Modelling battery

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Lesson 15 Modelling battery 29th April 2019 P a g . 1 | 4 Modelling battery Physical based approach Lithium-ion batteries and also other types of batteries have a complex relation between thermodynamic curve during discharge (so theoretical discharge at zero current) and SoC (state of charge). The shape of the curve could be complex because we can have some phase transition in the materials (phase transition will determine a change in the slope). When we draw current we are introducing overpotentials related to positive and negative electrode and to electrolyte (we have at least 3 main overpotentials). We need to describe them. Note: • When we define SoC, we have a certain activity of the two major reactants indicated with 𝑎𝐷+ and 𝑎𝐷−. These are the reactants that play a role during discharge. At SoC equal to 100% 𝑎𝐷+ and 𝑎𝐷− have the maximum value. If we consider Li battery 𝑎𝐷− = 𝑎𝐿𝑖𝐶 and 𝑎𝐷+ = 𝑎𝑀𝑂. • When battery is fully discharged 𝑎𝐷+ and 𝑎𝐷− will have the minimum value. • This means that 𝒂𝑫+ and 𝒂𝑫− are proportional to SoC but we have to define the proportionality between activities and SoC • Then we have the products of discharge reaction, 𝑎𝐶+ and 𝑎𝐶− (that are reactants during charge process), they reach maximum value when battery is fully discharged. • If you consider Li-ion battery: 𝑎𝐶− = 𝑎𝐶 and 𝑎𝐶+ = 𝑎𝐿𝑖𝑀𝑂 • 𝒂𝑪+ and 𝒂𝑪− are proportional to (1 – SoC) Now we try to describe thermodynamic potentials, to do that we consider a real case: Li-ion battery. We look at discharge process: • (-) 𝐿𝑖𝐶 → 𝐿𝑖+ + 𝐶 + 𝑒− • (+) 𝐿𝑖+ + 𝑀𝑂 + 𝑒− → 𝐿𝑖𝑀𝑂 Activity of species i has a complex function with SoC, we need to define this kind of function. Remember, we know that 𝑎𝑀𝑂 and 𝑎𝐿𝑖𝐶 are proportional to SoC, while 𝑎𝐿𝑖𝑀𝑂 and 𝑎𝐶 are proportional to (1-SoC). @ 100% SoC: this term will…