Li Ion Battery Research Paper

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5.2.3 The Mathematical Modeling of Li-Ion Battery For a combined solar cell-battery device classical liquid electrolytes are not able to guarantee long-term stability as temperature rises up to 1500 C on the backside of a solar cell. Switching to solid electrolytes with crystalline structure does not only provide thermal stability, long-term cycling stability and safety benefits, but also an improved diffusivity as temperature rises. A promising crystalline solid electrolyte is Li5+x BaLa2Ta2o11.5+0.5x , [x ϵ 0,2] with a lithium ion conductivity of 105 to 5.105 [s.Cm-1] To gain a better understanding of the limiting processes within the battery cell, a mathematical model which describes the transport of lithium ions in detail, is of great…show more content…
5.3 - Typical charge characteristic Similar to the discharge model, the exponential voltage for the Li-Ion battery is A*exp(-Bit) term. Hence, the battery voltage obtained can be described as (Tremblay & Dessaint 2009): V_batt=E_0-K Q/(Q-it) it-Ri-K Q/(0.1Q+it) i^*+Aexp(-B it) ------ (5.3) The main feature of this battery model is that the parameters can easily be deduced from a manufacturer’s discharge curve. Figure 5.4 shows a typical discharge characteristic for Li-Ion battery. As shown, the first section represents the exponential voltage drop when the battery is charged. Depending on the battery type, this area is more or less wide. The second section represents the charge that can be extracted from the battery until the voltage drops below the battery nominal voltage. Finally, the third section represents the total discharge of the battery when the voltage drops rapidly. Fig. 5.4 - Nominal current discharge characteristic The three necessary points used to extract the model parameters are: the fully charged voltage, the end of the nominal zone and the end of the exponential zone. With these three points, it is possible to solve, using Equation (5.1), the following set of Equations (5.4), (5.5) and (5.6). For the fully charged voltage (Vfull), the extracted charge is 0 (it = 0) and the filtered current (i*) is ‘0’ because the current step has just

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