1. Introduction
Recently, climate problem has emerged as a significant issue, primarily, caused by the greenhouse effect stemming from the mass consumption of fossil fuels. In response, renewable energy sectors such as wind and solar energy have been developed to replace fossil fuels. Addtionaly, electric vehicles are being promoted as alternative to fossil fuel-based internal combustion engines along with advancements in energy storage devices designed to store renewable energy. Lithium-ion batteries (LiBs) are widely utilized in energy storage systems and electric vehicles due to their compact size, high energy density, long lifespan, low self-discharge rate, high discharge current tolerance, and absence of memory effect. However, LiBs are sensitive to overcharging, over-discharging, and ambient temperature, and variations, leading to issues such as rapid increases in charging temperature, low charging efficiency (CE), and reduced lifespan. Consequently, ongoing research aims to address these challenges. Generally, battery performance is determined primarily by the selection of battery materials and manufacturing process technology. Once the battery is manufactured, its performance is influence by the effectiveness of the battery management system (BMS) and the operating conditions determined by the user. Among these factors, the most critical aspect of the BMS is that battery charging technology significantly impacts overall battery performance. Efficient charging technology is essential for sevral performance factors, including fast charging speed, lower charging temperature, extended battery life, and improved CE.
By utilizing an effective battery charging algorithm, charging times can be reduced. Elevated charging temperature can induce thermal stress within the battery, which is linked to safety concerns such as rapid performance degradation, battery expansion, and fire hazards. Implmenting appropriate charging technology can alleviate the increase in charging temperature. An improved battery charging technology can mitigate temperature increases during charning. Enhanced battery charging technology can also prolong lifespan by alleviating the decline in state of health (SOH) associated with the number of charge/discharge cycles. Furthermore, increased energy loss during the charging process can diminish CE, thereby reducing overall energy transfer efficicency. Therefore, optimal charging technology can significantly enhance the performances of lithium-ion batteries when integrated with BMS.
The constant current-constant voltage (CC-CV) charging method [
1,
2] is a commonly used technique that initially charges the battery using constant current (CC), gradually increasing the battery voltage until it reaches the upper limit of 4.2V. At this point, the charging method switches to constant voltage (CV), and the charging curent begins to decrease until it reaches the minimum set value. The CC-CV method combines the advantages of both CC and CV methods and is relatively simple and easy to implement, making it the most widely used charging technology to date. However, the CV charging stage requires a lengthy charging time, which extends the overall charging duration. Addtionally, it does not allow for direct control of the increase in charging temperature, leading to reductions in battery life and charging efficiency (CE). To address these issues, there has been significant in improving chraing time and CE while managing charging temperature. On such advancement, the modified CC-CV method known as the boost charging (BC) CC-CV method, which enhances charging speed compared to the traditional CC-CV approach [
3,
4]. The BC method differentiats itself from the standard CC-CV by incorporating a high CC or a constant power cycle during the charging process. In this approach, a current pump is utilized in the CC mode, while a pulse current is applied in the CV mode. Experimental results indicate that the BC method achieves a higher and CE while maintaining a total charging time similar to that of the traditional CC-CV method.
The pulse charging technique has been proposed by various researchers to reduce charging time, temperature rise, and extend the lifespan of lithium-ion batteries (LiBs) [5-8]. There are several types of current pulses, characterized by their frequency, amplitude, and duty cycle. Numerous pulse-charging patterns have been suggested in the literature as alternatives to the traditional CC-CV charging method. Pulse charging relies on periodic variations in current pulses with adjustable current speeds and directions. During the charging process, the charging current can be paused, increased, decreased, or replaced with short discharge pulses for a specific duration. This technique can significantly enhance the charging performance when appropriate parameters settings and operating conditions are applied; however, it often requires complex controllers and incurs high implementation costs.
