Introduction

Fossil fuels with severe greenhouse emissions are depleting. Meanwhile, the installed capacity of renewables continues to soar to help support the world’s transformation to a low-emission and more sustainable energy future. Up to now, renewable energy sources account for more than 30% of global electricity generation. This imposes critical challenges for the global grid system, which was built based on the power generation characteristics using conventional hydrocarbon fuels. Among others, one significant challenge is the intermittent nature of most renewables, such as solar and wind energy, that mismatches the electricity supply and demand from the end users. Battery energy storage systems (BESS) based on lithium-ion batteries (LIBs) are able to smooth out the variability of wind and photovoltaic power generation due to the rapid response capability of LIBs. It can also actively support grid frequency regulation requirements. As a result, BESS is seen as a promising solution for meeting new energy demands and ensuring grid security1.

The issue of heat generation in batteries will become increasingly critical in new energy and grid support scenarios. If the heat generated cannot be dissipated from the battery in a timely manner, it will result in an increase in battery temperature. Elevated temperatures can have significant negative impacts on the performance and lifespan of lithium-ion batteries, including accelerated degradation and heightened safety risks. Especially, increased temperatures can accelerate the formation of the Solid Electrolyte Interphase (SEI) layer, which contributes to increased internal resistance and capacity fade2. Cao et al.3 presented a forced convection calorimetry method to measure the continuous noise-free heat generation rate of batteries. A larger discharge current and lower ambient temperature of 20–45 °C caused a greater heat generation rate and faster temperature increase. The average heat generation rate over the discharge period exhibited a quadratic polynomial correlation with the discharge current and a negative quadratic polynomial correlation with the ambient temperature. Dong et al.4 studied the thermal behaviour of batteries during high magnification charging and discharging. They found that the heat production of batteries with the same magnification is higher than that of batteries with the same charging process. Excessive discharge magnification is likely to lead to rapid heating of batteries and trigger thermal runaway. Establishing good discharge conditions or effective active thermal control may be the key to thermal control and preventing thermal runaway in lithium-ion batteries. In addition, the large cell design and large multiplier operating conditions will additionally lead to temperature distribution inhomogeneity within the cell, and between the cells. Lin et al.5 explored the physiochemical and thermal behaviors of battery under different operational scenarios. They found that for a large format battery, the inhomogeneous electrochemical reactions lead to uneven heat generation and temperature within battery cell. In contrast to lumped model, fullsize coupled model demonstrates superior prediction accuracy in describing temperature inconsistency.

To deal with the high battery-generated heat load, appropriate thermal management strategies should be implemented. Normally, battery cooling technologies include air cooling6,7,8,9, phase change material (PCM) cooling10, and liquid cooling11,12. Air cooling has been widely used in early battery thermal management systems due to its low cost and simple structure. However, the cooling capacity of air is low because of its poor specific heat capacity and thermal conductivity; thus, air cooling is inadequate to meet the battery heat dissipation demand in fast charging and high-rate frequency regulation situations. For example, Chen et al.13 suggested that an air-cooling system needs to be designed to improve the temperature uniformity of the battery pack due to the low specific heat capacity of air, while the structural design of the system cannot meet the requirements of battery thermal management under dynamic operating conditions. PCM-based battery thermal management systems do not consume energy and have uniform temperature and fast temperature response14. However, PCMs have low thermal conductivity15, and the absorbed heat cannot be effectively dissipated. Ling et al.16 proposed a hybrid thermal management system for lithium-ion batteries that combines PCMs and forced air cooling. The passive thermal management system with PCM provides an effective solution for overheating Li-ion batteries, but the heat accumulation in the PCM due to the inefficient cooling of natural air convection leads to the thermal management system failure. By comparison, liquid cooling as an active cooling method is flexible and efficient in addressing the high thermal load concern for downsized BSS operating at high charging/discharging rates. For example, Yan et al.17 proposed a parallel liquid-cooled battery thermal management with different flow paths, and the results showed that when the inlet and outlet are located in the middle of the first collector pipe and second When the inlet and outlet are located in the middle of the first and second collector pipes, the system achieves the best thermal performance. Wang et al.18 proposed a silica-liquid-cooled plate (SLCP) cooling system, the idea of which is to utilize the high thermal conductivity of the thermal silica plate to dissipate the heat from the cell efficiently; the heat is then transferred to the liquid flowing into the copper tubes. The results showed that the new cooling system has good applicability.

