Heat Effects during the Operation of Lead-Acid Batteries

Citation: Baˇca, P.; Vanýsek, P.; Langer, M.; Zimáková, J.; Chladil, L. Heat Effects during the Operation of Lead-Acid Batteries. Batteries 2024,10, 148. https://doi.org/10.3390/ batteries10050148 Academic Editors: Adrian Calborean and Carlos Ziebert Received: 24 January 2024 Revised: 23 April 2024 Accepted: 26 April 2024 Published: 27 April 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). batteries Article Heat Effects during the Operation of Lead-Acid Batteries Petr Baˇca * , Petr Vanýsek , Martin Langer, Jana Zimákováand Ladislav Chladil Department of Electrotechnology, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická10, 616 00 Brno, Czech Republic; [email protected] (P.V.); [email protected] (M.L.); [email protected] (J.Z.); [email protected] (L.C.) *Correspondence: [email protected] Abstract: Thermal events in lead-acid batteries during their operation play an important role; they affect not only the reaction rate of ongoing electrochemical reactions, but also the rate of discharge and self-discharge, length of service life and, in critical cases, can even cause a fatal failure of the battery, known as “thermal runaway.” This contribution discusses the parameters affecting the thermal state of the lead-acid battery. It was found by calculations and measurements that there is a cooling component in the lead-acid battery system which is caused by the endothermic discharge reactions and electrolysis of water during charging, related to entropy change contribution. Thus, under certain circumstances, it is possible to lower the temperature of the lead-acid battery during its discharging. The Joule heat generated on the internal resistance of the cell due to current flow, the exothermic charging reaction, and above all, the gradual increase in polarization as the cell voltage increases during charging all contribute to the heating of the cell, overtaking the cooling effect. Of these three sources of thermal energy, Joule heating in polarization resistance contributes the most to the temperature rise in the lead-acid battery. Thus, the maximum voltage reached determines the slope of the temperature rise in the lead-acid battery cell, and by a suitably chosen limiting voltage, it is possible to limit the danger of the “thermal runaway” effect. The overall thermal conditions of the experimental cell are significantly affected by the ambient temperature of the external environment and the rate of heat transfer through the walls of the calorimeter. A series of experiments with direct temperature measurement of individual locations within a lead-acid battery uses a calorimeter made of expanded polystyrene to minimize external influences. A hitherto unpublished phenomenon is discussed whereby the temperature of the positive electrode was lower than that of the negative electrode throughout the discharge, while during charging, the order was reversed and the temperature of the positive electrode was higher than that of the negative electrode throughout the charge. The authors relate this phenomenon to the higher reaction entropy change of the active mass of the positive electrode than that of the negative electrode. Keywords: lead-acid accumulator; heat effect; thermal behavior; endothermic reactions; exothermic reactions; Joule heat; cooling effect 1. Introduction The aim of this study is to look at a less appreciated fact that during lead-acid battery discharge, an entropy-based phenomenon leads to a cooling effect, which may not be intuitively apparent as it is often negated by Joule heating due to large current flow. Understanding the thermal balance of a lead-acid battery is important for continuous useful application of this time-proven electrochemical technology. Energy storage research is presently a highly regarded and also highly competitive environment, varying in different application solutions from automobile SLI (starting, lights, ignition) to small power applications of daily use to large power applications ensuring energy stability and power grid quality [ 1 – 6 ]. Lead-acid batteries (LAB) still play an important part on the battery market, and are financially the best compromise in power, longevity and ability to be recycled in the circularity management [ 7 – 12 ]. In 2019, LAB dominated the market share, accounting Batteries 2024,10, 148. https://doi.org/10.3390/batteries10050148 https://www.mdpi.com/journal/batteries Batteries 2024,10, 148 2 of 18 for an estimated 32.29% of the total battery market with a further forecast growth of 5.2% by 2030. The above advantages will continue to lead to the application of LAB in major automotive sectors and in low-cost off-grid energy storage systems [13,14]. In the LAB performance issues, it is important to understand in detail the thermal processes that play a major role in the lifetime and other important parameters of LAB. When critical values are exceeded, an effect called the thermal runaway (TRA) can occur, which ultimately leads to the destruction of the LAB. Thermal runaway in LAB is related to both exoand endothermal electrochemical reactions during charging and discharging and to the flow of electric current through the internal structures of the LAB with a nonzero electrical resistance. It is also important to pay attention to the heat capacity of the individual parts of the LAB and the heat exchange of the LAB with the environment. A lead-acid electrochemical cell with a given heat capacity can be divided into three basic parts—the aqueous sulfuric acid solution with the highest thermal capacity and low thermal conductivity, the plastic battery pack with both low thermal capacity and low thermal conductivity, and the electrodes, where the actual electrochemical reactions take place at the active mass/electrolyte interface. The electrodes made of lead and its oxides and sulfates are relatively heavy and have good thermal conductivity. Their heat capacity is very low and, therefore, particularly in AGM batteries with a lower amount of sulfuric acid solution relative to these electrodes, heating to critical