Chaotic State Analysis and Voltage Correction with Ferroresonance Modeling

Yıl 2023, Cilt: 15 Sayı: 2, 714 - 721, 14.07.2023

Mehmet Taciddin Akçay Aysel Ersoy

https://doi.org/10.29137/umagd.1255685

Öz

Many undesirable risky situations such as short circuits, burns, explosions, various malfunctions, dangerous events and equipment losses can occur in transformer systems. While such faults may occur due to external factors, in some cases, they may be caused by the characteristics of the electrical load connected to the circuit. One of the most important causes of faults arising from the load characteristics is the Ferroresonance phenomenon that occurs in transformer systems. Ferroresonance is defined as non-linear resonance and can pose a critical level of danger to the system. In this study, the theory of chaos in electrical power systems is explained and an application is made over the ferroresonance circuit. The mathematical model of the ferroresonance circuit is given by analyzing it. While using nonlinear circuit elements, the system was examined over the related equivalent circuit. With the given mathematical model of the nonlinear dynamic system, the effects of the conditions in the ferroresonance state and the voltage source are shown. By examining the ferroresonance state behaviors caused by transformer losses, simulations of different states are made. These states include the normal state, the fundamental frequency ferroresonance state, the subharmonic ferroresonance state, and the chaotic state ferroresonance state. At the end of the study, voltage correction application was made to correct the voltage oscillation occurring on the load side of the chaotic state.

Anahtar Kelimeler

chaos, ferroresonance, harmonic, loss, nonlineer

Ferrorezonans Modellemesi ile Kaotik Durum Davranışının Analizi ve Gerilim İyileştirme

Öz

Transformatör sistemlerinde kısa devreler, yanmalar, patlamalar, çeşitli arızalar, tehlikeli olaylar ve ekipman kayıpları gibi bir çok istenmeyen riskli durumlar meydana gelebilmektedir. Bu tip arızalar dış kaynaklı hususlardan dolayı oluşabilirken bazı durumlarda ise devreye bağlı elektriksel yükün karakteristiğinden kaynaklanabilmektedir. Yük karakteristiğinden kaynaklı arızaların en önemli nedenlerinden biri de transformatör sistemlerinde gerçekleşen Ferrorezonans olayıdır. Ferrorezonans lineer olmayan rezonans olarak tanımlanmakta olup sistem için kritik seviyede tehlike oluşturabilmektedir. Bu çalışmada elektrik güç sistemlerinde kaos teorisi anlatılarak ferrorezonans devresi üzerinden uygulama yapılmıştır. Ferrorezonans devresinin analizi yapılarak matematiksel modeli verilmiştir. Nonlineer devre elmanları kullanılırken ilgili eşdeğer devre üzerinden sistem incelenmiştir. Nonlineer dinamik sisteme ait verilen matematiksel model ile ferrorezonans durumundaki koşulların ve gerilim kaynağının etkisi gösterilmiştir. Transformatör kayıplarının neden olduğu ferrorezonans durum davranışları incelenerek farklı durumlara ait benzetimler yapılmıştır. Bu durumlar normal durum, temel frekans ferrorezonans durumu, altharmonik ferrorezonans durumu ve kaotik durum ferrorezonans durumlarını içermektedir. Çalışmanın sonunda kaotik duruma ait yük tarafında meydana gelen gerilim osilasyonun düzeltilmesi için gerilim iyileştirici uygulaması yapılmıştır.

