Indonesian Journal of Innovation and Applied Sciences (IJIAS), 1 (3), 208-218 208 Volume 1 Issue 3 October (2021) DOI: 10.47540/ijias.v1i3.303 Page: 208 – 218 Comparative Analytical Modeling and Performance Investigation of Graphene-Based Super Capacitor with Four Traditional Batteries Arsal Mehmood Mehran University of Engineering and Technology, Jamshoro, Sindh, Pakistan Corresponding Author: Arsal Mehmood; Email: arsalmehmood0713@gmail.com A R T I C L E I N F O A B S T R A C T Keywords: Batteries, Comparative Study, Graphene, Lithium-Ion, Dynamic Model. Received : 26 July 2021 Revised : 25 September 2021 Accepted : 12 October 2021 Graphene, a magical development of 2004, has revolutionized today's energy storage technologies. It is nothing but a graphite two-dimensional (2D) allotropic pure carbon layer which is derived from a three-dimensional (3D) shape. Since batteries have been the most common storage device from the invention of the first electrical battery by an Italian physicist Alessandro Volta in 1799 A.D but batteries offer many drawbacks, such as length, weight, poor transient response, low power density, and high internal resistance. In this contrast, the impressive and unique properties of graphene supercapacitor such as high peak current, high surface area, high electrical conductivity, low internal resistance, high load current, long life cycle, high power density, low-temperature charging, and discharging make graphene supercapacitor a replacement of traditional energy storage devices and sets trend for the future. This analytical comparative analysis presents an overview between four traditional batteries and graphene-based supercapacitor. For this regard, dynamic models, modeling equations, and an integrated simulation model for batteries and graphene-supercapacitors under MATLAB/Simulink® 2020a environment is developed. In addition, the effect of temperature on battery output and graphene-supercapacitor is also addressed. INTRODUCTION Royal Swedish Academy of Science honored Noble Prize in Physics to Andre K. Geim and Konstantin S. Novoselov in 2010 for the efficient development, isolation, identification, and characterization of Graphene (Novoselov, et al., 2004; The Royal Swedish Academy of Sciences, 2010). Graphene is a 3-Dimensional (3D) isolated graphite layer to which 2-Dimensional (2D) honeycomb lattices are tightly packed (Novoselov, et al., 2005). Compared to the single atom diameter, Graphene layers are roughly 1/10 mm thin (graphenea.com, 2021). Three trivalent covalent bonds form graphite between the C-C atoms, where the length of the bond between the two carbon atoms is around 1.42A° (Geim & Novoselov, 2007). To form graphite, graphene layers combine with an internal planner spacing of 0.335nm (Khan, et al., 2020). Due to the unusual zero overlap difference between valance and conduction band, graphene is often called Unimetal (Mollik, et al., 2019; Prasad, et al., 2019). The young graphene modulus is approximate ~ 1 tera pascal. That makes graphene the stiffest material ever known to man. In addition, electron mobility up to 2500 (cm2)/vs (Baboselac, et al., 2017; Hinov, et al., 2018) is seen. Figure 1. Inner Structure of Graphene INDONESIAN JOURNAL OF INNOVATION AND APPLIED SCIENCES (IJIAS) Journal Homepage: https://ojs.literacyinstitute.org/index.php/ijias ISSN: 2775-4162 (Online) Research Article https://ojs.literacyinstitute.org/index.php/ijias http://issn.pdii.lipi.go.id/issn.cgi?daftar&1587190067&1&&2020 Indonesian Journal of Innovation and Applied Sciences (IJIAS), 1 (3), 208-218 