Open AccessImpact of fractional order over time response for DC-DC converters with fractional capacitors
Author(s) -
Jesús M. López-Lezama,
David Esteban Betancur Herrera,
Juan Bernardo Cano,
Nicolás Muñóz-Galeano
Publication year - 2020
Publication title -
scientia et technica
Language(s) - English
Resource type - Journals
eISSN - 2344-7214
pISSN - 0122-1701
DOI - 10.22517/23447214.23591
Subject(s) - capacitor , fractional calculus , ripple , inductor , control theory (sociology) , converters , mathematics , voltage , physics , mathematical analysis , computer science , control (management) , quantum mechanics , artificial intelligence
This paper analyses the impact of fractional orders of derivatives over the response of DC-DC converters which includes fractional capacitors and their parasitic losses for a more realistic approximation of the converter. A fractional model is proposed and is applied for a Boost DC-DC with a fractional capacitor in its DC bus. The fractional model is obtained using Kirchhoff laws and applying the conventional switching model. Then, the resulting set of fractional differential equations is in the Caputo’s sense and was solved using Wavelets method. Solutions were appropriately shown using 3D representations, varying the duty cycle and the fractional order to determine the behaviour of the fractional capacitor voltage, inductor current and output voltage. Ripples and steady state values were determined. Results show high dependence of the fractional order in the variables related to the voltage in the fractional capacitor. With respect to the current, results show that the fractional order does not significantly affect its steady state and ripple.