A novel analytical solution for the calculation of temperature in supercapacitors operating at constant power

Temperature evolution in supercapacitors (SCs) when they are charged or discharged at a constant current is a well-known process. However, it does not exist any mathematical equation for the calculation of the instantaneous temperature of the SC when it is charged or discharged at constant power. In this work, a new mathematical formulation is presented, which allows for the analytical calculation of temperature as a function of time (or alternatively, as a function of the current or the internal or the external voltage), considering the electrical and thermal properties provided by the manufacturer of the SC or obtained through laboratory tests. Highly accurate equations for the calculation of instantaneous current, power losses and other significant variables are also obtained. The validity of the proposal is demonstrated by comparing the results obtained with the new method with those yielded from the classical iterative, numerical resolution of the differential equations. The high accuracy of the proposed approach makes it useful to be used in the task of sizing the cooling systems of SC applications.