## 1 Introduction
Experimental results indicate that the BC method achieves a higher and consistent 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 the charging time and temperature rise, and extend the lifespan of lithium-ion batteries (LiBs) [5; 6; 7; 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 parameter 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 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 employees 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 MSCC charging strategy using the SOC values as the current transition threshold was proposed in [9; 10; 11; 12; 13]. In this approach, the SOCvalues facilitate the transition from one constant current stage to another. The process can be uniformly divided into ten stages [11], three stages [12], or optimized to four stages [13], which is then applied to LiBs to evaluate 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 challenging 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 simplifies 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 criterion is the most commonly used criterion for transitioning from one stage to the next and is typically determined in advance by the battery manufacturer.