While the liquid-cooling strategy can be efficient for proposed BSS batteries, it ought to be also effective in levelling off the internal temperature gradient for large-format cells along the flow length. Wu et al.19 conceived a step-allocated coolant scheme for a 10 Ah LiFePO4 cell, where the temperature spike and gradient of the 3S1P pack were controlled under 34 °C and 5 °C, respectively, over 5 C discharging process. This method turned out to be capable of resolving issues of insufficient cooling and large temperature differences at small rates and the coolant waste at large flow rates. Sheng et al.20 proposed a cellular cooling jacket for high-specific-energy Li(Ni0·8Co0·1Mn0.1)O2 21,700 battery cells, where the fluid flowing, channel dimension, and cooling medium on cell-level thermal profiles were simulated. The results pointed out that the cooling strategy could maintain cell core temperature difference under 5 °C for batteries operating at 2.5 C while the core centre temperatures were kept under 40 °C at the end of discharging. Akbarzadeh et al.21 compared air-based and liquid-based cooling systems for 43 Ah prismatic NMC batteries. The authors suggested that, for a certain amount of power consumption, the liquid-based cooling system outperformed the air-based one, providing lower module temperature and better thermal uniformity. The temperature gradients within the hottest cell were approximately 10 and 5 °C, respectively, for air-cooled and liquid-cooled modules.

In a nutshell, BSS for grid frequency regulation applications usually operate at high power and exceedingly dynamic operating conditions22,23. A full load of BSS batteries often reaches 2–4 C magnification24,25. During the frequency regulation process, the current fluctuated sharply within a high amplitude, leading to an ever-changing heat generation rate and intensive thermal gradient within battery cells, which introduces critical challenges for the corresponding thermal management system design. This work explores the design and multiscale modelling of energy-efficient cooling systems for a compact battery pack with large-format lithium iron phosphate (LFP) cells for grid frequency regulation applications. To start with, a numerical model of a single battery has been developed and validated against experimental observations, where the non-uniform heat generation within the battery cell will be revealed. Furthermore, different cooling configurations will be compared through the module-level modelling, and the effectiveness of the liquid-cooled thermal management and the accuracy of the model are validated through experimental tests. Finally, the cooling strategy is tested and evaluated for a full-scale 4 MW/1MWh BSS for grid frequency regulation.

Methodology

Experimental bench

Figure 1 illustrates the experimental bench utilized to examine the electrical and thermal behavior of the battery under high-rate operating conditions. The platform is equipped with a charging-discharging instrument, a data acquisition system, a computer, and a constant temperature chamber. Table 1 lists the basic specifications of the equipment used. Additionally, a subsystem for liquid cooling tests is integrated into the experimental bench, as depicted in Fig. 1. This subsystem comprises cooling tubes, a flow meter, a heat exchanger, a water pump, and a container. The experimental uncertainty can be determined in terms of the Coleman and Steele method26. The uncertainty is considered to originate from the error of the temperature measurement instrumentation. The measurement inaccuracy of the thermocouples is ± 0.5 °C. The measured minimum temperature in the present work is around 25 °C. Accordingly, the maximum relative uncertainty (0.5/25) is 2% at most.

