Fractional model of an electrochemical capacitor

Martynyuk, Valeriy; Ortigueira, Manuel Duarte

doi:10.1016/j.sigpro.2014.02.021

Cited by 107 publications

(48 citation statements)

References 13 publications

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“…This model is unique in that the order of the third CPE with impedance 1=C 3 s ða 1 þa 2 Þ is greater than 1, with a value of a 1 þ a 2 ¼ 0:2848 þ 0:866 ¼ 1:1508 reported in [22], which has not previously been explored in literature. The models given in Fig.…”

Section: Introductionmentioning

confidence: 98%

“…-Impedance modeling of nickel finer mesh for simulation and design of elements in pulse power systems [18]; -Modeling high power performance to characterize super-capacitor capabilities [19]; -Modeling the impedance of super-capacitors over finite frequency bands to reduce the required model parameters [20][21][22]; -Modeling the transient characteristics from very small (seconds) [23] to very large (months) timescales [24]; -Measurement of fractional characteristics from transient behavior [25,26]; -Modeling and control of super-capacitor systems using fractional state-space models [27] and fractional linear systems [28,29]; -Implementation in a buck-boost converter for power electronics [30].…”

Section: Introductionmentioning

confidence: 99%

“…This model was used to represent the behavior of an HE0120C-0027A 120F super-capacitor in the frequency band 1 mHz-1 kHz [22]. This model is unique in that the order of the third CPE with impedance 1=C 3 s ða 1 þa 2 Þ is greater than 1, with a value of a 1 þ a 2 ¼ 0:2848 þ 0:866 ¼ 1:1508 reported in [22], which has not previously been explored in literature.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fractional-order models of supercapacitors, batteries and fuel cells: a survey

Freeborn

Maundy

Elwakil

2015

Mater Renew Sustain Energy

166

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This paper surveys fractional-order electric circuit models that have been reported in the literature to best fit experimentally collected impedance data from energy storage and generation elements, including super-capacitors, batteries, and fuel cells. In all surveyed models, the employment of fractional-order capacitors, also known as constant phase elements, is imperative not only to the accuracy of the model but to reflect the physical electrochemical properties of the device.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fractional-order models of supercapacitors, batteries and fuel cells: a survey

Freeborn

Maundy

Elwakil

2015

Mater Renew Sustain Energy

166

View full text Add to dashboard Cite

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“…However, such similar phenomenon has been existing in many other systems such as electrode/electrolyte-based systems including the Warburg impedance and other similar interfaces [32,30,18], and those systems with electrodes connected in porous channels [17], where the total impedance follows a power law that is fractional degree in value. The realization of such fractional-power-law impedances was generally described by Wang [31] as a resistor-capacitor (RC) ladder network which can be mathematically expressed using continued fraction expansions which would end up in a circuit having a constant phase throughout the frequency spectrum, or basically a fractional-order element with a fractional-order impedance of the form Z (jω) = (jω) α , (2.1) where 0 < α < 1.…”

Section: General Theory Of Insulation Resistancementioning

confidence: 69%

Novel Polarization Index Evaluation Formula and Fractional-Order Dynamics in Electric Motor Insulation Resistance

Gonzalez¹,

Petráš

Ortigueira

2018

FCAA

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One of the common test metrics prescribed by IEEE Std 43 for testing motor insulation is the Polarization Index (P.I.) which evaluates the “goodness” of the machine’s insulation resistance by getting the ratio of the insulation resistance measured upon reaching t2 > 0 minutes (IRt2) from t1 > 0 minutes (IRt2) for t2 > t1 > 0, after applying a DC step voltage. However, such definition varies from different manufacturers and operators despite of decades of research in this area because the values of t1 and t2 remain to be uncertain. It is hypothesized in this paper that the main cause of having various P.I. definitions in literature is due to the lack of understanding of the electric motor’s dynamics at a systems level which is usually assumed to follow the dynamics of the exponential function. As a result, we introduce in this paper the fractional dynamics of an electric motor insulation resistance that could be represented by fractional-order model and where the resistance follows the property of a Mittag-Leffler function rather than an exponential function as observed on the tests done on a 415-V permanent magnet synchronous motor (PMSM). As a result, a new PMSM health measure called the Three-Point Polarization Index (3PPI) is proposed.

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“…All elements in the 2 × 2 impedance matrix are measured in Ω and if 11 = 22 the network is known to be symmetrical while if 12 = 21 it is known to be reciprocal. However, with the increasing use of fractional-order impedance models, particularly in representing supercapacitors [3,4], energy storage devices [5], oscillators [6], filters [7], and new electromagnetic charts [8], it is possible that the elements of ( ) are of fractional order. Consider the simple case of the grounded impedance , shown in Figure 2(a).…”

Section: Introductionmentioning

confidence: 99%