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In the charge-discharge test or actual use of lithium-ion batteries, voltage parameters mainly include platform voltage, median voltage, average voltage, cut-off voltage, etc. The typical discharge curve is shown in Figure 1.

Platform voltage refers to the voltage value corresponding to when the voltage change is minimal and the capacity change is large. Lithium iron phosphate and lithium titanate batteries have obvious platform voltages, and the voltage platform can be clearly identified in the charge-discharge curve. The voltage platform of most batteries is not obvious. During charge-discharge testing, data is collected at voltage intervals, and then the voltage curve is differentiated. The platform voltage is determined by the peak value of dQ/dV.

The median voltage is the voltage value corresponding to half of the battery capacity. For materials with obvious platforms, such as lithium iron phosphate and lithium titanate, the median voltage is generally the platform voltage.

The average voltage is the effective area of the voltage-capacity curve (that is, the charge/discharge energy of the battery) divided by the capacity. The calculation formula is Ü = ∫U(t)*I(t)dt / ∫I(t)dt. In charge-discharge test data, the charge or discharge energy divided by the capacity data is the average voltage. Conversely, the energy density of a battery is also estimated based on the average voltage of the battery, that is, energy = capacity * average voltage / battery mass (or volume).

The cut-off voltage refers to the lowest voltage allowed when the battery is discharging and the highest voltage allowed when the battery is charging. If the battery continues to discharge after the voltage is lower than the discharge cut-off voltage, the potential of the positive electrode of the battery continues to decrease, while the potential of the negative electrode will rise rapidly, resulting in over-discharge. Over-discharge may cause damage to the active electrode material, loss of reaction ability, and shorten the battery life; it may also lead to the decomposition of the negative copper foil and precipitation on the positive electrode, presenting a short-circuit risk. If the charging voltage is higher than the charging cut-off voltage, the potential of the positive electrode of the battery continues to rise, causing excessive lithium removal from the positive electrode material, failure of the crystal structure due to destruction, and decomposition of the electrolyte and consumption of lithium ions. While the potential of the negative electrode will continue to drop, resulting in excessive lithium intercalation, collapse of the graphite layered structure, and lithium precipitation on the surface of the electrode sheet.

In fact, the voltage U(battery) of the battery is determined by the difference between the electrode potential E(positive electrode) of the positive electrode and the electrode potential E(negative electrode) of the negative electrode, as represented by formula (1):

U(battery) = E(positive electrode) - E(negative electrode) Formula (1)

In the battery system, the standard lithium electrode is generally used as a reference electrode. The electrode potentials of positive and negative electrode materials are generally the potentials generated by the reaction between reactants and products and the reference lithium electrode. As shown in Figure 2, during the charge-discharge process, the positive and negative electrode materials de-lithiate or intercalate lithium, and the electrode potential changes. The battery voltage is the difference between the two.

Therefore, to understand the voltage of a battery, we must first understand the electrode potentials of various electrode materials. Understanding the equilibrium electrode potential curve of materials can better understand the voltage characteristics of the battery.

Open circuit voltage refers to the potential difference between the positive and negative electrodes of the battery when it is in a non-working state, that is, when there is no current flowing in the circuit. Assembling the electrode material and metallic lithium into a button half-cell, the open circuit voltage is the equilibrium potential of the electrode material.

Open circuit voltage test method
The test process for the equilibrium potential of electrode materials is as follows: The electrode material is prepared into an electrode sheet and assembled with metallic lithium into a button half-cell. The open circuit voltage of the button half-cell in different SOC states is measured, and the mathematical expression of the open circuit voltage curve is determined by polynomial or Gaussian fitting. The open circuit voltage test methods mainly include:

1. Galvanostatic intermittent titration technique (GITT). The basic principle is to apply a constant current to the measurement system under a specific environment for a period of time and then cut off the current. Observe the change of the system potential with time during the current application period and the voltage (that is, open circuit voltage) that reaches equilibrium after relaxation. For example of GITT test: (i) Charge at C/50 until the voltage reaches the upper limit voltage, such as 4.2 V; (ii) Stand for 2 hours; (iii) Discharge at 1C for 6 minutes and record the discharge capacity; (iv) Stand for 15 minutes and record the voltage; (v) Repeat steps (iii) and (iv) a total of 9 times; (vi) Discharge at C/50 until the voltage reaches the lower limit voltage, such as 3.0V; (vii) Normalize the capacity-voltage curve recorded in steps (iii) and (iv), make it into an SOC-voltage curve, and fit to obtain the mathematical expression of the open circuit voltage curve.

2. Small current charge-discharge curve. Charge and discharge at a particularly low rate (such as 0.01C) with constant current. Set the upper and lower voltage limits to obtain the small current charge-discharge curve of the battery. Take the point with the same charge as the starting point of the curve. Take the average value of the voltage in the charge-discharge curve. Normalize the abscissa of the curve according to the theoretical capacity, and then use curve fitting to obtain the open circuit voltage curve.

Battery polarization
When current passes through the electrode, the phenomenon that the electrode deviates from the equilibrium electrode potential is called battery polarization, and polarization generates overpotential. According to the causes of polarization, polarization can be divided into ohmic polarization, concentration polarization and electrochemical polarization.
Ohmic polarization: Caused by the resistance of various parts of the battery connection. Its voltage drop value follows Ohm's law. When the current decreases, the polarization immediately decreases and disappears immediately after the current stops.

