Method for measuring half-load internal resistance of battery capacity

At present, battery safety testing technology is facing such a dilemma: the capacity discharge test is detrimental to the battery, time-consuming and labor-intensive, and contains disturbing operating risks, so it should not be used frequently; the internal resistance test has poor judgment accuracy and is difficult to fully trust. Can we find a new method that can combine the high accuracy of the capacity discharge method and the convenience and safety of the internal resistance method? This is the "half-load internal resistance method" that is between the two and has the advantages of both. This article focuses on the theoretical basis and practical key of the half-load internal resistance method.

1. Voltage curve family of battery pack discharge

The discharge curve of a single cell has long been known as the most important performance indicator of a battery. The discharge curve intuitively shows the change pattern of the terminal voltage of the battery under a certain load current. After ignoring the details, it can be expressed as:

1) Steady and slow decline before the termination voltage;

2) Rapid drop after termination voltage;

3) The termination voltage is the inflection point between the above two line segments, and a voltage curve can be roughly expressed by the two-fold line method;

4) The product of the discharge time before the voltage inflection point and the load current is defined as the actual capacity of the battery.

Batteries are eventually used in groups in series. If the discharge curves of the batteries in the series battery group are plotted in the same coordinates, a family of curves can be formed, referred to as the "voltage curve family". Figure 1 shows a voltage curve family drawn using the two-fold line method.

The voltage curve family of the battery pack changes continuously during operation, and the changing rules are as follows: the consistency of each battery is good at the beginning of operation, and the curve family distribution is relatively concentrated. In long-term operation, the difference between the individual cells gradually increases, and the curve family distribution gradually moves to the left. The horizontal distribution of the voltage inflection point in Figure 1 represents the performance of the battery. The battery with the voltage inflection point to the left should be paid attention to or maintained. According to the specification, the battery whose voltage inflection point is still behind 80% of the nominal inflection point after maintenance should be replaced.

It should be noted that the above concept of voltage curve family is only suitable for theoretical analysis and has little value in maintenance practice, because it is sufficient to accurately monitor the time to reach the voltage inflection point, and there is no need to map the entire family of curves point by point.

2 Internal resistance curve family of battery pack discharge

The equivalent internal resistance is a real physical quantity that can be directly measured on the two poles of the battery. For the convenience of discussion, the differences between different internal resistance measuring instruments are ignored. Then, the internal resistance curve family of the battery pack under discharge can also be drawn in the same way as the voltage curve family.

The law of internal resistance change under discharge state is not as familiar as the law of voltage change, but after a lot of research, it is generally recognized that it has the following characteristics:

1) There is little change above 50% charge rate;

2) Rapid increase below 50% charge rate;

3) Before the discharge is terminated, the internal resistance may rise to 2 to 4 times the initial internal resistance;

4) The 50% charge rate is the inflection point of the internal resistance curve, referred to as the internal resistance inflection point. The internal resistance curve can be roughly represented by the two-fold line method.

The "charge rate" mentioned here is defined as the ratio of the actual power stored in a single cell to the actual capacity of the battery, which is a single cell variable; in addition, the ratio of the actual discharge capacity to the nominal capacity is defined as the "nominal discharge depth", which is a group-wide variable. It should be noted that due to the different definitions of the two, their values ​​change in opposite directions. In this way, during the discharge process, the entire battery pack implements a unified nominal discharge depth, and its value increases as it is discharged, while the charge rates of each single cell in the implementation are different, and their values ​​decrease as they are discharged.

In order to clearly express the changing law of the internal resistance curve family, a representative battery pack model is specially selected: the model group consists of 3 batteries with a nominal capacity of 1000A·h, and the actual capacities of 1000, 800, and 600A·h represent the three typical types of good, medium, and bad batteries in the battery pack, respectively. The floating charge internal resistances are 0.20mΩ, 0.20mΩ, and 0.27mΩ, respectively. Please note that the internal resistances of 1000A·h and 800A·h are both equal to 0.20mΩ. This value is definitely supported by the measured data, and it also deliberately indicates that the internal resistance distribution under full charge does have exceptions that do not conform to the correlation law of "large internal resistance and small capacity". Assuming that the internal resistance at the end of discharge is 3 times the initial internal resistance, Figure 2 is the internal resistance curve family drawn by the two-fold line method according to the above parameters.