Anahtar Kelimeler

ferrorezonans, harmonik, kaos, kayıp, nonlineer

Kaynakça

• AI Zahawi , B. A. T., Emin, Z. & Tong, Y. K. (1998). Chaos in ferroresonant wound voltage transformers: effect of core losses and universal circuit behaviour. IEE Proc.-Sci. Meas. Technol., 145 (1), 39-43.
• Araujo, A. E. A., SOUDACK, A. C. & Marti. (1993). Ferroresonance in power systems: chaotic behaviour. IEE PROCEEDINGS-C, 140 (3), 237-240. Bashar, Z. E., AL Zahawi, A. T., TONG, Y., K. & UGUR, M. (2001). Quantification of the Chaotic Behavior of Ferroresonant Voltage Transformer Circuits. IEEE , Transactions On Circuits And Systems—I: Fundamental Theory And Applications, 48 (6), 757-760.
• Cataliotti, A., Cosentiono, V., Crotti, G., Delle Femine, A., Di Cara, D., Gallo, D., Giordano, D., Landi, C., Luiso, M. & Modarres, M. et al. (2018). Compensation of Nonlinearity of Voltage and Current Instrument Transformers. IEEE Trans. Instrum. Meas., 68, 1322–1332.
• Crotti, G., D’Avanzo, G., Giordano, D., Letizia, P.S. & Luiso, M. (2021.) Extended SINDICOMP: Characterizing MV Voltage Transformers with Sine Waves. Energies, 14, 1715
• Huawei, L. & Yu, F. (2007). Impact of Breaker Operations on Ferroresonance in Power Systems. 8th International Conference on Electronic Measurement and Instruments, Xi'an, China, 3, 680-682.
• Jałmuzny, W. (2013). Analysis of the properties of HV voltage transformers in abnormal operating conditions with particular consideration ˙ of ferroresonance oscillations. Zesz. Naukowe. Rozpr. Nauk./Politech. Łódzka, 454, 1–185.
• Kpomahou, Y., Miwadinou, C. & Hinvi, L. (2018). Mathematical modelling and parametric resonances of a nonlinear RLC series circuit. Int. J. Nonlinear Dyn. Cont., 1, 133–153.
• Lei, Z. M., Liu, Z. J., Sun, H. X. & Liu, H., X. (2005). Control And Application Of Chaos In Electrical System. International Conference on Machine Learning and Cybernetics, Guangzhou, China, 3, 1477-1481.
• Milicevic, K., Vinko, D. & Emin, Z. (2011). Identifying ferroresonance initiation for a range of initial conditions and parameters. Nonlinear Dyn., 66, 755–762
• Mork, B. A. & Stuehm, D. L. (1994). Application Of Nonlinear Dynamics And Chaos To Ferroresonance In Distribution Systems. IEEE Transactions on Power Delivery, 9(2), 1009-1017.
• Mozaffari, S., Henschel, S. & Soudack, A. C. (1995) Chaotic ferroresonance in power transformers. IEE Proc.-Gener. Transm. Distrib., 42(3), 247-250.
• Radmanesh, H., Rostami, M. & Khalilpour, J. (2012). Ferroresonance in Voltage Transformer Considering Linear and Nonlinear Core Losses Effect. Int. J. Comput. Electr. Eng., 4, 789–793.
• Stojkovska, B., Stefanovska, A., & Golob, R. (2001). Time-delay feedback control of ferroresonant chaotic oscillations. IEEE Porto Power Tech Proceedings, Porto, Portugal, 2, 1-6.
• Toscani, S., Faifer, M., Ferrero, A., Laurano, C., Ottoboni, R. & Zanoni, M. (2020). Compensating Nonlinearities in Voltage Transformers for Enhanced Harmonic Measurements: The Simplified Volterra Approach. IEEE Trans. Power Deliv., 36, 362–370.
• Valverde, V., Mazón, A. J., & Zamora, I. (2013). Buigues, G. Ferroresonance in Voltage Transformers: Analysis and Simulations. In Proceedings of the International Conference on Renewable Energies and Power Quality, Bilbao, Spain, 20–22 March, 1 (5), 465-471.
• Heidary, A., Rouzbehi, K., Radmanesh, H. & Pou, J. (2020). Voltage Transformer Ferroresonance: An Inhibitor Device. IEEE Transactions on Power Delivery, 35(6), 2731-2733.
• Shiming, X. , Yao, S., Jianheng, L. , Xing, L., Yonglu, L.,Wenjing, X. & Mei, S,, (2022). Stabilized Negative Resistance Emulating Control for Grid-Connected Inverter. IEEE Transactions on Industrial Electronics, 69(8), 8599-8603