Finally, the multistage constant current (MSCC) charging method offers the advantages such as easy implementation, low temperature rise, and high CE compared to conventional CC-CV-based charging and pulse charging methods. Unlike traditional methods, the MSCC charging approach does not include a CV mode, which imposes constant stress on the battery, thereby helping to extend battery life. Instead of using the CV mode, MSCC employes multiple CC stages with varying current values. In this method, the charging current profile consists of multiple CC stages with different current amplitudes, where the current at each stage is applied to the battery until a specific criterion is met. The stage transition points in the MSCC charging method can be determined using the state of charge (SOC) or cut-off battery terminal voltage. An SOC-based MSCC charging strategy was proposed in [9-13]. In this approach, the SOC value facilitaes the transition from one constant current stage to another. The number of stages can be uniformly divided into ten stages [
11] or three stages [
12] or optimized to four stages [
13], which is applied to LiBs to evalute the charge time, charge efficiency, charge and discharge capacities, and temperature rise during charging. The SOC-based MSCC method can reduce charge time, improve charge efficiency, enhance charge/discharge capacities, reduce temperature rise, and extend the life of LiBs compared to the CC-CV method. However, because the SOC value, which is crucial for intermediate current transfer at each stage, cannot be directly measured, various methods such as Coulomb counting [
14], Kalman filtering [
15], Extended Kalman filtering [
16], and Unscented Kalman filtering [
17] have been utilized. Despite these techniques, SOC estimation remains challengng due to significant variations in battery parameters such as voltage, current, and operating temperature. Errors can arise from aging and nonlinear behavior during the battery’s operation life. Moreover, the SOC-based step transition method incurs computational costs and complexity due to the numerous parameters involved in LiB operation. Consequently, applying SOC-based transitions in practical applications can be challenging, as they rely on SOC parameters that are difficult to measure directly.
Therefore, in this study, the cut-off voltage was utilized as the transition criterion or the CC charging technology. This approach simplies the implementation of the MSCC charging method, as the cut-off voltage can be easily measured during the charging process. The cut-off voltage-based is the most commonly used criterion for transitioning from one stage to the next and is typically determined in advance by the battery manufacturer. For cobalt-based LiBs, this is generally set at 4.2V. In this method, when the cut-off voltage is reached during charging, the current is reduced, and the charging continues until the cut-off voltage is reached again. This process is repeated until a predefined number of stages is completed, making the implementation straightforward. Each CC stage can beexecuted in various configurations, including four stages [18-20], five stages [21-29], and ten stages [
30], to evaluate the life and performance of the LiB. However, dividing the charging process into five stages has been reported to be optimal in terms of computational efficiency and performance [
23]. The MSCC charging strategy has been shown to improve CE, shorten charging time, enhance charge and discharge capacities, reduce temperature rise, and extend the lifespan of LiBs compared to the traditional CC-CV method. Additionally, the cut-off voltage-based criterion is simpler and easier to implement than other SOC-based methods.
The performance indicators of the MSCC charging method, including total charging capacity, charging time, and CE, depend on the selection of current values for each stage. Thus, it is crucial to adopt an efficient method to determine the optimal charging pattern (OCP) to enhance the performance of the MSCC charging method. While mathematical techniques such as the Taguchi method [
21,
24] and Bayesian optimization [
26] have been employed to identify the optimal OCP, these methods necessitate experimental verification of candidate charging patterns, which can be time-consuming and significantly increase the time and cost associated with finding the optimal solution. In [
21], a Thevenin equivalent circuit model (ECM) was implemented, which does not require extensive experiments and time costs for lithium-ion batteries. In this study, the OCP was derived by differentiating a charging time equation consisting of mathematically derived current and voltage variables. This approach allows for easy implementation without using the CV mode to charge the battery to its maximum capacity. However, it is important to note that this method primarily optimized, neglecting various performance indicators, such as temperature rise and charging loss.
Metaheuristic optimization algorithms (MOAs) simulate the movements of plants and animals in search of food or survival, as well as the physical chaos phenomena of nature. They have been widely applied to optimization problems due to their advantages, including few parameters, ease to implementation, and the ability to achieve a balance between exploration and exploitation during optimization process. To explore the OCP in the MSCC method, the particle swarm optimization (PSO) algorithm [
31] was utilized in [
18,
23,
28], grey wolf optimization (GWO) algorithm [
32] was employed in [
27], and jellyfish search algorithm (JSA) [
33] was applied in [
28]. Furthemore, charging time (CT) and charging loss were selected as objective functions for each optimization of the performance indicators of the MSCC charging method [
27,
28]. However, CT, which is key objective of OCP, and charging loss indicator have an indirect relationship, complicating the optimization process. Additionally, calculating chraging loss during the optimization is complex.
