Dynamic modeling of the electrical and thermal behavior of ultracapacitors

The purpose of this paper is to establish a dynamic ultracapacitor model which consists of an equivalent circuit model with voltage and temperature effects on its parameters and a thermal model. Identification of parameters in the equivalent circuit model is conducted by alternative current impedance spectroscopy (ACIS) experiment, which uses the least squares method to obtain the ultracapacitor equivalent series resistance (ESR), capacitance (C) and RC parallel resistor-capacitor time constant (τ) at different voltages and temperatures. The least squares method is modified with weightings at different frequencies so as to achieve satisfactory prediction over the whole applicable frequency ranges. On the other hand, parameters in the thermal model is identified from temperature measurement of the ultracapacitor during charge/discharge tests at different heat transfer conditions. The ultracapacitor model is then validated against experimental data under different charge/discharge cycles and thermal conditions. A potential application of this model to fast warm-up of a ultracapacitor in cold weather is demonstrated via simulation. The ultracapacitor model developed in this paper can be applied to estimation of the state of charge (SOC) and temperature which is important for the power and thermal management of a power system including ultracapacitors.