Modelling the effects of charge redistribution during self-discharge of supercapacitors

Abstract

A recent study has shown that the process of self-discharge is determined by a number of parameters such as initial voltage, temperature, and charge duration. Depending on these parameters we observed a voltage decay of 5–15% within 48 h after charging. These observations hardly affect dynamic operations for supercapacitors, but have major implications for all static setups. A complex electrical model has been established to account for the redistribution effects of ions occurring in supercapacitors. Intense experimental studies suggest that these redistribution effects are in part responsible for the measured potential decays. Extended charging allows the ions to allocate themselves more homogeneously throughout the pores and therefore the voltage decay during the rest period following the charging is greatly reduced. The introduced model is capable of predicting the effects of charge duration, initial voltage, and temperature on the open circuit voltage decay.

Introduction

Electrochemical double layer capacitors (EDLC), also called supercapacitors or ultracapacitors, are energy-storage devices which deliver 100 times the power of batteries and store 10,000 times more energy than conventional capacitors [1], [2], [3]. This is primarily achieved by the utilization of high surface area electrodes with surface areas of up to 2500 m²/g [4]. One of the major drawbacks of this technology however is its low volumetric and gravimetric energy density in comparison with batteries or fuel cells. However EDLCs become an interesting option when it comes to highly dynamic charging or discharging profiles with high current rates. This is because of their exceptional high power capabilities (specific power densities of several kW/kg) [5] and cycle lives of up to 10⁶ [6]. But before this technology can be used for promising applications such as kinetic energy recovery systems it is an absolute necessity to develop a detailed model which is capable of predicting the supercapacitor's behaviour under numerous conditions. One major obstacle for the application of EDLCs is the charge loss due to self-discharge mechanisms. In recent years this issue has been investigated by a number of laboratories [7], [8], [9], [10], [11], [12], [13], [14]. Ricketts and Ton-That [12] came to the conclusion that self-discharge consists of a relatively fast diffusion process and a slower leakage current. The open circuit voltage decay due to charge losses can be caused by side reactions which may be due to overpotential decomposition of the electrolyte, redox-reactions caused by impurities or possible functional groups on the carbon surface. Another cause for the observed self-discharge is flaws during the production which may result in micro-short circuits between the anode and the cathode [15]. In this work a brief overview of conducted experiments under various conditions is given. These experiments mainly focused on analysing the self-discharge rate as a function of temperature, charge duration, state of charge and the short-term history. In a second step an equivalent circuit is developed which is based on the de Levie transmission model. A basic outline of the model can be seen in Fig. 1. This proposed model is capable of predicting the behaviour of an EDLC under various conditions with good accuracy.