How to calculate battery capacity? A thorough understanding of battery capacity monitoring technology in one article
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1.Basic knowledge of battery power monitoring
1.1 What is battery capacity monitoring technology?
Meaning: Battery fuel monitoring is a technique used to predict the battery capacity under all system operating and idle conditions.
- Time until battery is exhausted/fully charged
- Call time, limit time, etc.
b. Other data that can be used to reflect battery health and safety diagnosis
Battery charge monitoring technology is mainly used to report the capacity of the battery. It can also generally provide the battery health status and the battery's fully charged capacity.
a. Basic knowledge of battery chemical composition
b. Traditional battery power monitoring method
c. Impedance tracking technology and its advantages
1.3 Part 1: Basic knowledge of battery chemistry
First, let me introduce some knowledge about battery chemistry related to battery power measurement.
[Figure: Lithium-ion battery discharge curve: optimal operating time]
The three graphs here are the discharge curves of Li-ion batteries measured under different conditions. Changing the cut-off voltage with discharge rate, temperature and aging can provide the longest possible operating time.
From these figures, we can first see that at room temperature and low current, the battery voltage will drop quickly after 3.5V. Although the system can support a minimum voltage of 3.0V or 3.3V, the voltage will drop quickly after 3.5V. In order to avoid data loss caused by sudden shutdown or sudden interruption of the circuit for loading files, the customer's application system usually tends to set the reference point of the battery's minimum capacity to 3.5V. If it is at low temperature or high current, or when the battery is very aged, if 3.5V is still used as the reference point for zero power, then the available capacity of the battery will be greatly reduced. You can see from these curves that under high current, the curve of discharge is almost at 3.5V at the beginning, and it is similar under aging or low temperature. Therefore, if 3.5V is fixed as the reference point for zero capacity, then under low temperature or high current conditions, or when the battery is close to aging, the reported capacity will be reduced. In order to avoid this situation, the battery capacity needs to be adjusted according to the temperature, discharge rate, and battery aging.
1.4 Battery chemical capacity Qmax
Regarding battery power monitoring technology, there is a relatively important concept, which is the chemical capacity Qmax of the battery. In this figure, the intersection of the red curve and the horizontal axis of 3.0V corresponds to the value of Qmax.
This curve is measured when the load current is 0.1C, because to measure Qmax, the load current must be small enough. In theory, Qmax refers to the capacity that can be discharged when the current approaches zero, but in actual engineering technology, a very small current is used to measure Qmax. Here we use a current of 0.1C. So what is 0.1C?
The concept of C in battery power management refers to the discharge rate of the battery. 1C actually means that if the battery capacity is 2200mAh, the current is 2200mA, which is 1C. So conceptually, it is the current required to completely discharge a battery within 1 hour. Therefore, the discharge current corresponding to a 2200mAh battery is 2200mA, and the discharge current corresponding to 0.5C is 1100mA.
The EDV mentioned in this figure refers to the lowest voltage that the system or battery itself can support.
1.5 Available Capacity Quse
Another corresponding capacity is the available capacity. Because what we just talked about is the chemical capacity of the battery. The chemical capacity of the battery is the capacity measured when the current is very small. It is more determined by the characteristics of the battery itself. In the actual use of the battery, not all of this capacity can be discharged. In the actual use process, due to a certain discharge current, the discharge curve will be lower than the open circuit voltage curve. You can see this curve. Due to the internal resistance of the battery, the actual discharge curve is the blue curve. The corresponding values of the blue curve and the red curve give Quse. Quse actually refers to the available capacity of the battery. In this curve, we found that due to the existence of the internal resistance of the battery, the position of this curve has moved downward, so the discharge termination voltage will be reached earlier during discharge, that is, EDV will be reached earlier, so Quse is generally less than Qmax.
From this curve, we can also see that the larger the current, the smaller Quse will be. In this curve, I*Rbat refers to the drop in battery terminal voltage due to the existence of internal resistance.
The internal resistance of the battery has a significant impact on the monitoring of the battery voltage. The basic formula can be used to express the impact of the internal resistance of the battery on the battery capacity monitoring:
In this formula, Vocv refers to the open circuit voltage of the battery, I refers to the charge and discharge current, Rbat refers to the internal resistance of the battery, and V refers to the terminal voltage of the battery.
The impedance of the battery is actually affected by many factors, including the ambient temperature, the battery capacity, and the degree of battery aging. It is a very complex function among these variables. It is very difficult to obtain the specific expression of this function, so the impedance is often obtained by actual measurement, that is, the impedance is obtained by the differential table method. Then the internal resistance of this battery will usually increase by 1 time after 100 charge and discharge cycles, which is an empirical value. The deviation between the same batch of batteries can be controlled at about 10~15%, and the deviation of the internal resistance of batteries produced by different battery manufacturers is often greater. Therefore, the battery is a variable that is difficult to control its deviation to a small level during production. The internal resistance of the battery is a very difficult variable to control, and it is also a very important variable.
1.7 State of Charge (SOC)
What we just talked about is SOC. SOC actually refers to the capacity percentage, which is the capacity percentage on the corner of the screen when you use your mobile phone or tablet. The meaning of capacity percentage is how much power is left in the battery from a certain state to empty. The English abbreviation is SOC, which is State Of Charge, so it can also be directly translated into charge state, because Charge means charge. So obviously for a fully charged battery, the voltage percentage, or charge state, is equal to 1; for a completely empty battery, the voltage percentage is equal to 0. So the formula for voltage percentage.
SOC is equal to Q on this curve (the remaining capacity corresponding to state A) divided by the chemical capacity Qmax of the battery. A concept corresponding to the percentage of power is DOD, which refers to the depth of discharge. Obviously, when the charge percentage or capacity percentage is 1, the discharge depth should be 0; conversely, when the capacity percentage is 0, the discharge depth should be 1.
