The lithium-ion battery (LiB) is a common type of rechargeable battery due to its high energy density, long life cycle, and low self-discharge rate^[1]. It is widely used in various fields such as portable electronic devices, industrial energy storage systems, and electric transportation^[2,3]. Generally, the acceptable operating temperature region for LiBs is −20°C–60°C^[4], while the optimal operating temperature range for LiBs is 15°C–35°C^[5]. In a low-temperature environment, the LiB exhibits sluggish chemical reaction activity and slower charge transfer rates, which will lead to a reduction in the ionic conductivity of the electrolyte and a decrease in the diffusion rate of lithium ions within the electrodes, consequently diminishing the activity of LiBs^[6,7]. As a result, some reversible reactions cannot proceed adequately, weakening the battery’s discharge capacity and shortening its operational lifespan. At extremely high temperatures, the electrolyte undergoes severe evaporation or decomposition, resulting in electrolyte loss and reduced conductivity. This leads to an increase in the internal resistance of the battery, which in turn affects the migration rate of lithium ions, thereby slowing down the internal ion conduction within the battery. This ultimately affects battery performance, including capacity and power loss^[8,9]. Uncontrolled temperature escalation can trigger thermal runaway, which could lead to self-ignition or even explosion under certain circumstances^[10]. In this process, the LiB’s temperature can increase quite quickly during the charging and discharging process. The phenomenon known as thermal runaway occurs when the LiB approaches an unmanageable self-heating state. The temperature can actually increase dramatically in just a few milliseconds. This process is incredibly challenging to stop once it has begun. Extremely high temperatures, ferocious cell venting, smoke, and fire are possible outcomes of thermal runaway. Therefore, accurately monitoring the internal temperature of the battery is very important for preventing the occurrence of battery thermal runaway. Large battery packs, consisting of a large number of LiB cells, are used in transportation systems due to the continuous need for high energy^[11]. At present, the safety of LiBs is a major concern for electric vehicles, with the operating temperature of LiBs considered to be the most important aspect of safety^[12-16].

Accurate temperature measurement can take timely measures to prevent excessive temperature when the battery temperature is abnormal and reduce the risk of battery failure, and it is extremely important for protecting the performance and extending the service life of LiBs^[17-21].

Due to its low cost, high accuracy, and wide measurement range, the thermocouple has been widely used in battery temperature measurement. However, their larger dimensions pose a risk of electrolyte leakage at the sealing position^[22].

Compared to wire-based sensors, miniature wireless sensors offer a potential solution to the sealing issue in batteries, preventing internal environmental contamination. Nonetheless, miniature wireless sensors can only be inserted into batteries during the assembly process, and their performance within the complex internal structure of the battery relying on electro-sensing characteristics is also questionable^[23].

The fiber Bragg grating (FBG) is made of a fiber core with an alternating refractive index and constant periodicity^[24,25]. When the wavelength of an incident light matches the Bragg wavelength of an FBG, the light will be reflected by the FBG, while other wavelengths of the light will pass through the FBG. Surrounding environmental variations such as temperature or strain applied to the FBG will result in a shift of Bragg wavelength. By monitoring the reflected wavelength of the FBG, the temperature or strain applied to the FBG can be determined. Compared to other sensing technologies, the FBG has unique advantages, such as fast response, high sensitivity, non-conductive nature, immunity to electromagnetic interference, and multiplexing capabilities, and thus is an ideal sensing technique for monitoring the health of LiBs^[26-30]. Li et al. used tilted FBGs imprinted on commercial single-mode optical fibers and coated with nanoscale gold film as the working electrode to continuously monitor the sub-micron-level surface temperature near the liquid–solid catalyst interface in situ^[31]. They were able to decode the thermal effects in interface photoinduced catalysis with a temperature resolution of 0.1°C and a time resolution of 0.1 s, without interfering with the simultaneous measurement of catalytic operations, effectively solving various thermal monitoring problems in the rapid catalytic reaction process^[31]. Wang et al. inserted a fiber optic plasma sensor near the electrode surface of the working battery to monitor the electrochemical events during battery operation, which can help improve the electrochemical design of better batteries^[32]. The fiber optic sensor mentioned above is based on monitoring chemical reactions at the microscopic level of the battery. In addition, by integrating the FBG array in the battery, the internal temperature of the battery cell will be accurately monitored to reflect the real state of the battery during operation, which will provide accurate internal temperature information for improving battery performance^[33].

