Virtual Testbed for Economical and Reliability Analysis of Battery Thermal Management Control Strategies¹

Modern-day electric vehicles (EVs) consist of interlinked vapor compression systems with coolant circuits to meet the narrow range of battery thermal operating conditions [1–3]. A complete system-level thermal understanding is required to design such advanced battery thermal management systems (BTMS). However, performing system-level experiments is expensive and time-consuming. This limits the ability to optimize and analyze an individual component based on its effect on the system-level performance. Other important aspects like analyzing control algorithms and strategies at the system level are also left out. Having a virtual testbed framework consisting of reconfigurable individual component models helps by providing a platform to build and simulate system-level models. In this study, a virtual testbed is created for assessing the economical and reliability aspects of BTMS control strategies.

Batteries are a large component of the EV market price. As a result, a long battery lifetime is of critical importance for the economic viability of EVs [4,5]. Given the paramount role of temperature in battery lifetime [6], maintaining an optimal battery temperature could significantly improve its lifetime [2]. In this regard, devising thermal management strategies that are reliable under widely varying environmental and operating temperatures is a necessity. However, battery lifetime optimization requires the incorporation of a reliable battery degradation model in the system-level simulation. Battery degradation models can be broadly classified into two categories, physical modeling [7,8] and empirical modeling [9–12]. Empirical aging models are usually classified into two groups, cycle aging and calendar aging. Cycle aging occurs during battery operation when it is either charging or discharging. Calendar aging is the self-degradation of the battery when the battery is stored and there is no current flowing through the battery. Different battery degradation studies usually express either calendar loss or cycle loss with an empirical correlation as a function of operating conditions.

Some studies have focused on developing cycle capacity loss models, incorporating different cycle stress factors such as C-rate, temperature, and ampere-hour throughput into a single capacity fade correlation [5,6,13]. Wang et al. [6] gathered a large test matrix for lithium iron phosphate (LFP) cells under a wide range of operating conditions such as temperature, C-rate, and depth of discharge (DOD). They used the testing results to develop a semi-empirical aging model for cycle capacity loss of LFP cells. Omar et al. [14] identified charging rate, discharge rate, temperature, and DOD as the four main factors contributing to the cycle capacity loss of Li-ion cells. They performed extensive experimental analysis, varying each of these four factors in one set of experiments and developed models for the end-of-life (EOL) of the battery for each case. Although their model closely covers the experimental result, it is not suitable for system-level simulations where stress factors are dynamically changing.

Another important contributor to battery degradation and capacity loss is calendar aging. Numerous studies have aimed at developing a model for battery degradation under calendar aging conditions. Sarasketa-Zabala [15] developed their calendar aging model by testing cells under static calendar aging conditions. Their model indicates a square root dependency on time and an exponential dependency on temperature and state of charge (SOC). Petit et al. [5] used relevant experimental data to develop both calendar and cycle aging capacity loss models for two common Li-ion technologies, i.e., LFP and nickel cobalt aluminum oxide. They combined calendar and cycle aging models into one lifetime prediction model and employed it to assess the impact of charging rate, charging strategy, and vehicle-to-grid on battery lifetime under realistic operating conditions. Naumann et al. [16] conducted a comprehensive calendar aging study and developed models for both capacity loss and resistance increase of LFP cells. They validated their model against experimental data under both static and dynamic conditions. Schmalstieg et al. [12] performed many tests under accelerated aging conditions to develop a calendar aging model for nickel manganese cobalt oxides cells as a function of time as well as SOC and temperature.