temperature can occur much more rapidly within a short time. Heat issues, in particular, the temperature increase in a lead-acid battery during its charging has been undoubtedly a concern ever since this technology became used in practice, in particular in the automobile industry. However, it came to greater forefront when many batteries were grouped in a stack together for the purpose of energy storage and sole propulsion in electromobility [ 15 ]. A large volume of closely packed batteries has led to more difficult heat transfer to the surrounding environment and overheating and thermal runaway [ 16 , 17 ], causing severe issues in longevity, reliability and safety [ 18 ]. Interestingly, heat issues in lead-acid batteries became a subject of mathematical simulations, perhaps because of the complicated physical access of temperature probes into large stacks and the hostile chemical environment [19,20]. In 1995, Newman and Tiedemann [ 21 ] presented what is now a classical approach, a study showing the temperature increase inside a battery with constant heat generation. Cai and White [ 22 , 23 ] published an efficient electrochemical-thermal model for battery simulation. The model was specifically for a lithium-ion battery, although it can generally be used for other battery systems as well. However, in lead-acid battery there is one specific that needs careful treatment, which is the sulfuric acid electrolyte, which exists in the battery in variable quantities and directly enters the stoichiometry of the electrochemical reaction. This has been performed thoroughly via mathematical modeling [ 24 – 26 ], which also included comparisons with other studies. Broda and Inzelt investigated internal resistance increase and temperature change for both the negative and the positive electrode in a lead-acid battery [ 27 ]. Kˇrivík dedicated his effort to thermal events in lead storage batteries [ 28 – 31 ]. For the calculations, he used thermodynamic values for a 100% sulfuric acid. With those values, the discharge reaction came out erroneously as exothermic. Later in this paper, we demonstrate that the more realistic concentration of 30%mass will lead to an endothermic value. The work also lacked the validation of theoretically determined data by practical experiments. The aim of this contribution, where lies its novelty, is a deeper insight into the complex level of thermal processes of lead-acid batteries with the definition of the level of individual influences affecting the resulting temperature of the LAB electrodes. Here, we point out some errors of other authors [ 28 – 32 ], especially in relation to the theoretical calculations of the thermodynamic values assuming 100% sulfuric acid. It turns out that those values for a realistic acid concentration (30%mass) yield different values that significantly affect the overall thermal performance of the lead-acid battery system. In contrast to the findings in [ 28 – 31 ], we confirm the accuracy of the theoretical calculations by good agreement with Batteries 2024,10, 148 3 of 18 actual measurements on a real LAB. As a first step, based on the presented theoretical calculations and practical measurements, we write that by adjusting the charge/discharge mode, the magnitude of the thermal processes taking place in the LAB can be influenced to a certain extent, and thus the temperature of the LAB can be influenced to minimize the TRA hazard. The goal of this work is to propose regime measures that can affect the internal temperature of the LAB during operation. 2. Materials and Methods 2.1. Theoretical Foundation A good place to start when considering electricity and heat in a rechargeable battery is with thermodynamics. To be true, laws of classical thermodynamics apply to the state of equilibrium, thus they can be used only as guidance during charging and discharging of a battery, which is not an equilibrium process. It is useful to use thermodynamic parameters called the state functions which do not depend on the reaction path. They depend only on the difference in the values for the products and for the reactants, the final and initial components in the process. In our consideration, the state functions are the reaction enthalpy, ∆ H, which describes the amount of energy released during the process; the Gibbs free energy, ∆ G, which describes the maximum amount of chemical energy that can be converted into useful work (in batteries, into electrical energy), or work, that can be used to generate chemical compounds; and the entropy of the reaction, ∆ S, which describes reversible gain or loss of energy associated with ongoing chemical (or electrochemical) reaction. The state functions from the practical point of view describe the upper limits of performance. As the reactions proceed (in the case of a battery as the current flows), kinetic parameters reduce these upper limits [ 32 ]. The other parameter, which will interest us in this deliberation, is heat, Q, associated with electrochemical processes. Heat is not a state function, thus heat released or generated will depend on the manner with which the battery is charged or discharged. The basic relationship between the three mentioned state functions is ∆G=∆H−T∆S(1) where Tis the temperature in kelvins. This is a useful relationship in electrochemistry, as it relates to the cell potential U0 ∆G=−nFU0(2) where nis the number of exchanged electrons in the unity reaction and Fis the Faraday constant, a charge of one mole of electrons. Several basic thermal processes occur that affect the resulting battery temperature during operation. These processes include heat exchange with the environment, QZ , Joule heat generation at the internal resistance of the cells, QJ , and the change in heat from the thermochemical reactions at the electrodes themselves, QR. Q=QZ+QJ+QR(3) The exchange of thermal energy between the lead-acid battery and the surrounding environment QZis described by Newton’s law of cooling: QZ=kZ(Tair −Tbatt)t(4) where k z is a heat transfer coefficient, a constant characterizing a particular battery (is a function of heat transfer resistance