In the literatures, there are many introductions regarding the use of FBG arrays for detecting the internal temperature of LiBs, but the measurement methods they describe cannot achieve long-term and accurate monitoring of the temperature inside the battery^[34-36]. Using FBG arrays to detect the external temperature of the LiB, Forgez et al. developed a simplified single-state thermal model that could be used to determine the temperature inside the battery based on the external temperature measurements. This method is simple, but it cannot provide a precise estimate of the internal temperature of the battery^[37].

Li et al. proposed an intelligent LiB with integrated FBG sensors, which could measure the internal temperature of the battery and more accurately monitor the temperature changes during battery operation. However, it has not yet been applied to cylindrical 18650 LiB^[38]. Liu et al. used a femtosecond laser engraved FBG to monitor the internal temperature of LiBs and compared the implanted FBG sensor with the thermocouple sensor. They found that the two displayed very similar temperature curves, which could accurately monitor the internal temperature of LiBs^[39]. Due to the use of only a single FBG to measure the temperature at a single point inside the battery, no further research was conducted on the temperature distribution inside the battery. Using a metal conduit to package the fiber optic sensors engraved with four FBGs, McTurk et al. solved the problem of electrolyte corrosion on the optical fiber, eliminating strain as the cause. However, since metal conduits have high thermal conductivity, obvious heat transfer will occur on the conduits, resulting in temperature uniformity at each point measured by the fiber^[40,41].

Based on the shortcomings of the FBG arrays mentioned above, in this paper, we propose an FBG array encapsulated with a capillary glass tube. One FBG array is attached to the outer external of the battery, while another FBG array is inserted into a glass capillary, which is embedded inside the battery through a small hole drilled at the center of the negative electrode of the battery. This can obtain the difference between the internal temperature and external temperature of the battery. This sensor can effectively prevent the corrosion of electrolytes on the optical fiber and the influence of the internal pressure of the battery on the fiber strain. It can also clearly differentiate temperature differences in the direction above the battery axis, enabling accurate measurement of internal battery temperature.

In the next sections of this paper, the design of the FBG arrays and its detection of internal temperature and external temperature during the battery’s charging and discharging process will be presented, followed by a discussion of the results in the third section. Finally, a summary of the findings will be concluded.

The FBG arrays used for this work are prepared using traditional excimer laser exposure and the phase mask fabrication method^[42]. Considering the geometric size of the battery, Fig. 1(a) shows a schematic diagram of how the four FBGs are inscribed in the core of a single optical fiber. Each FBG has a length of 5 mm, and the interval between two adjacent FBGs is 12 mm. Figure 1(d) shows an example of the spectral response of the FBG arrays. The central wavelength of each FBG is shown in Table 1. The bandwidth of all FBGs is less than 0.3 nm, the side mode suppression ratio is greater than or equal to 15 dB, and the reflectivity is greater than or equal to 85%. In the experiment, we used a TV130 fiber grating demodulation instrument developed by Beijing Tongwei Technology Co., Ltd^[43]. The maximum acquisition frequency is 100 Hz and the wavelength resolution is 0.1 pm. In the experiment, we used the acquisition frequency of 1 Hz.