For this study, a 100 Ah prismatic LFP battery with a metal shell is employed. Table 2 presents the basic specifications of this battery cell. In the experiments, the temperature of individual battery cells was first tested during discharge processes at rates of 1 C and 4 C. Subsequently, temperature measurements for the 4 C discharge were carried out under liquid cooling conditions in conjunction with subsystem testing. The cutoff voltage for each discharge test was set at 2.5 V. Prior to each discharge test, battery cells were charged using a CC-CV mode to a cutoff voltage of 3.6 V, followed by a resting period of more than 4 h to ensure adequate temperature equilibration and the elimination of internal polarization. To obtain the electrical and thermal model of the battery under high C-rate operation, the open-circuit voltage (Uocv), ohmic internal resistance (RΩ), polarization internal resistance(Rp), polarization capacitance (Cp), entropic heat coefficient (dUocv/dT), of the battery were tested by the experimental bench. All the parameters, except entropic heat coefficient, can be obtained from the Hybrid Pulse Power Characterization (HPPC) test method27. After obtaining these parameters, a first-order equivalent circuit model can be constructed to calculate the battery electrical behavior. The entropic heat coefficient is the rate of change of the battery’s Uocv with respect to temperature28. It is a function of state-of-charge (SOC) and temperature and is often expressed in mV/K. For a SOC of interest, the entropic heat coefficient was measured by recording the Uocv under different temperature. A sufficiently long resting time is required at each temperature value to ensure that the Uocv is obtained in thermal equilibrium at that temperature. All equivalent circuit parameter test results are listed in the Appendix.

Fig. 1
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Example of the data collection process.

Table 1 Specifications of equipment used in this study.
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Table 2 Specifications of the battery cell.
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Mathematlcal modeling

In order to investigate the electrical and thermal behavior performance of the used batteries in the system scale, an electrical-thermal-fluid coupling model is established in this paper, as shown in Fig. 2. A first-order equivalent circuit is used for each cell to describe its electrical behavior, in which the cell is equated to an equivalent circuit consisting of a number of resistors, capacitors, power supplies, etc. The cell terminal voltage is calculated in real time based on the current profile, which in turn calculates the cell heat production. Equation (1) is the equation for calculating the terminal voltage.

Fig. 2
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Illustration of numerical model. (a) Coupling between the electrical and the thermal-fluidic model. (b) Non-uniform heat generation region division.

$$\:U={U}_{ocv}+I{R}_{\varOmega\:}+{U}_{P}\left(0\right)\cdot\:{e}^{\frac{t}{{R}_{p}{C}_{p}}}+I{R}_{p}\left(1-{e}^{\frac{t}{{R}_{p}{C}_{P}}}\right)$$
(1)

where the open-circuit voltage Uocv, the ohmic internal resistance RΩ, the polarization internal resistance Rp and the polarization capacitance Cp are measured by the HPPC method.

The governing equations describe three principles of conservation: mass continuity29, momentum30 and energy conservation equations31. The flow in the mini channels is assumed to be laminar32. The governing equations for the three subdomains-coolant fluid, mini channels and batteries are shown below.

Table 3 Conservation equations of coolant fluid, channels and batteries.
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In Table 3, ρ, t and u denote the density, time and velocity (vector), respectively. µ, cp, k are viscosity, heat capacity and thermal conductivity, respectively. T and \(\:\dot{Q}\) are the temperature and volumetric heat generation rate of the batteries. Vb represents the volume of the LFP battery cell (~ 1.44 × 10− 3 m3). Qir and Qre indicate the irreversible and reversible heat generation rates for this battery; I stands for the current; Uocv refers to the open circuit voltage (OCV) of the LIBs; U is the terminal voltage which can be calculated using Eq. (1) at each time step; T denotes the temperature of the LIBs; dUocv/dT is the derivative of the Uocv with respect to temperature, commonly referred to as the entropy coefficient.