To implement an accurate ECM, electrochemical impedance spectroscopy (EIS) is conducted to derive the internal resistance, polarization resistance, polarization capacity, and time constant values of the model. Since the cycler experimental equipment for battery charging and discharging only measures charging voltage, current, and temperature, a separate and costly potentiostat equipment is required to perform EIS analysis on LiBs.
Based on aforementioned background, this study adopted the ECM of lithium-ion batteries and the Dandelion optimizer (DO) algorithm [
34], a type of MOA. The OCP of the MSCC charging method simultaneously considers the performance indices of charging time and charging temperature. Unlike previous research methods, this study first esimated the ECM model parameters, such as internal resistance, polarization resistance, polarization capacity, and time constant, offline based on voltage measurement obtained using the hybrid pulse power characterization (HPPC) test [35-37] in the time domain. In this test, pulse charge/discharge current is applied, and only the output voltage is measured, allowing for a simpler and more cost-effective implementation of the ECM model compared to the EIS method. Second, charging time and temperature were selected as the objective functions for optimizing the performance indices of the MSCC charging method. Consequenlty, the charging temperature and the optimization objective function are direclty related, simplifying cacluation process since the charging temperature is measured diectly during optimization. Third, among the recently strudied metaheuristic algorithms, including PSO, GWO, and JSA, we selected other algorithms such as the war strategy optimization (WSO) algorithm [
38], beluga whale optimization (BWO) algorithm [
39], levy flight distribution algorithm (LFDA) [
40], and African gorilla troops optimizer (AGTO) algorithm [
41], which have been relatively frequently cited. We compared these with the DO algorithm applied in this study and evasluated their charging performance indices. By utilizing the DO, the OCP search can be conducted rapidly through application to the ECM-based platform without requiring nemerous lengthy experimental processes.
The remainder of this paper is organized as follows.
Section 2 provides a detailed description of the basic concepts of the proposed charging technique, including the construction of the battery ECM, estimation of ECM parameters using the HPPC in the time domain, derivation of the mathematical relations for the proposed MSCC charging method, formulation of the optimization problem, and definition of the objective function.
Section 3 describes the DO algorithm. Comparative simulations and experimental results against several existing methods are presented in
Section 4, demonstrating that the proposed method is more valid and effective than the current alternatives. Finally, Section 5 concludes the study.
Figure 1.
Thevenin equivalent circuit model.
Figure 1.
Thevenin equivalent circuit model.
Figure 2.
Experimental battery platform.
Figure 2.
Experimental battery platform.
Figure 3.
Current pulse charge/discharge variations.
Figure 3.
Current pulse charge/discharge variations.
Figure 4.
HPPC experimental voltage curves. (a) Pulse power tests. (b) Single pulse-power test.
Figure 4.
HPPC experimental voltage curves. (a) Pulse power tests. (b) Single pulse-power test.
Figure 4.
Identified characteristic curves. (a) OCV versus SOC. (b) , and vs. SOC. (c) vs. SOC.
Figure 4.
Identified characteristic curves. (a) OCV versus SOC. (b) , and vs. SOC. (c) vs. SOC.
Figure 5.
CC-CV charging curves. (a) Charging voltage (b) Charging current. (c) Charging temperature.
Figure 5.
CC-CV charging curves. (a) Charging voltage (b) Charging current. (c) Charging temperature.
Figure 6.
Conceptual diagram of the MSCC charging method.
Figure 6.
Conceptual diagram of the MSCC charging method.
Figure 7.
Dandelions in nature. (a) Dandelions growth. (b) Dandelion floating in wind.
Figure 7.
Dandelions in nature. (a) Dandelions growth. (b) Dandelion floating in wind.
Figure 8.
ECM model for simulation.
Figure 8.
ECM model for simulation.
Figure 9.
Charging configuration of FM . (a) Simulation. (b) Experiement.
Figure 9.
Charging configuration of FM . (a) Simulation. (b) Experiement.
Figure 10.
Charging configuration of PSO. (a) Simulation. (b) Experiement.