As shown in Fig. 1(c), the FBG array encapsulated in a glass capillary (using precision glass tube cold processing technology, where the original blank SiO2 tube is ground externally and bored internally to produce a single-ended tube with an outer diameter of 0.7 mm and an inner diameter of 0.4 mm) is used to measure the internal temperature of the battery. The response time of the capillary glass tube to the internal temperature of the battery is less than 0.5 s, which can be used for real-time monitoring of the internal temperature of the battery. For this experiment, a Panasonic 18650 nickel-cobalt-aluminum cathode and graphite anode battery cell with a rated capacity of 3400 mAh and a standard voltage of 3.6 V is used. The FBG is calibrated at 20°C–60°C in increments of 10°C using a thermostatic platform (BY-2020 Intelligent thermostatic platform). Figure 2 shows the measured wavelength shift for each FBG array over the selected temperature range, and the sensitivity of each FBG array is shown in Table 1. Then two FBG arrays are arranged inside and on the external of the battery, respectively, as shown in Fig. 1(b). To measure the external temperature of the battery, acrylic is used to attach the FBG array on the surface. We attach one end of the optical fiber to the battery using adhesive and connect the other end through a PVC tube to the battery, allowing the fiber to expand freely. To measure the internal temperature of the battery, a drill bit with a diameter of 0.8 mm is used to create a hole at the center of the negative electrode of the battery, and then the FBG array (sealed with an epoxy adhesive) is inserted into the battery through a small hole in the negative electrode.

This section mainly introduces the specific method and process of the battery charging and discharging tests. For the purpose of observing the response of the FBG to temperature variations during the process of charging and discharging, the battery is charged and discharged completely at different charging and discharging rates in every cycle. The charging and discharging rate of the battery refers to the ratio of the current to the rated capacity of the battery during the charging and discharging process. Using the BTS 55 battery test system made by BIDAO, we carried out measurements on charging and discharging cycles at three rates of 0.5C, 1C, and 1.25C, keeping the battery at room temperature around 25°C. Table 2 shows the steps involved in a complete charging and discharging cycle. During the experiment, the battery is charged and discharged at three different rates in order to observe the responses of FBG on the battery’s inner and outer temperatures. We repeated this 3 times for each complete charging and discharging cycle in the experiment. The time required for the complete charging and discharging experiments of the battery at three different rates of 0.5C, 1C, and 1.25C is 8.2, 5.1, and 4.5 h, respectively.

To compare the results obtained from the experimental study of temperature variation inside a battery, a simplified model is constructed to simulate how temperature changes within the battery. There are two main reasons for heat production within the battery, Joule heating and electrochemical operation^[44,45]. A commonly cited expression for calculating heat generation is given as^[46]q=I(U−V)−I(TdUdT),(1)where dUdT is the entropy change, U is the open-circuit voltage, and V is the terminal voltage.

Table 3 provides the materials used and their characteristics for the charging and discharging simulation of the battery. A finite element simulation is performed under an ANSYS static thermal condition. Figure 3(a) shows the geometry model used in the simulation, which consists of three parts: case, terminals, and electrode. Note that the temperature information used in the simulation is derived from another measurement, while the coefficients are obtained from the literature^[47] and the entropy values at different states of charge (SOC) are provided in Table 4. As shown in Fig. 3(b), the battery thermal performance undergoes isotropic thermal conductivity at cross-sections X-X and Y-Y.

