Analysis of the transient state in a circuit with supercapacitor

• Autorzy: Jakubowska A. , Walczak J.
• Konferencja: Computer Applications in Electrical Engineering (20-21.04.2015 ; Poznań, Polska)
• Języki publikacji: EN

Abstrakty

EN

The paper presents an analysis of the transient state in a simple circuit of RCα class with a supercapacitor. The behavior of supercapacitors differs from that of classic capacitors, which influences voltage and current waveforms in circuits containing them. The waveforms are described by relations of fractional-order integral-differential calculus. A simple fractional-order supercapacitor model, including its series internal resistance, has been assumed for the analysis. The obtained solution of the fractional-order differential equation describing the examined circuit is presented. The impact of different values of the parameter α on the solution has been analyzed too. The derived relations are illustrated by simulation examples for the circuit powered by a DC voltage source. This situation describes the supercapacitor charging process. Its charging time depends mainly on the value of fractional-order parameter α of the supercapacitor.

Słowa kluczowe

EN

fractional-order differential equation; first-order RCα circuit; supercapacitor

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Poznan University of Technology Academic Journals. Electrical Engineering
• Rocznik: 2015
• Tom: No. 81
• Strony: 71--77
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Jakubowska A.

• Silesian University of Technology

autor

Walczak J.

• Silesian University of Technology

Bibliografia

• [1] Burke A.: Ultracapacitors, why, how and where is the technology, Journal of Power Sources, Vol. 91, 2000, pp. 37-50.
• [2] Freeborn T.J., Elwakil A.S.: Measurement of supercapacitor fractional-order parameters from voltage-excited step response, IEEE Journal on Emerging and Selected Topics in CAS, Vol. 3, No. 3, September 2013, pp. 367-376.
• [3] Schafer J., Kruger K.: Modelling of lossy coils using fractional derivatives, Journal of Physics D: Applied Physics, Vol. 41, 2008 , pp. 367-376.
• [4] El-Sayed A.M.A., Nour H.M.: Fractional parallel RLC circuit, Alexandria Journal of Mathematics, Vol. 3, No. 1, June 2012, pp. 11-23.
• [5] Włodarczyk M., Zawadzki A.: RLC circuits in aspect of positive fractional derivatives, Scientific Works of the Silesian University of Technology Q, Electrical Engineering, vol.1, 2012, pp. 75-88 (in Polish).
• [6] Gomez F., Rosales J., Guia M.: RLC electrical circuit of non-integer order, Central European Journal of Physics, Springer, Vol. 11(10), 2013, pp. 1361-1365.
• [7] Ostalczyk P.: Zarys rachunku różniczkowo - całkowego ułamkowych rzędów. Teoria i zastosowanie w automatyce, Wyd. Politechniki Łódzkiej, Łódź, 2008.
• [8] Strona internetowa: http://pl.farnell.com/panasonic/eecf5r5h104 z dnia 28.11.2014.