The experimental results demonstrate that during high-rate operation of the battery, temperature changes are non-uniform. This is attributed to the uneven distribution of heat generated by the battery as the rate increases. Specifically, temperatures in the upper region near the tabs (collectors) (T1 to T3) are notably higher than those in the lower region at the bottom of the cell (T7 to T9), resulting in a maximum temperature difference of 5 K. This disparity is primarily caused by higher heat generation near the tabs compared to other regions. To analyze this phenomenon more accurately, the heat source distribution needs to be adjusted based on location and C-rate. Al-Zarrer et al.33 proposed a simplified method to account for non-uniform heat generation distribution using a geometric factor and concentration factors. The geometric factor divides the battery volume into three regions, with concentration factors indicating the percentage of total heat generation rate in each region. With the fixed current profile, the proposed method consistently predicted the heat generation distribution factors with an accuracy of ± 1 K in predicting the battery surface temperature against experimental data at different battery surface locations. In the frequency regulation conditions, it is crucial to consider the changing current and adjust the distribution factors for heat generation accordingly. To address this, we introduced a correction term based on Ref33 to account for the impact of current variations on the heat source distribution under frequency modulation conditions. Figure 2b illustrates the modeling of non-uniform heat generation regions. For different regions in the battery cell, the heat generation rate can be obtained by Eqs. (8–10).

$$\:{\dot{Q}}_{1}=\frac{{S}_{p}}{{\theta\:}_{p}}\bullet\:\dot{Q}$$
(8)
$$\:{\dot{Q}}_{2}=\frac{{S}_{n}}{{\theta\:}_{n}}\bullet\:\dot{Q}$$
(9)
$$\:{\dot{Q}}_{3}=\frac{1-{S}_{p}-{S}_{n}}{1-{\theta\:}_{p}-{\theta\:}_{n}}\bullet\:\dot{Q}$$
(10)
$$\:{S}_{p}=\alpha\:+\beta\:{exp}((\frac{I}{{I}_{ref}}+1.0)/2.0)$$
(11)
$$\:{S}_{n}=\gamma\:{S}_{p}$$
(12)

The non-uniform heat generation in batteries can be characterized using two sets of factors: a geometric factor θ and concentration factors S, where subscripts p and n denote positive and negative sides, respectively. The geometric factor θ divides the battery volume into three domains with fixed values θp = θn = 1/18. The concentration factors Sp and Sn quantify the heat generation concentrated within each region and are determined by Eqs. (11 and 12). The constant parameters α, β and γ can be determined through inverse heat transfer simulations. Parameter regression was conducted using 1 C and 4 C discharge experiments, resulting in optimal values of α, β and γ equals 0.015, 0.009, and 0.9, respectively. The reference current Iref was set at 100 A for this study.

Numeriacl strategies

The entire computational domain contains three sub-zones, i.e. batteries, channels, and coolant liquid. The initial temperature of the batteries, coolant fluids, channels and the ambient environment temperature is 298 K. The inflow boundary is specified with a fixed velocity, while the outflow is set at a constant relative static pressure, zero, and the inner channel wall is assumed to satisfy the no-slip condition. Both the interface of the battery/channel wall and channel wall/coolant are set as the coupled thermal boundary, indicating that both the heat flux and temperature are continuous at the interface. The outer boundaries, except the coolant inlet and outlet, are taken as thermally adiabatic.

The computational elements are hexahedral, and the corresponding volume of the mesh system ranges from 1.06 × 10− 12 m3 to 4.87 × 10− 8 m3. Figure 3 shows the grids the battery module and rack. Grid-independence tests based on the Richardson extrapolation approach32 were conducted to guarantee that the employed mesh system gives calculation results of adequate accuracy. The battery parameters used in the simulation are listed in Table 2. The coolant used in the simulation is water, and the wavy microchannels are made of aluminum alloy. The thermophysical properties of the coolant and the minichannels are listed in Table 4.

Table 4 Thermophysical properties of the coolant and channels.
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Fig. 3
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Numerical simulation grid model. (a) Single-module grid (b) Liquid-cooled line connection grid (c) Battery rack.