209 Graphene is a Wonder material, the electrical conductivity of graphene is 1×106 times the copper conductor while its mobility is 1×103 times the silicon material (Singh & Kumar, 2017), thermal conductivity (3000-5000 W⁄Mk times graphite, diamond, copper & silver) (Zuo, et al., 2017), also known as “high temperature”. Since conductivity is 133ºC (Kurniawan, et al., 2016), transparency (2.3%) (Haizhou, 2017), and strength (strongest ever known material, which is 40 times stronger than diamond, 300 times than A36 structural steel). This enables it to be used in the design and manufacture of various field applications, such as batteries, solar panels, fuel cells, supercapacitors, sensors, photodetectors, coatings, loudspeakers, radiation shields, thermal control, cloaking, lubrication, water purification, etc. Figure 2. Different applications of Graphene Pollution problems and environmental effects as a long-term goal have led green energy a necessity of today's green world. Nowadays, more research is going on minimization of the exhaust of carbon dioxide. Renewable energy sources storage batteries are a promising solution for environmental and economic benefits. Figure 3. Energy content by different batteries Graphene supercapacitor or ultra-capacitor has capacitance better capacitance than an ordinary capacitor, electrical double-layer capacitors (EDLC). There are 3 types of capacitors Double layer capacitor, Hybrid capacitance, and Pseudo- capacitor. Below fig 4 represents the energy and power density of energy storage devices. Figure 4. Energy & power densities of different storage devices Graphene Supercapacitor has electrolyte ions to produce a high charge as compared to standard capacitors (Poonsuk & Pongyupinpanich, 2016). https://ieeexplore.ieee.org/author/37086131154 Indonesian Journal of Innovation and Applied Sciences (IJIAS), 1 (3), 208-218 210 Table 1. Comparison of general characteristics between the battery and the supercapacitor Graphene. Source: Barua, S., et al. (2015). The global energy paradigm is rapidly changing from fossil fuel to renewables. For the development of the best energy storage device, significant effort has been made from Lithium-Ion batteries, supercapacitors to Lithium-Ion capacitors. This research aims to observe the performance investigation-based comparative analysis for dynamic modeling, equations modeling and simulation modeling for batteries and grapheme- supercapacitors under MATLAB/simulink® 2020a environment. METHODS Graphene-Based Supercapacitor and Other Energy Storage System Analytical Comparison The specific energy density of the supercapacitor with graphene-based electrodes is approximately 85.6Wh/kg, while 136 Wh/kg at 80 0C is estimated at a current density of 1 A/g. Its high capacitance of 550 F/g and real surface area of 2675 m2/g is a significant property of graphene. Table 2. Energy density and power density comparisons. Battery Model in MATLAB/Simulink® 2020a MATLAB/Simulink® 2020a is used to model batteries for lead-acid, lithium-ion, nickel-cadmium, and nickel-metal hydride batteries. Below is the parameterized model representation of batteries. Figure 5. The generic dynamic model of batteries The following Stern equation and Tafel equation are implemented by the Supercapacitor block in MATLAB [21, 22]: 𝑁 = 𝑁𝑁𝑆𝑄𝑋2 𝑁𝑃𝑁 2𝜀𝜀°𝐴 + 𝑁𝑁𝑆2𝑅𝑇 𝐹 𝛼𝑟 sinh 𝑄 𝑁𝑃𝑁 2𝐴 8𝑅𝑇𝜀𝜀°𝐶 −𝑖𝐶 𝑡 = 𝐴𝑖0𝑒𝑥𝑝 𝛼𝐹 𝑉 𝑁𝑆 − 𝑉𝑚𝑎𝑥 𝑁𝑆 − ∆𝑉 𝑅𝑇 𝑁 For graphene-based supercapacitor modeling, the two general equations for traditional supercapacitors are used. Where parameters are represented: N = Number of layers