An Equivalent Circuit of Carbon Electrode Supercapacitors

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1 An Equivalent Circuit of Carbon Electrode Supercapacitors Usman S.Sani*, Ibrahim H.Shanono* *Department of Electrical Engineering, Bayero University, Kano, P.M.B. 3011, Nigeria. Abstract Impedance spectroscopy test was performed on a commercial carbon electrode supercapacitor. Data obtained was presented in form of a Nyquist plot which was then modeled into an equivalent circuit. Six electro-chemical double layer supercapacitors were then fabricated. The fabricated supercapacitors were modeled in the same manner. All the supercapacitors fitted the equivalent model with errors in the form of chi square ranging from to , showing how the equivalent circuit models an approximate behavior of a supercapacitor. Unlike in most cases where by researchers show equivalent circuits of supercapacitors without accounting for the value of each circuit element, the value of each circuit element is shown in this work. Keywords:Equivalent circuit, Impedance spectroscopy, Tanhyperbole Introduction Supercapacitors are well known for their high energy and power densities, long lifetime as well as great cycle number. Typical applications of supercapacitors include memory backup to bridge short power interruptions, improving the current handling of a battery as well as regenerative braking on vehicles. In the field of telecommunication it is used to supply power during signal transmission because more power is needed during transmission than during reception. Though supercapacitors perform well, there is a need for improvement at higher frequencies. This is due to the fact that the supercapacitor no longer behaves as a capacitor at high frequencies rather its behaviour changes closely to that of a resistor. So also, resistances in supercapacitors have to be minimized to ensure maximum power delivery [1]-[7]. An important aspect of study in a supercapacitor is its impedance which has an imaginary part that is inversely proportional to its capacitance value. The impedance is frequency dependant making the capacitance to be dependant on frequency too. The impedance considered is thus a complex number consisting of a real part and a frequency dependant imaginary part indicated by equation 1. The impedance of the supercapacitor is determined by experimentation process known as the Impedance Spectroscopy Study from which analysis is done to obtain the supercapacitor s value and other parameters [7],[ 8]. (1) II. Impedance spectroscopy Impedance spectroscopy involves taking measurements of impedance for a device or material over a certain frequency range. It is applied in the field of electrochemistry for material characterization and new materials development, a process which requires continuous measurements until the target goal is achieved. It involves conversion of the signals involved from time domain to the frequency domain which are voltage and current. A sinusoidal signal generated by a signal generator is applied to the system/device/material and the resulting signal is recorded by a phase- sensitive recording device or by any other means. The input control signal may either be a voltage signal or a current signal. If the applied signal is a voltage source, the impedance spectroscopy is termed potentiostatic impedance spectroscopy. Likewise for an applied current signal it is termed galvanostatic impedance 631

spectroscopy. The impedance is determined by finding the ratio of the voltage to the current and doesn t matter on which parameter amongst them is the input or the output.

2 spectroscopy. The impedance is determined by finding the ratio of the voltage to the current and doesn t matter on which parameter amongst them is the input or the output. Thus any of the impedance spectroscopy measurement techniques can be used [7]-[12]. The results obtained from measurements are used to draw a Nyquist plot, which is a plot of the imaginary impedance (Z ) versus the real impedance (Z ) as a function of frequency. Oscilloscopes have been used to obtain plots in a case where the input and output signals are connected to the plates of an oscilloscope. The resulting plot is called a Lissajous figure which takes the form of an ellipse. Further analysis is done based on which of the signals is connected to the vertical plate and which is connected to the horizontal plate. This method is called the Lissajous analysis. Bode plots are often used in some cases [7]-[12]. Nowadays, computers are used in measuring impedance by the application of Fast Fourier Transform (FFT) in which the setup consists of an embedded measurement instrument connected to a computer workstation which has software installed for data presentation and analysis. The embedded measurement system contains analogue to digital converters, instrumentation amplifiers and a data acquisition board which transfers data to the work station computer as well as process any command issued via software in order to control the experimental setup [7]-[12]. Methodology Impedance spectroscopy was first carried out on a commercial supercapacitor using VersaSTAT 3 and its accompanying V3-studio software. The purpose was to model it first such that any other supercapacitor could be modeled based on results obtained. A GS113 capxxsupercapacitor was selected for the purpose. The supercapacitor is a thin prismatic packaged supercapacitor suitable for application in portable devices such as mobile phone, camera, digital music players, PCMCIA cards, notebook PCs, location tracking devices and other automotive applications etc. Due to the type of packaging used capxxsupercapacitors are well known for their low equivalent series resistance implying that they permit maximum power delivery [13]. An equivalent circuit model was generated for the data obtained using Zsimpwin software. Figure 1: Picture of the Capxx prismatic supercapacitor. The Nyquist plot from the impedance spectroscopy of the capxxsupercapacitor and data obtained from equivalent circuit fitting is shown below: 632