After specifying the initial and boundary conditions, the system of equations (Eqs. 2–6) is solved to obtain the unknowns: u (three velocity components), p, and T using the commercial computational fluid dynamics (CFD) software ANSYS Fluent, which utilizes the finite volume (FV) method. The solution is obtained through a “single domain of multiple sub-regions” approach, treating the simulated domains as sub-regions of a larger domain with automatic handling of internal surfaces/interfaces to enhance computational efficiency. To further improve efficiency, a two-step projection method is employed for solving the equations. Initially, the mass and Navier-Stokes equations for the coolant liquid are solved to determine a steady velocity field. The pressure-velocity coupling is addressed using the SIMPLE algorithm on a staggered Cartesian grid. Subsequently, thermal energy conservation equations for different sub-domains are calculated independently to obtain the transient temperature field. This approach reduces the two-way coupling between fluid flow and heat transfer to one-way coupling, enhancing calculation efficiency. Since the fluid temperature changes minimally in this study, this simplification of the fluid flow and heat transfer coupling does not introduce significant errors in the results. The iteration method with under-relaxation is applied to each equation, with second-order accuracy for spatial-derivative terms using a second-order upwind approximation and a fully implicit scheme for transient terms.

Results and discussion

In this section, experimental tests were initially conducted to investigate uneven heat generation within the battery cell at varying C-rates and the effectiveness of temperature control through liquid cooling. The validity of the simulation model was confirmed through these tests. The impact of liquid cooling topology on temperature inconsistencies was then studied in relation to the scale of the battery module. This methodology was further extended to analyze the evolution of temperature distribution over extended cycles in an energy storage system operating at a frequency regulation scenario.

Cell level simulation: experimental validation and nonuniform heat generation

Figure 4a and b show the temperature rise curves of the battery during 1 C and 4 C rate discharges under natural convection conditions. To analyze the battery temperature distribution, K-type thermocouples for temperature measurement points were placed at nine point orthogonally on the battery plane (labeled T1-T9), along with three points (labeled Ts1-Ts3) on the battery side. From Fig. 4a, the temperature change trend of each measurement point of the battery during 1 C times rate discharge is consistent. The rate of temperature rise is higher at the beginning and the end of the discharge, and the temperature rise tends to level off in the interval of 1200 –2400 s. This is because the polarization resistance and polarization capacitance are larger at the beginning and the end of the discharge process, which leads to a larger heat generation. The maximum temperature difference between each measurement point during the whole discharge process is about 0.5 K, indicating a uniform temperature distribution.

As shown in Fig. 4b, the surface temperature of the battery increases approximately linearly during 4 C-rate discharge. By the end of the discharge, the maximum temperature reaches 317 K. The irreversible ohmic heat generation is more significant under high-rate charging and discharging conditions. Since the ohmic internal resistance varies less throughout the SOC interval, the overall heat production does not change much with time, resulting in an approximately linear temperature rise. However, there is a notable difference in the temperature distribution under high- rate discharge conditions. The temperature in the region above the cell near the tabs (T1 to T3) is significantly higher than that in the region at the bottom of the cell (T7 to T9), with a maximum temperature difference of 5 K. This is due to the fact that the internal currents of the cell converge at the battery tabs, and the uneven distribution of currents on the collector leads to a larger difference in the ohmic heat production of the collector at high-rate of charging and discharging.

The simulation results presented in Fig. 4 demonstrate a strong agreement with the experimental observations. During 1 C discharging, the temperature variations at each measurement point exhibit notable consistency. However, when magnified to a 4 C rate, the temperature difference between measuring points gradually escalates as the discharge progresses. Notably, the largest error occurs at measurement points T7-T9 after discharging at a 4 C rate for 300 s, amounting to approximately 1.42 K. This difference may be attributed to the uniform heat source term utilized for the Q3 region without further differentiation of heat production variations across different regions. The experimental data reveals a certain level of inconsistency in heat production within the area, with changing heat production distribution throughout the discharge process leading to a larger error at the bottom during the initial discharge phase. Despite this, the absolute temperature simulation errors at the remaining measuring points are all below 1 K, underscoring the effectiveness of this approach. Additionally, Fig. 5 illustrates the cell temperature distribution upon discharge cutoff at both 1 C and 4 C rates. The visualization indicates that the peak temperature during a 1 C rate discharge is centered within the battery cell, with a minimal temperature difference of only 0.04 K. Conversely, a 4 C rate discharge cutoff positions the maximum temperature near the positive tab within the battery cell, resulting in a substantial temperature difference of approximately 5 K, aligning closely with the experimental observations.