While research has been done on simulating the performance of BTMS by exploring the effect of various conditions such as ambient temperature and battery configuration [17,18], there is a lack of research regarding system-level simulation of BTMS that incorporate the aging and degradation of the battery as an evaluation factor. This work leverages MATLAB-Simulink Simscape for the modeling, simulation, and analysis of the BTMS [19–21]. MATLAB-Simulink Simscape is a software tool developed by MathWorks Inc. for modeling and simulating multidomain physical systems. The Simscape component library along with custom-built components like the electrothermal battery model is used for modeling. Equivalent-circuit lumped parameter modeling is done using one-dimensional 2-RC circuits [22] for LFP lithium-ion cells. Temperature and SOC-dependent data of various cell parameters are obtained from the literature to capture the variation of battery performance with temperature and SOC. The heat generated by the battery is linked to thermal masses, which are connected to suitable components for thermal conditioning. The developed BTMS model allows for transient analysis of different thermal control strategies which are essential for automotive fast-charge and discharge cycles. To assess the effect of various thermal management strategies on battery lifetime, aging models from the literature are incorporated into the framework. The aging model combines cycle and calendar capacity loss to make a reliable prediction of battery capacity loss under dynamically varying conditions, relating the working conditions such as the temperature of the battery to its lifetime. Using the aging model, the economic benefit of thermal management strategies from extending battery lifetime is weighed against the corresponding energy cost of the operation, allowing for the adoption of economy-conscious strategies under different conditions. This analysis is performed on an LFP battery, and the corresponding results of battery lifetime extension and net cost saving are compared.

MATLAB-Simulink (R2023a) along with Simscape is used for the modeling and analysis of the virtual testbed for assessing battery thermal management strategies. All model files and scripts are publicly available online on Mendeley data [23]. The individual component-level models are first developed and then integrated with each other for system-level modeling. The reconfigurable individual components (Fig. 1) can be used to represent and study a wide set of system configurations by changing the interconnections and control algorithms. Simscape is used in this work because of its exhaustive component library like heat exchangers (evaporator, radiator, condenser), pumps, compressors, expansion valves, and more. Custom components can be built wherever required by using fundamental blocks or using Simscape language for coding physical equations represented as acausal implicit differential algebraic equations. The component and system-level models of the vapor compression system are based on previous work on integrated EV thermal management systems [24]. The modeling framework of that study which was validated against experimental data can be found in the online repository [25].

The components have various physical domains of operation like electrical, thermal, mechanical, moist air, single-phase thermal liquid, and two-phase fluid. Commonly used 50–50% mixture (by volume fraction) of water-ethylene glycol (WEG) is used as the coolant for the single-phase thermal liquid domain and R134a is used as the refrigerant for the two-phase domain. Automotive heat exchangers generally fall into three categories based on the fluid streams: thermal liquid—moist air (radiator), thermal liquid—two phase (evaporator, Fig. 1(a)) and two phase—moist air (condenser). The compressor (Fig. 1(c)) is a critical component of the refrigeration system and has a proportional-integral-differential controller for controlling the refrigerant mass flowrate based on the thermal conditioning requirements of the battery. The controller also has additional constraints such as maximum discharge pressure and minimum suction pressure to ensure that the compressor does not cross the operating pressure limits. The refrigerant expansion occurs through an expansion valve (thermostatic expansion valve (TXV), Fig. 1(b)), which has a bulb sensor connected to the compressor inlet. Process parameters like superheat, subcooling, evaporating, and condensing temperatures determine the opening fraction of the TXV. The receiver tank before the TXV (Fig. 1(b)), allows for the passage of liquid only and acts to maintain the required refrigerant charge in the system. Centrifugal pumps (Fig. 1(d)) are used for causing fluid flow in the thermal liquid domain and are characterized by their pressure drop as a function of flowrate curves.

