Constant Phase Element in the Time Domain: The Problem of Initialization
The constant phase element (CPE) is found in most battery and supercapacitor equivalent circuit models proposed to interpret data in the frequency domain. When these models are used in the time domain, the initial conditions in the fractional differential equations must be correctly imposed. The ini...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/15/3/792 |
| _version_ | 1797488172341395456 |
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| author | Juan Antonio López-Villanueva Salvador Rodríguez Bolívar |
| author_facet | Juan Antonio López-Villanueva Salvador Rodríguez Bolívar |
| author_sort | Juan Antonio López-Villanueva |
| collection | DOAJ |
| description | The constant phase element (CPE) is found in most battery and supercapacitor equivalent circuit models proposed to interpret data in the frequency domain. When these models are used in the time domain, the initial conditions in the fractional differential equations must be correctly imposed. The initial state problem remains controversial and has been analyzed by various authors in the last two decades. This article attempts to clarify this problem by proposing a procedure to prepare the initial state and defining a decay function that reveals the effect of the initial state in several illustrative examples. This decay function depends on the previous history, which is reflected in the time needed to prepare the initial state and on the current profile assumed for this purpose. This effect of the initial state is difficult to separate and can lead to the misinterpretation of the CPE parameter values. |
| first_indexed | 2024-03-09T23:59:13Z |
| format | Article |
| id | doaj.art-587e74bb105748a4b99f7d22871e8680 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-09T23:59:13Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-587e74bb105748a4b99f7d22871e86802023-11-23T16:19:59ZengMDPI AGEnergies1996-10732022-01-0115379210.3390/en15030792Constant Phase Element in the Time Domain: The Problem of InitializationJuan Antonio López-Villanueva0Salvador Rodríguez Bolívar1Department of Electronics and Computer Technology, CITIC, University of Granada, 18071 Granada, SpainDepartment of Electronics and Computer Technology, CITIC, University of Granada, 18071 Granada, SpainThe constant phase element (CPE) is found in most battery and supercapacitor equivalent circuit models proposed to interpret data in the frequency domain. When these models are used in the time domain, the initial conditions in the fractional differential equations must be correctly imposed. The initial state problem remains controversial and has been analyzed by various authors in the last two decades. This article attempts to clarify this problem by proposing a procedure to prepare the initial state and defining a decay function that reveals the effect of the initial state in several illustrative examples. This decay function depends on the previous history, which is reflected in the time needed to prepare the initial state and on the current profile assumed for this purpose. This effect of the initial state is difficult to separate and can lead to the misinterpretation of the CPE parameter values.https://www.mdpi.com/1996-1073/15/3/792constant phase element (CPE)fractional calculustime domaininitial conditionsZARCsupercapacitor and battery modeling |
| spellingShingle | Juan Antonio López-Villanueva Salvador Rodríguez Bolívar Constant Phase Element in the Time Domain: The Problem of Initialization Energies constant phase element (CPE) fractional calculus time domain initial conditions ZARC supercapacitor and battery modeling |
| title | Constant Phase Element in the Time Domain: The Problem of Initialization |
| title_full | Constant Phase Element in the Time Domain: The Problem of Initialization |
| title_fullStr | Constant Phase Element in the Time Domain: The Problem of Initialization |
| title_full_unstemmed | Constant Phase Element in the Time Domain: The Problem of Initialization |
| title_short | Constant Phase Element in the Time Domain: The Problem of Initialization |
| title_sort | constant phase element in the time domain the problem of initialization |
| topic | constant phase element (CPE) fractional calculus time domain initial conditions ZARC supercapacitor and battery modeling |
| url | https://www.mdpi.com/1996-1073/15/3/792 |
| work_keys_str_mv | AT juanantoniolopezvillanueva constantphaseelementinthetimedomaintheproblemofinitialization AT salvadorrodriguezbolivar constantphaseelementinthetimedomaintheproblemofinitialization |