA) applied to groups defined by the quartiles of installed capacity. The ANOVA results revealed statistically significant differences among the analyzed groups, which were subsequently confirmed by the Games-Howell post-hoc test. The findings contribute to the development of more accurate statistical models for estimating exported power and may support distribution system operators in the integration, monitoring, and planning of prosumers within smart electricity networks.