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UYUMLU KESİRLİ MERTEBEDEN TÜREVLE MODELLENEN KONDANSATÖRÜN SPICE MODELİ VE PARALEL R-L-C_∝ DEVRESİNİN SİMÜLASYONUNDA KULLANIMI

Yıl 2023, Cilt: 24 Sayı: 2, 49 - 56, 28.12.2023
https://doi.org/10.59314/tujes.1396358

Öz

Buçuklu türev ile elektrik devrelerinin ve devre elemanlarının modellenmesi 20. yüzyılda ortaya çıkmıştır ve devre elemanlarının modellenmesinde de kullanılmıştır. Son yıllarda Konformal Buçuklu Türev (KBT) popüler bir yöntem haline gelmiştir. Literatürdeki bazı çalışmalarda superkapasitörler başarılı şekilde modellenmiştir. Yine de KBT kondasatörleri barındıran devreler için analitik bir çözüm bulmak oldukça zordur. Devre simulatörleri analizi zor devrelerin analitik çözümlerini bulma konusunda başarılıdır. KBT kondansatörler henüz bir Spice modeline sahip değildir. Bu çalışmada KBT kondansatör Spice modeli LTspice programında oluşturuldu. Ayrıca model parallel R-L-C_∝ devresinin simulasyonu için kullanıldı. Simulasyon sonuçları verildi.