Fig. 4
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Temperature profiles of the LFP battery under different C-rate. (a) 1 C-rate discharge. (b) 4 C-rate discharge.

Fig. 5
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Temperature distribution of the LFP battery at the end of discharge. (a) 1 C-rate discharge. (b) 4 C-rate discharge.

The temperature of the battery increases by approximately 20 K during the 4 C-rate discharge, as illustrated in Fig. 4b. High battery temperature and temperature variations can have a detrimental impact on the battery’s lifespan and safety. Therefore, it is crucial to implement an effective thermal management system to maintain optimal performance, especially for high-rate frequency regulation. Prismatic batteries can have cooling surfaces on the bottom, sides, and plane of the battery33. Choosing the bottom and sides for cooling surfaces provides the benefit of high thermal conductivity in these directions. However, this choice also comes with the drawback of longer heat transfer distances and the potential presence of gaps and diaphragms inside the battery, which can lead to increased local thermal resistance. Additionally, the temperature rise test results from the 4 C discharge process indicate that heat generation is higher near the electrode tabs in the battery. Therefore, dissipating heat from the battery proves challenging when using the bottom and side faces as cooling surfaces. Despite the battery’s low thermal conductivity in the thickness direction, the heat dissipation performance improves due to the shorter heat transfer distance and larger heat dissipation area. Therefore, choosing the battery plane as the heat dissipation surface is more suitable for high-rate charging and discharging scenarios. In this study, a flat liquid cooling plate with internal microchannels is implemented in the battery system. To account for variations in heat production along the height of the battery under high-rate conditions, two narrower cooling channels are utilized to cover the battery’s cooling surface. These cooling channels are positioned close to the battery surface and can be placed between two batteries to utilize the liquid-cooling plates effectively.

Figure 6 illustrates the impact of liquid cooling with a flow rate of 3 L/min on both the maximum temperature and temperature uniformity of the battery cell. As shown in the figure, the battery undergoes a temperature increase of around 5 K during a 4 C discharge, while maintaining a temperature uniformity of less than 2 K. The results indicate that liquid cooling can lower the maximum temperature by approximately 15 K, enabling the battery to function effectively under 4 C-rate conditions. The simulation results were also compared with experimental results in Fig. 6. The temperature rise patterns and maximum temperature obtained in the simulation closely matched the experimental data, with a maximum error of 0.5 K. This demonstrates the reasonableness and effectiveness of the simulation model. Figure 7 illustrates the distribution of battery cell temperatures at a 4 C discharge cutoff with liquid cooling conditions. The highest temperature of the battery cell remains near the positive electrode region. By utilizing a dual-channel design, the temperature variance can be decreased even further by regulating the flow rate of the positive electrode area flow channel.

Fig. 6
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Temperature profiles of the LFP battery under 4 C-rate discharge with liquid cooling.

Fig. 7
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Temperature distribution of the LFP battery at the end of 4 C-rate discharge with liquid cooling.

Module level simulation: comparison of different cooling configurations

The arrangement of the liquid cooling channel affects the temperature uniformity between cells and also the additional power consumption of the pump34. In this paper, the thermal management performance of two typical liquid cooling channel topologies is discussed for a battery module consisting of selected LFP batteries. The battery module utilizes a 1P12S connection method and is arranged in a configuration of three rows and four columns. The liquid cooling channel features a 65 mm wide, 5 mm thick mini-channel aluminum flat tube, which is assembled by bending and welding joints into a group. Figure 8 illustrates the two topologies of grouping the series and parallel flow channels. One pair of inlet and outlet boundary is set for the series topology. In contrast, the parallel topology includes five pairs of inlet and outlet boundaries. The total flow rate is set to 3 L/min for both topologies, and the temperature of the inflow medium is 298 K.

