A Hybrid Model Combining Neural Learning and Uncertainty Modeling for Estimating the Average Phase Voltage in Three-Phase IGBT Inverters

Faruk Kürker

doi:10.29130/dubited.1907458

EN TR

A Hybrid Model Combining Neural Learning and Uncertainty Modeling for Estimating the Average Phase Voltage in Three-Phase IGBT Inverters

Abstract

Accurate modeling of power electronics-based inverter systems is very important in the analysis of electric drive systems, as well as in the development of sophisticated control systems and condition monitoring systems. Nevertheless, the non-linear nature of inverter systems, owing to their switching characteristics, and the variability in system parameters make it difficult to accurately model average phase voltages using analytical models. In this study, a hybrid data-driven model is presented, which combines residual learning with heteroscedastic uncertainty modeling in the estimation of average phase voltages using the pulse width modulation (PWM) period in two-level three-phase insulated gate bipolar transistor (IGBT) inverters. In this study, the reference voltage is estimated using the physical operating principle of the inverter system, and this is combined with the use of an artificial neural network in the development of the residual learning model. In addition, probabilistic voltage estimation is performed in this study to assess the reliability of the model outputs. The framework is validated using an open-access three-phase inverter dataset. The results show that the physics-guided residual model substantially improves the standalone physical reference and direct MLP estimation, achieving RMSE values in the range of 1.05–1.11 V, MAE values in the range of 0.59–0.62 V, and (R²≈ 0.99990) for three-phase voltage estimation. The uncertainty-aware extension provides reliability-related uncertainty indicators that may be useful for monitoring, diagnostic, and supervisory-level applications; however, these uncertainty estimates should be interpreted as practical reliability indicators rather than perfectly calibrated probabilities.

Keywords

Three-phase IGBT inverter, Physics-based learning, Residual learning, Heteroscedastic uncertainty modeling, Average phase voltage estimation, Data-driven inverter modeling

Supporting Institution

This research has not received any external financial support.

Project Number

None

Ethical Statement

This study does not involve human or animal subjects. All scientific and ethical rules have been followed within the scope of the study, and all sources used have been properly cited.

Thanks

The author declares that there are no individuals or institutions to whom he/she wishes to express gratitude in connection with this work.

Abstract

Güç elektroniği tabanlı inverter sistemlerinin doğru modellenmesi, elektrikli sürücü sistemlerinin analizi, gelişmiş kontrol ve durum izleme uygulamaları açısından önemlidir. Ancak inverter anahtarlama davranışının doğrusal olmayan yapısı ve sistem parametrelerindeki değişkenlik, ortalama faz gerilimlerinin analitik olarak doğru modellenmesini zorlaştırmaktadır. Bu çalışmada, iki seviyeli üç fazlı IGBT inverterlerde PWM periyodu bazlı ortalama faz gerilimlerinin tahmini için fizik yönlendirmeli artık öğrenme ve heteroskedastik belirsizlik modellemesini birleştiren hibrit bir veri güdümlü model önerilmektedir. Önerilen yaklaşım, inverterin fiziksel çalışma prensiplerinden elde edilen referans gerilim bileşenini yapay sinir ağı tabanlı artık öğrenme modeli ile birleştirmektedir. Ayrıca model çıktılarının güvenilirliğini değerlendirmek amacıyla olasılıksal gerilim kestirimi gerçekleştirilmiştir. Yöntem, açık erişimli üç fazlı inverter veri seti üzerinde değerlendirilmiştir. Sonuçlar, önerilen yaklaşımın doğrudan veri güdümlü modellere kıyasla daha yüksek tahmin doğruluğu sağladığını göstermektedir. Üç faz gerilim tahminlerinde RMSE değerinin 1.05–1.11 V, MAE değerinin 0.59–0.62 V aralığında olduğu ve determinasyon katsayısının R2≈0.99990 seviyesine ulaştığı görülmüştür. Ayrıca model tüm fazlar için güvenilir belirsizlik tahminleri üretmiştir. Bulgular, hibrit modelleme yaklaşımlarının inverter tabanlı güç elektroniği sistemlerinin modellenmesinde kullanılabileceğini göstermektedir.

Keywords

Üç fazlı IGBT inverter, fizik yönlendirmeli öğrenme, artık öğrenme, heteroskedastik belirsizlik modellemesi, ortalama faz gerilimi tahmini, veri güdümlü inverter modelleme

Supporting Institution

Bu araştırma herhangi bir kurum veya kuruluş tarafından finansal olarak desteklenmemiştir.

Project Number

None

Ethical Statement

Bu çalışma insan veya hayvan denekler içermemektedir. Çalışma kapsamında tüm bilimsel ve etik ilkelere uyulmuş olup kullanılan tüm kaynaklara uygun şekilde atıf yapılmıştır.

Thanks

Yazar teşekkür etmek istediği herhangi bir kişi veya kurum bulunmadığını beyan eder.