Figure 10.
Charging configuration of PSO. (a) Simulation. (b) Experiement.
Figure 11.
Charging configuration of WSO. (a) Simulation. (b) Experiement.
Figure 11.
Charging configuration of WSO. (a) Simulation. (b) Experiement.
Figure 12.
Charging configuration of JSA. (a) Simulation. (b) Experiement.
Figure 12.
Charging configuration of JSA. (a) Simulation. (b) Experiement.
Figure 13.
Charging configuration of GWO. (a) Simulation. (b) Experiement.
Figure 13.
Charging configuration of GWO. (a) Simulation. (b) Experiement.
Figure 14.
Charging configuration of BWO. (a) Simulation. (b) Experiement.
Figure 14.
Charging configuration of BWO. (a) Simulation. (b) Experiement.
Figure 15.
Charging configuration of LFDA. (a) Simulation. (b) Experiement.
Figure 15.
Charging configuration of LFDA. (a) Simulation. (b) Experiement.
Figure 16.
Charging configuration of AGTO. (a) Simulation. (b) Experiement.
Figure 16.
Charging configuration of AGTO. (a) Simulation. (b) Experiement.
Figure 17.
Charging configuration of DO. (a) Simulation. (b) Experiement.
Figure 17.
Charging configuration of DO. (a) Simulation. (b) Experiement.
Figure 18.
Experimental result for charging temperature.
Figure 18.
Experimental result for charging temperature.
Figure 19.
Bar chart of performance indicator. (a) FC. (b) CT. (c) MCT. (d) EL. (e) Total score.
Figure 19.
Bar chart of performance indicator. (a) FC. (b) CT. (c) MCT. (d) EL. (e) Total score.
Table 1.
Specification of Panasonic NCR18650PF LiB.
Table 1.
Specification of Panasonic NCR18650PF LiB.
Parameter |
Value |
Nominal Capacity |
|
Nominal Voltage Cut-off Voltage |
|
Standard Charge |
|
Dimensions |
|
Temparature |
|
Table 2.
Data obtained by CC-CV charge method.
Table 2.
Data obtained by CC-CV charge method.
C-rate |
Charge Time (sec) |
Temperature (°C) |
0.5 |
9910 (Tc,max) |
26 (tc,max) |
2 |
4250 (Tc,min) |
42 (tc,max) |
Table 3.
Range setting of the objective current parameter.
Table 3.
Range setting of the objective current parameter.
|
|
Table 4.
Selected parameter values of the applied MOAs.
Table 4.
Selected parameter values of the applied MOAs.
Algorithm |
Particle No. Iteration No. Tuning parameter |
PSO |
|
WSO JSA |
N/A
|
GWO BWO LFDA AGTO |
N/A N/A N/A |
DO |
|
Table 5.
Simulation CPEI results.
Table 5.
Simulation CPEI results.
Algorithm |
FC CT(sec) MCT(deg) EL(J) |
1C CC-CV |
|
FM |
|
PSO |
|
WSO JSA |
|
GWO BWO LFDA AGTO |
|
DO |
|
Table 6.
Simulation OCC results.
Table 6.
Simulation OCC results.
Algorithm |
|
1C CC-CV FM |
- - - -
|
PSO |
|
WSO JSA |
|
GWO BWO LFDA AGTO |
|
DO |
|
Table 7.
Experimental CPEI results.
Table 7.
Experimental CPEI results.
Algorithm |
FC CT(sec) MCT(°C) EL(J) |
1C CC-CV |
|
FM |
|
PSO |
|
WSO JSA |
|
GWO BWO LFDA AGTO |
|
DO |
|
Table 8.
Obtained Experiment OCC values.
Table 8.
Obtained Experiment OCC values.
Algorithm |
|
1C CC-CV FM |
- - - -
|
PSO |
|
WSO JSA |
|
GWO BWO LFDA AGTO |
|
DO |
|
Table 9.
Normalized score of the charging performance for each method.
Table 9.
Normalized score of the charging performance for each method.
Algorithm |
FC CT MCT CE Total Score |
1C CC-CV |
|
FM |
|
PSO |
|
WSO JSA |
ab |
GWO BWO LFDA AGTO |
|
DO |
|