3 Figure 2: Impedance spectra of capxxsupercapacitor with fitted equivalent circuit data. Figure 2 above showed a legend composed of Z, Msd and Z, Calc. Z, Msd is the measured impedance spectra, while Z, Calc is the data for the fitted equivalent circuit. It will be noticed that the data was almost the same indicating how matched the measured data is to the fitted equivalent circuit data. The fitted circuit model resulted by matching the data obtained by measurements against all the circuit models available in the software and selecting the best among them. The software Zsimpwin by iteration process computes the global minimum chi square ( ) for a selected circuit and shows the optimal circuit parameters using the Down-hill Simplex Method [14]. Since is the sum of squared errors divided by the variance [15], the circuit that gave the least chi square was selected as the appropriate model. A kind of circuit coding system was used to indicate a circuit by symbols rather than by figures. In such codes, elements in series are represented by a concatenation of their symbol letters. Parallel components are bracketed and concatenated with other series or parallel elements. In the case where the first element or first set of elements in series are in parallel with the remaining circuit components, the whole expression is put into bracket. Table I below shows the list of circuit elements used for equivalent circuit fitting. Table 1: Circuit elements used for modelling impedance spectroscopy data. Description Symbol Parameter Resistance R R Capacitance C C Inductance L L Warburg W Yo Constant phase Element Q Yo, α Tanhyperbole T Yo, B Cothyperbole O Yo, B Gerischer G Yo, B 633

4 . The equivalent circuit model for the capxxsupercapacitor and its code is shown below: Circuit code: R(CR)(CR)T Figure 3: Equivalent circuit model of capxxsupercapacitor. For easy identification, each of the circuit components was given a number designation. Numbers 0 to 5 were used as shown below: R(CR)(CR)T Table 2 shows each parameter, its designated number and value. Table 2: Equivalent circuit parameters of the capxxsupercapacitor Number designation Component Parameter Value 0 R( ) Solution resistance C(F) Double layer capacitance R( ) Solution resistance C(F) Double layer capacitance R( ) Solution resistance T Yo(S) Admittance B(s) Time constant Six carbon electrode supercapacitors were fabricated, each of which was given a letter designation from A to F. Impedance spectroscopy test was performed on each supercapacitor and the results were fitted unto the equivalent circuit that matched the capxxsupercapacitor. The results are shown below: 634

5 Figure 4: Impedance spectra of supercapacitor A with fitted equivalent circuit data. Figure 5: Impedance spectra of supercapacitor B with fitted equivalent circuit data. Figure 6: Impedance spectra of supercapacitor C with fitted equivalent circuit data. 635

6 Figure 7: Impedance spectra of supercapacitor D with fitted equivalent circuit data. Figure 8: Impedance spectra of supercapacitor E with fitted equivalent circuit data. 636

7 Figure 9: Impedance spectra of supercapacitor F with fitted equivalent circuit data. The equivalent circuit parameters of each supercapacitor are shown in the table below: Table 3: Values of equivalent circuit parameters of the fabricated supercapacitors N0. Component Supercapacitor A B C D E F 0 R( ) C(F) µ µ R( ) C(F) µ µ µ 4226µ 233.3µ 4 R( ) T Yo(S) B(s) The chi-square ( ) value obtained from the equivalent circuit fitting of each supercapacitor is shown below: Table 4:Chi square values obtained from the equivalent circuit fitting of each supercapacitor Supercapacitor capxx A B C D E F Chi-square X

