## 5 Conclusions  
For the upcoming SG utilities adopting the dynamic (d-ToU or f-ToU) pricing program, we have proposed a modified gradient boosting-based theft detector (DETD) that has a good detection capability for highly probable window-based theft cases. In the presented ML procedure, we have broken down the daily samples with two theft windows (\"theft window\" and \"non-theft window\"), generated such synthetic theft cases in advance, and trained and tested the DETD based on the usage data of the consumers and their corresponding ToU prices. The simulation results proved that our DETD algorithm that has additional training and provides fine tuning of hyperparameters, which improves the performance of theft detection over existing ML schemes.  
While electricity theft is directly dependent on actual power consumption, it can be indirectly affected by other window factors that influence real usage such as the pricing scheme used in the SG, temperature data, seasonal trends, and so on. Taking that into consideration, in our proposed algorithm DETD, we have reported a ToU pricing scheme-based theft activity effect via simulation. As a classifier in our algorithm, alternatives to XGBoost, such as CatBoost and LightGBM, have been tested for their respective performances.  
Further work may include creating a global theft detector for the entire grid that detects theft irrespective of the user (one detector for the whole grid instead of one for each consumer) is another important step towards futuristic and practical theft detection. Additionally, automated parameter tuning using Bayesian processes or a better replacement of gradient boosting techniques with other ML/AI techniques can further help in optimizing theft detection using DETD.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**DETD** & **3-Month Summer Window** \\ \hline DR [\%] & 97.3 \\ FPR [\%] & 8.1 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average theft detection performance of DETD when using the weather-dependent theft cases for an average of 1000 consumers (trained and tested on 3-month data).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**LightGBM** & **d-ToU** & **f-ToU** \\ \hline DR [\%] & 97 & 97 \\ FPR [\%] & 7 & 5 \\ \hline
**CatBoost** & **d-ToU** & **f-ToU** \\ \hline DR [\%] & 98 & 98 \\ FPR [\%] & 3 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average theft detection performance of LightGBM- and CatBoost-based DETD when using the d-ToU window-based theft cases for an average of 1000 consumers.  
**Author Contributions:** Conceptualization, R.P. and S.C.; methodology, R.P.; software, R.P.; validation, R.P. and S.C.; formal analysis, R.P.; investigation, R.P. and S.C.; resources, R.P. and S.C.; data curation, R.P.; writing--original draft preparation, R.P.; writing--review and editing, S.C.; visualization, R.P.; supervision, S.C.; project administration, S.C.; funding acquisition, S.C. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported in part by the NRF grant funded by the Korea Government Ministry of Science and ICT (MSIT) under Grant 2017R1A2B4005840, and in part by the Catholic University of Korea, Research Fund, 2020.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.