Fig. 8
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Cooling channel for the battery module. (a) Serial topology. (b) Parallel topology.

The comparison of pressure and velocity distribution is illustrated in Fig. 9. The pressure distributions of the coolant in the two channel topologies are compared in Fig. 9a and b. It is evident that the pressure loss is higher in the series flow channel compared to the parallel flow channel. The maximum fluid pressure at the inlet is 4170 Pa for the serial topology, while it is only 160 Pa for the parallel topology, indicating that the pumping power of the serial flow channel is greater for the same flow rate. However, the velocity of the coolant in the series channel is significantly higher than that in the parallel channel, as depicted in Fig. 9c and d. In the mini-channel region, the average velocity in the serial flow channel is approximately 0.04 m/s, whereas in the parallel flow channel it is only 0.008 m/s. Accordingly, the calculated Reynolds numbers are 233.2 and 46.6. This indicates that the flow in the cold plate is in the laminar state in this work. It is important to note that the serial flow channel features a circular arc-shaped bending region. The difference in flow velocity between the inner and outer sides of the arc can lead to the formation of a secondary vortex in the mini-channel cross-section, enhancing convective heat transfer in the laminar flow state and improving the thermal management performance of the series topology.

Figure 10 shows the variation of the maximum and minimum cell temperatures as well as the variation of the temperature difference during the 4 C-rate discharge process for both channel topologies. In both topologies, the cell temperature rises rapidly at the beginning of discharge. The rate of temperature rise decreases at about the depth of discharge (DOD) of 0.4. At discharge cut-off, the maximum temperature of the series topology circuit was 303.3 K and the maximum temperature difference was 2.5 K. The maximum temperature and maximum temperature difference of the parallel channel circuit increased to 304.2 K and 3.5 K. The minimum temperature variation of the cells for both topologies was very close to each other. The temperature distribution of the battery module at discharge cut-off for both topologies is given in Fig. 11. In the parallel channel case, the highest temperature battery is inside the module near the outlet of the channel. In contrast, the temperature distribution of the series flow channel cell is more uniform.

Fig. 9
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Comparison of flow field variables. (a) Pressure distribution in the serial channel. (b) Pressure distribution in the parallel channel. (c) Velocity magnitude and vector of coolant in the serial channel. (d) Velocity magnitude and vector of coolant in the parallel channel.

Fig. 10
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Comparison of temperature distribution at the end of 4 C-rate discharge.

Fig. 11
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Comparison of temperature distribution at the end of 4 C-rate discharge. (a) Serial channel case. (b) Parallel channel case.

To analyze the heat transfer performance of the two flow path topologies, the heat flux of each cell cooling surface in the flow path was further compared, as illustrated in Fig. 12. To facilitate understanding, one cell width is considered as the unit length for all horizontal axis units in Fig. 11. In the series topology, 15 cell faces need to be traversed from the inlet to the outlet, whereas in the parallel topology, only 3 cell faces need to be passed along the flow path of each channel. It is important to note that certain channel faces on both sides contact the battery. To represent this, a red dash curve is utilized to indicate the lower side of the pipeline in the figure. From Fig. 12a, the heat flux on the heat exchanger surface of the channel in the series topology is characterized by periodic pulses. The heat flux on the channel reaches 5500 W/m2 when contacting the first cell heat exchange surface, rapidly decays to 3200 W/m2 and then gradually decays in a parabolic shape to 2000 W/m2. However, the heat flux rapidly rebounds above 5000 W/m2 after every three cell surfaces, which is related to the vortex at the arcs shown in Fig. 9c. This feature allows the coolant to better maintain the heat transfer performance, ultimately leading to a further reduction in the maximum module temperature and temperature difference. Figure 12b shows the variation of heat flux on the parallel runner path. The heat exchanger faces F1, and F8 have the highest heat flux in the parallel topology module, with an average value close to 3000 W/m2, which is because these two faces correspond to the channel with batteries on only one side, which can keep the coolant at a low temperature very well. F2 and F7 have the lowest heat flux. This is mainly due to the fact that the F1 and F2 sides and F7 and F8 sides act together on the same battery. More heat from the battery is dissipated by the F1 and F8 faces. Overall, the serial flow channel locally has higher heat flow. The maximum temperature and temperature inhomogeneity of the serial flow channel topology are lower for the same flow rate, which improves the cooling efficiency of the thermal management system.