Kaynakça

  • Abdeljawad, T. (2015). On conformable fractional calculus. Journal of computational and Applied Mathematics, 279, 57-66.
  • Alagöz, B. B., & Alisoy, H. (2018). Estimation of reduced order equivalent circuit model parameters of batteries from noisy current and voltage measurements. Balkan Journal of Electrical and Computer Engineering, 6(4), 224-231.
  • Arapi, M., & Mutlu, R. (2022). Analysis of an Oscillation Circuit with a Linear Time-invariant Inductor and a Capacitor Modelled with Conformal Fractional Order Derivative. European Journal of Engineering and Applied Sciences, 5(1), 22-28.
  • Babacan, Y. (2017, July). Memristor: Three MOS transistors and one capacitor. In IEEE Conference Paper. Babiarz, A., Czornik, A., Klamka, J., & Niezabitowski, M. (2017). Theory and applications of non-integer order systems. Lecture Notes Electrical Engineering, 407.
  • Bentley, P., Stone, D. A., & Schofield, N. (2005). The parallel combination of a VRLA cell and supercapacitor for use as a hybrid vehicle peak power buffer. Journal of power sources, 147(1-2), 288-294.
  • Ciocan, I., Farcăş, C., Grama, A., & Tulbure, A. (2016, October). An improved method for the electrical parameters identification of a simplified PSpice supercapacitor model. In 2016 IEEE 22nd International Symposium for Design and Technology in Electronic Packaging (SIITME) (pp. 171-174). IEEE.
  • Devecioğlu, İ., & Mutlu, R. (2022). A Conformal Fractional Derivative-based Leaky Integrate-and-Fire Neuron Model. Sakarya University Journal of Science, 26(3), 568-578.
  • Fărcaş, C., Petreuş, D., Ciocan, I., & Palaghiţă, N. (2009, September). Modeling and simulation of supercapacitors. In 2009 15th International Symposium for Design and Technology of Electronics Packages (SIITME) (pp. 195-200). IEEE.
  • Freeborn, T. J., Elwakil, A. S., & Allagui, A. (2018, May). Supercapacitor fractional-order model discharging from polynomial time-varying currents. In 2018 IEEE International Symposium on Circuits and Systems (ISCAS) (pp. 1-5). IEEE.
  • Freeborn, T. J., Maundy, B., & Elwakil, A. S. (2013). Measurement of supercapacitor fractional-order model parameters from voltage-excited step response. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 3(3), 367-376.
  • Gualous, H., Bouquain, D., Berthon, A., & Kauffmann, J. M. (2003). Experimental study of supercapacitor serial resistance and capacitance variations with temperature. Journal of power sources, 123(1), 86-93.
  • Ionescu, C., Vasile, A., & Negroiu, R. (2015, October). Accurate modeling of supercapacitors for DC operation regime. In 2015 IEEE 21st International Symposium for Design and Technology in Electronic Packaging (SIITME) (pp. 303-306). IEEE.
  • Iordache, M., Dumitriu, L., Perpelea, M., Sîrbu, I. G., & Mandache, L. (2013). SPICE-like Models for Nonlinear Capacitors and Inductors. International Journal Of Computers & Technology, 12(2), 3228-3240.
  • Johansson, P., & Andersson, B. (2008). Comparison of simulation programs for supercapacitor modelling. Master of Science Thesis. Chalmers University of Technology, Sweden.
  • Karakulak, E., & Mutlu, R. (2020). SPICE Model of Current Polarity-Dependent Piecewise Linear Window Function for Memristors. Gazi University Journal of Science, 33(4), 766-777.
  • Karakulak, E. (2023). Conformable fractional-order derivative based adaptive FitzHugh-Nagumo neuron model. Journal of Electrical Engineering, 74(4), 282-292.
  • Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. (2014). A new definition of fractional derivative. Journal of computational and applied mathematics, 264, 65-70.
  • Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of fractional differential equations (Vol. 204). Elsevier.
  • Koseoglu, M., Deniz, F. N., Alagoz, B. B., & Alisoy, H. (2022). An effective analog circuit design of approximate fractional-order derivative models of M-SBL fitting method. Engineering Science and Technology, an International Journal, 33, 101069.
