1. Introduction

2. Materials and Methods

2.1. Study Methods

2.1.1. Battery Bank of the Electrical Vehicle

There can be an infinite number of shapes, sizes, and storage capacities for batteries. The main differences lie in the electrochemical characteristics needed to meet specific requirements. Consequently, there is a specific battery for every need and application. This is why solutions are often based on the use of basic storage units that are commercial and standardized. One of these units is the 18650 battery, named because it is standardized in shape and size: 18 mm in diameter, 65 mm in length, with the "0" indicating its cylindrical shape. The only aspects that have changed with the improvement of electrolyte technology are its storage capacity and charging technology. Other battery types have been developed, but the 18650 remains one of the most widely used. In fact, the energy storage in the first versions of the well-known electric vehicle Tesla Roadster was obtained from a special configuration of 18650 battery packs.

The energy storage system studied can be seen in Figure 1. It consists of basic 18650 battery units with a nominal capacity of 2500mAh at 3.6V. The configuration includes a small pack of four batteries connected in parallel, equivalent to a 3.6V and 10Ah battery. Thirteen of these packs are connected in series to obtain a total pack or equivalent battery of 10Ah at 46.8V.

The actual battery configuration is shown in Figure 2. This battery arrangement also necessitates an external physical protection system. The pack is encased in a 1.1mm thick aluminum casing to enhance isolation between the casing and the batteries. This aluminum cover not only encloses and shields the batteries from impact but also provides a surface to dissipate the heat generated inside the battery pack. The configuration includes a lithium battery protection system (BMS 48V 13S) and a PCB 13S protection plate rated up to 30A.

The internal structure of a lithium battery is shown in Figure 3. The stack of electrodes of commercial lithium-ion batteries in the current market is a multi-layered structure. A single repeatable unit consists of a cathode, an anode, and two layers of separator. The cathode is made of an aluminium foil coated on both sides by an active material with a binder. Similarly, the anode is composed of a copper foil coated with graphite (or silicon) particles.[8]

One of the most critical factors affecting battery performance is the operating temperature of the batteries. Each individual cell or unit behaves as a heat source due to the heat released from the electrochemical process and the inherent internal resistance of the battery itself. The energy balance of the cell is expressed by the equation 1 [9].

$$\rho c_v\frac{\partial T}{\partial t}=q_{cell}-h(T_s-T_{am})$$

(1)

Where h is the convective heat transfer coefficient, and $T_s$ and $T_{am}$ are the surface and ambient temperatures, respectively, $q_{cell}$ is the average rate or total heat generation, which includes the sum of all heats generated in the battery: the heat of reaction, ohmic heat, active polarization heat, and secondary or lateral heat, respectively, as shown in the equation 2 [10].

$$q_{cell}=q_{rea}+q_{ohm}+q_{pol}+q_{sid}$$

(2)

Although the latter heat,$q_{sid}$ in equation 3, is usually not taken into account.

$$q_{sid}=h_f(T_s-T_{am})+{ϵ}_{r}kB(T_1^4-T_2^4)$$

(3)

2.1.2. Telemetry

Table 1. Description of Variables and Units of Measurement.

Table 1. Description of Variables and Units of Measurement.

Variable	Description	Unit of Measurement
Temperature	Temperature measured by MCP9701 sensor	Celsius (°C)
Current	Current measured by ACS709 sensor	Amperes (A)
Voltage	Voltage measured by Analog Voltage Divider module	Volts (V)

The implementation of an efficient and accurate telemetry system is crucial for ensuring proper monitoring of the battery bank in electric vehicle applications. In this context, various sensors and devices have been employed for the acquisition of crucial data, including temperature, current, and voltage measurements. Each of these components plays a critical role in real-time tracking of the battery bank’s operational status, providing vital information for optimizing the charging and discharging processes, as well as preventing potential failures and maximizing energy efficiency. This section will detail the technical aspects and key features of the MCP9701 temperature sensors, ACS709 current sensors, and Analog Voltage Divider module for voltage measurement, as well as the ESP32 controller with LoRa module used for data acquisition and transmission. Additionally, the Raspberry Pi 4 with LoRa module acts as a Node-RED server for storing and visualizing the collected information.