Each curve in Figure 2 starts at 100% true charge rate and initial internal resistance, ends at 0% true charge rate and 3 times of initial internal resistance, and turns at 50% true charge rate and slightly larger initial internal resistance. Actual measurement experience shows that the error between the internal resistance change curve drawn by the two-fold line method and the actual data will not affect the analysis results of this article.

The practical significance of the internal resistance curve family is much greater than that of the voltage curve family. The key to its practical significance lies in its real-time comparability: because in the voltage curve family, what is of comparative significance is the time when each battery reaches the termination voltage, which is shown as the horizontal spacing between the inflection points in Figure 1. In the internal resistance curve family, what is of comparative significance is the different internal resistance values ​​at different discharge depths, which is shown as the vertical spacing between the curves at a certain horizontal value in Figure 2. In terms of measurement methods, the former must sample and time continuously and uninterruptedly, while the latter only needs to sample once at a specified time. In particular, the various groups of sampled values ​​at different times in the latter have very useful comparison value, that is, real-time comparability.

If the internal resistance curve family is not intuitive enough, we can learn from the idea of ​​image processing and introduce the concept of "contrast" of internal resistance distribution. Contrast is a single real-time variable that can be calculated. The introduction of the contrast concept will give the internal resistance curve family more positive academic significance and practical value than the voltage curve family.

3 Contrast curve of internal resistance distribution of battery pack under discharge

In image processing, a large contrast means a "clear" image, and a small contrast means a "chaotic" image. Similarly, for the purpose of battery testing, a large contrast means a "clear" distribution of internal resistance, which inevitably means an increase in the accuracy of discrimination.

The internal resistance contrast Fcr can be defined as:

Fcr=(Rmax－Rmin)/Rmin（1）

Where: Rmax is the maximum value in the internal resistance distribution;

Rmin is the minimum value in the internal resistance distribution.

Then, according to Figure 2, the contrast values ​​of each point from 0% nominal discharge depth to 60% nominal discharge depth are roughly calculated and listed in Table 1. Figure 3 is a single Fcr curve drawn based on the data in Table 1, where the data in Table 1 and the curve in Figure 3 both stop at 60% nominal discharge depth. The reason is that the 600A·h monomer in the model group has reached the over-discharge point, and its actual charge rate is equal to 0%.

Table 1 Fcr point-by-point calculation table The single Fcr curve shown in Figure 3 reflects the corresponding law between the discharge depth and the internal resistance contrast more intuitively than the internal resistance curve family: when the discharge depth exceeds 50% of the minimum real capacity monomer (300A·h in this case), Fcr begins to increase rapidly and usually reaches the maximum value at 50% of the nominal discharge depth (500A·h). In addition, it can be seen from Figure 3 that if the Fcr value (for example, Fcr=1.0) that is sufficient for discrimination is used as the boundary condition, the satisfaction range of the discharge depth is greatly relaxed, which means that there is no need to accurately control the discharge depth; in other words, after reaching a certain contrast, the size of the discharge depth only affects the contrast without reducing the accuracy.

Finally, it can be seen from Figure 3 that all discharge depths included in the Fcr after the contrast is enhanced are still far away from the over-discharge zone. This is the scientific basis for the safety of the half-charge method compared to the capacity discharge method.

4 Half-load internal resistance method and judgment accuracy

Based on the discharge internal resistance curve family alone, at least two new test methods can be designed.

4.1 The first method can be called "internal resistance timing method"

The idea of ​​this method is similar to the capacity discharge method, except that the monitoring timing of the voltage inflection point (i.e., the termination voltage) is changed to the monitoring timing of the internal resistance inflection point. Since the voltage inflection point has a 2-fold dependence on the internal resistance inflection point, the actual capacity can be easily calculated by simply multiplying the timing value of the internal resistance inflection point by 2.

The advantages of this method are: safer than the capacity discharge method and more accurate than the floating charge internal resistance method.