The component-level models described above are integrated together to form subsystems and system. The system-level model for the analysis of battery thermal conditioning is shown in Fig. 2. It has a refrigeration subsystem consisting of condenser, compressor, evaporator, and TXV. This is used for the active cooling of the battery. The evaporator cools down the WEG coolant (thermal liquid), which in turn cools down the battery by running through channels inside the cold plate which is located underneath the battery. A radiator is also connected in parallel with the evaporator for passive cooling of the battery. It should be noted that our use of the terms “active cooling” and “passive cooling” solely refers to the inclusion or exclusion of the vapor compression cycle in the cooling process, respectively. The naming is not meant to imply free convection in the air-cooled condenser or radiator as both the condenser and radiator are fan cooled. Based on the cooling strategy, the evaporator or the radiator can be disconnected from the loop. The evaporator is only used for active cooling and the radiator is only used for passive cooling. The centrifugal pump causes the coolant to flow along the thermal liquid circuit consisting of the radiator, evaporator, battery, and tank. Ambient conditions are defined by the user input and include parameters such as temperature, pressure, and relative humidity to characterize the environmental moist air, which flows over the condenser and the radiator. The Autonomie Signals block provides the relevant signals such as power. These signals are obtained by simulating an EV in the Autonomie software [26], which is a vehicle system simulation tool developed by Argonne National Lab for vehicle dynamics simulation and analysis. For this study, a regular-sized passenger EV with a fixed-gear transmission is used. The signals from Autonomie simulations are fed as inputs to the virtual testbed model for total energy that needs to be extracted from the battery for a particular drive cycle. The charging algorithm provides the relevant signals during charge for a constant-current constant-voltage (CC–CV, Fig. 3) charging protocol.

A lumped-parameter electrothermal approach adopted from the work of Lin et al. [22] is used for battery modeling. The cell and battery pack characteristics are summarized in Table 1. The LFP cell electrical characterization is based on a 2-RC [22] equivalent-circuit models as shown in Fig. 4. Critical cell parameters like resistance and capacitance are dependent on temperature and SOC, thus enabling a coupled electrical analysis with the thermal aspects.

Where $Q ˙$ is the cell heat generation, $I$ is the cell current, $VOCV$ is the open circuit voltage of the cell when there is no electric current through the cell, $VT$ is the terminal voltage of the cell, and $T$ is the temperature of the cell.

The cell-level component model is then used to represent battery packs as shown in Fig. 5(b). The battery comprises of four battery packs connected in series, and the configuration of battery packs have been chosen to result in a similar nominal capacity of ∼83 kWh as indicated in Table 1. The battery packs are connected to a cold plate which models the heat exchange between the coolant and the packs. Further specific details about the cell and battery models can be found in Refs. [22,30] and the online model repository [23].

In the case of battery charging, the CC–CV algorithm (Fig. 3) is used with a user-defined C-rate. The cell is charged at a specified constant current until it reaches the threshold voltage after which the current decreases gradually and charging takes place at constant voltage.

Three different thermal management strategies are compared by evaluating their effectiveness in regulating battery pack temperature and the subsequent impact on the battery lifetime. The first strategy (case 1) uses a fan-cooled radiator to cool the battery which we categorize as passive cooling. This is the base case in which the coolant absorbing heat from the battery is cooled by an air-cooled radiator as shown in Fig. 2. The second strategy (case 2) is categorized as active cooling in which a vapor compression system (blue box in Fig. 2) is used to cool the battery during fast-charging or discharging while driving. The vapor compression cycle allows for cooling of the battery to temperatures below the ambient temperature. The desired set point temperature of the battery is kept at 25 °C, mainly because experimental cycle life studies on Li-ion batteries have shown that battery lifetime decreases when temperatures reach above 25 °C [14]. The third strategy (case 3) is categorized as active cooling with preconditioning. The only difference between this case and case 2 is that here the battery is precooled to 25 °C prior to fast charging.

There are two important aspects to the case 3 strategy. The first one is the time it takes for precooling to the desired setpoint. This can be useful for saving time because battery precooling can kick in before the user reaches the fast-charging station. The second is the amount of energy required to precool the battery which would affect economic aspects. The time required for precooling and BTMS energy consumption for preconditioning the battery are plotted in Fig. 6 for ambient temperatures ranging from 30 to 40 °C. Precooling time and energy consumption for the precooling of the battery vary between 14 and 37 min and 0.8–2.8 kWh. It is important to note that although these values are specific to the component sizing of the coolant and vapor compression system used in this work, they still provide a reasonable approximation for estimating these process parameters.

where $Qlosscyc.$ is the cycle capacity loss in percentage, $B$ is the pre-exponential factor, which is a function of the C-rate, $Ea$ is the activation energy in $J mol−1$ as a function of C-rate, $R=8.314 J mol−1 K−1$ is the gas constant, $T$ is temperature of the battery in K, $Ah$ is the ampere-hour throughput of the battery, and $zcyc.$ is the exponent constant which is equal to 0.55. Among these parameters B, $Ea$⁠, and $zcyc.$ are empirical parameters that are determined by minimizing the error between the modeled and measured capacity losses and can be found in Ref. [6].

where $Ea$ is the activation energy in $J mol−1$⁠, $Tref.=25 °C$ is reference temperature, and $R=8.314 J mol−1 K−1$ is the gas constant. These values along with values of $kref$⁠, $c$⁠, and $d$ are presented in Table 2.

