The continuous increase in energy consumption and the harmful impacts of fossil fuels to the environment have stimulated the efforts to develop the devices and systems for the storage of green and renewable energies. Supercapacitors, which are known as electrochemical capacitors, have considerable advantages over metal-ion batteries, including high power density, fast charging/discharging rate and environment-friendly [[1], [2], [3], [4], [5], [6]]. Various techniques have been used to measure the performance of supercapacitors, including capacitance, resistance, energy and powder densities. Generally, the electrochemical performance of supercapacitors can be characterized with electrochemical impedance spectroscopy (EIS), cyclic voltammetry (CV) and galvanostatic charge/discharge (GCD) [7]. EIS is an effective technique to discern different storage mechanisms [8], while the interpretation of the EIS data remains a great challenge. CV and GCD techniques play important roles in analyzing the performance of the devices and systems for energy storage and can be used to characterize the capacitive and resistive behaviors of supercapacitors.

Pell et al. [9] studied the effects of non-aqueous electrolyte of four different concentrations on the performance of supercapacitors with CV and GCD techniques. They [10] later evaluated the internal resistance of the porous electrodes of supercapacitors from the distribution of electrolyte, using CV and GCD curves. Their results show that both the charge-storage capacity and the energy density of the porous electrodes decrease with the increase of the CV sweep rate under constant and variable electrolyte resistances. Boonpakdee et al. [11] examined the non-ideal behavior of micro-supercapacitors, using an equivalent circuit and attributed the asymmetrical behavior of the CV curves to the redistribution of electrolyte ions near the electrodes. They suggested that the capacitance obtained from the equivalent circuit is more accurate than that from the conventional method. Gu et al. [12] evaluated the capacitance and resistance of solid-supported bilayer lipid membrane from the CV curves, using a proposed equivalent circuit. Qi et al. [13] presented an equivalent circuit for asymmetric hybrid supercapacitors, which consisted of a battery and a capacitor in series. Their model showed a good agreement between the experimental and analytical results. Considering two different charge transport mechanisms, Sedlakova et al. [14] proposed an equivalent circuit of supercapacitors with three resistors and two capacitors for the Helmholtz layer and the diffusion layer, respectively. Their results indicated that the temporal variation of voltage is an exponential function of the root square of time. Graydon et al. [15] used a two-branch equivalent circuit to account for the redistribution of charges in supercapacitors. Their results showed that a significant number of charges are trapped in micropores, as represented by the second branch in their model. Realizing that the conventional techniques, such as CV and GCD, neglect the nonlinear behavior of supercapacitors, Allagui et al. [16] presented an equivalent circuit with a resistor and a constant phase element (CPE) to account for the nonlinear response of supercapacitors. Their results indicated that the equivalent circuit can be used to describe the electrochemical behavior of supercapacitors. Wang et al. [17] used a modified Poisson-Nernst-Plank (MPNP) model to simulate the transport of ions and the dynamics of electric double layer capacitors for CV measurements. They found that the specific surface capacitance obtained from the CV measurements was constant and not affected by the electrode for the scan rate less than a critical value.

Machine learning has been used to analyze the performance and lifetime of engineering devices and systems. Wang et al. [18] used an improved neural network with anti-noise adaptive long short-term memory to predict the remaining useful life and optimize the multi-scale parameters of lithium-ion batteries (LIBs). They commented that the proposed model reduces the maximum root-mean-square error, the mean absolute error, the maximum mean absolute percentage error and increases the R-square. They later provided an improved model with robust multi-time scale singular filtering-Gaussian process regression-long short-term memory [19] to analyze the remaining capacity of LIBs. Their approaches laid a theoretical foundation to estimate the remaining capacity of the life cycle of LIBs at extremely low temperatures. Zhang et al. [20] presented a state-of-charge estimator with a physics-driven dual-stage attention-based bidirectional recurrent neural network to determine important driving variables for the battery measurements in time and frequency domains. Currently, machine learning has exhibited great potential in analyzing the performance of devices and systems for energy storage. However, it cannot provide a simple, straightforward method to determine the capacitance and resistance of supercapacitors from the CV and/or GCD curves.

The aim of this work is to explore the feasibility of using a three-element equivalent circuit in the determination of the capacitance and resistance of supercapacitors from the CV and/or GCD curves. The results from the equivalent circuit were compared to the corresponding ones from the conventional approaches to validate the effectiveness and applicability of the equivalent circuit. The effects of the pre-compression of the electrode materials on the performance of the associated supercapacitors were presented in contrast to the studies of the effects of concurrent compression of symmetrical supercapacitors during electrochemical cycling reported in the literature [[21], [22], [23]].