Estimation of State-of-Charge and Energy Efficiency of Supercapacitors Using a 1-D Electrochemical Model

Abstract

Supercapacitors (SCs) have found a broad application spectrum due to their unique characteristics, including high power density and long cycle life [1]. Supercapacitors have been extensively studied to be used with Li-ion batteries for electric vehicle applications due to their complementary characteristics [1]. The energy management system of these applications relies on accurate information about the state-of-charge (SOC) and energy efficiency of the storage device at the cell level for effective monitoring and control. In the case of SCs, coulomb counting is the most commonly used SOC identification method; however, it entails certain challenges, including initial SOC information, effects of leakage current, and measurement noise [1]. Alongside improving the capacitive health diagnosis, it is critical to identify utilizable capacitance. During rapid charge/discharge of an SC, the ions in the electrolyte are immediately adsorbed/desorbed within the macro-pores, which leads to achieving the desired terminal voltage level instantaneously. However, this hinders ions’ penetration in the micropores, causing an inhomogeneous distribution of the ions across the electrodes, increasing the electrolyte resistance, resulting in poor utilizable capacitance and a drop in its energy efficiency [2]. Derived from a one-dimensional model [2, 3], a simplified SOC and energy efficiency estimation scheme of the SCs is proposed in this study. In the solid phases, the charge density of the SC is approximated as a function of its electrodes’ specific surface area, double-layer differential capacitance, and the potential drop across the double-layer. The SOC of the SCs can be expressed as a function of the solid phase charge density in the positive electrode or negative electrode, as defined in Eqn. (1). The energy efficiency (Eeff ) of the SCs can be expressed as a function of the ratio of bulk double-layer potential difference of the electrodes to the output terminal voltage change, as defined in Eqn. (2). SOC(t)=(ρ(t)/ρmax)×100 ...............(1); Eeff=(ΔΦ/ΔΦd/ΔV)×CrΔV2/2 ..............(2) where ρ and ρmax are the electrode charge density at t time and a fully charged state, respectively; ΔΦd is the bulk double-layer potential difference; ΔV is the terminal voltage change; and Cr is the rated capacitance.The electrochemical model is used to analyze the effectiveness of the proposed SOC and energy efficiency model considering a galvanostatic charge and discharge. In this limited scope, a concise response of the model compared to their respective standard methods is shown in Fig. 1. A SAFT 3500 F SC cell parameters are considered to perform the simulations [2, 3]. The results show that the SOC estimation scheme identifies the remaining charge without considering the initial SOC information. Similarly, the energy efficiency model calculates the energy received/delivered by the SC effectively. Figure 1