We encounter the concept of DOD in many TI documents. DOD is actually a relative concept to SOC. They actually mean the same thing, that is, how much power is left in the battery, or how much power the battery has discharged from a fully charged state. It indicates this degree.
1.8 Impedance is related to temperature and DOD
The impedance of the battery is greatly affected by temperature and capacity percentage, which can also be expressed by the depth of discharge mentioned earlier, that is, DOD. From this curve, we can see some basic trends. From the figure, we can see that the greater the discharge percentage and the greater the discharge depth, the greater the internal resistance of the battery, because the ordinate on this curve refers to the internal resistance of the battery, its unit is ohm; the abscissa refers to the discharge percentage, that is, DOD. Curves of different colors represent data measured at different temperatures. Obviously, at the same temperature, the greater the discharge percentage, that is, the deeper the discharge, the greater the internal resistance of the battery. Then we can also see from this figure that under the same DOD, that is, the same capacity percentage, the lower the temperature, the greater the internal resistance of the battery. This is a basic concept, and this is a basic understanding that everyone should form about batteries.
1.9 Changes in resistance and capacitance with aging
In addition to temperature and capacity percentage, another factor that has a significant impact on the internal resistance of the battery is the age of the battery, that is, the degree of battery aging. Generally, after 100 heavy discharges, the chemical capacity of the battery will decrease by 3~5%. This capacity reduction is not very significant, but its impedance change is more significant. After 100 charge and discharge cycles, the impedance can increase by almost 1 times. You can see from these two pictures that the picture on the left is a picture of the 1st and 100th discharge curves drawn together. From this picture, it can be seen that the increase in the number of discharges does not have a great impact on the reduction in capacity.
However, the increase in discharge rate has a great impact on internal resistance. The figure on the right refers to the relationship between the internal resistance of the battery and the increase in the number of discharges. There are many curves here. The horizontal axis of this figure is the frequency used to measure the internal resistance of the battery, and the vertical axis refers to the internal resistance of the battery. In this figure, we can see that when the frequency is very low, the bottom curve is a curve measured at different frequencies for the first time, and the top curve is the curve of the battery internal resistance measured at different frequencies for the 100th time. The values of the intersection of the two curves at the vertical axis are basically 1 times different, so after 100 cycles, the internal resistance of the battery has increased by 1 times. The horizontal axis of the internal resistance here uses frequency, which means that when the frequency is very low, the change of internal resistance is very significant with the increase of the number of cycles, but conversely, with the increase of frequency, for example: when the change frequency of the test load increases to 1KHZ, the change of internal resistance can be basically ignored. You can see that so many curves basically converge to the same point. So what kind of impedance actually has a great impact on our battery power monitoring?
It is the impedance under low frequency or DC conditions, so we should look at the two intersection points of the curve on the right and the vertical axis. From this intersection point we can see the effect of the number of cycles on the DC internal resistance of the battery.
1.10 Impedance Difference of New Batteries
This picture shows the difference in impedance of new batteries. The process structure of the battery is stacked or rolled up layer by layer, so from the outside, the positive and negative electrodes of the battery have the characteristics of capacitance, resistance, and inductance. So for the entire battery, if you want to measure its impedance, the impedance can be divided into real and virtual. In this picture, we use an alternating load to measure the internal resistance of the battery. The frequency of change of this battery, that is, the frequency of change of the load current, changes from 1KHZ to 1mHZ. The concept of 1KHZ is often encountered, which means 1000 changes in 1 second; 1mHZ means 1 change in 1000 seconds. This change frequency is quite slow, which means that what is measured is actually a DC impedance.
In these two pictures, you can see that the DC impedance increases linearly with decreasing frequency, but the AC impedance has a changing trend, starting small, then slowly increasing, then decreasing again, and finally increasing again, which is caused by the combined effects of the capacitor and inductor inside the battery. However, the DC impedance increases monotonically, and as the frequency decreases, the DC impedance becomes larger and larger.
As for battery charge monitoring technology, we are concerned about the DC impedance at 1mHZ. From this figure, we can see that at 1mHZ, the deviation of battery impedance is still about 15%. This 15% impedance deviation will cause a 40mV voltage difference between the terminal voltage and the open circuit voltage of the battery under 1C current discharge and low temperature conditions. If the algorithm you use is to judge the capacity based on voltage, it will probably cause a capacity error of about 26%.
1.11 Remaining battery capacity (RM)
The following is an introduction to the remaining capacity of the battery. The remaining capacity refers to the battery capacity at the current state when it is discharged to EDV, which is the end-of-discharge voltage. In the current state A in the figure, the battery is discharged at a given current. When it is discharged to 3.0V, the corresponding remaining capacity is marked as RM1 in the figure. If the battery is discharged at a relatively large current in state A,
At this time, the position of this curve will be lower than the open circuit voltage, and also lower than the position corresponding to RM1 of the small current discharge just now. The remaining capacity obtained at this time is RM2. The difference between the discharge curves corresponding to RM2 and RM1 is that the discharge current used is different. The larger the discharge current, the lower the position of the curve, and the smaller the remaining capacity. Therefore, the remaining capacity of the battery is related to the discharge rate, and the remaining capacity of the battery is different under different currents.
Some users find that the battery capacity changes from less to more during discharge during actual use of the battery, which they find incomprehensible. In fact, this situation can be explained here. This situation is caused by the change of discharge current. When we see the battery capacity change from less to more, this is usually caused by a sudden decrease in discharge current, because the capacity that the battery can discharge is different under different currents. When the discharge current becomes smaller, the capacity it can discharge can increase.
1.12 Summary of Battery Chemistry
Let’s now briefly review the concepts we just introduced.
Qmax refers to the chemical capacity of the battery. The value of this capacity has nothing to do with the load. It refers to the capacity that the battery can discharge under extremely small load current conditions, and its unit is usually expressed in mAh.