Fig. 12
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Comparison of heat flux under different cooling channel topology. (a) Serial channel case. (b) Parallel channel case.

Pack level simulation: cooling performance under high C-rate frequency regulation

The above battery modules are connected through electrical connections and thermal management pipework to form a 4 MW/1MWh energy storage system, as shown in Fig. 2. Twelve battery modules are connected in series to form a cluster of batteries, which are placed in two layers of trays on the battery shelf to facilitate modular maintenance. Eight battery racks are set up in the container, which are listed on both sides of the container and independently equipped with water pumps and heat exchanges. Since the flow pattern of each battery layer is consistent, one of the battery racks was selected to build the simulation model.

Figure 13 shows the current and heat source profiles of the 4 MW/1MWh energy storage system under real frequency regulation conditions. The calculation of the lumped heat source of the battery during the 15,000 s operation is derived from Eq. 7. Additionally, the adaptive determination of the inconsistent heat generation distribution within the battery under varying current conditions is achieved through Eqs. (8–10). When the system is in a 4 C times rate charging and discharging cycle for a long time, the peak value of the heat source can reach 65,000 W/m3.

Fig. 13
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Current and heat generation profiles of the battery cell under actual AGC frequency regulation working conditions. (a) Current profile (b) Heat source profile.

Figure 14 shows the battery temperature evolution and the coolant temperature at the outlet boundary under actual frequency regulation operating conditions. Since the response time of the heat transfer process is much larger than the rate of change of current, the temperature change of the battery and the outlet water temperature in the system is smoother compared to the current curve and the heat source curve. Under the specified conditions, the battery’s peak temperature can reach 306.5 K, while the lowest temperature recorded is below 300 K. The temperature distribution across the battery layer is illustrated in Fig. 15 during both peak and valley moments. Remarkably, even at the highest temperature, the temperature variance among cells remains under 2 K, showcasing the effectiveness of the thermal management system in ensuring the sustained and stable operation of the energy storage system under high-rate frequency regulation conditions.

Fig. 14
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Profiles of maximum battery temperature and fluid temperature at outlet during AGC frequency regulation.

Fig. 15
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Temperature distribution during 4 C-rate frequency regulation. (a) At valley point a. (b) At peak point b.

Conclusions

This study examines the electrical and thermal properties of a single battery and proposes a liquid-cooled thermal management system for high C-rate applications. Experimental testing and inconsistent heat generation modelling and simulation revealed that the inconsistency in heat distribution increases with increasing operation rate. The maximum temperature rise and temperature difference of the battery cell under 4 C rate discharge conditions are 20 K and 5 K, highlighting the importance of implementing an efficient thermal management system for optimal performance, particularly for high-rate frequency regulation. The arrangement of the liquid cooling channels not only impacts the temperature uniformity between cells but also influences the additional power consumption of the pump. Despite the serial topology having higher flow resistance compared to the parallel topology at the same flow rate, it exhibits superior convective heat transfer performance. Applying this design to the system level ensures that the maximum battery temperature is below 306.5 K. The maximum temperature difference between the battery cells is 2 K when it is operated in 4 C times frequency modulation working condition. This ensures the long-term stable operation of the battery system.

Future work will focus on regulating flow rates in different cooling channels in accordance with internal thermal gradient characteristics under high C-rate discharging. This will lead to reduced pump power consumption while keeping equivalent cooling performance for the proposed battery pack.