Temperature: The telemetry system implemented for the battery bank utilizes temperature probes based on the MCP9701 sensor. This sensor can accurately measure temperature over a wide range, from -10°C to +125°C. The output of the MCP9701 is calibrated with a slope of 19.53 mV/°C and has a DC offset of 400 mV. These features enable reliable and precise temperature measurement of both the battery bank and the surrounding environment. The temperature data captured by the MCP9701 is integrated with the rest of the telemetry data and transferred to the central database with a sampling frequency of 1 second, allowing for real-time monitoring and the generation of detailed logs for further analysis.

Current:

The battery bank telemetry system employs the Allegro ACS709 sensor for precise current measurement. This sensor is specifically designed for real-time current monitoring applications. The board used is a simple carrier for the ACS709 sensor, which utilizes the Hall effect to measure current over a range of up to ±75A. The sensor offers a low-resistance current path of approximately 1.1 m and provides electrical isolation of up to 2.1 kV RMS. The ACS709 has been optimized for optimum accuracy in currents ranging from -37.5 A to 37.5 A. Its analog voltage output is linear for current magnitudes up to 75 A, with the output voltage centered at $VCC/2$ and a typical error of $\pm 2\%$.

Additionally, it can operate in a voltage range of 3 V to 5.5 V, allowing it to connect directly to 3.3 V and 5 V systems. This precise measurement capability and wide operating range make the ACS709 sensor an ideal choice for monitoring the battery bank’s charging current with high reliability and accuracy. The current data captured by the ACS709 is integrated with the rest of the telemetry data and logged into the central database, facilitating continuous monitoring and optimization of the battery bank’s charging process.

Voltage: The Analog Voltage Divider module was employed for voltage measurement in the battery bank telemetry system. This module can detect the supply voltage over a wide range, from 8V to 100V. Its operation is based on the principle of the voltage divider, which allows the input voltage to be reduced by a factor of 20. Since the ESP32’s analog input typically has a maximum of 5V, the input voltage of the analog voltage detection module cannot exceed 5V * 20, which is equivalent to 100V. This feature ensures that the input voltage is within the safe range and compatible with the ESP32. The ability to detect voltages over a wide range, combined with compatibility with the ESP32’s analog input, makes the Analog Voltage Divider module a suitable option for accurately measuring the battery bank voltage. The voltage data captured by this module is integrated with other telemetry data and logged into the central database, facilitating continuous monitoring and efficient management of the battery charging process.

Controller: The ESP32 controller, equipped with a LoRa module enabling its connection to a Raspberry Pi 4, is used for data acquisition. The Raspberry Pi 4, in turn, is equipped with a LoRa module serving as a Node-RED server responsible for storing and visualizing the collected information. The ESP32 acts as a remote node that collects data from the battery bank’s telemetry system, utilizing its LoRa module to transmit this data to the Raspberry Pi 4 wirelessly. The Raspberry Pi 4, functioning as a Node-RED server, receives this data and processes it for storage in a database and subsequent visualization in the form of graphs or tables. This configuration allows for efficient and wireless communication between the ESP32 and the Raspberry Pi.

2.1.3. Response Surface Methods

The response surface methodology (RSM) is a set of mathematical and statistical tools whose main objective is to optimize a response of interest influenced by a variety of variables and determine the optimal operating conditions of the system. The modeling is carried out through the estimation of a polynomial of first order or higher, generally applying the ordinary least squares method, to develop a second-order model on a response surface in equation 4.

$$y={\beta }_0+\sum _{i=1}^k{\beta }_i{x}_i+\sum _{i=1}^k{\beta }_{ii}{x}_i^2+\sum \sum _{i<j}{\beta }_{ij}{x}_i{x}_j+ϵ$$

(4)

RSM is a sequential procedure where current operating conditions are considered non-optimal if the appropriate model is not first order. The objective is, starting from the current operating conditions, to find the trajectory towards the optimum, applying an algorithm such as the one with the highest rise to maximize the response (or descent to minimize), through a second order model where the top represents the point of maximum response [7]. Response surfaces are plotted in two (contour) or three dimensions (response surface) in order to characterize the shape of the surface and locate the optimum, the coefficients of the second-order model can be estimated through regression analysis and analysis of variance ANOVA applied in order to interpret the effect that the input variables have on the response.