Quse refers to the available capacity of the battery. This capacity is related to the load. Under different load conditions, the available capacity of the battery is different. The larger the load current, the smaller the available capacity of the battery.
Why is there such a difference between Quse and Qmax? This is mainly due to the internal resistance of the battery and the load on the battery.
The electromotive force and terminal voltage directly produce a voltage drop. Another concept is the battery capacity percentage, or the charge state. Its unit is %. This % is actually the remaining capacity of the battery divided by the chemical capacity of the battery.
The remaining capacity is called RM. The size of RM also depends on the load. The greater the load, the smaller the remaining capacity under the same state.
Another concept is that battery aging will affect the impedance and capacity of the battery. The effect of aging on impedance is more obvious, and the impedance will increase by 1 time after 100 cycles. The effect of aging on capacity is not as obvious as impedance, but there will be a 3~5% drop after 100 cycles.
2. Traditional battery power monitoring method
2.1 Goal: Make full use of available battery capacity
The main purpose of battery power monitoring is to maximize the use of the battery capacity. Generally speaking, it is difficult to utilize 100% of the battery capacity. Why?
There are 2 factors here
First, when charging, the charging voltage is rarely exactly the full charging voltage of the battery. Usually, in order to prevent the battery from overcharging, the charging voltage error is biased downward. That is to say, for a 4.2V battery, the charging voltage may be 4.18V or 4.15V. In this way, if charging is performed at this low charging voltage, the charged capacity may become smaller;
In addition, due to the inaccuracy of battery power monitoring, for safety reasons and to prevent data loss caused by sudden critical events, users may make conservative power estimates. That is to say, when the actual battery power has not reached 0%, it will be reported as 0% in advance, allowing the system to shut down in advance. This can at least avoid user data loss. Of course, the user experience feels that the battery capacity has become smaller, which is a disadvantage. The consequence of this is that the battery capacity cannot be fully utilized. The battery power monitoring technology is to maximize the monitoring of battery power so that users can use the current battery capacity to the maximum extent. The blue section actually refers to the effective capacity of the battery. Our technology is to expand the actual effective capacity as much as possible up or down.
2.2 Traditional battery pack side fuel gauge
Traditional battery pack power monitoring technology has such a framework structure. The power monitoring chip is generally placed inside the battery pack. The part surrounded by dotted lines in this picture is the battery pack. This battery pack generally has lithium battery cells, which is the battery electrical symbol seen here, and the power monitor represented by the red square, which is where the TI device is located.
There is also a protector that controls the MOS tube. This protector switches the MOS to protect the battery cell when the battery is overcharged or over-discharged. Generally, a thermistor is placed in the battery pack to monitor the temperature of the battery pack. In addition to the system board of the mobile phone or tablet computer on the left, the main things related to the fuel gauge on this system board are the power management chip and the host processor. The host processor usually reads the power information in the fuel gauge through I2C or the single-line HDQ bus.
With this power information, we can decide how much time it will take for the battery to be fully discharged. When some users want to do something, we can remind them whether the battery has enough power. This is a traditional solution, that is, putting the fuel gauge inside the battery pack. TI's main devices in this regard are the two main chips BQ27541 and BQ27545. We have subsequently launched the BQ27441, which is a relatively low-cost solution. We also have the BQ27741, which is a solution that combines a fuel gauge and a protector. We also have the BQ28z560, which is also a solution that combines a fuel gauge and a protector.
2.3 System-side Impedance Tracking Fuel Gauge
With the advancement of technology, or the introduction of TI's impedance tracking technology, there is now such an application, which puts the fuel gauge on the side of the device's motherboard. On the battery side, there is only a protector and MOS tube, as well as a thermistor, and of course a battery cell in it. What are the benefits of this? The cost of the battery pack is greatly reduced, and it is easier to find suppliers of battery packs, because he moved the fuel gauge from the battery pack to the host side, so such solutions are now feasible, and TI provides support for both solutions. There is also BQ28z550, which is a solution to put the fuel gauge on the system board of the portable device, so that the battery pack does not need a discharge gauge, which can reduce the cost of the battery pack and make it easier to find suppliers. This type of TI fuel gauge mainly includes BQ27510, BQ27520, BQ27441 can also be used in this occasion, and there are also BQ27425, BQ27421... and other chips.
2.4 What are the functions of the fuel gauge?
a. Communication between battery and user
- Charging or discharging current
- Battery runtime and remaining capacity
- Battery health information
- Overall battery power management (operating mode)
What are the main functions of a fuel gauge?
The fuel gauge must first complete the communication between the system and the battery. If the system wants to know how much power the battery has, it needs to communicate with the fuel gauge through the bus. I just mentioned that I2C and the single-line HDQ bus communication are used to obtain this information. During the communication process, what main information can the system obtain?
The first is the measured analog information, such as battery voltage, battery charge and discharge current, and battery temperature. These basic analog information, as a fuel gauge, are more important to provide battery capacity information, that is, the remaining battery capacity, battery operating time, and battery health information. Another is that the chip itself must be able to complete the transition of working conditions, that is, it must switch from normal working mode to low power mode. What is the purpose of achieving this transition? To save power.
2.5 How to implement a fuel gauge
How to realize power monitoring?
The first method is voltage-based power monitoring. The power percentage or capacity percentage is regarded as a function of the battery voltage. This is a formula obtained from experience. Of course, the expression of the function itself does not have to be obtained. It only needs to obtain a table corresponding to the open circuit voltage and capacity percentage. The data between each point in this table can be obtained by the difference compensation method.
Another method is coulomb counting, which is the energy obtained by integrating the current charged into or discharged from the battery. We can think of the battery as the fuel tank of our car. The amount of fuel charged into and discharged from the tank can be used to calculate the amount of fuel left in the tank. This is also a relatively intuitive algorithm based on life experience.