of the whole system) and T air − T batt is the difference in temperatures between the battery and the environment and tis the time during which the heat exchange between the battery and the surroundings takes place. The Joule heat, or the thermal energy generated at the individual internal resistances, QJ, is given by: QJ=RI2t(5) Batteries 2024,10, 148 4 of 18 where Ris the internal resistance of the lead-acid battery, Iis the magnitude of the current and tis the discharge time. Because of the gradual increase in internal resistance during discharge, this heat will be most pronounced towards the end of the discharge. In the latter case, it is the thermochemical heat generated (or consumed) by the electrochemical reaction at the electrodes during discharge, i.e., the conversion of lead and lead oxide to lead(II) sulfate. The discharge reaction is described as: Pb +PbO2+2 H2SO4→2 PbSO4+2 H2O (6) The reaction entropy of battery discharge ∆ S dis can be calculated as the difference of the sum of entropies of all the products, minus the sum of entropies of all reactants [ 33 , 34 ] with the entropy values obtained from [ 34 ]. In further calculations, we will use for Equation (6) ∆ S dis = − 10.4 J · mol −1· K −1 . The product with absolute temperature T ∆ Scorresponds to energy bound into the system and reflects the change of the structure of the atomic bonds of the compounds [ 35 ]. The corresponding entropic voltage or potential of the reaction at room temperature [36] is calculated from the reaction entropy: UR=T∆Sdis nF =−0.016 V (7) where Tis the temperature, n= 2 is the number of exchanged electrons and F= 96,485 C · mol −1 is the Faraday constant. The relationship (8) comes directly from the referenced work [ 28 ] a relationship which was sourced from a seldom quoted work by Berndt [ 37 , 38 ]. The idea is that the U R is defined as a new variable, the entropic potential, i.e., potential contribution due to entropy, thus independent of enthalpy changes. The thermochemical heat is then calculated from the entropic potential of the reaction [28]: QR=−T∆Sdis nF It =−URIt (8) The value of the thermochemical heat is positive, so heat is released during the electrochemical reaction. In other words, if the entropy difference ∆ Sis negative, the battery will heat up during discharge [29]. The above value from Equation (7) is, however, calculated for 100% sulfuric acid. If we consider for the calculations the actual concentration of sulfuric acid used in lead-acid batteries, the resulting values will differ. Sulfuric acid in lead-acid batteries is usually a 30% aqueous solution in the fully charged state, so its entropy will be different. The entropy value for this diluted sulfuric acid is 128.1 J · K −1· mol −1 [ 34 ] and it will significantly affect the conclusions about cell heat balance [ 39 ]. The resulting ∆ S dis for the discharge in appropriately concentrated sulfuric acid is ∆ S dis = 47.2 J · mol −1· K −1 , and the corresponding entropic potential of the reaction therefore will be UR= 0.0726 V. Ultimately, the value of the thermochemical heat (see Equation (8)) will be negative, i.e., the heat is consumed by the electrochemical reaction. Thus, during discharge, the generated Joule heat heats up the battery, while the electrochemical conversion of lead-based active materials with sulfuric acid to lead sulfate and water is accompanied by an endothermic reaction that cannot be neglected in terms of thermal management of the battery. During charging, in addition to the above-mentioned discharge reactions (now working in the opposite direction), other parallel reactions occur according to the reached charging voltage. When the second charging stage (this is the second voltage charging plateau after overcoming the inflection point of approximately 2.45 V) is reached, electrolysis begins to occur to a significant extent and the decomposition of water into hydrogen and oxygen takes place. In the case of VRLA battery designs, an internal oxygen cycle begins to occur, with oxygen recombining back to water at the negative electrode to form water and generate heat. When charging, the value of the polarization resistance further increases and therefore additional polarization losses by Joule heat occur [29]. Batteries 2024,10, 148 5 of 18 At the beginning of charging, Joule heating losses again occur due to the internal resistances of the battery and the electrochemical charging reactions generate heat of the same magnitude as the heat of discharge, but of the opposite sign. The battery will be heated by both of these sources during charging. In the case of charging, the heat consumed for electrolysis (water decomposition) must also be taken into account, which is particularly applicable after a ‘gassing’ voltage of approximately 2.4 V (or when approximately 70% of the surrendered charge from the previous discharge has been received) has been reached per cell. The chemical reaction describing this process is: H2O→1 2O2+H2(9) ∆Sdec =163.4 J·mol−1·K−1(10) QRP =−T∆Sdec nF It (11) This heat value will be received by the system to accompany the electrolysis of the water (the battery will be cooled). When charging with increasing voltage, the polarization resistance increases. If we consider a breakdown voltage of 2.4 V per cell, we calculate the polarization resistance as: Rpol =U−UEMF −U0 I=2.4 −2.035 −0.25 I(12) where U EMF [ 40 ] is the electromotive force of the cell and U 0 is the entropic potential of decomposition of water [29]. As the cell voltage increases, the polarization resistance will increase, and thus the total polarization thermal energy will also increase. For polarization resistance, at cell potential of 2.40 V, the thermal energy released QJpol will be in the form of Joule heat: QJpol =Rpol I2t=0.115 I·t(13) For batteries where the oxygen cycle is not enabled (flooded types), we obtain the total heat of charge without considering the losses to the environment: Q=QJ+QR+QRP +QJpol (14) For batteries with an internal oxygen cycle (VRLA, GEL batteries), we must also consider the heat generated by the recombination of oxygen on the negative