Electrochemical polarization: Polarization caused by the sluggishness of the electrochemical reaction on the electrode surface. As the current decreases, it decreases significantly within microseconds.

Concentration polarization: Due to the sluggishness of the ion diffusion process in the solution, a concentration difference between the electrode surface and the bulk solution occurs under a certain current, resulting in polarization. This polarization decreases or disappears on a macroscopic second scale (several seconds to tens of seconds) as the current decreases.

The internal resistance of the battery increases with the increase of the battery discharge current. This is mainly because a large discharge current makes the polarization trend of the battery increase, and the larger the discharge current, the more obvious the polarization trend, as shown in Figure 2. According to Ohm's law: V = E0 - I×RT. As the overall internal resistance RT increases, the time required for the battery voltage to reach the discharge cut-off voltage is correspondingly reduced, so the discharged capacity is also reduced.

Lithium-ion batteries are essentially a lithium-ion concentration difference battery. The charge-discharge process of lithium-ion batteries is the process of lithium ions embedding and de-embedding in the positive and negative electrodes. Factors affecting the polarization of lithium-ion batteries include:

2.1 Influence of electrolyte: Low conductivity of the electrolyte is the main reason for the polarization of lithium-ion batteries. In the general temperature range, the conductivity of the electrolyte for lithium-ion batteries is generally only 0.01 to 0.1 S/cm, which is one percent of that of an aqueous solution. Therefore, when a lithium-ion battery is discharged at a high current, it is too late to supplement Li+ from the electrolyte, and polarization will occur. Improving the conductivity of the electrolyte is a key factor in improving the high-current discharge capability of lithium-ion batteries.

2.2 Influence of positive and negative electrode materials: Large particles of positive and negative electrode materials lengthen the channel for lithium ion diffusion to the surface, which is not conducive to high-rate discharge.

2.3 Conductive agent: The content of conductive agent is an important factor affecting high-rate discharge performance. If the content of conductive agent in the positive electrode formula is insufficient, electrons cannot be transferred in time during high-current discharge, and the polarization internal resistance increases rapidly, causing the battery voltage to quickly drop to the discharge cut-off voltage.

2.4 Influence of electrode sheet design:
Electrode sheet thickness: In the case of high-current discharge, the reaction speed of active materials is very fast, requiring lithium ions to be able to quickly embed and de-embed in the material. If the electrode sheet is thick, the diffusion path of lithium ions increases, and a large lithium ion concentration gradient will be generated in the thickness direction of the electrode sheet.
Compaction density: If the compaction density of the electrode sheet is large, the pores become smaller, and the path for lithium ion movement in the thickness direction of the electrode sheet becomes longer. In addition, if the compaction density is too large, the contact area between the material and the electrolyte is reduced, the electrode reaction site is reduced, and the internal resistance of the battery will also increase.

2.5 Influence of SEI film: The formation of the SEI film increases the resistance at the electrode/electrolyte interface, resulting in voltage hysteresis, that is, polarization.

Working voltage of the battery
The working voltage, also known as the terminal voltage, refers to the potential difference between the positive and negative electrodes of the battery when the battery is in a working state, that is, when there is current flowing in the circuit. In the working state of battery discharge, when current flows through the battery, it is necessary to overcome the resistance caused by the internal resistance of the battery, which will cause ohmic voltage drop and electrode polarization. Therefore, the working voltage is always lower than the open circuit voltage. The opposite is true during charging. The terminal voltage is always higher than the open circuit voltage. That is, as a result of polarization, the terminal voltage of the battery during discharge is lower than the electromotive force of the battery. During battery charging, the terminal voltage of the battery is higher than the electromotive force of the battery.

Due to the existence of polarization phenomenon, there will be a certain deviation between the instantaneous voltage and the actual voltage during the charge-discharge process of the battery. During charging, the instantaneous voltage is slightly higher than the actual voltage. After charging is completed, polarization disappears and the voltage drops back; during discharging, the instantaneous voltage is slightly lower than the actual voltage. After discharging is completed, polarization disappears and the voltage rises back.

As mentioned above, the composition of the battery terminal voltage is shown in Figure 3, and the expression is:

Charging: VCH = (E+ - E-) + VR = (E+0 + η+) - (E-0 - η-) + VR

Discharging: VD = (E+ - E-) - VR = (E+0 - η+) - (E-0 + η-) - VR

Why do some materials have obvious voltage platforms while others do not?

In thermodynamics, degrees of freedom F is when the system is in an equilibrium state, without changing the number of phases, the factors that can be independently changed (such as temperature and pressure). The number of these variables is called the number of degrees of freedom. The relationship between the degrees of freedom of the system and other variables:

F = C - P + n

Where F: represents the degrees of freedom of the system; C: the number of independent components of the system; P: the number of phases; n: external factors. Most of the time, n = 2, representing pressure and temperature.

For the lithium-ion electrochemical system, the external factor n = 2, and voltage and temperature are taken respectively. Assume that the temperature and pressure of the lithium-ion electrode material are constant during the charge-discharge process. Here, we discuss the binary system (C = 2). If there is one phase in a particle, that is, P = 1, then F = 1. The chemical potential is one degree of freedom and changes with the change of lithium concentration (for example, lithium cobalt oxide in solid solution has one phase and the lithium concentration is constantly changing).

If the particle contains two phases, that is, P = 2, then F = 0. When two phases coexist, there is a flat voltage platform in a binary electrode material (for example, lithium iron phosphate, two phases coexist, and the lithium concentration in each phase is constant).

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