The latest algorithm now is the impedance tracking algorithm. This algorithm actually obtains the battery capacity based on the real-time measurement of the battery's internal resistance. Its formula is the formula in the figure, which has been listed just now. That is, the battery terminal voltage V is equal to the battery's open circuit voltage minus the current multiplied by the battery's internal resistance. This current refers to the total current flowing into or out of the battery.
2.6 Voltage-Based Fuel Gauge
Next, I will introduce the voltage-based fuel gauge. This figure is a battery open circuit voltage curve. The basic idea of this method is to use different grids to represent the battery capacity for different voltages. For example, at 4.2V, 4 grids are used to represent a full-grid battery; at 3.8V, I may use 3 grids to represent the battery capacity, 3.6V uses 2 grids; 3.2V may use 1 grid to represent the battery capacity, that is, different grids are used to correspond to different battery voltages to represent the battery capacity. This method has poor accuracy and is usually used in the earliest low-end cellular phones or early digital cameras. What is the problem with this method?
That is to say, when the current fluctuates, it will jump up and down. For example, when I have a discharge current, or when the current is relatively large, during the discharge process, you can see at the red arrow, if the current suddenly decreases at this point, or suddenly becomes 0, the voltage will obviously rise. Generally, when the voltage is raised to this point, its number of grids will become 2 grids, and the change will be more obvious when it goes down. When it goes down further, the number of battery grids may be close to 0 grids or the number of battery grids may be represented by red. At this time, the jump will change from red to 2 grids, and it will jump back and forth. If the current changes, for example, he just made a phone call and it was stopped here, and there were only 2 grids left in the battery. He thought there was still power, and then suddenly another call came in, and it suddenly became 0. Therefore, the error of this representation will be relatively large, because you can see that 4 grids are actually used to represent the battery capacity here, because 1 grid corresponds to 25% of the capacity, so jumping one grid will have a capacity difference of 25%, and jumping 2 grids will have a capacity difference of 50%, so this method has a relatively large error. The reason for the large error is that the battery has internal resistance. When the current is large, the number of cells will jump more frequently.
This is a formula for the open circuit voltage and terminal voltage of the battery. As mentioned earlier, the internal resistance of the battery is a function of temperature, charge state and battery aging. The internal resistance of the battery will double after 100 charge and discharge cycles. The impedance deviation of the same batch of batteries may be 10~15%. The internal resistance deviation of different battery manufacturers or manufacturers with poorer quality will be greater.
2.8 Impedance is related to temperature and DOD
The information that has the greatest impact on the capacity calculation or is the most difficult to obtain is I*Rbat. Of course, I is relatively easy to obtain, as long as the current flowing in and out is measured. With current technology, this can be measured with an accuracy of ±1mA. Rbat is relatively difficult to measure because it is calculated based on two quantities. This is the relationship between impedance, temperature, and capacity percentage. This relationship has been discussed just now. Basically, impedance increases with decreasing temperature and increases with decreasing capacity percentage. This is the concept.
2.9 Impedance Difference of New Batteries
This is the impedance deviation. What is the concept of this? That is to say, the impedance used in general has a greater impact on the power measurement. The impedance refers to the impedance in the low-frequency state, which is the impedance at 1mHZ. In fact, it is the DC impedance, not the impedance measured by the internal resistance tester we usually see on the market. That impedance is the battery internal resistance measured at 1KHZ, which usually looks smaller. The above are the three factors that have been introduced that affect the accuracy of capacity calculation, which are temperature, capacity percentage and aging degree. These will affect the calculation of capacity. This impact refers to the impact of the method of using voltage to monitor power. In addition to the influence of these factors, if the voltage monitoring method is used, there is another impact that cannot be ignored, and this impact is also difficult to deal with. This is a headache for many power management engineers, that is, the problem of transient response of the battery.
2.10 Battery-Transient Response
From these two pictures, you can see that the battery is discharged when it is fully charged. The curve in front shows a discharge process. At this time, the voltage is relatively low, and then the load is removed. At this time, the battery voltage does not immediately return to the current of 0, because you think that the current becomes 0 when the load is removed. Does the voltage at this time return to the voltage of 0 current? No. It slowly goes back up, and it takes a long time to go back up, as you can see from this curve. Your usual experience can also prove this point. That is to say, after a battery is discharged, and you remove the load, its voltage is constantly changing. So how long does it take for this voltage change to stabilize? You can see that this point is about 1600 seconds. It basically takes 3500 seconds to stabilize, and it takes about 2000 seconds to stabilize. This is a discharge at a voltage of about 3.8V to 3.9V, which means that the battery is not full at this time. According to what I just said, when the battery is full, that is, when the battery capacity percentage is high, the internal resistance of the battery is relatively small at this time, and it recovers relatively quickly when the internal resistance of the battery is relatively small. In the following figure, you can see that the voltage here is relatively low. It starts discharging from about 3.3V. After a period of time, this time is also very short, because when the voltage of the lithium battery is relatively low, it will be close to the lowest acceptable voltage of 3.2V system after a short discharge. At this time, if it stops discharging, how long will it take for the voltage to return? Basically, it takes a longer time, such as more than 3000 seconds to stabilize the voltage. Therefore, during this period of time, its voltage is not stable enough, but there is no load, and the current is always 0. At this time, when you read the voltage, the voltage is constantly changing. What is the corresponding capacity percentage? At this time, errors will occur.
2.11 Voltage Relaxation and Charge State Error
You can see that the voltage difference between 20 and 3000 seconds can exceed 20mV. So when calculating the capacity, the voltage value of 20mV can cause a large capacity deviation, especially in the flat area of voltage discharge. It can cause a large capacity deviation. Therefore, the transient response of the battery will cause a relatively large error in the measurement method using voltage monitoring.