electrode back to water and the Joule heat, which is also generated by the enabled oxygen cycle [ 41 ]. The heat generated in the recombination of oxygen (the internal oxygen cycle) can be found from the basic equation of the reaction: Pb +H2SO4+1 2O2→PbSO4+H2O (15) The change in standard molar entropy for reaction (15) is ∆Soc =−77.05 J·mol−1·K−1(16) With corresponding entropic heat generated during the oxygen cycle (OC): QROC =−T∆Soc nF It (17) The measured system consisting of the electrochemical cell within the insulating box can be viewed as heat-accumulating elements. If we assume for simplicity that the temperatures of the electrolyte, both electrodes and the cell container are the same, then Batteries 2024,10, 148 6 of 18 from the known masses and heat capacities of the active masses, electrolyte and cell packaging, we can calculate the total value of thermal energy absorbed by the cell: Qcell =Qelectrolyte +QABS +QPb =melectrolyte·celectrolyte +mABS·cABS +mPb·cPb·∆T(18) where Q electrolyte is the total heat received by the electrolyte of the battery, Q ABS is the heat stored by the used cell pack and spacers, Q Pb is the heat received by the electrodes, and ∆ T is the temperature change within the studied time span. The other heat-accumulating elements are the air in the insulating box space and the polystyrene foam box itself. Similar to the first case, assuming equal air temperatures inside the insulating box and the walls of the insulating box, we calculate accumulated heat of the insulating box as: Qcal =Qair +Qbox =(mair·cair +mbox·cbox)·∆T(19) where Q air is the total heat received by the air in the insulating box, Q box is the heat stored by the walls of the insulating box, and ∆ Tis the temperature change within the studied time span. 2.2. Equipment and Materials Used The cell of the lead-acid battery was constructed from two commercially available electrodes of the 60 · 130 · 1 mm dimensions and placed in an ABS cell container (Figure 1). The electrodes were separated by an AGM separator Recomat F2140XP, manufactured by Bernard Dumas. ABS spacers were used to ensure compression of the cell. The capacity of the cell was 6.7 Ah. The Pt 100 temperature microsensors with special treatment against effect of sulfuric acid were placed on the surface of both the positive and negative electrodes at 1/3 of the electrode height. The finished cell was placed into a commercially available thermally insulated box made of expanded polystyrene with dimensions of 280 · 230 · 280 mm, with a wall thickness of 35 mm, was used as a calorimeter (Figure 1). Additional temperature sensors were placed in the same position as the temperature sensors of the positive and negative electrode on the inside and outside of the thermally isolating box. The potential difference measurement was made against the mercury-mercurous sulfate reference electrode MRSE (615 mV vs. NHE). Batteries 2024, 10, x FOR PEER REVIEW 6 of 18 peratures of the electrolyte, both electrodes and the cell container are the same, then from the known masses and heat capacities of the active masses, electrolyte and cell packaging, we can calculate the total value of thermal energy absorbed by the cell: 𝑄 =𝑄  +𝑄  +𝑄  =𝑚  ∙𝑐  +𝑚  ∙𝑐  +𝑚  ∙𝑐 ∙∆𝑇 (18) where Qelectrolyte is the total heat received by the electrolyte of the battery, QABS is the heat stored by the used cell pack and spacers, QPb is the heat received by the electrodes, and ΔT is the temperature change within the studied time span. The other heat-accumulating elements are the air in the insulating box space and the polystyrene foam box itself. Similar to the first case, assuming equal air temperatures inside the insulating box and the walls of the insulating box, we calculate accumulated heat of the insulating box as: 𝑄 =𝑄  +𝑄  =󰇛𝑚 ∙𝑐  +𝑚  ∙𝑐 󰇜∙∆𝑇 (19) where Qair is the total heat received by the air in the insulating box, Qbox is the heat stored by the walls of the insulating box, and ΔT is the temperature change within the studied time span. 2.2. Equipment and Materials Used The cell of the lead-acid battery was constructed from two commercially available electrodes of the 60·130·1 mm dimensions and placed in an ABS cell container (Figure 1). The electrodes were separated by an AGM separator Recomat F2140XP, manufactured by Bernard Dumas. ABS spacers were used to ensure compression of the cell. The capacity of the cell was 6.7 Ah. The Pt 100 temperature microsensors with special treatment against effect of sulfuric acid were placed on the surface of both the positive and negative electrodes at 1/3 of the electrode height. The finished cell was placed into a commercially available thermally insulated box made of expanded polystyrene with dimensions of 280·230·280 mm, with a wall thickness of 35 mm, was used as a calorimeter (Figure 1). Additional temperature sensors were placed in the same position as the temperature sensors of the positive and negative electrode on the inside and outside of the thermally isolating box. The potential difference measurement was made against the mercury-mercurous sulfate reference electrode MRSE (615 mV vs. NHE). Figure 1. Conceptual diagram of the experiment design. The measuring workstation consisted of an Agilent 34980A multifunction switch, Agilent N6700B power supplies (all Agilent instruments obtained from Agilent, Santa Clara, California, USA) and a control PC. It allowed monitoring voltage and current, poFigure 1. Conceptual diagram of the experiment design. The measuring workstation consisted of an Agilent 34980A multifunction switch, Agilent N6700B power supplies (all Agilent instruments obtained from Agilent, Santa Clara, CA, USA) and a control PC. It allowed monitoring voltage and current, potentials of Batteries 2024,10, 148 7 of 18 both electrodes, and temperature of the sensor embedded in the cell at the set modes of operation. The resolution of the data acquisition system is 6.5 digits (22 bits). The location and miniaturization of the temperature sensor allows the normal function of the lead cell without affecting its response. Measurement of the internal resistance of the in situ cell was carried out with a laboratory instrument of domestic provenance, which superimposes the sinusoidal component of the current at a frequency of 1 kHz on the DC discharge/charge current and the internal resistance is calculated from the ratio of the AC voltage response to the current. The magnitude of the AC perturbing voltage is set to 10 mV. Measuring of the AC components of voltage and current was carried out simultaneously with collecting other parameters, using the Agilent work station. 