References

Akın, M., Canbay, Y., & Ocak, C. (2024). Deep learning based phase current prediction model in three-phase IGBT two-level inverter for electrical drives. In 2024 IEEE 18th International Conference on Compatibility, Power Electronics and Power Engineering (CPE-POWERENG) (pp. 1–6). IEEE. https://doi.org/10.1109/CPE-POWERENG60842.2024.10604414
Andelić, N., Lorencin, I., Glučina, M., & Car, Z. (2022). Mean phase voltages and duty cycles estimation of a three-phase inverter in a drive system using machine learning algorithms. Electronics, 11(16), Article 2623. https://doi.org/10.3390/electronics11162623
Athari, H., Niroomand, M., & Ataei, M. (2017). Review and classification of control systems in grid-tied inverters. Renewable and Sustainable Energy Reviews, 72, 1167–1176. https://doi.org/10.1016/j.rser.2016.10.030
Babakmehr, M., Harirchi, F., Dehghanian, P., & Enslin, J. H. (2021). Artificial intelligence-based cyber–physical events classification for islanding detection in power inverters. IEEE Journal of Emerging and Selected Topics in Power Electronics, 9(5), 5282–5293. https://doi.org/10.1109/JESTPE.2020.2980045
Chai, T., & Draxler, R. R. (2014). Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature. Geoscientific Model Development, 7, 1247–1250. https://doi.org/10.5194/gmd-7-1247-2014
Chicco, D., Warrens, M. J., & Jurman, G. (2021). The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation. PeerJ Computer Science, 7, Article e623. https://doi.org/10.7717/peerj-cs.623
Divina, F., Gilson, A., Gómez-Vela, F., García Torres, M., & Torres, J. F. (2018). Stacking ensemble learning for short-term electricity consumption forecasting. Energies, 11(4), Article 949. https://doi.org/10.3390/en11040949
Gal, Y., & Ghahramani, Z. (2016). Dropout as a Bayesian Approximation: Representing model uncertainty in deep learning. In M. F. Balcan & K. Q. Weinberger (Eds.), Proceedings of the 33rd International Conference on Machine Learning (Vol. 48, pp. 1050–1059). PMLR. https://proceedings.mlr.press/v48/gal16.html
He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep residual learning for image recognition. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (pp. 770–778). IEEE. https://doi.org/10.1109/CVPR.2016.90
Ho, T.-Y., Peng, S.-W., & Su, S.-F. (2025). Enhanced modeling of three-phase IGBT two level inverter for electric drives using LM algorithm in artificial neural networks. In 2025 IEEE International Conference on Consumer Electronics - Taiwan (ICCE-Taiwan) (pp. 195–196). IEEE. https://doi.org/10.1109/ICCE-Taiwan66881.2025.11208034

Kendall, A., & Gal, Y. (2017). What uncertainties do we need in Bayesian deep learning for computer vision? arXiv. https://doi.org/10.48550/arXiv.1703.04977
Kingma, D. P., & Ba, J. (2015). Adam: A method for stochastic optimization. In Y. Bengio & Y. LeCun (Eds.), Proceedings of the International Conference on Learning Representations (ICLR 2015). https://doi.org/10.48550/arXiv.1412.6980
Krishnan, R. (2001). Electric motor drives: Modeling, analysis, and control. Prentice Hall.
Lorencin, I., Anđelić, N., Mrzljak, V., & Car, Z. (2019). Genetic algorithm approach to design of multilayer perceptron for combined cycle power plant electrical power output estimation. Energies, 12(22), Article 4352. https://doi.org/10.3390/en12224352
Liu, Y., Sangwongwanich, A., Zhang, Y., Ou, S., & Wang, H. (2024). A transferable deep learning network for IGBT open-circuit fault diagnosis in three-phase inverters. In 2024 IEEE Applied Power Electronics Conference and Exposition (APEC) (pp. 1229–1234). IEEE. https://doi.org/10.1109/APEC48139.2024.10509151
Lu, B., & Sharma, S. K. (2009). A literature review of IGBT fault diagnostic and protection methods for power inverters. IEEE Transactions on Industry Applications, 45(5), 1770–1777. https://doi.org/10.1109/TIA.2009.2027535
Masrur, M. A., Chen, Z., & Murphey, Y. (2010). Intelligent diagnosis of open and short circuit faults in electric drive inverters for real-time applications. IET Power Electronics, 3(2), 279–291. https://doi.org/10.1049/IET-PEL.2008.0362
Popescu, M. C., Balas, V., Perescu-Popescu, L., & Mastorakis, N. (2009). Multilayer perceptron and neural networks. WSEAS Transactions on Circuits and Systems, 8(7), 579–588.
Rajeswaran, N., Swarupa, M. L., Rao, T. S., & Chetaswi, K. (2018). Hybrid artificial intelligence-based fault diagnosis of SVPWM voltage source inverters for induction motor. Materials Today: Proceedings, 5(1), 565–571. https://doi.org/10.1016/j.matpr.2017.11.119
Santhoshi, B. K., Sundaram, K. M., Padmanaban, S., Holm-Nielsen, J. B., Prabhakaran & K. K. (2019). Critical review of PV grid-tied inverters. Energies, 12(10), Article 1921. https://doi.org/10.3390/en12101921
Stender, M., Wallscheid, O., & Böcker, J. (2020a). Data set description: Three-phase IGBT two-level inverter for electrical drives [Technical report]. University of Paderborn. https://doi.org/10.13140/RG.2.2.23335.37280
Stender, M., Wallscheid, O., & Böcker, J. (2020b). Three-phase IGBT two-level inverter for electrical drives [Data set]. Kaggle. https://www.kaggle.com/stender/inverter-data-set
Stender, M., Wallscheid, O., & Böcker, J. (2021). Comparison of gray-box and black-box two-level three-phase inverter models for electrical drives. IEEE Transactions on Industrial Electronics, 68(9), 8646–8656. https://doi.org/10.1109/TIE.2020.3018060
Szwarc, K. J., Szczepankowski, P., Nieznański, J., Swinarski, C., Usoltsev, A., & Strzelecki, R. (2020). Hybrid modulation for modular voltage source inverters with coupled reactors. Energies, 13(17), Article 4450. https://doi.org/10.3390/en13174450
Wen, B., Boroyevich, D., Burgos, R., Mattavelli, P., & Shen, Z. (2016). Analysis of D-Q small-signal impedance of grid-tied inverters. IEEE Transactions on Power Electronics, 31(1), 675–687. https://doi.org/10.1109/TPEL.2015.2398192