Where $Qlosstot.$ is the total capacity loss, $Qlosscal.$ is the calendar capacity loss under rest conditions, and $Qlosscyc.$ is cycle capacity loss during charge and discharge of the battery.

The parameters and details of the cycling conditions and economic analysis are summarized in Table 3. The cycling conditions include the charge and discharge protocols used in the simulation. For charging we use a C-rate of 2 in the fast charging process for the main results section. A mixture of 50–50% between fast and slow charging is also presented in the Appendix. For discharge, a combination of highway and city driving conditions are considered. Highway driving conditions are represented by the standard US06 drive cycle while city driving conditions are modeled by using the Urban Dynamometer Driving Schedule (UDDS), hereafter referred to as UDDS drive cycle [33]. Each discharge cycle includes five separate trips, one of which is a highway trip for 63.5 min and the other four are city driving trips, each lasting for 40 min. The battery power required for a regular-sized passenger EV under US06, and UDDS drive cycles are obtained from Autonomie simulations as explained in Sec. 2.1 and is fed into the battery to discharge it from 80% back to 20% SOC. It is assumed that the vehicle rests between these trips long enough so that the battery temperature reaches the ambient temperature at the beginning of the next trip.

The average miles driven per year (12,724 miles) is obtained from the data released by the Federal Highway Administration, a division of the U.S. Department of Transportation [34]. Given that the miles driven by the vehicle under the described highway and city trips is 100.94 miles, in total the battery undergoes 126 cycles of charge and discharge per year, which is when we apply the cycle capacity described in Eq. (2). Since the focus of this study is to analyze the economic benefit of applying different thermal management strategies to batteries in hot climate conditions, the ambient temperature is varied between 30 °C and 40 °C for cycling the battery including both charging and discharging. The rest of the time when the battery is neither charging nor discharging it is under rest condition. Since a significant part of the rest time is in nighttime and some of the rest time is when the vehicle is parked in a garage and is exposed to a lower temperature, for capacity loss under rest condition or calendar aging we assume that the resting temperature is on average 5 °C below the ambient (working) temperature of the battery. For instance, when we are cycling the battery at an ambient temperature of 30 °C, the average rest time temperature of the battery is 25 °C. In addition, since we are cycling the battery in the SOC range of 20–80%, we assume an average SOC of 50% when the battery is at rest condition. The parameters and details of the cycling conditions and economic analysis are summarized in Table 3. It is noteworthy that the cycling conditions in this study are not meant to exactly represent the working condition of a particular vehicle. However, the modeling framework can be applied to other cycling conditions in a similar fashion.

Where “$Net Savings$” is the total saving in $/year that is resulted from applying active cooling to the battery, “$EOL extension savings$” is the saving in $/year from extending battery lifetime from Eq. (8), and “$Extra operating cost$” is the additional operating cost from Eq. (7).

The results section is divided into two parts. In the first part, profiles of parameters of interest such as compressor power, battery heat generation, evaporator cooling, battery temperature, and voltage are discussed for charging and discharging scenarios. In the second part, the results of the economic analysis are reported and compared. Two cases of active cooling and preconditioned active cooling are compared against the base case of passive cooling.

The profiles of parameters during the charging process of the battery in a hot ambient condition of 35 °C for active cooling with preconditioning (case 3) strategy are shown in Fig. 7. Three most important parameters energy-wise are how much heat is being generated in the battery because of fast-charging, how much heat is being removed from the battery coolant by the evaporator, and how much energy the compressor consumes to run the vapor compression cycle since most of the BTMS energy is consumed by the compressor. Energy-related parameters are shown in Fig. 7(a). The average temperature of the four battery packs plotted in Fig. 7(b) shows a temperature increase of about 4 °C during the 18 min of fast charging.

