DOI: https://doi.org/10.15587/2312-8372.2017.107664

### Mathematical model of high-voltage instrument autotransformer intended for use in smart grid networks

Volodymyr Brzhezitsky, Yaroslav Haran, Yevgeniy Trotsenko

#### Abstract

The object of the research is a mathematical model of the active part of the high-voltage instrument autotransformer with several output windings. The most challenging task in this model is leakage inductance calculation of single winding turns or groups of autotransformer winding turns. Also, a significant problem when calculating the parameters of the autotransformer are those operating conditions, that are close to no-load conditions.

To create a mathematical model of the active part of a high-voltage autotransformer, taking into account the leakage inductance of each single winding turn (or groups of winding turns), and also the magnitude and type of the load, it is proposed to modify the known system of transformer equations detailed to the level of single turns (or groups of turns) and use the proposed method for determining the partial self- and mutual- leakage inductances by numerical methods.

With a help of the developed mathematical model of the active part of a high-voltage autotransformer, a prototype of a 10 kV autotransformer with high metrological characteristics was designed and manufactured. Positive results of metrological certification of the created high-voltage autotransformer confirmed the possibility of calculating the parameters of such primary high-voltage transformers that can be used in Smart Grid networks in conjunction with analog-to-digital converters, thus unifying the electromagnetic primary high-voltage transformers.

It is shown that the operating conditions of high-voltage autotransformers, close to no-load conditions, allow easily achieve high accuracy of high voltage transformation.

#### Keywords

autotransformer; voltage transformer; Smart Grid; mathematical model; leakage inductance

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#### References

Brzhezytskyi, V., Haran, Ya., Masliuchenko, I. (2016). Detailing of the transformer equation to the single winding turns (groups of the winding turns). Technology Audit and Production Reserves, 1(1(27)), 32–37. doi:10.15587/2312-8372.2016.59101

Xu, Q., Deng, C., Chen, L. (2013). Real-Time Generation Dispatch and Communication Architecture of Smart Grid with Renewable Energy. Journal of Communications, 8 (8), 497–504. doi:10.12720/jcm.8.8.497-504

Yilmaz, C., Albayrak, S., Lützenberger, M. (2014). Smart Grid Architectures and the Multi-Agent System Paradigm. Energy 2014: The Fourth International Conference on Smart Grids, Green Communications and IT Energy-aware Technologies, 90–95.

Anderson, K., Du, J., Narayan, A., Gamal, A. E. (2014). GridSpice: A Distributed Simulation Platform for the Smart Grid. IEEE Transactions on Industrial Informatics, 10 (4), 2354–2363. doi:10.1109/tii.2014.2332115

Arya, A. K., Chanana, S., Kumar, A. (2013). Role of Smart Grid to Power System Planning and Operation in India. Proceedings of International Conference on Emerging Trends in Engineering and Technology, 793–802.

Miceli, R., Favuzza, S., Genduso, F. (2013). A Perspective on the Future of Distribution: Smart Grids, State of the Art, Benefits and Research Plans. Energy and Power Engineering, 05 (01), 36–42. doi:10.4236/epe.2013.51005

Vijayapriya, P., Bapna, G., Kothari, D. P. (2015). Smart Tariff for Smart Meters in Smart Grid. International Journal of Engineering and Technology, 2 (5), 310–315.

Khandekar, N., Thube, K., Patil, N., Mane, P. B. (2014). Non-Intrusive Appliance Load Monitoring System Using Zigbee Protocol. International Journal of Engineering Research & Technology (IJERT), 3 (4), 2415–2417.

Janjic, A., Stajic, Z., Radovic, I. (2011). Power Quality Requirements for the Smart Grid Design. International Journal of Circuits, Systems and Signal Processing, 5 (6), 643–651.

Maitra, S. (2016). Smart Energy meter using Power Factor Meter and Instrument Transformer. Communications on Applied Electronics, 4 (1), 31–37. doi:10.5120/cae2016652015

Brzhezitsky, V. O., Garan, Ja. O., Desjatov, O. M. (2014). Leakage Inductance Calculation of High-Voltage Transformer Windings by Means of the Software using the Finite Elements Method. Technical Electrodynamics, 4, 61–63.