  • Kopka, R. (2017). Estimation of supercapacitor energy storage based on fractional differential equations. Nanoscale research letters, 12(1), 636.
  • Lewandowski, M., & Orzyłowski, M. (2017). Fractional-order models: The case study of the supercapacitor capacitance measurement. Bulletin of the Polish Academy of Sciences Technical Sciences, 65(4), 449-457.
  • Makaryshkin, D. A. (2010). Investigation of the Supercapacitor Mathematical Model by Means of LTspice IV. In Xth International Conference on Modern Problems of Radio Engineering, Telecommunications and Computer Science (TCSET’2010).–Lviv-Slavsko, Ukraine (pp. 40-42).
  • Mohammed, A. A. H. A., Kandemir, K., & Mutlu, R. (2020). Analysis of parallel resonance circuit consisting of a capacitor modelled using conformal fractional order derivative using Simulink. European Journal of Engineering and Applied Sciences, 3(1), 13-18.
  • Morales-Delgado, V. F., Gómez-Aguilar, J. F., & Taneco-Hernandez, M. A. (2018). Analytical solutions of electrical circuits described by fractional conformable derivatives in Liouville-Caputo sense. AEU-International Journal of Electronics and Communications, 85, 108-117.
  • Moreles, M. A., & Lainez, R. (2016). Mathematical modelling of fractional order circuits. arXiv preprint arXiv:1602.03541.
  • Negroiu, R., Svasta, P., Vasile, A., Ionescu, C., & Marghescu, C. (2016, October). Comparison between Zubieta model of supercapacitors and their real behavior. In 2016 IEEE 22nd International Symposium for Design and Technology in Electronic Packaging (SIITME) (pp. 196-199). IEEE.
  • Palaz, U., & Mutlu, R. (2021). Analysis of a Capacitor Modelled with Conformable Fractional Derivative Under DC and Sinusoidal Signals. Celal Bayar University Journal of Science, 17(2), 193-198.
  • Palaz, U., & Mutlu, R. (2021). Two capacitor problem with a lti capacitor and a capacitor modelled using conformal fractional order derivative. European Journal of Engineering and Applied Sciences, 4(1), 8-13.
  • Palaz, U., & Mutlu, R. (2022). A Two-capacitor Problem with a Memcapacitor and a Conformal Fractional-Order Capacitor Put Together. European Journal of Engineering and Applied Sciences, 5(1), 9-15.
  • Palaz, U., & Mutlu, R. (2022). Energy Consideration of a Capacitor Modelled Using Conformal Fractional-Order Derivative. Kocaeli Journal of Science and Engineering, 5(2), 117-125.
  • Pantazica, M., Drumea, A., & Marghescu, C. (2017, October). Analysis of self discharge characteristics of electric double layer capacitors. In 2017 IEEE 23rd International Symposium for Design and Technology in Electronic Packaging (SIITME) (pp. 90-93). IEEE.
  • Piotrowska, E., & Rogowski, K. (2017, October). Analysis of fractional electrical circuit using Caputo and conformable derivative definitions. In Conference on Non-integer Order Calculus and Its Applications (pp. 183-194). Springer, Cham.
  • Piotrowska, E. (2019). Analysis of fractional electrical circuit with sinusoidal input signal using Caputo and conformable derivative definitions. Poznan University of Technology Academic Journals. Electrical Engineering, (97), 155-167.
  • Podlubny, I. (1998). Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier.
  • Ross, B. (1977). The development of fractional calculus 1695–1900. Historia Mathematica, 4(1), 75-89.
  • Sikora, R. (2017). Fractional derivatives in electrical circuit theory–critical remarks. Archives of Electrical Engineering, 66(1), 155-163.
  • Tariboon, J., & Ntouyas, S. K. (2016). Oscillation of impulsive conformable fractional differential equations. Open Mathematics, 14(1), 497-508.
  • Tsirimokou, G., Kartci, A., Koton, J., Herencsar, N., & Psychalinos, C. (2018). Comparative study of discrete component realizations of fractional-order capacitor and inductor active emulators. Journal of Circuits, Systems and Computers, 27(11), 1850170.
  • Yang, X. J. (2019). General fractional derivatives: theory, methods and applications. Chapman and Hall/CRC.
  • Zhao, D., & Luo, M. (2017). General conformable fractional derivative and its physical interpretation. Calcolo, 54(3), 903-917.