The temperature response of the FBG inside and outside the battery cell at different charging and discharging rates is tested during the full constant current (CC)/constant voltage (CV) charging and CC discharging cycles. Figures 4(a), 4(d), and 4(g) show the voltage and current changes of the battery at 0.5C, 1C, and 1.25C charging and discharging rates, respectively. The temperature of both the internal and external surfaces of the battery increases with the charging and discharging rates. Figures 4(b), 4(e), and 4(h) show that the maximum internal temperature of the battery reaches 35.5°C, 48.5°C, and 56°C when the battery is charged and discharged at 0.5C, 1C, and 1.25C, respectively. Note that (i) the temperature changes during the entire charging and discharging process and (ii) during constant discharge, the internal and external surfaces of the battery reach the highest temperatures. This is because when the battery charge reaches its maximum level, the internal resistance also increases to its maximum value, resulting in higher power loss and temperature under a constant load^[48]. Note that the corresponding relationship between the temperature change rate of the internal and external surfaces of the battery and the voltage and current during battery charging and discharging is shown in Figs. 4(c), 4(g), and 4(k). Taking the second complete charging and discharging cycle of the battery at 1C charging and discharging rate as an example for analysis, from the graph, it can be observed that when the battery enters the CC charging stage from the rest state [point a in Fig. 4(e)], the rate of temperature rise on the internal and external surfaces of the battery is the highest throughout the entire CC charging process. As the temperature on the internal and external surfaces of the battery continues to rise, the corresponding rate of the temperature change also decreases. When the battery transitions from CC charging to CV charging [point b in Fig. 4(e)], the temperature on the internal and external surfaces of the battery reaches its maximum. As the CV charging begins, the decrease in battery charging current causes the temperature on the internal and external surfaces of the battery to begin to decrease, and it can be seen from the graph that the rate of temperature change also decreases. When CV charging is completed, the temperature of the internal and external surfaces of the battery drops to the lowest level. Then the battery enters the CC discharging stage from CV charging [point c in Fig. 4(e)], at which point the temperature of the internal and external surfaces of the battery rapidly begins to rise again. However, unlike CC charging, the rate of temperature change in the battery during this process increases as the CC discharging progresses until the battery temperature reaches its maximum value at the end of discharging. Finally, the battery enters the shelving stage from CC discharging [point d in Fig. 4(e)]. At this time, the temperature on the internal and external surfaces of the battery rapidly decreases, and the initial rate of the temperature decrease is the highest. As the temperature decreases, the rate of temperature decrease continuously decreases. Note that there is a temperature difference between the internal and external surfaces of the battery. The temperature difference between the internal and external surfaces of the battery during charging and discharging is shown in Figs. 4(c), 4(f), and 4(i). The internal temperatures of the battery is always higher than the external temperature, and this temperature difference exhibits a certain pattern. During constant discharging, the temperature difference between the internal and external surfaces reaches its maximum value near the negative electrode of the battery. Furthermore, this temperature difference increases as the charging and discharging rate of the battery increases. The maximum temperature differences between the internal and external surfaces at charging and discharging rates of 0.5C, 1C, and 1.25C are 1.85°C, 4.1°C, and 5°C, respectively. This shows that the traditional method of detecting the external temperature cannot accurately reflect the internal state of the battery and may not be able to successfully protect the battery in time. In contrast, the proposed FBG based approach can offer the benefits of precise internal temperature measurement. Moreover, along the axis of the battery, the temperature gradually decreases from the positive electrode to the negative electrode, and the observed maximum temperature differences are 1.5°C, 3.0°C, and 4.5°C, respectively. This may be caused by anisotropic heat conduction within the battery, which will result in the formation of a localized hot spot^[49].

Figure 5 shows a contrast between the measured and simulated internal temperatures at different voltages at the position of FBG4 when the battery is charged and discharged in the second cycle at 0.5C. Comparing the simulated and measured temperature values when the battery is charged and discharged, the average value of the discrepancy is about 1.5°C, which is less than 5% of the average temperature in the experiments. The initial difference is about 4.7°C, and the discrepancy is reduced to about 1°C at most of the remaining charging stage. The discrepancy is increased a bit to 2°C in the first half discharging stage, and then it reduces to less than 0.5°C during most of the second half of the discharging stage. The differences may be due to the simplification of the simulation model, where the internal thermal conductivity differs from the actual one, as well as the selection of the entropy thermal coefficient, which varies depending on the individual battery. Nevertheless, the consistent trends shown in the results indicate that FBG can be used to monitor the internal temperature of the battery.

