Lambert W function based closed-form expressions of supercapacitor electrical variables in constant power applications

Pedrayes, Joaquín F.; Melero, M.G.; Cano, José M.; Norniella, Joaquín G.; Duque, Salvador B.; Rojas, C.H.; Orcajo, Gonzalo A.

doi:10.1016/j.energy.2020.119364

Cited by 13 publications

(25 citation statements)

References 33 publications

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“…A complete mathematical formulation for the electrical analysis of SCs operating at constant power is presented in [46] by the authors of this paper. Nevertheless, the main electrical variables involved in the charge and discharge of an SC cell at constant power will be hereafter described for the sake of clarity.…”

Section: Electrical Analysis Of An Sc Cell Operating At Constant Powermentioning

confidence: 99%

“…A discharge at constant power, P > 0, is assumed to begin at t = 0. From the mathematical formulation obtained in [46], a dimensionless variable, g (t), can be defined as: The initial internal voltage of the cell is called U 0 . A discharge at constant power, P > 0, is assumed to begin at t = 0.…”

Section: Electrical Analysis Of An Sc Cell Operating At Constant Powermentioning

confidence: 99%

“…Moreover, Burke gave an alternative formula that produces excellent results in [45]. J. F. Pedrayes et al presented in [46] a complete analysis of the main electrical variables involved in the constant-power charge and discharge operation that enables the expression of any of those variables as a function of the rest.…”

Section: Introductionmentioning

confidence: 99%

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Supercapacitors in Constant-Power Applications: Mathematical Analysis for the Calculation of Temperature

et al. 2021

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A set of analytical equations for the calculation of the temperature in supercapacitors operating in constant-power applications is presented in this paper. Although the main operation modes of supercapacitors are constant-current and constant-power charge and discharge, this study was focused on the latter, since both sources and loads act as constant-power systems in a wide range of power conversion facilities. The starting point of this study is the classical supercapacitor model based on electrical and thermal parameters provided by manufacturers or also obtained by experimental means. The proposed mathematical analysis is based on the so-called incomplete gamma function that presents two major advantages over previously existing methods. Firstly, it is not necessary to solve any differential equations system by means of numerical methods, which reduces the required computational effort. Secondly, no simplifications to relief the calculations are made in the computation of any variable. The new formulation renders valid solutions even for high-power demand situations. Moreover, the temperature of the supercapacitor can be expressed as a function of time or any other electrical variable in the charging and discharging processes. Therefore, the proposed formulas are especially remarkable for the electrical and thermal dimensioning of supercapacitors.

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Section: Electrical Analysis Of An Sc Cell Operating At Constant Powermentioning

confidence: 99%

Section: Electrical Analysis Of An Sc Cell Operating At Constant Powermentioning

confidence: 99%

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Supercapacitors in Constant-Power Applications: Mathematical Analysis for the Calculation of Temperature

et al. 2021

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“…The array of capacitors was dimensioned and simulated. The dimensioning procedure was the result of previous studies in this field done by our research group [35][36][37]. A thorough Simulink™ model was developed, and the cells were selected to obtain the calculated energy with the minimum weight.…”

Section: Energy Storage System: Sc Array Dimensioning and Operationmentioning

confidence: 99%

“…As with all the other parts of the prototype, the SC array and the two-way converter, which managed the stored energy under the control of the FPGA, were simulated using Simulink™. The simulation model presented different levels for electrical and thermal analysis, as validated in [35][36][37]. The SCs' internal resistance and temperature were inputted into the model in order to analyse the behaviour of different types of SCs with different specifications.…”

Section: Energy Storage System: Sc Array Dimensioning and Operationmentioning

confidence: 99%

Preliminary Results of a Hybrid Thermoelectric Propulsion System for a Multirotor UAS with Active Rectifying, Electronic Throttle Control and Supercapacitors

et al. 2021

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The main drawback of unmanned aerial systems (UAS) is that almost their entire field of application is autonomous in terms of energy. Flights beyond 50 min are nearly impossible when using conventional energy storage systems (lithium-ion polymer or lithium-ion batteries). Several commercial products have been developed using hybrid systems (H-UAS). Although the improvement they have provided is undeniable, H-UAS in the present market are strongly limited by their low thrust vs. weight ratio, which is caused by limited electrical power generation and a non-optimal energy conversion with relatively low efficiencies. This paper reviews these systems to show the preliminary results of a prototype of hybrid generator which state-of-the-art electronics as well as a new approach using a supercapacitor (SC) array are used to save fuel, increase the thrust vs. weight ratio, optimize losses during conversion and prevent the overheating of the internal combustion unit (ICU). Whereas current generators mostly operate with the ICU at a constant speed, delivering maximum power, the presented prototype includes a throttle control system, and the engine works with a variable regime according to the power demand. Thus, fuel consumption is reduced, as well as heating and wear. The lifespan of the engine is also increased, and the time between maintenance operations is lengthened. The designed system provides almost twice the power of the hybrid current generators. The reduction in the RPM regime of the engine is achieved by means of a supercapacitor array that provides the necessary energy to keep the DC output power constant during the engine acceleration when the flight envelope experiences a perturbation or a sudden manoeuvre is performed by the pilot. To obtain maximum efficiency, the diode rectifiers and conventional converters used in the reviewed products are replaced by synchronous converters and rectifiers. The whole system is controlled by means of a FPGA where a specific control loop has been implemented for every device: ICU’s throttle, DC bus converter, charge and discharge of the SC’s array, cooling and monitoring of temperature for the cylinders heads, and on-line transmission, by means of a XBEE™ module, of all the monitored data to the flight ground station.

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Novel analytical STFT expressions for nonlinear power engineering problem solving

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2024

J Comput Electron

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Lambert W function based closed-form expressions of supercapacitor electrical variables in constant power applications

Cited by 13 publications

References 33 publications

Supercapacitors in Constant-Power Applications: Mathematical Analysis for the Calculation of Temperature

Supercapacitors in Constant-Power Applications: Mathematical Analysis for the Calculation of Temperature

Preliminary Results of a Hybrid Thermoelectric Propulsion System for a Multirotor UAS with Active Rectifying, Electronic Throttle Control and Supercapacitors

Novel analytical STFT expressions for nonlinear power engineering problem solving

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