Spice Model of a Capacitor Modelled Using Conformal Fractional Order Derivative and its Usage in Simulation of a Parallel R-L-C_∝ Circuit

Yıl 2023, Cilt: 24 Sayı: 2, 49 - 56, 28.12.2023
https://doi.org/10.59314/tujes.1396358

Öz

Fractional-order (FO) components have emerged as a necessary method to model electrical and electronic circuits in the 20th century. In recent decades, the conformable fractional derivative has become a very popular mathematical tool. In the literature, it is used to model supercapacitors successfully. However, it is usually difficult to find analytical solutions for the circuits having a CFD capacitor. Circuit simulation programs make it easy to inspect the circuits hard to analyze. A CFD capacitor does not have a spice model yet. In this study, the Spice model of a CFD capacitor is constructed in the LTspice program. The model is also used to simulate an R-L-C_∝ parallel circuit with a CFD capacitor. Its simulation results are given.

Kaynakça

  • Abdeljawad, T. (2015). On conformable fractional calculus. Journal of computational and Applied Mathematics, 279, 57-66.
  • Alagöz, B. B., & Alisoy, H. (2018). Estimation of reduced order equivalent circuit model parameters of batteries from noisy current and voltage measurements. Balkan Journal of Electrical and Computer Engineering, 6(4), 224-231.
  • Arapi, M., & Mutlu, R. (2022). Analysis of an Oscillation Circuit with a Linear Time-invariant Inductor and a Capacitor Modelled with Conformal Fractional Order Derivative. European Journal of Engineering and Applied Sciences, 5(1), 22-28.
  • Babacan, Y. (2017, July). Memristor: Three MOS transistors and one capacitor. In IEEE Conference Paper. Babiarz, A., Czornik, A., Klamka, J., & Niezabitowski, M. (2017). Theory and applications of non-integer order systems. Lecture Notes Electrical Engineering, 407.
  • Bentley, P., Stone, D. A., & Schofield, N. (2005). The parallel combination of a VRLA cell and supercapacitor for use as a hybrid vehicle peak power buffer. Journal of power sources, 147(1-2), 288-294.
  • Ciocan, I., Farcăş, C., Grama, A., & Tulbure, A. (2016, October). An improved method for the electrical parameters identification of a simplified PSpice supercapacitor model. In 2016 IEEE 22nd International Symposium for Design and Technology in Electronic Packaging (SIITME) (pp. 171-174). IEEE.
  • Devecioğlu, İ., & Mutlu, R. (2022). A Conformal Fractional Derivative-based Leaky Integrate-and-Fire Neuron Model. Sakarya University Journal of Science, 26(3), 568-578.
  • Fărcaş, C., Petreuş, D., Ciocan, I., & Palaghiţă, N. (2009, September). Modeling and simulation of supercapacitors. In 2009 15th International Symposium for Design and Technology of Electronics Packages (SIITME) (pp. 195-200). IEEE.
  • Freeborn, T. J., Elwakil, A. S., & Allagui, A. (2018, May). Supercapacitor fractional-order model discharging from polynomial time-varying currents. In 2018 IEEE International Symposium on Circuits and Systems (ISCAS) (pp. 1-5). IEEE.
  • Freeborn, T. J., Maundy, B., & Elwakil, A. S. (2013). Measurement of supercapacitor fractional-order model parameters from voltage-excited step response. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 3(3), 367-376.
  • Gualous, H., Bouquain, D., Berthon, A., & Kauffmann, J. M. (2003). Experimental study of supercapacitor serial resistance and capacitance variations with temperature. Journal of power sources, 123(1), 86-93.
  • Ionescu, C., Vasile, A., & Negroiu, R. (2015, October). Accurate modeling of supercapacitors for DC operation regime. In 2015 IEEE 21st International Symposium for Design and Technology in Electronic Packaging (SIITME) (pp. 303-306). IEEE.
  • Iordache, M., Dumitriu, L., Perpelea, M., Sîrbu, I. G., & Mandache, L. (2013). SPICE-like Models for Nonlinear Capacitors and Inductors. International Journal Of Computers & Technology, 12(2), 3228-3240.
  • Johansson, P., & Andersson, B. (2008). Comparison of simulation programs for supercapacitor modelling. Master of Science Thesis. Chalmers University of Technology, Sweden.
  • Karakulak, E., & Mutlu, R. (2020). SPICE Model of Current Polarity-Dependent Piecewise Linear Window Function for Memristors. Gazi University Journal of Science, 33(4), 766-777.
  • Karakulak, E. (2023). Conformable fractional-order derivative based adaptive FitzHugh-Nagumo neuron model. Journal of Electrical Engineering, 74(4), 282-292.
  • Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. (2014). A new definition of fractional derivative. Journal of computational and applied mathematics, 264, 65-70.
  • Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of fractional differential equations (Vol. 204). Elsevier.
  • Koseoglu, M., Deniz, F. N., Alagoz, B. B., & Alisoy, H. (2022). An effective analog circuit design of approximate fractional-order derivative models of M-SBL fitting method. Engineering Science and Technology, an International Journal, 33, 101069.
