Frequency dependent piecewise fractional-order modelling of ultracapacitors using hybrid optimization and fuzzy clustering

Kumar, Mano Ranjan; Ghosh, Subhojit; Das, Shantanu

doi:10.1016/j.jpowsour.2016.10.024

Cited by 25 publications

(16 citation statements)

References 19 publications

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“…The technique of multiple swarms of particles used in Hu et al optimizes the parameters of the SC modeled with twelve different approaches. The hybrid optimization based approach was introduced in other works …”

Section: Introductionmentioning

confidence: 99%

“…The hybrid optimization based approach was introduced in other works. [13][14][15] In this article, the behavior of an SC is modeled using a basic electrical circuit with an equivalent resistance in parallel (Rp), an equivalent resistance in series (Rs), and a capacitor (C). These three parameters are estimated for five different mathematical approaches by applying interior point optimization and using a set of experimental data.…”

Section: Introductionmentioning

confidence: 99%

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Comparative analysis to determine the accuracy of fractional derivatives in modeling supercapacitors

Carreño

Rosales

Merchan

et al. 2019

Circuit Theory & Apps

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Summary In this paper, we study a supercapacitor model represented by an equivalent RC circuit considering five different types of derivatives: Caputo, Caputo‐Fabrizio, and Atangana‐Baleanu fractional derivatives and the conformable and integer‐order derivatives. A set of experimental data from six commercial supercapacitors are used to estimate the parameter values for each derivative model by applying interior point optimization. The results show that the most accurate approach is achieved with the conformable derivative followed by the Caputo fractional derivative.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparative analysis to determine the accuracy of fractional derivatives in modeling supercapacitors

Carreño

Rosales

Merchan

et al. 2019

Circuit Theory & Apps

View full text Add to dashboard Cite

show abstract

“…Considering different dimensions and orders of magnitude, the data must be standardized as Equation (1) [27].…”

Section: Fuzzy Clusteringmentioning

confidence: 99%

Short-Term Load Forecasting for Electric Bus Charging Stations Based on Fuzzy Clustering and Least Squares Support Vector Machine Optimized by Wolf Pack Algorithm

Zhang

2018

Energies

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Accurate short-term load forecasting is of momentous significance to ensure safe and economic operation of quick-change electric bus (e-bus) charging stations. In order to improve the accuracy and stability of load prediction, this paper proposes a hybrid model that combines fuzzy clustering (FC), least squares support vector machine (LSSVM), and wolf pack algorithm (WPA). On the basis of load characteristics analysis for e-bus charging stations, FC is adopted to extract samples on similar days, which can not only avoid the blindness of selecting similar days by experience, but can also overcome the adverse effects of unconventional load data caused by a sudden change of factors on training. Then, WPA with good global convergence and computational robustness is employed to optimize the parameters of LSSVM. Thus, a novel hybrid load forecasting model for quick-change e-bus charging stations is built, namely FC-WPA-LSSVM. To verify the developed model, two case studies are used for model construction and testing. The simulation test results prove that the proposed model can obtain high prediction accuracy and ideal stability.

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“…This fractional derivative Expression (5) gives a new capacitor theory [5] and we utilize this above Formula (5) to find characteristics of super-capacitors, like the variation of n with the current excitation, and the efficiency of the energy discharged to the energy stored [13] [17], has implication in dissipation [5] theory of di-electrics that we will not cover here. We state that while classical capacitor unit is in Farad, the n C the "fractional capacity" is in units of…”

Section: Obtaining Fractional Derivative Directly From Curie-von Schwmentioning

confidence: 99%

“…The observations of power law relaxation are also made in the experiments and studies with super-capacitors [13] [14] [15] [16] [17]. These studies also indicate the fractional calculus is used as constituent expression to describe super-capacitors.…”

Section: Introductionmentioning

confidence: 97%

Revisiting the Curie-Von Schweidler Law for Dielectric Relaxation and Derivation of Distribution Function for Relaxation Rates as Zipf’s Power Law and Manifestation of Fractional Differential Equation for Capacitor

Das¹

2017

JMP

Self Cite

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The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric-as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19 th Century. This relaxation law is also regarded as "universal-law" for dielectric relaxations; and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf's power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.

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Frequency dependent piecewise fractional-order modelling of ultracapacitors using hybrid optimization and fuzzy clustering

Cited by 25 publications

References 19 publications

Comparative analysis to determine the accuracy of fractional derivatives in modeling supercapacitors

Comparative analysis to determine the accuracy of fractional derivatives in modeling supercapacitors

Short-Term Load Forecasting for Electric Bus Charging Stations Based on Fuzzy Clustering and Least Squares Support Vector Machine Optimized by Wolf Pack Algorithm

Revisiting the Curie-Von Schweidler Law for Dielectric Relaxation and Derivation of Distribution Function for Relaxation Rates as Zipf’s Power Law and Manifestation of Fractional Differential Equation for Capacitor

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