Brzhezytskyi, V., Haran, Ya. (2016). Analysis of capacitive currents in the winding of a high voltage measuring autotransformer. Technology Audit and Production Reserves, 4(1(30)), 70–76. doi:10.15587/2312-8372.2016.74694

#### GOST Style Citations

Brzhezytskyi, V. Detailing of the transformer equation to the single winding turns (groups of the winding turns) [Text] / V. Brzhezytskyi, Ya. Haran, I. Masliuchenko // Technology audit and production reserves. – 2016. – Vol. 1, No. 1(27). – P. 32–37. doi:10.15587/2312-8372.2016.59101

Xu, Q. Real-Time Generation Dispatch and Communication Architecture of Smart Grid with Renewable Energy [Text] / Q. Xu, C. Deng, L. Chen // Journal of Communications. – 2013. – Vol. 8, No. 8. – P. 497–504. doi:10.12720/jcm.8.8.497-504

Yilmaz, C. Smart Grid Architectures and the Multi-Agent System Paradigm [Text] / C. Yilmaz, S. Albayrak, M. Lützenberger // Energy 2014: The Fourth International Conference on Smart Grids, Green Communications and IT Energy-aware Technologies. – 2014. – P. 90–95.

Anderson, K. GridSpice: A Distributed Simulation Platform for the Smart Grid [Text] / K. Anderson, J. Du, A. Narayan, A. E. Gamal // IEEE Transactions on Industrial Informatics. – 2014. – Vol. 10, No. 4. – P. 2354–2363. doi:10.1109/tii.2014.2332115

Arya, A. K. Role of Smart Grid to Power System Planning and Operation in India [Text] / A. K. Arya, S. Chanana, A. Kumar // Proceedings of International Conference on Emerging Trends in Engineering and Technology. – 2013. – P. 793–802.

Miceli, R. A Perspective on the Future of Distribution: Smart Grids, State of the Art, Benefits and Research Plans [Text] / R. Miceli, S. Favuzza, F. Genduso // Energy and Power Engineering. – 2013. – Vol. 05, No. 01. – P. 36–42. doi:10.4236/epe.2013.51005

Vijayapriya, P. Smart Tariff for Smart Meters In Smart Grid [Text] / P. Vijayapriya, G. Bapna, D. P. Kothari // International Journal of Engineering and Technology. – 2010. – Vol. 2, No. 5. – P. 310–315.

Khandekar, N. Non-Intrusive Appliance Load Monitoring System Using Zigbee Protocol [Text] / N. Khandekar, K. Thube, N. Patil, P. B. Mane // International Journal of Engineering Research & Technology (IJERT). – 2014. – Vol. 3, No. 4. – P. 2415–2417.

Janjic, A. Power Quality Requirements for the Smart Grid Design [Text] / A. Janjic, Z. Stajic, I. Radovic // International Journal of Circuits, Systems and Signal Processing. – 2011. – Vol. 5, No. 6. – P. 643–651.

Maitra, S. Smart Energy meter using Power Factor Meter and Instrument Transformer [Text] / S. Maitra // Communications on Applied Electronics. – 2016. – Vol. 4, No. 1. – P. 31–37. doi:10.5120/cae2016652015

Brzhezitsky, V. O. Leakage Inductance Calculation of High-Voltage Transformer Windings by Means of the Software using the Finite Elements Method [Text] / V. O. Brzhezitsky, Ja. O. Garan, O. M. Desjatov // Technical Electrodynamics. – 2014. – No. 4. – P. 61–63.

Brzhezytskyi, V. Analysis of capacitive currents in the winding of a high voltage measuring autotransformer [Text] / V. Brzhezytskyi, Ya. Haran // Technology audit and production reserves. – 2016. – Vol. 4, No. 1(30). – P. 70–76. doi:10.15587/2312-8372.2016.74694

Copyright (c) 2017 Yevgeniy Trotsenko, Volodymyr Brzhezitsky, Yaroslav Haran