BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

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108 Vlad Marţian et al that all the components are constant, whereas in reality all these characteristics are dependent of the SOC, and the dicharge current. The circuit diagram can be seen in the Fig. 2. Fig. 2 – Thervein model. 2.3. Non linear Dynamic Model A more realistic model has been created by extending the Thervein model. This new model takes into account the nonlinearities in the components of the Thervein model. As we said earlier the internal resistance of the battery R+R 0 and the open circuit voltage E 0 are dependent on the SOC of the battery, and also on the temperature T of the battery. Since we are interested in how the temperature of the battery changes in time we will use a modification of this later model, which can be seen in a simplified version in Fig. 3. In this model different form Thervein model we have included the internal resistance in the overvoltage resistance, for simplification purpose, and the internal resistance R and the open circuit voltage E 0 are dependent on some function of SOC. Fig. 3 – Non linear dynamic model. 3. Modeling Implementation If we want to know how the current and the voltage in the battery are modified in time we have to solve a system of equations that include first order differential equations and also algebraic equations. Doing it by hand it takes a long time, and if one of the parameter is changed we will have to do it again.
Bul. Inst. Polit. Iaşi, t. LVIII (LXII), f. 3, 2012 109 There is a faster and error free method anyway doing this with the help of the computer. In the following we will present the modeling implementation steps with the help of the OpenModelica (OpenModelica, 2012) software package. The first step in modeling the battery was to model the equivalent electric circuit of tha battery. Since OpenModelica has a diagram development interface, and because the Modelica language (Modelica, 2012) is an equation based language, the implementation of the electrical model was straithforward. In the Fig. 4 can be seen the end result of the model. Fig. 4 – Battery model. The battery model is composed from different components, which are electrical components represented by: V oc that implements a signal voltage source, R int that implements a variable resistor, the internal rezistor of the battery, C that implements a capacitor, ISens that implements a measuring sensor for curent drawn. To complete the battery model it was necesarry to include non electric components such as: mCp implements a heat capacitor, Temp implements a temperature sensor, Soc implements the SOC parametter acording to Eq. (2), ExpDataVoc,ExpDataR implements experimental functions for open circuit voltage and respectively for internal rezistor of the battery
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