BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

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110 Vlad Marţian et al The battery model is linked with the rest of the circuit by three connectors: a positive (p) and negative (n) electric connectors, and a heat connector (heatPort). Let us explain the thermal part of the battery: It is well known that the energy conservation law stipulates that the energy that is stored in a domain must equal the energy that comes in minus the energy that goes out plus the energy generated inside the domain. The equation form per unit time, of this law can take the form dE d st dEin dE E out g = − + , (3) dt dt dt dt and in the case of a solid domain as the battery, and where we do not have phase change the Eq. (3) becomes dT mCp R i () t hA[ T T ] d 2 int amb t = − − , (4) where m – mass of the battery, Cp – specific heat capacity of the battery, T – battery temperature, R int – internal battery resistance, h – thermal convection coefficient with the outside medium, A – exchange surface of the battery, and i(t) – the current intensity. The Eq. (4) is implemented in the battery model as in Fig. 5, except the Temp sensor, which it is used for linking the temperature to the other components Fig. 5 – Thermal model. 4. Simulations For simulations we have choose a Winston Li-ion battery (Winston, 2011) with a capacity of 60 Ah. The internal resistances and the open circuit voltage where determined by fitting the charts form the manufacturers data. The capacitor value was taken to be 4.047kF (Valerie, Ahmad, & Thomas, 2000). Because we wanted only to test the model, first we have simulated the model
Bul. Inst. Polit. Iaşi, t. LVIII (LXII), f. 3, 2012 111 without any cooling and with a constant resistor taken to be the load on the battery. You can see the modeling in the Fig. 6 Fig. 6 – Battery without cooling. The simulation was done for a time of 1 hour in which the battery has been drained for almost the entire energy. In the following charts we can see the most important parameters of the battery function of time. Battery Temperature [°C] 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 Time [min] Fig. 7 – Battery temperature. As it is observed from the Fig. 7 the temperature is rising and in an hour of using the battery with a constant load the temperature rises with almost 40 o C.
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