The disadvantages of this method are:

1) The internal resistance monitoring point is not easy to grasp, and inaccurate monitoring points will still cause large errors or even misjudgment;

2) It is still necessary to continuously monitor and time the internal resistance inflection point, that is, it is necessary to develop a special internal resistance monitoring and timing instrument.

The above two shortcomings need to be improved after obtaining a large amount of measured data, and this article will not discuss them in depth.

4.2 The second method is the "half-load internal resistance method"

The idea of ​​this method is: after the battery pack is roughly discharged at half load, each single cell is inspected normally and then a judgment is made based on the internal resistance.

From the test process, the half-load internal resistance method only adds half-load discharge, and the other operation methods and requirements are exactly the same as the floating charge internal resistance method. The following analysis shows which factors improve the accuracy of the half-load internal resistance method:

1) Increased internal resistance contrast The enhanced contrast makes detection easier and interpretation more reliable. Half-charge discharge can be figuratively understood as the "development" process in film photography technology. Obviously, the fully developed photo image is the clearest.

2) The small contrast of the effective sorting of internal resistance is not a fatal weakness, and it can be overcome by appropriately improving the instrument's resolution; however, the objective partial disorder of the floating charge internal resistance is the root cause of confusion and misjudgment, and this defect cannot be compensated by simply improving the instrument's resolution. Half-load discharge allows the internal resistance value to be sorted correctly, effectively correcting the initial disorder of the floating charge internal resistance, which is a key factor in improving the accuracy of judgment.

3) Closely linked to the real capacity The most important thing for battery maintenance professionals is the real capacity of the battery. The more the method can reflect the real capacity, the more reliable it is. The relationship between the floating charge internal resistance and the real capacity can be summarized as: "highly correlated but with exceptions", and it is easy to understand that the judgment accuracy is poor. The internal resistance inflection point objectively exists at 50% of the real capacity, which has been linked to the real capacity to the greatest extent. It should be said that the correct sorting and direct link with the real capacity are the most attractive points of the half-load internal resistance method.

4) Reduce the impact of non-chemical internal resistance. The equivalent internal resistance of the battery is the equivalent sum of all electrochemical internal resistances and non-chemical internal resistances. Non-chemical internal resistance also carries important information (such as internal bus bar welding defects or corrosion cracks, etc.), but it has nothing to do with the actual capacity, which makes it very difficult to correctly extract capacity information. This is also the main source of the initial disorder of floating charge internal resistance. Under the objective premise that existing instruments cannot separate different internal resistances, half-load discharge can significantly improve the proportional relationship between electrochemical internal resistance and non-chemical internal resistance, which makes an important contribution to improving the accuracy of discrimination.

The half-load internal resistance method is essentially just changing the test working point from the floating full load point to the half-load point. This small step improvement in the selection of the working point brings about the above 4 very practical improvements in indicators, and ultimately achieves a big leap in the accuracy of judgment.

Based on a large amount of measured data from home and abroad, no matter which principle or instrument is used, the single-cell accuracy of the floating charge internal resistance method generally remains at around 90% and is difficult to break through. In addition, the industry rule (barrel rule) requires that a single-cell misjudgment must be counted as a whole-group misjudgment, so the accuracy of the whole group is generally around 80%. Considering the importance of backup battery packs, it is normal and reasonable that such an accuracy rate is difficult to trust.

The half-load internal resistance method just corrects this 20% misjudgment, achieving the long-sought goal of reaching or exceeding the accuracy of the capacity discharge method. The above conclusions have been verified by preliminary experiments.

5 Discussion on key practical issues of half-load internal resistance method

Before the half-load internal resistance method can be put into practical use, there are obviously many practical problems that need to be explored and solved.

5.1 Applicable constraints

The half-load internal resistance method naturally requires the following constraints:

1) The battery pack operates normally and in accordance with the regulations, including compliance with the installation and maintenance regulations;

2) Ensure that the discharge starting point is fully float charged to ensure full charge;

3) The internal resistance meter has sufficient measurement accuracy and good online resistance

Interference capability;

4) There are other auxiliary monitoring means (such as voltage) to prevent single cell over-discharge.

These constraints are completely consistent with normal maintenance specifications and are nothing special. The emphasis on the constraints is simply to draw attention to the fact that any test beyond the above conditions may exceed the scope of application of the half-load method and produce unknown results that are inconsistent with this article.

