Even if you don’t need the highest accuracy from your lithium-ion (Li-ion) battery gauge, some insights into the electrochemical process inside the cells will help you understand the suitability and limits of various approaches to gauging.
Gauging for Li-ion batteries is the process of estimating the state of charge in the battery. The state of charge is the remaining capacity as a fraction of the total usable capacity in the battery. The remaining capacity of a battery is typically given in milliamp-hour (mAh) or milliwatt-hour (mWh) units.
To calculate the remaining capacity, you’ll need to know the zero point at which the battery is considered empty. This is the minimum voltage to sustain a certain current for a system. Total usable capacity in the battery is just the remaining capacity once the battery is fully charged.
Many methods exist to gauge Li-ion batteries. The simplest form of gauging is to measure the voltage and associate the voltage to a pre-determined state of charge. This method can accurately determine the capacity of a fully relaxed battery; however, in a real system, getting a relaxed-voltage measurement is often difficult. The voltage-only method ignores the battery’s internal impedance. As the load or temperature changes, the loaded-voltage measurement will match the same state of charge.
Coulomb counting is another method to measure state of charge. This method typically “learns” the battery capacity in the first couple of discharges and will initialize to some initial state of charge upon first connection. The state of charge will increase or decrease depending on the direction of current flow until it reaches the zero point, or full capacity. Some coulomb-counting gauges attempt to track impedance with approximation factors that scale the capacity. Each battery in a system will undergo different use and aging so the approximations may become inaccurate after some cycling. Both of these methods treat the Li-ion battery as if it is a simplistic electrical model and measure voltage and current without attempting to model the battery’s internal dynamics.
Figure 1: Simplified lithium ion battery schematic
In order to properly gauge a Li-ion battery, you need to look at the battery as an electrochemical device and not purely an electrical device. Li-ion batteries consist of an anode, cathode and separator. Figure 1 shows a simplified schematic of a typical lithium ion battery. The cathode is typically a strong oxidizer such as manganese dioxide or cobalt dioxide that is very capable of accepting an electron. The anode is a strong reducer such as graphite or graphene, which is very capable of donating electrons. When the battery is connected to a system load, the electrons flow from anode to cathode through the system load; the Li-ions diffuse from anode to cathode internal to the Li-ion battery through the separator and solution surrounding the cathode and anode (electrolyte).
This diffusion process is responsible for the internal impedance of a Li-ion battery and is temperature-dependent. As the temperature decreases, the diffusion slows and the internal impedance increases; conversely, as temperature increases, diffusion speeds up and internal impedance decreases. The diffusion process is not only affected by temperature, but by frequency of the load and state of charge in the battery. Figure 2 and 3 show the impedance versus depth of discharge (inverse of state of charge) and impedance vs frequency respectively.
Figure 2: Depth of discharge vs battery impedance at certain temperatures. The depth of discharge is the inverse of state of charge. 100% depth of discharge corresponds to 0% state of charge. As temperature decreases, we can see the impedance increase.
Figure 3: Impedance spectra of a lithium ion battery. Starting from the bottom left, is the high frequency impedance, we move across the impedance curve until we get to the upper right, where we have the DC resistance. There are 5 regions on the plot. Region 1 and 2 correspond to ohmic contact and SEI impedance respectively. Region 3 is the charge transfer resistance. Region 4 is the distributed resistance of active material and ionic resistance of electrolyte in pores. Region 5 is the diffusion effects. Region 6 is the DC resistance at a constant load.
The equation below shows the reaction for the anode and cathode of a LiCoO2 battery:
Ideally, as you cycle the Li-ion battery, the equation is completely reversible. But in a real Li-ion battery, the electrodes – especially the anode – will react with the electrolyte at the interface, causing the formation of a solid electrolyte interface (SEI). The SEI layer will eventually lead to an impedance increase and loss of lithium due to growth that blocks the pores of the electrode from cycling the battery. High temperatures and high states of charge will cause this growth to be elevated.
The anode can expand and contract from the diffusion of Li-ions and cause mechanical deformations that result in contact loss between the current collector and active anode material to further increase cell impedance. This can be further worsened by low states of charge or overdischarge.
The Li-ion battery is not just a simple electrical source, but a chemical power plant that requires a more complex modeling scheme than voltage, current or temperature alone. Impedance Track™ gas gauges from Texas Instruments look at the Li-ion battery using a more chemistry-based model. They use the internal impedance in all predictions of usable capacity.
Impedance Track gas gauges also use voltage, current and temperature information to determine the loss of lithium (chemical capacity or Qmax) as well as the rise in impedance throughout the life of the battery. Advanced thermal models that factor in self-heating and surface-temperature changes during charge and discharge account for the temperature effects on impedance. When an Impedance Track gas gauge is properly configured for the system it supports, it will maintain proper accuracy across the life of the battery due to the advanced nature of the model.
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