8 Discussion of Results From the equivalent circuit fitting it was seen that the supercapacitor could be represented with a resistance in series with 2 time constants and a Tanhyperbole (T) element. The presence of the T element indicates that finite diffusion takes place in the supercapacitor. This is a sort of an impurity in an electrochemical double layer supercapacitor. But the level of diffusion is not much because a T element describes a process with a limited number of electro-active species. The moment they are finished, they can t be replenished. Resistors with designation numbers 0, 2 and 4 are solution resistances together with contact resistance and separator resistance. By mentioning the term solution resistance, the electrolyte resistance and charge transfer resistance are being referred to. This is because the fitting was done using software and one can t differentiate the contributions of each resistance. Meanwhile a totality of there effects is shown by the resistors. The same also applies to the double layer capacitors. Conclusions Impedance spectroscopy tests were carried out on seven supercapacitors, the result of which was used in determining an equivalent circuit that models the behavior of a supercapacitor. Results showed that a supercapacitor can be represented by an equivalent circuit consisting of a resistor in series with two time constants and a Tanhyperbole. References F.B. Sillars, S. I. Fletcher, M. Mirzaeian, P.J. Hall, Ionic Liquid Electrolytes toenhance Supercapacitor Performance, Department of Chemical and Process Engineering, University of Strathclyde, Glasgow, G1 1XJ, Scotland, UK, pp1, duler/abstracts/215/0151.pdf, retrieved may 31, A. Schneuwly, R. Gallay, Properties and applications of supercapacitors from the state-ofthe- art to future trends, 2000, Proceeding PCIM, pp1-8, f, retrieved June 1, I. Buchmann, What's the role of the Supercapacitor?, BatteryUniversity.com, 2005, 8.htm, retrieved June 1, P. Dewsbury, Designing with Super Capacitors, Advanced Analogic Technologies, Inc, pp1, nicalarticles/ta-111.pdf, retrieved June 4, 2010 J. Dong, T.H.Xu, H.M. Chen, S.L. Qiu, Development & Application Of Ultra- Capacitor Separator, Shanghai Shilong Hi-Tech Co., Ltd Chinese Academy of Sciences (CAS), P.R China, pp7-32, ong.pdf, retrieved June 4, L. Guzella, A. Sciarretta, Vehicle propulsion systems:introduction to modelling and optimization, Vol. 10, Springer, 2007, pp330. B.E Conway, Electrochemical Supercapacitors:ScientificFundamentals and Technological Applications, Kluwer academic/ Plenum publishers, 1999, pp Gamry Instruments, Electrochemical ImpedanceSpectroscopy Theory: A Primer, GamryInstruments, retrieved May 30, Claude Gabrielli, Identification of Electrochemical Processes by Frequency Response Analysis, Centre National de la RechercheScientifique, France, 1984, pp

9 E. Barsoukov, J. R. Macdonald, Impedance spectroscopy: theory, experiment and applications, John Wiley and sons, Inc, Hoboken, New Jersey, 2005, pp M.E. Orazem, B. Tribollet, ElectrochemicalImpedance Spectroscopy, John Wiley and sons, Inc, Hoboken, New Jersey, 2008, pp VersaSTAT3 & V3-Studio Hardware and Software Manual (product document). Zsimpwin software User manual, pp3-7. J. E. Nesbitt, Statistical Guides in educational Research No.2: Chi-square, Manchester University Press, 1966, pp1. 639

173 Electrochemical Impedance Spectroscopy Goals Experimental Apparatus Background Electrochemical impedance spectroscopy

Goals 173 Electrochemical Impedance Spectroscopy XXGoals To learn the effect of placing capacitors and resistors in series and parallel To model electrochemical impedance spectroscopy data XXExperimental