Given that the C-rate is equal to 2 (Fig. 7(c)) and the fact that the battery is being charged from 20% to 80% SOC, the charging takes only 18 min. Moreover, the C-rate of the battery during the charging process remains constant since the battery does not reach the maximum voltage threshold during this time. The battery heat generation in Fig. 7(a) shows a general increasing trend since the resistors in the 2-RC bridges in the ECM model [22] (R1 and R2 in Fig. 4) have an increasing trend with increasing SOC during charging. The battery heat generation increases with time for most of the charging period to a maximum of 9.6 kW, while the evaporator cannot reject all the heat generated in the battery leading to a temperature rise of the battery from 25 °C to 29 °C.

The discharge profiles at ambient temperature of 35 °C for the highway trip using the US06 driving cycle are presented in Fig. 8. It should be noted that since the duration of US06 drive cycle is only 596 s, we apply the drive cycle repeatedly during the 63.5 min of driving time. It is worth mentioning that the discharge profiles for case 2 (active cooling) and case 3 (preconditioned active cooling) are the same since the preconditioning is only applied before fast charging in case 3. The discharge profiles at ambient temperature of 35 °C for one city trip using the UDDS driving cycle are presented in Fig. 9. Comparing the heat generations during a highway trip (Fig. 8(a)) and city trip (Fig. 9(a)), we observe that peaks of the heat generation plot are significantly larger during the more intensive US06 drive cycle, mainly because the current demand on the battery is higher during highway driving relative to city driving. In each driving trip, whether highway or city driving, the battery starts at the ambient temperature and the thermal management system controls the battery temperature to the setpoint temperature of 25 °C over time.

This section presents the economic analysis comparing the active cooling and preconditioned active cooling strategies (cases 2 and 3) against passive cooling (case 1). The economic analysis considers the benefit from extending battery lifetime and the cost of increased operating energy consumption for the two active cooling cases relative to the passive cooling case. This economic analysis enables the adoption of economy-conscious decision-making to choose the right thermal management strategy under different conditions. Since the purpose of this study is to evaluate the effect of thermal management strategies under cycling conditions, the calendar aging stress factors , i.e., temperature and SOC are fixed for all three thermal management cases investigated in this study (Table 3).

Figure 10(a) shows the battery EOL for different thermal management strategies for ambient temperatures varying from 30 °C to 40 °C. The battery EOL for passive cooling shows a significant decrease from 8.3 to 4.8 (42% reduction) years for an ambient temperature increase from 30 °C to 40 °C. This value reduces to 40% for active cooling, and 31% for preconditioned active cooling. This comparison shows that precooling the battery before fast charging has a more significant impact on minimizing the battery EOL reduction than applying active cooling during both charge and discharge. In terms of improving battery EOL, active cooling alone improves lifetime by 0.8–0.9 years relative to the passive cooling case. However, precooling the battery before fast charging could increase the lifetime extension to 1.4–1.9 years, almost doubling the lifetime gain relative to passive cooling. The net saving, presented in Fig. 10(b), considers both the annual energy cost and annual savings from improving the battery lifetime. Net saving from active cooling varies between 30 and 60 $/year for the ambient temperature range of 30–40 °C. The preconditioned active cooling has a much higher net saving of 140–550 $/year, which shows a significant improvement that can be achieved by precooling the battery before fast charging.

The results presented in Fig. 10 indicate that the combined application of precooling before fast charging and active cooling, aimed at maintaining an optimal battery temperature, results in an extended battery lifetime compared to passive cooling. Moreover, this approach is effective in minimizing the reduction in battery lifetime at higher ambient temperatures, thereby enhancing the overall reliability of the battery. Furthermore, the economic analysis presented in Fig. 10(a) and shows that applying active cooling to the battery is economically justifiable as it is shown that the benefits gained from extending battery EOL exceed the cost of the active cooling operation. It should be noted that while the results of this analysis are dependent on specifications of the battery including factors such as battery chemistry, size, nominal energy, and energy density, similar analyses can be performed on other batteries depending on the availability of reliable calendar and cycle aging correlations. Such analyses offer valuable insights for making decisions regarding the thermal conditioning strategy applied to the battery, ensuring both the reliability of the battery, i.e., having a more stable lifetime regardless of climate conditions and economic feasibility.