2.3. Measurement Methodology and Experimental Conditions The experimental cell was placed in the insulating box and kept in a closed hood at room temperature. For cycling the experimental cell, 100% depth of discharge (100% DOD) mode constant current/constant voltage (CC/CV) was used. The current for discharging and charging the cell was set to C5 (1.2 A), the end of discharging was at a set point when the voltage of the cell dropped below 1.6 V. Charging current started to limit when the limiting value of 2.45 V was reached. During the experiment, the total voltage, the potentials of both electrodes, the current flowing through the cell, the temperatures of both electrodes, and the temperature of the inner and outer surface of the insulating box, as well as the internal resistance of the cell, were recorded. All monitored values were recorded every 30 s. The set period was one cycle per day. 3. Results 3.1. Cycling of the Cell CC/CV Figure 2shows the outputs of all the monitored parameters of the experimental cell. The discharge/charge cycle was performed entirely under fairly constant external conditions. Batteries 2024, 10, x FOR PEER REVIEW 7 of 18 tentials of both electrodes, and temperature of the sensor embedded in the cell at the set modes of operation. The resolution of the data acquisition system is 6.5 digits (22 bits). The location and miniaturization of the temperature sensor allows the normal function of the lead cell without affecting its response. Measurement of the internal resistance of the in situ cell was carried out with a laboratory instrument of domestic provenance, which superimposes the sinusoidal component of the current at a frequency of 1 kHz on the DC discharge/charge current and the internal resistance is calculated from the ratio of the AC voltage response to the current. The magnitude of the AC perturbing voltage is set to 10 mV. Measuring of the AC components of voltage and current was carried out simultaneously with collecting other parameters, using the Agilent work station. 2.3. Measurement Methodology and Experimental Conditions The experimental cell was placed in the insulating box and kept in a closed hood at room temperature. For cycling the experimental cell, 100% depth of discharge (100% DOD) mode constant current/constant voltage (CC/CV) was used. The current for discharging and charging the cell was set to C5 (1.2 A), the end of discharging was at a set point when the voltage of the cell dropped below 1.6 V. Charging current started to limit when the limiting value of 2.45 V was reached. During the experiment, the total voltage, the potentials of both electrodes, the current flowing through the cell, the temperatures of both electrodes, and the temperature of the inner and outer surface of the insulating box, as well as the internal resistance of the cell, were recorded. All monitored values were recorded every 30 s. The set period was one cycle per day. 3. Results 3.1. Cycling of the Cell CC/CV Figure 2 shows the outputs of all the monitored parameters of the experimental cell. The discharge/charge cycle was performed entirely under fairly constant external conditions. Figure 2. Reading of temperature responses of the lead-acid cell during the second cycle of the experiment (top) and the corresponding voltage and current (bottom) as a function of time. Figure 2. Reading of temperature responses of the lead-acid cell during the second cycle of the experiment (top) and the corresponding voltage and current (bottom) as a function of time. The temperature characteristics give us information about the temperature course on the positive and negative electrode and on the inner and outer wall of the insulating box. At the end of the previous charging (first cycle) we observe cooling at different rates of the individual components and the equalization of all temperatures at the beginning of the discharge. As the cell discharges, there is a linear increase in the temperature of both the Batteries 2024,10, 148 8 of 18 positive and negative electrodes until approximately 70–80% of discharge, when the temperature increase becomes exponential, with the positive electrode increasing significantly faster than the negative. We attribute this phenomenon to the order of magnitude higher increase in internal resistance of the positive electrode than the negative electrode at the end of the discharge [ 42 , 43 ], when lead sulfate accumulates on the surface of the active materials and blocks the active surface of the porous structure of the materials. The difference in electrical resistance (resp. conductivity) of positive and negative electrodes was discussed by Calábek and Micka [ 44 ], who, although in this work they did not yet distinguish between the resistance of the active matter and the contact resistance of the collector/active matter transition, they nevertheless concluded that for the positive electrode the conductivity was in the single digits of siemens, while for the negative electrode of the same concept the conductivity was in the hundreds of siemens. Similarly, in a follow-up paper with an advanced experimental electrode concept by Calábek and Micka [ 42 , 45 ] have already been able to experimentally distinguish between the active mass resistance and the transient resistance of the two electrodes and have shown that both resistances are one to two orders of magnitude higher for the positive electrode than for the negative electrode. This temperature rise persists even at the moment of switching to the charging phase (approximately the first 5% of charge supplied during charging), which we attribute