1. Introduction
Steadily increasing pollution is especially harmful to urban areas [
1,
2,
3,
4] and the health of the people living in them [
5,
6,
7]. The EU Parliament agreed on a regulation for the transport sector which calls for a 30% reduction in CO
2 emissions by 2030 relative to 1990 [
8]. To achieve this goal, electrification of the private and especially the public transport sectors is of great importance. Primarily through the electrification of buses and trains, it has become possible to reduce emissions in urban areas [
9]. Local public transportation services are usually well established in regard to their structure. Problems such as the range of the battery electric vehicles and the required charging infrastructure, which are quoted frequently as exclusion criteria for electrification in the private transport sector, are rated differently in the microsystems of public transportation [
10].
Due to high loads and long daily periods of use, battery systems used in commercial vehicles face much greater challenges than those in passenger cars. Market success is closely linked to durability [
11,
12,
13], which makes constant monitoring of the battery’s operating conditions indispensable [
14,
15,
16]. Consequently, existing monitoring concepts such as those suggested by Pop et al. [
17] need to be enhanced. This is especially the case for battery-aging monitoring systems to achieve a more sustainable battery lifecycle [
18,
19,
20].
In principle, two main effects can be observed in battery aging: battery capacity losses by losing lithium inventory, and active material and increasing internal resistances, where the former leads to a loss in drive range and the latter to a reduction in performance. This work focuses on the estimation of state of health (SoH) in terms of capacity losses over a battery’s lifetime.
We define capacity SoH
according to Bauer [
21] and Jossen et al. [
22] as the ratio of the actual capacity
and the nominal capacity
:
Closely related to SoH is the state of charge (SoC) of a battery, which we define according to Fleckenstein and Jossen et al. [
15,
22] as the ratio of the charge
currently stored in the battery and the actual capacity
:
A good SoH estimation is important for two reasons in particular. First, safety risks arise when a battery is operated outside its specified SoH limits; that is, the cells are used longer than agreed with the cell manufacturer. Second, a poor SoH estimate affects the SoC estimation, as can be seen in Equation (2). This can lead, for example, to the battery being discharged more deeply than intended, which in turn can cause permanent damage to the battery.
SoH estimation methods can typically be divided into three groups. Yao et al. [
23] distinguishe between model-based-, data-driven- and fusion-technology-methods. The group of model-based methods includes equivalent circuit models as well as electrochemical models. Neural networks and statistical filtering methods belong to the data-driven methods. The last group describes a combination of several methods. Some concepts are listed below.
Soon et al. [
24] describe an energy throughput-based method for SoC and SoH calculation. The authors show the dependency of the SoC accuracy on the precision of the residual capacity estimation. If the SoH confidence level is low, SoC deviations of up to 10% can occur. Both variables interact with each other, demonstrating the necessity of an additional function which recalibrates SoH and SoC.
Zou et al. [
25] choose an approach for SoC and SoH estimation based on two Extended Kalman Filters (EKF) with different time scales. One of them is running online to calculate SoC and the other one is used offline to estimate SoH. The EKF for SoC estimation is very accurate, with an average relative error of 0.7%. But the EKF for SoH is also precise: within a few hours, the estimation error is less than 3%. This method is highly dynamic. It only needs a few cycles to predict the correct remaining capacity value. However, due to its complexity, it needs to be computed offline instead of being directly computed on the vehicle’s battery management system (BMS). Similar results are provided by Fang et al. [
26] and Sun et al. [
27].
Li et al. [
28] introduce some different analysis methods, like differential analysis (DA), differential voltage analysis (DVA) or differential thermal voltammetry (DTV). With the results of these measurements, they train neural networks (NN) and give an outlook over the advantages and disadvantages.
Wen et al. [
29] analyze the correlation between the characteristics of the incremental capacity (IC) curve and SOH at different ambient temperatures. They establish a SoH prediction model at different temperatures by using a least square method.
Other studies focus on SoH estimation based on changes in the characteristic open-circuit voltage (OCV) curve or the final charging and discharging characteristic curve. Both Weng et al. [
30] and Wang et al. [
31] use the incremental capacity analysis (ICA) derived from the OCV curve to detect and interpret the changes. One disadvantage of the suggested approaches is that a broad SoC window must be charged or discharged at a constant current rate, which is unfeasible in most real operations.