5.2 Selection of discharge depth

You can pursue the goal of maximum contrast (most reliable accuracy) or minimum discharge depth (shortest test time). The key is to meet maintenance needs and continuously summarize and improve. Deliberately pursuing zero discharge depth, or even stubbornly believing that there is no new value as long as discharge is carried out, is extremely unscientific.

Here, we need to rationally think about the true meaning of "linked to the actual capacity": under the condition that the actual capacity is an unknown number, no discharge is equivalent to no linkage, that is to say, a certain amount of electricity must be discharged to build a functional relationship between the two, so that the mathematical factor of the actual capacity can appear in the calculation formula.

We should not ignore the essential difference between the half-load method and the capacity discharge method because the half-load method cannot be separated from discharge: the capacity discharge method theoretically requires that at least one battery be discharged to the critical point of over-discharge, which has already damaged the safety of the battery pack; while the half-load discharge method theoretically always stays away from the over-discharge danger zone and can also retain some power for emergency use.

5.3 Implementation of Discharge Depth

The discharge current can be large or small, and a dedicated load can be used, or the AC power supply can be cut off and the real load can be used; the power calculation can be manually timed, or the voltage can be automatically monitored; in short, there is no accuracy requirement for discharge measurement, and the conditions are extremely loose. In the verification experiment, the discharge depth was monitored by monitoring the voltage of the single battery less than 2.00V, and the accuracy rate was very ideal. It is particularly important to point out that the best solution should be to combine the "regular maintenance discharge system" in the original regulations, without increasing the workload or revising the regulations. Just add a test to achieve twice the result with half the effort.

5.4 Instrument accuracy requirements

The increase in contrast reduces the requirements for instrument accuracy, which means that the existing instruments are fully sufficient; an internal resistance tester that can perform well in the floating charge internal resistance test (note: the poor judgment accuracy is not the fault of the instrument itself) should be sufficient to perform the half-load internal resistance test task, no matter what principle or brand it is originally based on.

6. The evolution of battery detection technology from the perspective of the piezoresistive curve family of battery packs

The internal resistance curve family of battery pack discharge provides us with some knowledge that we were not familiar with before. New knowledge can bring about new technological breakthroughs. Future battery manuals should add data and charts of internal resistance curves. If the voltage curve family of Figure 1 and the internal resistance curve family of Figure 2 are combined into a new "piezoresistance curve family" as shown in Figure 4, it will bring more complete knowledge about batteries.

Interestingly, we can also see the evolution of battery testing technology from the piezoresistive curve family, which can also deepen our understanding of the essence of the half-load internal resistance method:

1) The oldest open circuit voltage method is located at the left starting point of the voltage curve and must be supplemented with acid measurement;

2) The capacity discharge method, which must be emphasized because the sealed battery cannot measure acid, is located in the right half of the voltage curve and must be monitored continuously;

3) The fast capacity test method that attempts to shorten the test time is located in the left half of the voltage curve. It is intended to use large current and large slope to extrapolate the voltage inflection point, but it ultimately fails due to the small voltage contrast and lack of accuracy.

4) The floating charge internal resistance method is located at the left starting point of the internal resistance curve. It is convenient and practical, but it is not suitable for the initial internal resistance.

It is difficult to fully trust.

5) The half-load internal resistance method in this paper appropriately occupies the wide area in the middle of the internal resistance curve family, intuitively demonstrating its advantages such as large data contrast, high accuracy, wide adaptability, and safe operation.

7 Conclusion

Internal resistance data is a very valuable information resource for batteries. Sealed batteries can be regarded as black boxes in physics. The two poles on the black box can only provide two independent electrical physical parameters: voltage and internal resistance. The internal resistance reflects the real situation inside the battery better than the voltage. However, such precious resources have not been reasonably developed and utilized so far. The half-load internal resistance method has made a bold attempt in this regard. Its core is to actively release part of the electricity in exchange for the "opening and sorting" of the internal resistance contrast to obtain a satisfactory judgment accuracy. It is hoped that the topic of this article can help open up a new academic idea for battery safety testing.