RSM is a sequential procedure where current operating conditions are considered non-optimal if the appropriate model is not of first order. The objective is to find the trajectory towards the optimum starting from the current operating conditions, applying an algorithm such as the one with the steepest ascent to maximize the response (or descent to minimize it), through a second-order model where the peak represents the point of maximum response [7]. Response surfaces are plotted in two dimensions (contour) or three dimensions (response surface) to characterize the shape of the surface and locate the optimum. The coefficients of the second-order model can be estimated through regression analysis, and analysis of variance (ANOVA) is applied to interpret the effect that the input variables have on the response.

We selected the initial, the final voltage and, the current as input variables, the charge time is the response variable. The levels and variables in Table 2.

3. Results

4. Discussion

5. Conclusions

References

1. IPCC.; others. Climate Change 2014: Mitigation of Climate Change. Contribution of Working Group III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change; Cambridge University Press, 2014; p. 147. ISBN: 978-1-107-05821-7.
2. IPCC.; others. Climate Change 2022: Impacts, Adaptation and Vulnerability. Contribution of Working Group II to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change; Cambridge University Press, 2022; p. 3056 [CrossRef]
3. Mothilal Bhagavathy, S.; Budnitz, H.; Schwanen, T.; McCulloch, M. Impact of charging rates on electric vehicle battery life. Findings 2021, 2021. [Google Scholar] [CrossRef]
4. Ding, Y.; Cano, Z.P.; Yu, A.; Lu, J.; Chen, Z. Automotive Li-Ion Batteries: Current Status and Future Perspectives. Electrochemical Energy Reviews 2019, 2, 1–28. [Google Scholar] [CrossRef]
5. Sanguesa, J.A.; Torres-Sanz, V.; Garrido, P.; Martinez, F.J.; Marquez-Barja, J.M. A review on electric vehicles: Technologies and challenges. Smart Cities 2021, 4, 372–404. [Google Scholar] [CrossRef]
6. Balasingam, B.; Avvari, G.; Pattipati, B. and Pattipati, K.B.Y. A robust approach to battery fuel gauging, part II: Real time capacity estimation. Journal of Power Sources 2014, 269, 949–961. [Google Scholar] [CrossRef]
7. Myers, R.H.; Montgomery, D.C.; Anderson-Cook, C.M. Response surface methodology: process and product optimization using designed experiments; John Wiley & Sons, 2016; p. 856. ISBN: 9781118916032.
8. Zhu, J.; Wierzbicki, T.; Li, W. A review of safety-focused mechanical modeling of commercial lithium-ion batteries. Journal of Power Sources 2018, 378, 153–168. [Google Scholar] [CrossRef]
9. Xia, Q.; Wang, Z.; Ren, Y.; Yang, D.; Sun, B.; Feng, Q.; Qian, C. Performance reliability analysis and optimization of lithium-ion battery packs based on multiphysics simulation and response surface methodology. Journal of Power Sources 2021, 490, 229–567. [Google Scholar] [CrossRef]
10. Sato, N. Thermal behavior analysis of lithium-ion batteries for electric and hybrid vehicles. Journal of power sources 2001, 99, 70–77. [Google Scholar] [CrossRef]
11. Zhang, C.; Jiang, J.; Gao, Y.; Zhang, W.; Liu, Q.; Hu, X. Charging optimization in lithium-ion batteries based on temperature rise and charge time. Applied energy 2017, 194, 569–577. [Google Scholar] [CrossRef]
12. Sun, J.; Ma, Q.; Liu, R.; Wang, T.; Tang, C. A novel multiobjective charging optimization method of power lithium-ion batteries based on charging time and temperature rise. International Journal of Energy Research 2019, 43, 7672–7681. [Google Scholar] [CrossRef]
13. Ghaeminezhad, N.; Monfared, M. Charging control strategies for lithium-ion battery packs: Review and recent developments. IET Power Electronics 2022, 15, 349–367. [Google Scholar] [CrossRef]
14. Abdollahi, A.; Han, X.; Avvari, G.; Raghunathan, N.; Balasingam, B.; Pattipati, K.R.; Bar-Shalom, Y. Optimal battery charging, Part I: Minimizing time-to-charge, energy loss, and temperature rise for OCV-resistance battery model. Journal of Power Sources 2016, 303, 388–398. [Google Scholar] [CrossRef]
15. Abdollahi, A.; Raghunathan, N.; Han, X.; Pattipati, B.; Balasingam, B.; Pattipati, K.; Bar-Shalom, Y.; Card, B. Battery health degradation and optimal life management. 2015 IEEE AUTOTESTCON. IEEE, 2015, pp. 146–151.