Although the FBG array has unique advantages for detecting the internal temperature of batteries, it is necessary to evaluate the impact of the FBG array on battery performance. Therefore, a reproducibility test is performed on the improved and original batteries. The comparison results shown in Fig. 6(a) are crucial to show that the FBG array has no effect on the performance of the battery. Figure 6(a) compares the change in battery capacity during the 60-cycle [where the voltage variation of a single charging and discharging cycle is shown in Fig. 6(b), mainly composed of discharging and charging parts] charging and discharging tests with the FBG array inserted and the original battery. The results show that the original battery has a capacity of 3070 mAh and the battery inserted into the FBG array has a capacity of 3067 mAh. A capacity differential change of 3 mA had little effect on the performance of the cells in this experiment. This indicates that the insertion of the FBG array does not adversely affect the electrochemical performance of the battery, verifying the feasibility of monitoring the internal temperature of the battery.

We accrued cyclic charging and discharging on the battery to verify the repeatability of the FBG array’s response to changes in battery temperature 10 days later with the results depicted in Fig. 7. Figures 7(a), 7(c), and 7(e) show the changes in battery voltage and current at 0.5C, 1C, and 1.25C charging and discharging rates, respectively. Comparing Figs. 7(b), 7(d), and 7(f) with Figs. 4(b), 4(e), and 4(h), respectively, we can observe that, when the external temperature environment is the same, the temperature changes inside and outside the battery during charging and discharging are almost the same. It is evident that the FBG array has high stability in monitoring the temperature of the inner and outer surfaces of the battery, and it can be used to monitor the temperature of a LiB for a long time.

We conducted an overcurrent charging and discharging temperature test on the battery. In our experiments, the charging and discharging rate was set at 2C, the cut-off voltage of CC discharging was set to 2.5 V, and other parameters remained unchanged as in the previous test. To calibrate the FBG measurement results, a thermocouple was inserted into the battery, which is close to the position of IFBG2. Figure 8(a) shows the voltage-current variation of the battery and the temperature response of the FBG arrays under overcurrent charging and discharging. It can be seen that, as the charging and discharging rate increases, the single charging and discharging time significantly shortens from 2.8 h at 0.5C rate to 1.2 h. The maximum temperature of the battery during abnormal charging and discharging is 78°C, which is 22°C higher than that under normal charging and discharging at 1.25C. The maximum temperature difference between the internal temperature and external temperature of the battery also increases to 8.6°C. As shown in Fig. 8(b), the thermocouple and IFBG2 have almost the same temperature response to the charging and discharging process, indicating that the FBG arrays can accurately monitor the temperature change of the battery under abnormal working conditions, thereby providing an early warning for the abnormal working conditions of the battery.

In this paper, we propose embedding optical fiber FBG arrays inside and outside the battery to measure the internal temperature and monitor temperature gradients at different parts of each battery cell as it charges and discharges. In accordance with the LiB structure model, the finite element software (ANSYS) is used to simulate and analyze the heat generation and temperature gradient within the battery cell. The temperature changes inside the battery during different charging and discharging states are simulated and compared with the experimental results obtained when using the FBG array. Comparing and verifying the experimental results with the simulation results, both experimental and theoretical results exhibit similar trends. In addition, we have presented a promising method for monitoring the internal temperature of a LiB in real time. The insertion of an FBG array has been shown to have no effect on the capacity and charging and discharging performance of the battery, enabling long-term monitoring of the LiB’s temperature. We show that the maximum temperature difference between the internal and external temperature of the battery reaches 1.85°C, 4.1°C, and 5°C at charging and discharging rates of 0.5C, 1C, and 1.25C, respectively. This temperature difference increases with the charging and discharging rates, and it is more noticeable near the negative electrode. The results obtained in this study indicate that the proposed FBG arrays have an accuracy of ±0.5°C and can accurately measure the temperature differences, and this can provide a better understanding of the battery’s behavior during the charging and discharging process as well as provide valuable data for real-time battery management and smart charging/discharging. It can help in developing smart charging controllers that can help reduce battery degradation and extend battery life.