to the dissolution of the surface blocking sulfate structure and the formation of a supersaturated layer of sulfate ions in the immediate vicinity of the active surface of the masses. Continued charging leads to a reduction in the steepness of the temperature rise (5–70% supplied charge during charging), yet this temperature rise is higher than during the discharge phase (despite the fact that there is now more heat dissipation to the surroundings). After reaching a voltage value of approximately 2.35 V, the temperature of the electrodes gradually increases steeply. This rise in electrode temperature reached a maximum after the limiting voltage of 2.45 V was reached and the charging current started to be limited. Subsequently, a gradual almost linear decrease in cell temperature occurs over a period of 12 h, followed by another discharge/charge cycle. In Figure 3we can see the voltage, current, potentials of both electrodes and the internal resistance of the cell. From the electrode potential response it can be seen that there is a uniform utilization of both electrodes. It can be seen that the decrease in the total cell voltage during discharge is given by the summation of the potential drops of both electrodes towards zero value (i.e., towards the potential of the reference electrode). Batteries 2024, 10, x FOR PEER REVIEW 9 of 18 Figure 3. Time change of potential, current, temperature and resistance in the course of the second cycle. The internal resistance of the cell during discharge shows an increase in its magnitude by approximately 250%, while in the last 1/3 of the discharge, the steepness of the increase in cell resistance increases with the progressive transformation of the charged form of the active materials into non-conductive lead sulfate. During charging, the value of the internal resistance returns to its original value, but the decrease in cell resistance at the beginning of charging is significantly steeper than during discharging, which is attributed to the dissolution of the surface blocking sulfate structure, vide supra. 3.2. Discharging Figure 4 shows in detail the changes of all four monitored temperatures (positive and negative electrode, inner and outer wall of the insulating box), along with the internal resistance during the discharge. The curves show that during the first 2/3 of the discharge there is a gradual linear increase in the temperatures of both electrodes and the inner wall of the insulating box. The apparent initial slight drop in the temperature of the positive electrode is due to its higher temperature reached during the previous charging. The temperature change in the outer wall of the insulating box is independent of the temperature rise inside the insulating box and is due to the temperature fluctuation in the external environment. The magnitude of the internal resistance shows a slight linear increase over this interval for the first approximately 2/3 of the discharge. During approximately the last third of the discharge, there is a significant temperature increase with a partially exponential pattern for both electrodes and the inner wall of the insulating box. The positive electrode shows the steepest temperature rise, followed by the negative electrode. In this discharge interval, the internal resistance shows a sharp increase with an exponential pattern, with the final value of the internal resistance showing an increase of approximately 250% of the initial value. Figure 3. Time change of potential, current, temperature and resistance in the course of the second cycle. Batteries 2024,10, 148 9 of 18 The internal resistance of the cell during discharge shows an increase in its magnitude by approximately 250%, while in the last 1/3 of the discharge, the steepness of the increase in cell resistance increases with the progressive transformation of the charged form of the active materials into non-conductive lead sulfate. During charging, the value of the internal resistance returns to its original value, but the decrease in cell resistance at the beginning of charging is significantly steeper than during discharging, which is attributed to the dissolution of the surface blocking sulfate structure, vide supra. 3.2. Discharging Figure 4shows in detail the changes of all four monitored temperatures (positive and negative electrode, inner and outer wall of the insulating box), along with the internal resistance during the discharge. The curves show that during the first 2/3 of the discharge there is a gradual linear increase in the temperatures of both electrodes and the inner wall of the insulating box. The apparent initial slight drop in the temperature of the positive electrode is due to its higher temperature reached during the previous charging. The temperature change in the outer wall of the insulating box is independent of the temperature rise inside the insulating box and is due to the temperature fluctuation in the external environment. The magnitude of the internal resistance shows a slight linear increase over this interval for the first approximately 2/3 of the discharge. During approximately the last third of the discharge, there is a significant temperature increase with a partially exponential pattern for both electrodes and the inner wall of the insulating box. The positive electrode shows the steepest temperature rise, followed by the negative electrode. In this discharge interval, the internal resistance shows a sharp increase with an exponential pattern, with the final value of the internal resistance showing an increase of approximately 250% of the initial value. Batteries 2024, 10, x FOR PEER REVIEW 10 of 18 Figure 4. Changes of the internal resistance of the cell and increase in the detected temperatures during the discharge cycle. To calculate the thermal processes during discharge, the discharge curve (see Figure 4) is divided into two segments (shown by the orange vertical lines). These will be linearized to simplify the calculations. Analysis of both parts of the discharge is summarized in Table 1. The total time of discharge was 338 min and the internal resistance