In this curve, the discharge curve of the battery is reversed. The ordinate becomes the capacity percentage, and the abscissa is the battery voltage. What does this picture mean? That is to say, at this stage, the battery is actually in the middle stage. If you stretch this platform a little bit, you can see that the voltage changes slowly during this period, and the capacity changes greatly. In other words, if you use voltage to monitor the capacity during this period, a slight error in the voltage will cause a large error in the capacity. The picture on the right refers to the error in the corresponding capacity under different voltages. You can see that at the middle point of the voltage, that is, the voltage of the discharge curve is flat, which is about 3.7 to 3.8V. The error corresponding to this period is the largest, and the error corresponding to this period can reach 15%. This is the error caused by the voltage method to calculate the capacity.
Therefore, the errors based on voltage monitoring and measurement are mainly caused by the following aspects. One is the relaxation error, which is the voltage recovery time of the battery after the load is removed. A typical value here is a relaxation measurement error of 20mV. The actual error will be much larger than this relaxation error. You can take a look after the battery is discharged. From the time the discharge is just finished to the time the voltage stabilizes, their voltage error is actually very large.
There is also a 15% resistance error between batteries. As I just said, if the same batch of batteries produced by the same supplier has better process control, the internal resistance deviation of these batteries may be 15%, which is still a relatively good situation. If different suppliers or suppliers have poor process control, the resistance error between batteries will be greater. In the figure on the left, we can see that the red refers to the relaxation error caused by the transient effect of the battery, and the light blue curve above is the error caused by the deviation between the individual impedances of the battery. The total deviation of these two combined can be about 15%. This is 15% for new batteries, or a test result obtained when the current is well controlled.
2.12 SOC Error Based on Voltage-Based Power Monitoring
As you know, another factor that has a big impact on the calculation of battery capacity is the age of the battery. In this figure, the errors measured under different ages of use, the red one represents the error curve obtained in the first or 0th cycle, which is about 15% of this graph. The last one marked here is 15%. After 100 times, you know that the impedance has actually increased by 1 times. You can also see from the previous figure that after 100 cycles, the internal resistance of the battery has increased by 1 times. According to this rule, the error will become larger and larger, and the error caused by the impedance error to the capacity will also become larger and larger accordingly. Therefore, basically after 300 cycles, the error caused by the relatively low capacity will be very large, 75% or more. Therefore, the power calculation technology based on voltage measurement can only be used in those occasions with low requirements. Its error is relatively large, usually in the early diqital camera The capacity of the battery inside is calculated using this method, so the biggest influence on this capacity calculation is the internal resistance of the battery. The reason for the large change in the internal resistance of the battery is that the battery manufacturing process causes the deviation of the internal resistance of the battery. Another reason is that the delay in battery use time will cause a large change in the internal resistance of the battery. It is difficult for engineers to know an accurate model for these changes, and they can only estimate based on experience. The estimated results will have a large deviation from the actual results.
3. Voltage-based fuel gauge
3.1 Voltage-Based Fuel Gauge
a. Advantages
- Learning without fully discharging
- Self-discharge does not require correction
- Very accurate at low load currents
b. Disadvantages
- Poor accuracy due to internal battery impedance
- Impedance is a function of temperature, aging and state of charge
To summarize, the disadvantage of the voltage-based fuel gauge is that it has poor accuracy due to the internal impedance of the battery. There is a functional relationship between impedance, temperature, aging status and battery capacity percentage. This functional relationship is quite complicated. Only professionals who specialize in batteries can find a relatively approximate functional relationship. It is difficult to find an accurate functional relationship. Therefore, this model is quite complicated. It is difficult for general electronic engineers or software engineers to write a very accurate relationship. Therefore, the calculation of capacity in software calculations is the most headache for engineers. Then it also has some advantages. The advantage is that it can get the current capacity of the battery without full discharge.
Because anyone who has worked in battery and battery pack production, or has used a fuel gauge knows that a fuel gauge generally needs to be fully charged and discharged before it leaves the factory. Why do we need to charge and discharge? This is to determine the current battery capacity and the full charge capacity of the battery, especially the full charge capacity of the battery. Different batteries have different full charge capacities. Of course, you can choose a battery design capacity, but the deviation between different batteries and the design capacity is still relatively large. To obtain this full charge capacity, you still need to do a complete charge and discharge. Then the specific charge and discharge requirements for the production process are relatively high, and a lot of direct costs will be added.
In addition, the battery has the characteristic of self-discharge. When the battery is placed there, even if the load is not working, the battery will leak electricity. After a long time, the power will become less and less, and the voltage will become lower and lower. Then the voltage monitoring fuel gauge only needs to judge the capacity based on the voltage, so the capacity is reported according to the voltage, so the self-discharge does not need to be too concerned. Therefore, this voltage-based fuel gauge can still achieve a certain degree of accuracy if the current is very small. However, at present, various applications are becoming more and more complex, and the current changes are getting larger and larger, so it is a bit difficult for the voltage-based fuel gauge to meet customer requirements.
3.2 Power Monitoring Based on Coulomb Counting
In addition to voltage-based fuel gauges, there is another type of fuel gauge, which is coulomb counting fuel gauge technology.
The idea of this fuel gauge is to first charge a battery to full, and during the charging process, you can know the current capacity of the battery, that is, the full charge capacity of the battery, and then during the discharge process, subtract the discharge capacity of the battery from the current capacity to get the remaining capacity of the battery. Its idea is actually to integrate the current over time to get the amount of capacity discharged, and thus get the remaining capacity of the battery.
With this technology, a record of the discharged capacity will be kept at the end of each discharge, and this recorded capacity will be used as the full charge capacity of the battery. Therefore, Qmax will be updated at the end of each discharge, that is, the chemical capacity and maximum capacity of the battery will be updated.