of electrodes NS = Number of series supercapacitor NP = Number of parallel supercapacitors Q = Electric charge in colomb ε = Permittivity of material in coloumb ε = Permittivity of free space -8.85 x 1012 F⁄m A = Interfacial area between electrodes and electrolyte (m2) R = Ideal gas constant -5.189 x 1019 eVK-1 mol -1 X2 = Helmholtz layer length (m) Indonesian Journal of Innovation and Applied Sciences (IJIAS), 1 (3), 208-218 211 T = Operating temperature (in Celsius) α = Charge transfer coefficient, Tafel equation (0< α <1) r = Molecular radius =X2 NA = Avagado constant -6.02214129 x 10 23 mol-1 i0 = Exchange current density = 𝑖𝑓 𝐴 𝐴𝑚 2 if = Leakage current in Ampere Vmax = Surge voltage – Maximum voltage of the supercapacitor (V) V = Supercapacitor rated voltage ∆V = Over potential (V) It is possible to measure the supercapacitor State of charge (SOC) using: 𝑆𝑂𝐶 = 𝑄𝑖𝑛𝑖𝑡 − 𝑖 𝜏 𝑑𝜏 𝑡 0 𝑄𝑇 × 100 Hypotheses taken for modeling are: 1. No impact on temperature. 2. No ageing results. 3. Cell balancing has not been planned. The Charging Model Overview 1. Lead-Acid 𝐸𝑏𝑎𝑡𝑡 = 𝐸° −𝐾 𝑄 𝑖𝑡0.1. 𝑄 . 𝑖∗ −𝐾 𝑄 𝑄 −𝑖𝑡 . 𝑖𝑡 + 𝐸𝑥𝑝(𝑡) 2. Lithium-Ion 𝐸𝑏𝑎𝑡𝑡 = 𝐸° −𝐾 𝑄 𝑖𝑡0.1. 𝑄 . 𝑖∗ −𝐾 𝑄 �㠸 −𝑖𝑡 . 𝑖𝑡 + 𝐴𝑒𝑥𝑝(−𝐵∙ 𝑖𝑡) 3. NiMH and NiCd 𝐸𝑏𝑎𝑡𝑡 = 𝐸° −𝐾 𝑄 |𝑖𝑡|0.1. 𝑄 . 𝑖∗ −𝐾 𝑄 𝑄 −𝑖𝑡 . 𝑖𝑡 + 𝐸𝑥𝑝(𝑡) Different Batteries Mathematical Equations 1. Lead Acid Model Discharge Model (i*>0) 𝑓 1 𝑖𝑡,𝑖 ∗ , 𝑖, 𝐸𝑥𝑝 = 𝐸° − �ਗ਼ ∙ 𝑄 𝑄 − 𝑖𝑡 ∙ 𝑖 ∗ 𝐾∙ 𝑄 𝑄 − 𝑖𝑡 𝑖𝑡 + 𝐿𝑎𝑝𝑙𝑎𝑐𝑒 −1 𝐸𝑥𝑝 𝑠 𝑆𝑒𝑐 𝑠 ∙ 0 Charge Model (i*<0) 𝑓 2 𝑖𝑡, 𝑖 ∗ , 𝑖, 𝐸𝑥𝑝 = 𝐸° − 𝐾 ∙ 𝑄 𝑖𝑡 + 0.1𝑄 ∙ 𝑖 ∗ −𝐾 ∙ 𝑄 𝑄 −𝑖𝑡 ∙ 𝑖𝑡 + 𝐿𝑎𝑝𝑙𝑎𝑐𝑒 −1 𝐸𝑥𝑝 𝑠 𝑆𝑒𝑐 𝑠 ∙ 1 𝑠 2. Lithium-Ion Model Discharge Model (i*>0) 𝑓 1 𝑖𝑡, 𝑖 ∗ , 𝑖 = 𝐸° − 𝐾∙ 𝑄 𝑄 − 𝑖𝑡 ∙ 𝑖 ∗ −𝐾∙ 𝑄 𝑄−𝑖𝑡 ∙ 𝑖𝑡 + 𝐴𝑒𝑥𝑝 −𝐵, 𝑖𝑡 Charge Model (i*<0) 𝑓 2 𝑖𝑡, 𝑖 ∗ , 𝑖 = 𝐸° − 𝐾∙ 𝑄 𝑖𝑡 + 0.1𝑄 ∙ 𝑖 ∗ −𝐾∙ 𝑄 𝑄 −𝑖𝑡 ∙ 𝑖𝑡 + 𝐴𝑒𝑥𝑝 −𝐵, 𝑖𝑡 3. Nickel-Cadmium & Nickel-Metal-Hydride Model Discharge Model (i*>0) 𝑓 1 𝑖𝑡, 𝑖 ∗ , 𝑖, 𝐸𝑥𝑝 = 𝐸° − 𝐾 ∙ 𝑄 𝑄−𝑖𝑡 ∙ 𝑖 ∗ −𝐾 ∙ 𝑄 𝑄 − 𝑖𝑡 ∙ 𝑖𝑡 + 𝐿𝑎𝑝𝑙𝑎𝑐𝑒 −1 𝐸𝑥𝑝 𝑠 𝑆𝑒𝑐 𝑠 ∙ 0 Indonesian Journal of Innovation and Applied Sciences (IJIAS), 1 (3), 208-218 212 Charge Model (i*<0) 𝑓 2 𝑖𝑡, 𝑖 ∗ , 𝑖, 𝐸𝑥𝑝 = 𝐸° − 𝐾∙ 𝑄 | 𝑖𝑡 | + 0.1𝑄 ∙ 𝑖 ∗ −𝐾∙ 𝑄 𝑄 −𝑖𝑡 ∙ 𝑖𝑡 + 𝐿𝑎𝑝𝑙𝑎𝑐𝑒 −1 𝐸𝑥𝑝 𝑠 𝑆𝑒𝑐 𝑠 ∙ 1 𝑠 When: E° = Battery Constant Voltage (V) Exp(s) = Exponential Zone dynamic (V) Sel(s) = Battery Mode Sel(s) = 0 (Represent battery discharging) Sel(s) = 1(Represent battery charging) K = Polarization Constant 𝐴𝐻 −1 = 𝐸𝐹𝑢𝑙𝑙 − 𝐸𝑁𝑜𝑚 + 𝐴 𝑒𝑥𝑝 −𝐵, 𝑄𝑁𝑜𝑚 − 1 ∙ 𝑄 −𝑄𝑁𝑜𝑚 𝑄 𝑁𝑜𝑚 Q = Maximum battery capacity (Ah) it = Extracted capacity (Ah) A = Exponential voltage (V) B = Exponential capacity (Ah-1) i = Battery current (A) RESULTS AND DISCUSSION Discharging Characteristics of Batteries after Simulation For various batteries, the discharge characteristics were analyzed. Three sections form a standard discharge curve: Discharge curve, Nominal area, and Exponential area. Lead Acid Battery Figure 6. Lead Acid Battery Discharge Characteristics Indonesian Journal of Innovation and Applied Sciences (IJIAS), 1 (3), 208-218 213 Lithium-Ion Battery Figure 7. Characteristics of Lithium-Ion Battery Discharge Nickel-Cadmium Battery Figure 8. Nickel Cadmium Battery Discharge Characteristics Indonesian Journal of Innovation and Applied Sciences (IJIAS), 1 (3), 208-218 214 Nickel-Metal-Hydride Figure 9. Nickel Metal Hydride Battery Discharge Characteristics When the battery current is negative, the battery will display the charge functionality. Using the following equations. 𝑂𝐶𝑃𝑝𝑜𝑠 = 4.19829 + 0.0565661 tanh −14.556𝑦 + 8.60942 − 0.0275479 1 0.998432 − 𝑦 0.492465 − 1.90111 − 0.157123𝑒 −0.04738 𝑦 8 + 0.810239𝑒 −40 𝑦−0.133875 Range of y is: 0.4