## Battery characteristics

**capacity**

The capacity of a battery refers to the total amount of charge generated by a complete discharge under a given condition and time. The theoretical capacity CT depends on the amount of active substance and is calculated as follows:

CT=xF (19)

In the formula, F is the Faraday constant; x is the number of moles of electrons produced during the discharge process. The actual capacity Cp is smaller than the theoretical capacity because the reactants cannot be used 100% during the discharge process. As the charge-discharge rate increases, the drop in iR makes the actual capacity further decrease.

The charge and discharge rate is usually expressed by Crate. The relationship between battery capacity and charge and discharge current can be expressed as follows:

h = Cp/i(20)

In the formula, h is the time required for the battery to fully discharge (or charge) (unit is h); i is the current (unit is A); Cp is the battery capacity (unit is Ah), and the reciprocal of h is Crate, which means , When the Crate increases, the time required to charge and discharge the battery decreases. The battery capacity can be expressed by mass specific capacity (Ah/kg, (mAl/g) or volume specific capacity (Ah/l, (mAl/cm3)).

**Energy Density**

Energy density is the energy stored per unit mass or unit volume, and it is an important parameter to measure battery performance. The maximum capacity that 1 mol reactant can provide can be expressed as follows:

△G=–FE= εT (21)

In the formula, E is the electromotive force of the battery; εT is the theoretical energy (unit wh, 1Wh = 3600J) for the battery reaction of 1 mol substance.

The actual energy εp varies according to the discharge mode. The actual energy of 1 mol reactant is derived as follows:

εp=∫Edq =∫(Ei)dt=-F(Eeq-η) (22)

As the discharge rate or discharge current per unit time increases, the potential of the battery further deviates from the equilibrium potential.

Similar to battery capacity, energy density can be expressed in Wh/kg, mWh/g or Wh/1, mWh/cm3.

**power**

The power of a battery refers to the energy available per unit time. Power P is the product of current i and voltage E.

P=iE (23)

Electric power is the measurement of the current value passed under a given voltage. When the current increases, the power will decrease after the increase reaches the maximum value. This is because when the current exceeds a certain range, the battery voltage decreases, which in turn causes the power to decrease. This polarization phenomenon is related to the diffusion of lithium ions and the internal resistance of the battery. In order to increase the power, it is necessary to increase the diffusion rate of lithium ions and the electronic conductivity. Similar to battery capacity and energy, power density is expressed in terms of unit mass power or volume power.

**Cycle life**

Cycle life is the number of charge and discharge cycles that a battery can complete before its capacity is exhausted. High-performance batteries must be able to maintain a certain capacity after multiple charge and discharge cycles. The cycle life of lithium secondary batteries largely depends on the structural stability of the electrode active material during charge and discharge. Usually, irreversible capacity is observed after the first charge-discharge cycle, that is, the number of charges lost. This is because a new film layer is formed at the electrode and electrolyte interface.

After N charge/discharge cycles, the capacity retention rate is expressed as CN/C1 (%), and the relative capacity reduction rate is expressed as (C1－CN)/C1o. The capacity after N cycles of charge and discharge and 1 cycle are respectively CN And C1 cycle life is affected by the depth of discharge and is related to the battery type. If the shallow discharge is repeated, the cycle life of the lithium secondary battery is longer, and the capacity of the battery will not be completely depleted in this case.

**Discharge curve**

Repeated charging and discharging will affect the discharge characteristics of the battery. Discharge conditions, electrical performance and other test variables are different, the discharge curve can have different forms. Constant current, constant power and constant external resistance are commonly used discharge conditions. The electrical properties to be tested include battery voltage, current and power, while the test variables are discharge time, capacity and lithium content. The same type of battery made from the same material and the same design may have different discharge curves depending on the test conditions. To have a more accurate understanding of battery performance, it is necessary to compare these discharge curves. An actual battery can give a variety of discharge curves according to different battery components. Figure 1.1 below shows a typical discharge curve of a battery.

Figure 1.1 is the curve of voltage versus capacity when the battery is discharged under constant current conditions. Since the capacity is proportional to time when current is applied, Figure 2.4 also shows the voltage change over time. In addition, when the battery is not connected to an external load, the battery voltage is the open circuit voltage, and when the circuit is closed, it is the operating voltage. The battery voltage when the discharge is completed is the so-called cut-off voltage.

As for the curve I in Figure 1.1, the battery voltage is almost unaffected by the reaction in the battery during the discharge. Curve II shows two plateau areas caused by changes in the reaction mechanism. On curve III, the reactants, products, and internal resistance of the battery are constantly changing during the entire discharge process.

For lithium secondary batteries, the battery voltage change after charging and discharging can be expressed by the Armand equation.

Ecall= Eocell－(nRT/F) In(γ/1－γ) + kγ (24)

In the formula, γ is the lithium content; kγ is the influence of the interaction between the inserted lithium ions on the battery voltage. The battery voltage change based on capacity depends on direct factors such as lithium ion diffusion rate, phase change, lattice structure change and dissolution, as well as indirect factors such as the particle size, temperature, electrolyte characteristics and separator porosity of the electrode active material. These factors may change the values of γ and k in the Armand equation.

Under the condition of low current density, the voltage and discharge capacity of the working battery are close to the theoretical balance. From the change trend of ①~④ in Figure 1.2, we can see that the battery voltage during the discharge process continues to drop. This is because the iR drop and overpotential caused by the polarization increase with the increase of the discharge current. Even if the battery is discharged beyond the cut-off voltage, the capacity is also reduced, which is due to the obvious increase in the gradient of the discharge curve. The characteristics of the discharge voltage have a great relationship with the temperature.

As shown in Figure 1.3, when the battery is discharged at a low temperature, the decrease in the chemical activity of the reactants will increase the internal resistance, which will cause the battery voltage to drop sharply and reduce the battery capacity. At high temperatures, the decrease in internal resistance and the increase in discharge voltage will increase the battery capacity. But if the temperature is too high, too high chemical activity may cause self-discharge and other harmful chemical reactions