  • Kopka, R. (2017). Estimation of supercapacitor energy storage based on fractional differential equations. Nanoscale research letters, 12(1), 636.
  • Lewandowski, M., & Orzyłowski, M. (2017). Fractional-order models: The case study of the supercapacitor capacitance measurement. Bulletin of the Polish Academy of Sciences Technical Sciences, 65(4), 449-457.
  • Makaryshkin, D. A. (2010). Investigation of the Supercapacitor Mathematical Model by Means of LTspice IV. In Xth International Conference on Modern Problems of Radio Engineering, Telecommunications and Computer Science (TCSET’2010).–Lviv-Slavsko, Ukraine (pp. 40-42).
  • Mohammed, A. A. H. A., Kandemir, K., & Mutlu, R. (2020). Analysis of parallel resonance circuit consisting of a capacitor modelled using conformal fractional order derivative using Simulink. European Journal of Engineering and Applied Sciences, 3(1), 13-18.
  • Morales-Delgado, V. F., Gómez-Aguilar, J. F., & Taneco-Hernandez, M. A. (2018). Analytical solutions of electrical circuits described by fractional conformable derivatives in Liouville-Caputo sense. AEU-International Journal of Electronics and Communications, 85, 108-117.
  • Moreles, M. A., & Lainez, R. (2016). Mathematical modelling of fractional order circuits. arXiv preprint arXiv:1602.03541.
  • Negroiu, R., Svasta, P., Vasile, A., Ionescu, C., & Marghescu, C. (2016, October). Comparison between Zubieta model of supercapacitors and their real behavior. In 2016 IEEE 22nd International Symposium for Design and Technology in Electronic Packaging (SIITME) (pp. 196-199). IEEE.
  • Palaz, U., & Mutlu, R. (2021). Analysis of a Capacitor Modelled with Conformable Fractional Derivative Under DC and Sinusoidal Signals. Celal Bayar University Journal of Science, 17(2), 193-198.
  • Palaz, U., & Mutlu, R. (2021). Two capacitor problem with a lti capacitor and a capacitor modelled using conformal fractional order derivative. European Journal of Engineering and Applied Sciences, 4(1), 8-13.
  • Palaz, U., & Mutlu, R. (2022). A Two-capacitor Problem with a Memcapacitor and a Conformal Fractional-Order Capacitor Put Together. European Journal of Engineering and Applied Sciences, 5(1), 9-15.
  • Palaz, U., & Mutlu, R. (2022). Energy Consideration of a Capacitor Modelled Using Conformal Fractional-Order Derivative. Kocaeli Journal of Science and Engineering, 5(2), 117-125.
  • Pantazica, M., Drumea, A., & Marghescu, C. (2017, October). Analysis of self discharge characteristics of electric double layer capacitors. In 2017 IEEE 23rd International Symposium for Design and Technology in Electronic Packaging (SIITME) (pp. 90-93). IEEE.
  • Piotrowska, E., & Rogowski, K. (2017, October). Analysis of fractional electrical circuit using Caputo and conformable derivative definitions. In Conference on Non-integer Order Calculus and Its Applications (pp. 183-194). Springer, Cham.
  • Piotrowska, E. (2019). Analysis of fractional electrical circuit with sinusoidal input signal using Caputo and conformable derivative definitions. Poznan University of Technology Academic Journals. Electrical Engineering, (97), 155-167.
  • Podlubny, I. (1998). Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier.
  • Ross, B. (1977). The development of fractional calculus 1695–1900. Historia Mathematica, 4(1), 75-89.
  • Sikora, R. (2017). Fractional derivatives in electrical circuit theory–critical remarks. Archives of Electrical Engineering, 66(1), 155-163.
  • Tariboon, J., & Ntouyas, S. K. (2016). Oscillation of impulsive conformable fractional differential equations. Open Mathematics, 14(1), 497-508.
  • Tsirimokou, G., Kartci, A., Koton, J., Herencsar, N., & Psychalinos, C. (2018). Comparative study of discrete component realizations of fractional-order capacitor and inductor active emulators. Journal of Circuits, Systems and Computers, 27(11), 1850170.
  • Yang, X. J. (2019). General fractional derivatives: theory, methods and applications. Chapman and Hall/CRC.
  • Zhao, D., & Luo, M. (2017). General conformable fractional derivative and its physical interpretation. Calcolo, 54(3), 903-917.
Toplam 40 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Bilgi Sistemleri Geliştirme Metodolojileri ve Uygulamaları
Bölüm Araştırma Makalesi
Yazarlar

Ertuğrul Karakulak 0000-0001-5937-2114

Reşat Mutlu 0000-0003-0030-7136

Yayımlanma Tarihi 28 Aralık 2023
Gönderilme Tarihi 26 Kasım 2023
Kabul Tarihi 6 Aralık 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 24 Sayı: 2

Kaynak Göster

IEEE E. Karakulak ve R. Mutlu, “Spice Model of a Capacitor Modelled Using Conformal Fractional Order Derivative and its Usage in Simulation of a Parallel R-L-C_∝ Circuit”, TUJES, c. 24, sy. 2, ss. 49–56, 2023, doi: 10.59314/tujes.1396358.