increased for the original 99 mΩ at the onset of the discharge to 150 mΩ at the end of the discharge. Table 1. Discharge parameters. Discharging interval t R QJ Q R Q cell Q cal Q z min mΩ J J J J J 1 245 99.5 2106 −1278 474 227 128 2 93 150 1205 −485 545 129 99 In the table t is the duration of the given segment, R is the internal resistance of the cell, Q J is the Joule heat, Q R is the thermochemical heat, Q cell is the thermal energy absorbed by the cell, Q cal is thermal energy absorbed by the calorimeter, and Q z is the heat loss to the surroundings. From the analysis of the first segment, the heat energy released to the surroundings due to Joule hear losses was 2106 J and the endothermic reaction involving the conversion of lead and lead oxide electrodes to lead sulfate resulted in the absorption of 1278 J. Thus, as a result of these two effects (heating by Joule heat and cooling by electrochemical conversion), 828 J of thermal energy was transferred to our system under investigation. Heat-accumulating elements of the system [electrochemical cell—insulating box] in the first segment of discharge accumulated total heat energy (Q cell + Q cal ) equal to 701 J. Considering the fact that this is not a perfectly insulated system, it is necessary to take into account the losses to the surroundings. Due to the stable conditions inside the insulating box with a slow temperature rise homogeneously throughout the interior space, we can assume that the difference of the thermal energy transferred to the system Figure 4. Changes of the internal resistance of the cell and increase in the detected temperatures during the discharge cycle. To calculate the thermal processes during discharge, the discharge curve (see Figure 4) is divided into two segments (shown by the orange vertical lines). These will be linearized to simplify the calculations. Analysis of both parts of the discharge is summarized in Table 1. The total time of discharge was 338 min and the internal resistance increased for the original 99 m Ω at the onset of the discharge to 150 mΩat the end of the discharge. Batteries 2024,10, 148 16 of 18 Although the common perception among experts is that lead-acid batteries only release heat during chemical reactions, this article explains that this perception is not entirely correct. Here, we have shown that at certain stages of lead-acid cell use (during discharge and during CV charging mode), endothermic reactions may prevail over exothermic reactions in the cell and that the thermal state of the LAB depends not only on the internal structure of the LAB but also on the set operating parameters. In this paper, we also outline strategies for monitoring the parameters and operation of the LAB to avoid risky conditions that may lead to the TRA effect. In future experimental work, we will look at other modes of charging and their effect on the overall temperature profile. We also want to focus on other types of battery design arrangements (VRLA AGM, GEL) and their effect on the significance of thermal processes. Author Contributions: Conceptualization, P.B. and P.V.; methodology, P.B., P.V., L.C. and J.Z.; software, M.L.; validation, P.B., P.V. and J.Z.; formal analysis, P.B., P.V., L.C. and M.L.; investigation, P.B., P.V., J.Z., L.C. and M.L.; resources, P.B. and P.V.; data curation, J.Z. and M.L.; writing—original draft preparation, P.B., P.V., J.Z., L.C. and M.L.; writing—review and editing, P.B. and P.V.; visualization, M.L. and L.C.; supervision, P.B. and P.V.; project administration, P.B.; funding acquisition, P.B. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the specific graduate research of the Brno University of Technology No. FEKT-S-23-8286. Data Availability Statement: The original contributions presented in this study are included in the article materials; further inquiries can be directed to the corresponding author. Conflicts of Interest: The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. References 1. Dimopoulou, S.; Oppermann, A.; Boggasch, E.; Rausch, A. A Markov Decision Process for managing a Hybrid Energy Storage System. J. Energy Storage 2018,19, 160–169. [CrossRef] 2. Mugyema, M.; Botha, C.D.; Kamper, M.J.; Wang, R.J.; Sebitosi, A.B. Levelised cost of storage comparison of energy storage systems for use in primary response application. J. Energy Storage 2023,59, 106573. [CrossRef] 3. Laaksonen, H. Improvement of Power System Frequency Stability with Universal Grid-Forming Battery Energy Storages. IEEE Access 2023,11, 10826–10841. [CrossRef] 4. Choi, D.; Shamim, N.; Crawford, A.; Huang, Q.; Vartanian, C.K.; Viswanathan, V.V.; Paiss, M.D.; Alam, M.J.E.; Reed, D.M.; Sprenkle, V.L. Li-ion battery technology for grid application. J. Power Sources 2021,511, 230419. [CrossRef] 5. Poullikkas, A. A comparative overview of large-scale battery systems for electricity storage. Renew. Sustain. Energy Rev. 2013,27, 778–788. [CrossRef] 6. Shamsi, S.S.M.; Barberis, S.; Maccarini, S.; Traverso, A. Large scale energy storage systems based on carbon dioxide thermal cycles: A critical review. Renew. Sustain. Energy Rev. 2024,192, 114245. [CrossRef] 7. Salem, M.H.; Mansouri, K.; Chauveau, E.; Ben Salem, Y.; Abdelkrim, M.N. Multi-Power System Electrical Source Fault Review. Energies 2024,17, 1187. [CrossRef] 8. Krishnamoorthy, M.; Periyanayagam, A.; Kumar, C.S.; Kumar, B.P.; Srinivasan, S.; Kathiravan, P. Optimal Sizing, Selection, and Techno-Economic Analysis of Battery Storage for PV/BG-Based Hybrid Rural Electrification System. IETE J. Res. 2022,68, 4061–4076. [CrossRef] 9. Dietz, A.; Hörlin, S.; Graß, N. High voltage Battery storage system for multiuse. In Proceedings of the 11th International Conference on Ecological Vehicles and Renewable Energies (EVER), Monte Carlo, Monaco, 6–8 April 2016. 10. Wecel, D.; Jurczyk, M.; Uchman, W.; Skorek-Osikowska, A. Investigation on System for Renewable Electricity Storage in Small Scale Integrating Photovoltaics, Batteries, and Hydrogen Generator. Energies 2020,13, 6039. [CrossRef] 11. Oancea, C.D. Aspects of Renewable Energy Supply to Small Consumers. In Proceedings of the International Conference and Exposition on Electrical and Power Engineering (EPE), Iasi, Romania, 25–27 October 2012; pp. 964–967. 