Kong et al. [
32] performed a regression for an aging model based on the changing voltage curves by observing a fixed voltage value. The authors assume that at one SoC-OCV point there is a linear correlation between the gradient and the aging. Maher et al. [
33] show the behavior of the OCV across the SoC and the amount of charged energy as a function of aging using a Lithium Cobalt Oxide cell. As the differently aged OCV capacity curves are plotted on top of each other, the partial gradient of the curves can be observed to become steeper. This effect is to be exploited in the SoH estimator presented in this paper. Maher et al. themselves do not use the dependence on the capacity but look at the temperature behavior of the OCV and the resulting entropy and enthalpy over SoC to rate the state of the cell. Lavigne et al. [
34] also give an example of state estimation via OCV modelling.
More detailed studies on the evaluation and classification of different SoH estimation methods can be found in the reviews of Ungurean et al. [
35] and Komsiyska et al. [
16].
In contrast to most of the methods mentioned before, the SoH estimation approach presented in the remainder of this paper is designed to run during normal operation of the battery. Its functionality is demonstrated on real field data available for a period of two years. Additionally, the data are complemented by two full-capacity checkup measurements, allowing the evaluation of the SoH estimate at these points in time. Another distinguishing feature is the low computational complexity of the estimator, which favors its use on common BMS hardware.
The remainder of this article is structured as follows: First, the basic idea and the concept behind the presented SoH estimator are explained in
Section 2. Next, the experimental data used to evaluate and parameterize the estimator are presented in
Section 3. The results are then presented and discussed in
Section 4. Finally, the paper is concluded in
Section 5.
4. Result and Discussion
After all parameters have been chosen, the resulting SoH estimation performance on pack level is evaluated and discussed in the following two subsections.
4.1. Result
Figure 11 shows the simulatively determined SoH course of the presented estimator (red solid line) based on the available field data (see also
Section 3). For comparison, a lookup table (LUT)-based approach similar to the one from Huynh [
47] is shown (blue dashed line). This approach is chosen for comparison, as it is another SoH estimation method which can also be implemented directly in BMS because of its low computational complexity. Additionally, both available checkup measurement results are shown:
%, measured at the production end of line test in June 2016, and
%, measured in February 2019.
Both algorithms started with an initial SoH of 99.3%, which is the value determined by the LUT-based approach at the beginning of the operation. It results from the calendric aging that occurred within the six months that elapsed between production and operation of the pack. Cyclic aging of the pack is not present during this period.
The SoH of the LUT-based approach continuously decreases at an almost constant rate. This is not surprising, since an increase in SoH is not possible with this approach. In contrast to that, the value estimated by the observer increases within the first four months to a value of 101.3% before it then decreases at an approximately constant rate. We consider this initial behavior with an increasing SoH to be plausible, since the first checkup measurement at the end of production showed a SoH of 101.1%. The value is over 100% because the battery pack’s capacity at the start of life is determined from the cell’s datasheet. However, more charge could be drawn from the battery pack during the first checkup measurement. This explains the SoH value of over 100%. The SoH observer thus goes through a transient phase within the first four months from an initial value that is lower than the true SoH, a value of 101.3% that is most likely closer to the real value, as it is in the range of the first checkup measurement.
From April 2017 on, both the curve of the estimator and the curve of the LUT-based approach decrease almost in parallel, where the estimator’s values are about 1.9% higher than the LUT-based values. Additionally, the estimated SoH almost always remains in the envelope defined by the two checkup measurements depicted by the dashed horizontal lines. Therefore, the transient behavior and the subsequent constant progression of the estimated SoH seem to be plausible, since the battery was delivered with a SoH of more than 100% and is operated with a recurring daily duty cycle from which continuous aging can be expected. In contrast, the LUT-based approach cannot compensate for the initial deviation, as an increase in SoH is not modeled and therefore yields a too-low SoH value.
However, the estimated SoH is not strictly monotonically decreasing after April 2017. A “ditch” in the curve can be observed shortly before the second checkup measurement in February 2019. It cannot be said whether this behavior reflects the true SoH development or whether it is a dynamic phenomenon of the estimator. But, at the time of the second checkup measurement, the estimator meets exactly the measured value of 95.9%, whereas the LUT-based approach reports a lower value of 94.2%. This clearly shows that the new estimator approach outperforms the LUT-based approach, which is not able to compensate for initial deviations or individual aging mechanisms occurring depending on the respective application.
4.2. Discussion
4.2.1. Dynamic Behavior
The estimator is capable of compensating for initial SoH deviations. With the chosen parameters, the initial deviation of approximately 2% is compensated for in about four months. This might seem slow, but compared to the expected lifetime of the battery used it is rather a short period. The dynamic parameters were intentionally chosen to be conservative to avoid overshooting and to obtain a smooth curve. In practice, unknown initial deviations significantly larger than 2% are not to be expected.