3.3 Learning before full discharge
In theory, this is true, but in practice, when updating the full charge capacity or chemical capacity of the battery, it is not necessary to completely discharge the battery before updating, because the battery voltage will be very low at this time, and the system may have to shut down or something happens. At this time, it is too late. The usual update is to update the battery capacity when it is about 7%. The idea of this update is that when the capacity reaches 7%, it means that 93% of the capacity has been discharged. If the capacity just discharged is integrated, the mAh number of the capacity will be discharged. Dividing this mAh number by 93% can get the full charge capacity, which also achieves the effect of learning. Therefore, learning is generally not done when it is 0%, but generally at 7%. As for learning, what is learned is the full charge capacity of the battery. After the full charge capacity is obtained, the discharge current is integrated to calculate how much capacity is left, so the power of the fully charged battery is also important for the calculation of power. As for the voltage corresponding to 7% and 3%, it depends on the current, temperature and impedance at the time. Generally, when the current is constant at room temperature and the impedance of the same batch of batteries does not differ too much, this voltage can also be considered basically constant, because it is 3.5V at 7%. At this time, the voltage deviation will not cause too much deviation in capacity, so it can be corrected at 7%.
3.4 Compensated End-of-Discharge Voltage (CEDV)
The 7% mentioned just now actually means that under given temperature, current or the same batch of batteries, the voltage at this point is basically fixed, but in fact its current cannot be a fixed current. During use, the current will always change, so the voltage corresponding to 7% is also different, that is, the 7% corresponding to different currents is different.
In this curve, the discharge current is I1, and the voltage corresponding to I1 is 3.5V in this curve, which is represented by CEDV2. CEDV2 is a function of I1. If the current changes, and the voltage is corrected by 7%, the error will be large. From the CEDV curve, we can see that the voltage corresponding to 7% actually has 30% remaining capacity. If we synchronize or learn according to 7% to correct the full charge capacity, 23% of the capacity will be lost, which will cause a large error. Therefore, the algorithm must correct the voltage at 7% based on the current. I call the voltage at 7% CEDV2. Find the functional relationship between the voltage at this point and the current, and get different voltages under different currents. So in the case of current I2, we get CEDV2. In fact, its voltage is a little lower than 3.5V. CEDV2(I2) is actually obtained based on complex calculations. Its formula is roughly as follows: CEDV=OCV(T,SOC)-I*R(T,SOC). The C in CEDV is compensation, and EDV is the termination discharge voltage, that is, the compensated termination discharge voltage is actually equal to the open circuit voltage of the battery minus the voltage drop caused by internal resistance. The key is that in this formula, OCV(T,SOC) can find a function that matches the curve better, and this curve will not change much, but the latter curve is a function of T and SOC, and it is difficult to find a matching function for this curve, so this formula is quite complicated.
Due to the existence of internal resistance differences, the accuracy of this formula is limited during use. This does not mean that this formula is universal throughout the entire discharge process. Usually, when we use this formula to calculate below 7%, it is used, that is, a functional relationship of R (T, SOC), which can be found in our datasheet. The applicable range is only after 7% or 12%. This is actually enough, because the correction finger only needs to be corrected at around 7%, so the problem of its small applicable range is not big. Then before 12%, Coulomb calculation is still used for integration. The error caused by Coulomb calculation integration can be compensated by voltage correction after 12%. This is the simple idea of the CEDV algorithm. This formula actually reflects the relationship between impedance, temperature and SOC. This relationship reflects the impedance of the battery. Once the general parameters in this formula are determined, the relationship between impedance, temperature and capacity percentage is determined. In fact, as the battery ages, the internal resistance will definitely change, but this formula does not actually reflect the difference between the internal resistance of the battery and the age of use. This formula cannot reflect this difference. Of course, we have made improvements to our subsequent algorithms and added some linear compensation. This can be done in our chips with CEDV, such as TI's BQ3060, and the earlier BQ2084 and BQ2085, which are made using the CEDV algorithm.
3.5 Battery Management Products - Battery Capacity Monitoring - BQ3060
3.6 Power Monitoring Based on Coulomb Counting
-Not affected by voltage measurement distortion
-Accuracy determined by current integration hardware
- Monitoring error: 3-10% (depending on working conditions and usage)
- Requires a learning cycle to update Qmax: Battery capacity decreases with aging, Qmax less: 3-5% (100 charges)
- Without learning, the monitoring error will increase by 1% for every 10 charges, and self-discharge must be modeled: inaccurate
Main parameters related to aging: Impedance
What are the advantages of coulomb counting-based power monitoring?
Because it mainly calculates the amount of electricity based on current integration, the distortion of voltage measurement has a relatively small impact on it. The accuracy of the current is determined by the hardware of the circuit integration. If you control the parameters of the entire CEDV algorithm well, the error can be controlled within 3% or even lower. If the parameters match the actual battery model, the error may be larger. The overall error is probably around 3~10%, depending on the working conditions and usage.
Its disadvantage is what I just said, because it uses coulomb counting, that is, the capacity is calculated by how much electricity is charged and how much electricity is discharged. The premise is that it needs to know the full charge capacity of the battery to calculate the remaining capacity of the battery. This full charge capacity is generally updated before leaving the factory, because the deviation between the full charge capacity and the remaining capacity of the battery is still relatively large, and the remaining capacity of the battery cannot be directly used as the full charge capacity. Therefore, before the battery leaves the factory, a charge and discharge cycle must be performed to obtain the full charge capacity of the battery. The full charge capacity is obtained based on the cycle. The cycle requires special tools to be equipped on the production line, so this is more time-consuming.
