Ultracapacitors self discharge modelling using a physical description of porous electrode impedance

The main goal of this paper is to establish a link between the ultracapacitors impedance at low frequency and slow phenomena such as self-discharge and charge recovery. Usually these phenomena are studied in the time domain. However, additional information can be extracted from specific characterization methods in the frequency domain like impedance spectroscopy. In this way, we intend to introduce an analytical method to characterize the ultracapacitors only by using impedance spectroscopy results and so to simplify some ultracapacitors tests like power cycling and calendar life tests. Firstly, we introduce a complete impedance model of ultracapacitor, which is based on the main physical behaviour in the porous electrodes and at the electrode- electrolyte interface. A specific identification method is used in order to determine the model parameters from the impedance spectroscopy results. This model has a good accuracy, especially in the low investigated frequency range [1 mHz,100 Hz]. Then, we focus only in the dynamic behaviour in the low frequency range using some justified simplifications. The link with voltage decay is discussed and validated by using experimental results of self-discharge tests. Then a mathematical relation is introduced in order to predict the self-discharge rate from impedance spectroscopy results. Finally, a time domain identification procedure of the ultracapacitors model is introduced. It allows obtaining an accurate model of the dynamic behavior without using the impedance spectroscopy. The proposed model has been validated thanks to experimental results. The validation tests have been performed using a large cell 2700F/2.7 V for a significant test duration. The results show a good agreement between measured and simulated results during the relaxation periods over few hours.