The recorded data used for the evaluation have a sample time of 6 s. Typically, BMS tasks have a cycle time in the range of several milliseconds. Therefore, we expect to see a different dynamic behavior when the observer runs directly on a BMS, as the observer will be acting on more dynamic data because of the higher sample rate. This will primarily affect the data being selected by the weighting rules (Equations (5a) and (5b)), which in turn results in a different calculation of the mean correction factor mmean (Equation (13)). Therefore, it is expected that it is necessary to adapt the dynamic parameters of the algorithm when the observer is run directly on a BMS.
The accuracy and dynamic behavior of the estimator needs to be better verified. The presented results are initial validation results that give an impression of the performance and behavior of the estimator. The two available checkup measurements are not enough to evaluate the accuracy of the estimator in general. It was not possible to carry out more checkup measurements because the bus with the battery pack under consideration was in operational use most of the time and the workshop routine for carrying out the checkup measurement (see
Section 3.3) is time-consuming. Therefore, the fleet operator did not agree to any further checkup measurements. But a new field study has already been started to validate the estimator, integrated in a BMS, with more frequent checkup measurements. The results will be published in future work.
It must be noted that the observed period of about two years is short in comparison to the expected lifetime of the battery examined. Therefore, the dynamic behavior in the future cannot fully be inferred from the assessed data. It is planned to further monitor the system and to perform additional checkup measurements to obtain more confidence in the dynamic interpretation.
4.2.2. Parametrization
The parameterization demonstrated in
Section 3.4 is based on statistical analysis of the available real operating data. In cases where this is not possible, it might be an option to use synthetic data from simulations to find a suitable parameter set for the respective system. Ultimately, the option remains to set the parameters based on know-how about the system used, as the rule-based design of the estimator gives an intuitive way to understand the influence of each parameter.
4.2.3. Alternative Methods and Possible Extensions
A common approach to SoH estimation is to use a Kalman filter (KF) [
48]. The difference to the approach chosen in this work lies in the calculation of the feedback term
L (see also
Figure 2). In the Kalman filter, the feedback is computed recursively by a computational rule which results from minimizing the mean square estimation error while considering uncertainties in the system model as well as in the measurements. It can be proved that the KF gives the optimal minimum mean square error estimate under some specific conditions. While in practice these conditions are often violated, the KF still results in acceptable performance in most cases. Thus, the KF is widely used in practice. The “magic” to acquire an acceptable dynamic behavior lies mainly in the parameterization of the system noise covariance matrix. However, there is no universal approach to this, leaving engineers with a lengthy trial-and-error process. In contrast, our motivation was to develop feedback that could be parametrized in an intuitive way, since the meaning of each parameter is directly interpretable.
Currently, the internal resistance Ri in Equation (9) is considered to be constant over the battery’s lifetime, which is not true, as the resistance increases significantly as the battery ages. Therefore, the estimate of SoHc unintentionally also compensates for aging effects originating from the resistance increase. The solution would be to implement a separate estimator for the aging effects in Ri and to use the estimate in Equation (9). For example, the structure shown here could also be applied to implement such an Ri estimator.
Another possible extension to the estimator would be to add an additional model which accounts for calendric aging during long standstill phases where the estimator is not updated. However, in the commercial vehicle applications the standstill phases are significantly lower in comparison to passenger car applications, so that the estimator would be most probably able to self-correct for these deviations during the runtime after standstill phases.
5. Conclusions
In this paper, an on-board applicable estimator for capacity SoH estimation for NMC lithium-ion batteries which exploits changes in the OCV curve that occur as the battery ages is presented. Its structure is motivated by the observer concept from control theory. However, deviating from the standard structure, a rule-based feedback is introduced. This allows for an intuitive way to parameterize the estimator. Additionally, the utilized observer structure is computationally beneficial, which favors its use on BMS hardware.
The estimator is evaluated in MATLAB/Simulink with the help of real data collected over more than two years on an electrified bus fleet. Additionally, two checkup measurements were performed for one of the used battery packs: one directly after the production of the battery pack and one after roughly two years of operation. By that, at the time of the checkup measurements, the battery’s real capacity could be determined, which serves as ground-truth reference points helping to evaluate the estimator’s behavior.
By running the estimator in MATLAB/Simulink using the recorded data, its basic functionality could be demonstrated. The estimated SoH at the time of the second checkup measurement deviates less than ±0.5% from the measured SoH. Furthermore, it is demonstrated that the estimator is capable of correcting for initialization offsets. The next step we want to address in the future is to evaluate the estimator’s behavior when it is running directly on a BMS.