The capacity of the battery will also decrease with the increase of years of use. Of course, the decrease is not as significant as the impedance, but there will be a 3~5% decrease after 100 charge and discharge cycles. This decrease must also be compensated. Why? Because in actual use, not every discharge can be learned, because our electrical equipment (mobile phone or laptop) is discharged, it may not be discharged from full charge to empty, or below 93% to let you update the full charge capacity. Generally, it may be discharged to half, or the adapter is plugged in immediately after a slight discharge. In this case, the discharge is very shallow, and it may not have the opportunity to update the full charge capacity. In the absence of an update, the error of monitoring will increase by 1% for every 10 charges. In this case, the error of Qmax will become larger and larger if it is not updated. Therefore, in actual use, if you use an old-fashioned power meter, if you have such experience, you may let the laptop be fully charged and discharged once a month to let it continuously update the Qmax parameters inside, so that it can be relatively accurate. Another one is to estimate the self-discharge of the battery, which is inaccurate because, as mentioned earlier, the voltage-based power monitoring technology determines how much power the battery has, and then checks to see how much is left. As for how much power the battery has discharged internally, it does not care.
If it is a coulomb meter, it does not judge the capacity mainly based on voltage, but on the charge and discharge of current. The coulomb meter's monitoring chip cannot monitor the charge and discharge of the battery, because the coulomb meter is connected to the outside of the battery and can only monitor the current flowing in and out of the battery. It cannot measure the current consumed inside the battery, so it can only use a simple model to estimate how much is discharged each time, so the result is not very accurate. The delay in the service life will also cause an increase in errors, so there is a relatively large factor here, which is the aging of the battery. The coulomb meter is more limited in dealing with aging. The impact caused by aging is that the capacity will decrease with the increase of aging, and the battery impedance will increase after aging. As mentioned earlier, when the impedance of the battery increases, the error in the calculation of the CEDV of the battery will also increase, because in this formula, the impedance is only related to the temperature and the capacity percentage. The estimation of the capacity is added, which is actually a linear estimate, and there is still a certain difference with the actual battery. Therefore, the error in the contribution of the impedance to the capacity will increase with the increase of the battery age. Therefore, the CEDV algorithm takes into account the correction of battery impedance to voltage, but it does not take into account the factor of battery impedance changing over time, or it considers it in a relatively simple way.
Therefore, the traditional power monitoring method can use the voltage monitoring method to obtain a relatively accurate capacity when there is no load, and can use coulomb counting to obtain the capacity when there is a load, so these two methods are complementary. In fact, the chips available on the market basically use these two methods in combination.
3.7 Advantages over Typical Fuel Gauges
3.8 Battery Management Products - Battery Capacity Monitoring - BQ3060
Therefore, no matter it is a voltage-based power meter or a current integration-based power meter, the impedance has the greatest impact on the calculation of capacity. The impact of aging in this impedance is based on a simple linear model, or in other words, there was no such impact of aging in the early days. Since the model it is based on is relatively simple, the actual matching success with the battery is relatively poor, that is to say, the error caused will become more and more obvious as time goes by. Therefore, the factor that has the greatest impact on battery power calculation is actually the battery impedance. If we can get the battery impedance anytime and anywhere, then we can get a more accurate calculation of the battery capacity.
4. Advantages of impedance tracking technology
Next, we will introduce TI's power monitoring technology (which we call impedance tracking technology) and its advantages.
4.1 Current Monitoring
- Voltage-based power monitoring: provides accurate monitoring under no-load conditions
- Coulomb counting based power monitoring: provides accurate monitoring under load conditions
-Combines the advantages of voltage-based and current-based monitoring methods
-Real-time impedance measurement
- Uses open circuit voltage and impedance information to calculate remaining run time at given average load conditions
I just mentioned that voltage-based power monitoring technology can provide relatively accurate power monitoring under no-load conditions, and coulomb counting-based power monitoring can provide accurate power monitoring under load. Our impedance tracking technology actually integrates the advantages of voltage and current monitoring methods. Why can it obtain the advantages of both methods?
Because it measures the impedance of the battery in real time, it does not find a formula for battery impedance and then compensate for some factors. It finds a method to measure impedance in real time. Because it is measured in real time, there is no need to compensate it according to the model. Knowing the battery impedance, the open circuit voltage and impedance information can be used to estimate how long the system or battery can provide or how much capacity it can provide for system operation under a given current. This formula is a little more detailed here, that is, the terminal voltage of the battery is equal to the open circuit voltage of the battery minus the voltage drop on the internal resistance. The voltage drop on the internal resistance is mainly caused by the internal resistance of the battery. The internal resistance is determined by three factors: temperature, capacity percentage, and age. However, if you want to use a formula to express this internal resistance, it will be quite complicated and the effect is not ideal. Our method is actually to measure the impedance in real time.
4.2 Comparison of OCV curves
What is the basic idea of impedance measurement? In the actual use of the battery, the battery terminal voltage will change with many situations. As mentioned earlier, the battery terminal voltage may change with the current size, and of course the battery terminal voltage will change with the capacity percentage. At the same percentage and the same current, the battery terminal voltage may also be related to the temperature and the degree of battery aging, but this is only a surface phenomenon we see. In fact, more fundamentally, the open circuit voltage curve or the electromotive force of the battery is relatively not so obvious with the influence of these external factors. We can find some common things. Batteries produced by different manufacturers under given test conditions, such as at the same temperature, the curve error is very small.
This curve is the open circuit curve measured by the batteries made by 5 battery manufacturers. You can see that these open circuit curves are basically the same. They are measured at the same temperature. Because it is the open circuit voltage, there is no current. Of course, its measurement process is also quite cumbersome, because it needs to obtain the open circuit curve when the current is approximately 0. Its testing process is still quite cumbersome. From this curve, we can see that this curve basically does not change with different manufacturers. The impedance may change greatly due to different processes, but this open circuit voltage curve is basically the same for everyone. Most of the voltage offsets are less than 5mV. The prediction error of SOC based on this voltage is generally within 1.5%. So once such a curve is found, the same curve can be used to calculate the batteries made by different battery cell suppliers. The calculation of this curve can know the open circuit voltage of the battery, and can reversely find the battery capacity percentage. It is mainly such a curve. After knowing the battery capacitance capacity percentage, knowing the chemical capacity or full charge capacity of the battery, you can know how much mAh of power it has left, then you can calculate how long it will run, and the subsequent capacity percentage can be further calculated.
