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## An analytical approximation of the transient response of a voltage dependent supercapacitor model

Barić, Tomislav; Glavaš, Hrvoje; Kljajić, Ružica
An analytical approximation of the transient response of a voltage dependent supercapacitor model // Engineering review (Technical Faculty University of Rijeka), 39 (2019), 3; 310-319 doi:10.30765/er.39.3.12 (recenziran, članak, znanstveni)

Naslov
An analytical approximation of the transient response of a voltage dependent supercapacitor model

Autori
Barić, Tomislav ; Glavaš, Hrvoje ; Kljajić, Ružica

Izvornik
Engineering review (Technical Faculty University of Rijeka) (1330-9587) 39 (2019), 3; 310-319

Ključne riječi
Differential equation ; Supercapacitor ; Ultracapacitor ; Voltage dependent model

Sažetak
Supercapacitors are well known for their voltage dependent capacity. Due to this, it is not possible to obtain the exact analytical solution of the nonlinear differential equation which describes the transient charging and discharging. For this reason, approximations of differential equations must be carried out in order to obtain an approximate analytical solution. The focus of this paper is on a different approach. Instead of approximating the differential equation and obtaining analytical expressions for such approximations, an intuitive approach is chosen. This approach is based on the separation of the initial response from the rest of the transient phenomenon. Both parts of the transient phenomenon are described with adequate functions. Using appropriate weight functions, both functions are combined into a single function that describes the whole transient phenomenon. As shown in the paper, such an approach gives an excellent description of the whole transient. Also, it provides simpler expressions compared to those obtained by approximation of the nonlinear differential equation. With respect to their accuracy, these expressions do not lag behind the aforementioned approach. The validity of the presented analytical expressions was confirmed by comparing their results with those obtained by numerically solving the nonlinear differential equation.

Izvorni jezik
Engleski

Znanstvena područja
Elektrotehnika

Ustanove
Fakultet elektrotehnike, računarstva i informacijskih tehnologija Osijek

#### Časopis indeksira:

• Web of Science Core Collection (WoSCC)
• Emerging Sources Citation Index (ESCI)
• Scopus