Details

Primary Language

English

Subjects

Electrical Machines and Drives, Electrical Engineering (Other)

Journal Section

Research Article

Authors

Faruk Kürker ^*
0000-0003-1544-9743
Türkiye

Publication Date

October 23, 2026

Submission Date

March 11, 2026

Acceptance Date

July 1, 2026

Published in Issue

Year 2026 Volume: 14 Number: 4

DOI

https://doi.org/10.29130/dubited.1907458

IZ

https://izlik.org/JA24ZP27AY

APA

Kürker, F. (2026). A Hybrid Model Combining Neural Learning and Uncertainty Modeling for Estimating the Average Phase Voltage in Three-Phase IGBT Inverters. Duzce University Journal of Science and Technology, 14(4), 954-979. https://doi.org/10.29130/dubited.1907458

AMA

1.Kürker F. A Hybrid Model Combining Neural Learning and Uncertainty Modeling for Estimating the Average Phase Voltage in Three-Phase IGBT Inverters. DUBİTED. 2026;14(4):954-979. doi:10.29130/dubited.1907458

Chicago

Kürker, Faruk. 2026. “A Hybrid Model Combining Neural Learning and Uncertainty Modeling for Estimating the Average Phase Voltage in Three-Phase IGBT Inverters”. Duzce University Journal of Science and Technology 14 (4): 954-79. https://doi.org/10.29130/dubited.1907458.

EndNote

Kürker F (October 1, 2026) A Hybrid Model Combining Neural Learning and Uncertainty Modeling for Estimating the Average Phase Voltage in Three-Phase IGBT Inverters. Duzce University Journal of Science and Technology 14 4 954–979.

IEEE

[1]F. Kürker, “A Hybrid Model Combining Neural Learning and Uncertainty Modeling for Estimating the Average Phase Voltage in Three-Phase IGBT Inverters”, DUBİTED, vol. 14, no. 4, pp. 954–979, Oct. 2026, doi: 10.29130/dubited.1907458.

ISNAD

Kürker, Faruk. “A Hybrid Model Combining Neural Learning and Uncertainty Modeling for Estimating the Average Phase Voltage in Three-Phase IGBT Inverters”. Duzce University Journal of Science and Technology 14/4 (October 1, 2026): 954-979. https://doi.org/10.29130/dubited.1907458.

JAMA

1.Kürker F. A Hybrid Model Combining Neural Learning and Uncertainty Modeling for Estimating the Average Phase Voltage in Three-Phase IGBT Inverters. DUBİTED. 2026;14:954–979.

MLA

Kürker, Faruk. “A Hybrid Model Combining Neural Learning and Uncertainty Modeling for Estimating the Average Phase Voltage in Three-Phase IGBT Inverters”. Duzce University Journal of Science and Technology, vol. 14, no. 4, Oct. 2026, pp. 954-79, doi:10.29130/dubited.1907458.

Vancouver

1.Faruk Kürker. A Hybrid Model Combining Neural Learning and Uncertainty Modeling for Estimating the Average Phase Voltage in Three-Phase IGBT Inverters. DUBİTED. 2026 Oct. 1;14(4):954-79. doi:10.29130/dubited.1907458

A Hybrid Model Combining Neural Learning and Uncertainty Modeling for Estimating the Average Phase Voltage in Three-Phase IGBT Inverters

Abstract

Keywords

Supporting Institution

Project Number

Ethical Statement

Thanks

Abstract

Keywords

Supporting Institution

Project Number

Ethical Statement

Thanks

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite