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Commonly Used Lithium Battery Parameter Calculation Formula

Sep 29, 2020

(1) Theoretical capacity of electrode material


The theoretical capacity of the electrode material, that is, the capacity provided by assuming that all lithium ions in the material participate in the electrochemical reaction, and its value is calculated by the following formula:


Therefore, the mainstream material theoretical capacity calculation formula is as follows:

The molar mass of LiFePO4 is 157.756 g/mol, and its theoretical capacity is:


In the same way, the ternary material NCM (1:1:1) (LiNi1/3Co1/3Mn1/3O2) has a molar mass of 96.461g/mol, its theoretical capacity is 278 mAh/g, and a LiCoO2 molar mass of 97.8698 g/mol, If all lithium ions are removed, its theoretical gram capacity is 274 mAh/g.


In the graphite anode, when the amount of lithium insertion is the largest, a lithium-carbon intercalation compound is formed, the chemical formula LiC6, that is, 6 carbon atoms are combined with one Li. The molar mass of 6 C is 72.066 g/mol, and the maximum theoretical capacity of graphite is:


For the silicon anode, it can be seen from 5Si+22Li++22e- ↔ Li22Si5 that the molar mass of 5 silicon is 140.430 g/mol, and 5 silicon atoms combine with 22 Li, then the theoretical capacity of the silicon anode is:


These calculated values are the theoretical gram capacity. To ensure the reversibility of the material structure, the actual lithium ion deintercalation coefficient is less than 1. The actual gram capacity of the material is: the actual gram capacity of the material = lithium ion deintercalation coefficient × theoretical capacity.


(2) Battery design capacity


Battery design capacity = coating area density × active material ratio × active material gram capacity × pole piece coating area.


Among them, the areal density is a key design parameter, mainly in the coating and rolling process control.


When the compaction density is constant, the increase in the surface density of the coating means that the thickness of the pole piece increases, the electron transmission distance increases, and the electron resistance increases, but the increase is limited. In thick pole pieces, the increase in the migration resistance of lithium ions in the electrolyte is the main reason that affects the rate characteristics.


Taking into account the porosity and the twists of the pores, the migration distance of ions in the pores is many times longer than the thickness of the pole piece.


(3) N/P ratio


Anode active material gram capacity × anode surface density × anode active material content ratio ÷ (positive electrode active material gram capacity × anode surface density × anode active material content ratio)


The N/P of graphite anode batteries should be greater than 1.0, generally 1.04~1.20. This is mainly for safety design, mainly to prevent lithium from the anode, and process capabilities such as coating deviation should be considered when designing.


However, when the N/P is too large, the irreversible capacity of the battery will be lost, resulting in low battery capacity and lower battery energy density.


For the lithium titanate negative electrode, the positive electrode excess design is adopted, and the battery capacity is determined by the capacity of the lithium titanate negative electrode.


The excessive design of the positive electrode helps to improve the high-temperature performance of the battery: the high-temperature gas mainly comes from the negative electrode.


When the positive electrode is excessively designed, the negative electrode potential is lower, which makes it easier to form an SEI film on the surface of the lithium titanate.


(4) Compacted density and porosity of the coating


In the production process, the calculation formula for the compaction density of the coating of the battery pole piece:


Considering that the metal foil is stretched when the pole piece is rolled, the areal density of the coating after rolling is calculated by the following formula:


The coating is composed of a living substance phase, a carbon glue phase and pores. The porosity calculation formula:


Among them, the average density of the coating is:


(5) First effect


First effect = first discharge capacity / first charge capacity.


In daily production, it is generally formed first and then the capacity is divided, the conversion is charged with a part of the electricity, and the capacity is divided and recharged before discharging, so:

First effect = (formed into charging capacity + sub-capacity supplementary capacity) / sub-capacity first discharge capacity.


(6) Energy density


Volume energy density (Wh/L) = battery capacity (mAh) × 3.6 (V) / (thickness (cm) * width (cm) * length (cm)) Mass energy density (Wh/KG) = battery capacity (mAh) ×3.6(V)/battery weight.