This study focuses on the assessment of different thermal conditioning strategies for battery thermal management systems from an economic and reliability point of view. A virtual testbed framework was developed in MATLAB using the Simscape library and a custom electrothermal cell model is used for the simulation and analysis of the BTMS. Active battery cooling using a vapor compression system with preconditioning can maintain the desired optimal battery temperature even in hot conditions but costs an additional 170–530 $/year. However, the additional cost of operation is much less than the net saving of 140–550 $/year achieved by the increase in battery EOL by 1.4–1.9 years due to optimal thermal operation. Moreover, comparing the results of active cooling (case 2) with preconditioned active cooling (case 3) indicates that precooling the battery before fast charging can significantly extend battery lifetime in hot ambient conditions.

The authors gratefully acknowledge funding for this work in part from the U.S. National Science Foundation Engineering Research Center for Power Optimization of Electro-Thermal Systems (POETS). N.M. acknowledges funding support from the International Institute for Carbon Neutral Energy Research (WPI-I2CNER), sponsored by the Japanese Ministry of Education, Culture, Sports, Science, and Technology.

• National Science Foundation Engineering Research Center for Power Optimization of Electro-Thermal Systems (POETS) (Agreement No. EEC-1449548; Funder ID: 10.13039/100000149).

• International Institute for Carbon Neutral Energy Research (No. WPI-I2CNER).

The authors declare that there are no conflicts of interest regarding this research.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Ah =

ampere-hour throughput

B =

pre-exponential factor

BTMS =

battery thermal management system

CC–CV =

constant-current constant-voltage

DOD =

depth of discharge

EOL =

end of life

EV =

electric vehicle

I =

current

$kSOC$ =

state of charge influence factor

$ktemp$ =

temperature influence factor

LFP =

lithium iron phosphate

$Qlosscal.$ =

calendar capacity loss

$Qlosscyc.$ =

cycle capacity loss

$Qlosstot.$ =

total capacity loss

R =

gas constant

RC =

resistor–capacitor

SOC =

state of charge

T =

temperature

$Tref.$ =

reference temperature

TXV =

thermostatic expansion valve

UDDS =

Urban Dynamometer Divining Schedule

V_OCV =

open circuit voltage

V_T =

terminal voltage

WEG =

water ethylene-glycol

$zcyc.$ =

exponent constant

In this section a case study is performed by considering a percentage between fast and slow charging protocols which we refer to as the mixed charging case. Here we assume the battery charging occurs at a C-rate of 2 in half of the charging instances and at a C-rate of 0.5 in the other half. The exact ratio between fast and slow charging is dependent on many factors including driving habits and the availability of the charging infrastructure, but here we use a one-to-one ratio to see how the combination of slow and fast charging impacts the lifetime and economic analysis. The selection of the C-rate of 0.5 is mainly because of the limitation of cycle capacity loss model developed by Wang et al. [6] which covered a C-rate range of 0.5–10. The rest of the cycling conditions are the same as presented in Sec. 2.5. The EOL and net saving for the mixed charging case is presented in Fig. 11(a). Comparing the results of the mixed charging case with results presented in Fig. 10 for the fast charging case, we see that the general trends in battery lifetime for different thermal conditioning strategies are the same for both active cooling and preconditioned active cooling, and both strategies still lead to net savings which indicates they are economically justifiable. However, a noticeable difference can be observed between Figs. 10(b) and 11(b). The difference shows that the net saving of the active cooling thermal strategy is significantly improved for the mixed charging case study. The main reason for this difference is that slower charging rates enable longer charging time, which ensures that the thermal management system is able to cool down the battery during charging and minimize the capacity loss that happens due to high temperatures in charging.