12. Makola, C.S.; Le Roux, P.F.; Jordaan, J.A. Comparative Analysis of Lithium-Ion and Lead-Acid as Electrical Energy Storage Systems in a Grid-Tied Microgrid Application. Appl. Sci. 2023,13, 3137. [CrossRef] 13. Sajjad, M.; Zhang, J.; Zhang, S.; Zhou, J.; Mao, Z.; Chen, Z. Long-Life Lead-Carbon Batteries for Stationary Energy Storage Applications. Chem. Rec. 2024,24, e202300315. [CrossRef] Batteries 2024,10, 148 17 of 18 14. Wang, W.; Yuan, B.; Sun, Q.; Wennersten, R. Application of energy storage in integrated energy systems—A solution to fluctuation and uncertainty of renewable energy. J. Energy Storage 2022,52, 104812. [CrossRef] 15. Choi, K.W.; Yao, N.P. Heat Transfer in Lead-Acid Batteries Designed for Electric-Vehicle Propulsion Application. J. Electrochem. Soc. 1979,126, 1321. [CrossRef] 16. Torabi, F.; Esfahanian, V. Study of Thermal–Runaway in Batteries I. Theoretical Study and Formulation. J. Electrochem. Soc. 2011, 158, A850. [CrossRef] 17. Torabi, F.; Esfahanian, V. Study of Thermal-Runaway in Batteries: II. The Main Sources of Heat Generation in Lead-Acid Batteries. J. Electrochem. Soc. 2013,160, A223. [CrossRef] 18. May, G.J.; Davidson, A.; Monahov, B. Lead batteries for utility energy storage: A review. J. Energy Storage 2018,15, 145–157. [CrossRef] 19. Khan, M.R.; Swierczynski, M.J.; Kær, S.K. Towards an ultimate battery thermal management system: A review. Batteries 2017,3, 9. [CrossRef] 20. Henke, M.; Hailu, G. Thermal Management of Stationary Battery Systems: A Literature Review. Energies 2020,13, 4194. [CrossRef] 21. Newman, J.; Tiedemann, W. Temperature Rise in a Battery Module with Constant Heat Generation. J. Electrochem. Soc. 1995,142, 1054. [CrossRef] 22. Cai, L.; White, R.E. Reduction of model order based on proper orthogonal decomposition for lithium-ion battery simulations. J. Electrochem. Soc. 2008,156, A154. [CrossRef] 23. Cai, L.; White, R.E. An efficient electrochemical–thermal model for a lithium-ion cell by using the proper orthogonal decomposition method. J. Electrochem. Soc. 2010,157, A1188. [CrossRef] 24. Ansari, A.B.; Esfahanian, V.; Torabi, F. Discharge, rest and charge simulation of lead-acid batteries using an efficient reduced order model based on proper orthogonal decomposition. Appl. Energy 2016,173, 152–167. [CrossRef] 25. Esfahanian, V.; Shahbazi, A.A.; Torabi, F. A real-time battery engine simulation tool (BEST) based on lumped model and reduced-order modes: Application to lead-acid battery. J. Energy Storage 2019,24, 100780. [CrossRef] 26. Ansari, A.B.; Esfahanian, V.; Torabi, F. Thermal-electrochemical simulation of lead-acid battery using reduced-order model based on proper orthogonal decomposition for real-time monitoring purposes. J. Energy Storage 2021,44, 103491. [CrossRef] 27. Broda, B.; Inzelt, G. Internal resistance and temperature change during over-discharge of lead-acid battery. J. Electrochem. Sci. Eng. 2018,8, 129–139. [CrossRef] 28. Kˇrivík, P. Novépoznatky ve vývoji, výzkumu a optimalizaci olovˇených akumulátor˚u (New Findings in Research, Development And Optimization Of Lead-Acid Batteries). Vˇed. Sp. Vysok. Uˇc. Tech. V Brnˇe Edice HabilitaˇcníInaug. Sp. 2015,495, 1–29. (In Czech) 29. Kˇrivík, P.; Vanýsek, P. Changes of temperature during pulse charging of lead acid battery cell in a flooded state. J. Energy Storage 2017,14, 364–371. [CrossRef] 30. Kˇrivík, P. Temperature Changes of Lead Acid Battery Cell with Pulse Charging in a Flooded State. ECS Trans. 2016,74, 123. [CrossRef] 31. Kˇrivík, P. Influence of the Oxygen Cycle on the Temperature of the Lead Acid Battery Cell. ECS Trans. 2014,48, 273. [CrossRef] 32. Kiehne, H.A. Battery Technology Handbook (Electrical & Computer Engineering), 2nd ed.; Kiehne, H.A., Ed.; CRC Press: Boca Raton, FL, USA, 2003; p. 542. 33. Treptow, R.S. The Lead-Acid Battery: Its Voltage in Theory and in Practice. J. Chem. Educ. 2002,79, 334. [CrossRef] 34. NIST. NIST Chemistry WebBook. Available online: https://webbook.nist.gov/ (accessed on 13 January 2024). 35. Pavlov, D. Energy balance of the closed oxygen cycle and processes causing thermal runaway in valve-regulated lead/acid batteries. J. Power Sources 1997,64, 131–137. [CrossRef] 36. Spingler, F.B.; Naumann, M.; Jossen, A. Capacity Recovery Effect in Commercial LiFePO 4 /Graphite Cells. J. Electrochem. Soc. 2020,167, 040526. [CrossRef] 37. Berndt, D. Electrochemical Energy Storage. In Battery Technology Handbook, 2nd ed.; Kiehne, H.A., Ed.; Marcel Dekker: New York, NY, USA, 2003. 38. Berndt, D.; Spahrbier, D. Batteries, 1. General. In Ullmann’s Energy: Resources, Processes, Products; Elvers, B., Ed.; Wiley-VCH: Weinheim, Germany, 2015; Volume 1, pp. 3–25. 39. Giauque, W.F.; Hornung, E.W.; Kunzler, J.E.; Rubin, T.R. The Thermodynamic Properties of Aqueous Sulfuric Acid Solutions and Hydrates from 15 to 300◦K. J. Am. Chem. Soc. 1960,82, 62–70. [CrossRef] 40. Pavlov, D. Lead-Acid Batteries: Science and Technology–A Handbook of Lead-Acid Battery Technology and Its Influence on the Product, 2nd ed.; Elsevier: Amsterdam, The Netherlands, 2017; pp. 621–662. 41. Hu, J.; Guo, Y.; Zhou, X. Thermal runaway of valve-regulated lead-acid batteries. J. Appl. Electrochem. 2006,36, 1083–1089. [CrossRef] 42. Calábek, M.; Micka, K.; Baˇca, P.; Kˇrivák, P.; Šmarda, V. Analysis of positive-plate resistance during cycling and the effect of compression. J. Power Sources 1997,67, 85–91. [CrossRef] 43. Vinod, M.P.; Vijayamohanan, K. Effect of gelling on the impedance parameters of Pb/PbSO 4 electrode in maintenance-free lead-acid batteries. J. Power Sources 2000,89, 88–92. [CrossRef] Batteries 2024,10, 148 18 of 18 44. Calábek, M.; Micka, K. Time effects in conductivity measurements of lead/acid battery electrodes. J. Power Sources 1990,30, 309–314. [CrossRef] 45. Micka, K.; Calábek, M.; Baˇca, P.; Kˇrivák, P.; Lábus, R.; Bilko, R. Studies of doped negative valve-regulated lead-acid battery electrodes. J. Power Sources 2009,191, 154–158. [CrossRef] Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.