Online proceedings - EDA Publishing Association

24-26 September 2008, Rome, Italyany size and shape of capacitors exposed to various boundaryconditions. Performance of the compact modeling has beendemonstrated in terms of accuracy and computational cost.An example of temperature calculated is shown in figure 5.A rectangular capacitor placed in a surrounding medium wasconsidered with 10W as dissipated power. Electrical cableconductance and heat transfer coefficient applied to theexternal surface were chosen as 50W.m -2 .K -1 . Thesurrounding medium was isothermal and its temperaturetaken as a reference. Thermal conductivity and thickness ofthe cell are reported on Table I.One observes that temperature calculated by the compactmodel, reported in figure 5a, is in good agreement with thesimulation, shown in figure 5b. However figure6 showstemperature as a function of time for a rectangular capacitor.A good agreement is observed between the compact modeland the FEM simulation.b)Figure 5: Steady state temperature distribution in the volume of activecomponents with stainless steel current collectors (λ x=0.3W.m -1 .K -2 andλ y=1W.m -2 .K -1 , L=H=0.01m). a) As calculated by the compact model b) Ascalculated by the Finite Elements Method.TABLE IThermal conductivity and thickness of layers considered in the device.ThicknessThermal conductivityW.m -1 . K -1Collector(aluminum) 60 µm 200Collector(stainless steel) 60 µm 20Electrode 150 µm 0.3Separator 50 µm 0.3temperature1,00,80,60,40,2as calculated by the compact modelas calculated by the Finite Elements Method0,00 100 200 300 400 500time (s)Figure 6: Temperature as function of time as calculated by the compactmodel and by the simulation at the point (x=0.03m, y=0.03m) (λ x=1W.m -1 .K -2 and λ y=1W.m -2 .K -1 , L=H=0.06m).Table II reports temperature calculated in steady state for acapacitor module constructed with four 2V elementsgenerating 5W each. A thermal circuit was developed bycombining circuit referring to each individual elementrepresented in Figure 4. As indicated in Table II, it is found agood agreement with simulations (see Figure 7).a)TABLE IITemperatures as calculated by the compact model and the simulation, insteady state for a capacitor module (see figure 7).Maximumtemperature (K)Compact Model Finite ElementMethodSupercapacitor n°1 14 14Supercapacitor n°2 15.8 16.6©EDA Publishing/THERMINIC 2008 121ISBN: 978-2-35500-008-9