The following figure is an enlarged diagram of the error. This error is a voltage error during the entire discharge process, including the influence of the measuring equipment. This error is between ±15mV. Such an error is probably within ±1.5% of the capacity error and SOC calculation error. Why? Because the voltage error in this place is also related to the measurement accuracy of the instrument. After taking the measurement accuracy of the instrument into consideration, the resulting capacity percentage error is within 1.5%.
This picture is the same, this picture is not a new battery, but a relatively old battery. It is also turned off at 3.5V and turned off when there is 10mAh capacity left. In this case, its time is increased by about 58%.
This is the case at low temperatures. The effect of extended time at low temperatures is more obvious because the internal resistance at low temperatures increases significantly. The time used here is extended by 121%.
Under this test condition, its load current changes more, in this case it can even be extended to 290%, why? Because if it is in low temperature and in this place, it will shut down, this time is quite short, it will shut down not long after the discharge, then if the impedance tracking technology is used, it can continue to discharge for more than 80 minutes before shutting down, because as long as the 10mAh capacity is retained, it is enough to shut down, so this can extend a lot of time, I do not absolutely decide whether to shut down based on the voltage as a rigid indicator, but decide whether to shut down based on the remaining capacity, in this case, only the impedance tracking technology can calculate how long it must shut down, so the use of impedance tracking technology can greatly improve the user experience, user experience in the current portable consumer electronics products to expand sales, bring competitive advantages it is a very important factor.
So the advantage of impedance tracking technology is that, to be more specific, it can be used in some places. What I just introduced are some of the more intuitive advantages that can be thought of. In fact, with the continuous improvement of the algorithm in the impedance tracking technology, the impedance change caused by the continuous rise and fall of the battery temperature during use has added the estimation of the temperature model, introduced thermal simulation to adjust the heating of the battery, and also learned the change of the load during use. That is to say, under the usage habits of a user, the change of the current of an electrical device has a certain law. Then the impedance tracking chip will slowly learn this law during use, and grasp the voltage drop caused by the load change. These voltage drops are actually considered for capacity calculation, and these factors must also be considered. Of course, as mentioned before, for aging batteries, since impedance tracking calculates the impedance of the battery in real time, it does not need to use a model to estimate the aging battery. It is the impedance measured, so the impact of aging is relatively small. Because it accurately calculates the capacity, it can maximize the use time, which can be clearly seen from the pictures just now. With the impedance tracking chip, our host system no longer needs any algorithm to calculate the battery capacity, and can simply read the specified register to get the capacity. With impedance tracking technology, you can also conduct some thorough analysis of the battery, such as the battery aging degree, battery health status, etc.
5.2 What does it mean to get the used battery capacity?
Another advantage is that with the use of impedance tracking technology, the battery capacity can be calculated more accurately. With more accurate calculation of battery capacity, this fuel meter can actually bring you cost savings.
For batteries, the cost of a 100mAh battery is about $0.15. For example, a battery with a larger capacity can be obtained by reducing the discharge termination voltage. Here, the TV value is the discharge termination voltage. Reducing 500mV can increase the capacity by about 5%. For example, if the original 3.5V is reduced by 3V, the capacity can be increased by 5% by 500mV. For a 1500mAh battery, it actually saves about 5%, 75mAh capacity, which saves you $0.1.
Of course, this is only 0.1 USD, but as the battery ages, reducing 500mV will increase the capacity by 50% instead of 5%, so the savings is about 1 USD. Of course, this is for a capacity of 1500mAh. As the battery capacity gets larger, the amount of money saved will increase because the power consumption of smart devices is getting higher and higher.
5.3 Losses caused by inaccurate monitoring
Therefore, when designing a system, customers should not only consider the cost of a chip, but also consider how much cost it reduces for you to choose a battery. Because of the impedance tracking technology, a more accurate power calculation chip, the selected battery capacity can be more accurate, and there is no need to leave too much margin. There are many losses to customers due to inaccurate monitoring in real life. For example, if the customer charges and discharges every day, 3 months is about 90 days, and about 90 charges, the internal resistance of the battery will increase by 1 times. At this time, the battery will age by 100 times. If you do not use an impedance tracking power meter, the impedance of the battery will increase by 1 times, which will cause errors in power calculation. Since its original power meter calculates power according to a relatively small internal resistance, the actual internal resistance has increased by 1 times, so the internal resistance it calculates is bound to have a relatively large error. What kind of situation will it cause? It will tell you more running time, but the actual running time is much smaller than this, resulting in a sudden shutdown. This sudden shutdown has a great impact on the system. The sudden shutdown of our laptop may cause the system to crash. Then the user will feel that the battery life is greatly shortened, and this shortening may not be caused by battery aging.
The shelf life of the battery may be 1 to 2 years, but the system suddenly crashed after only 3 months of use. The customer may ask for a refund, which will cause financial losses to the company. This is just an example of economic losses caused by an inaccurate power meter.
a. For portable electronics, accurate metering is just as important to achieving long operating time as reducing power consumption and using strong batteries.
b. There are many types of fuel gauges available, which use different monitoring methods and different trade-offs.
So for portable battery products, accurate monitoring is just as important as reducing the power consumption of the design and using a strong battery to achieve long operating time. Because if you want a strong battery, you need more mAh, which actually increases the cost. If you use an accurate fuel gauge to calculate the maximum available capacity of the system, you can use a relatively low-capacity battery, which can save costs.
There are many available fuel gauge solutions, which are generally based on a compromise between voltage monitoring and coulomb counting. Only voltage monitoring or coulomb counting is rarely used. Our TI method is basically the best combination of the advantages of both methods to create a fuel gauge method.
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Disclaimer: This article is from TI Document-SSZB130B. The copyright belongs to the original author. If there are any copyright issues, please contact us in time. Thank you!
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