The precise thermal management of lithium-ion batteries is paramount for ensuring their safety, longevity, and performance, particularly in demanding applications like electric vehicles. Central to any effective thermal management strategy is an accurate thermal model of the lithium-ion battery. The fidelity of this model hinges critically on the accuracy of its core parameters: the heat capacity and the thermal resistances. These parameters are intrinsically linked to the battery’s fundamental thermophysical properties—specific heat capacity and thermal conductivity. Traditionally, measuring these properties requires sophisticated and costly equipment like Accelerating Rate Calorimeters (ARC) or specialized thermal flux meters, which also entail lengthy testing cycles. This presents a significant barrier to rapid prototyping and system-level modeling.
This work presents a novel, efficient, and cost-effective methodology for identifying the thermal model parameters of a laminated, soft-pack lithium-ion battery. The approach cleverly utilizes the battery’s own heat generation during controlled electrical operation in tandem with the natural heat transfer to an adjacent cell, eliminating the need for external heaters or expensive instrumentation. By designing specific current excitation profiles and employing an optimization algorithm, we can rapidly and accurately extract the necessary thermal parameters, enabling high-fidelity thermal modeling for system simulation and state estimation.
Accurate thermal modeling of a lithium-ion battery is not merely an academic exercise; it is a practical necessity. The internal temperature of a lithium-ion battery directly influences its electrochemical kinetics, internal resistance, aging rate, and safety limits. An oversimplified or inaccurate thermal model can lead to poor predictions, resulting in inefficient cooling, accelerated degradation, or in worst-case scenarios, thermal runaway. Therefore, developing accessible methods to characterize the thermal behavior of a lithium-ion battery is of great engineering significance.
The proposed method specifically addresses the challenge for large-format, laminated pouch-type lithium-ion batteries. For such cells, a simple lumped thermal model is often insufficient because significant temperature gradients can develop across the battery’s thickness during operation, especially under high loads or poor cooling conditions. To capture this gradient, a distributed thermal network model is essential. This model discretizes the battery into several layers along its thickness direction, each represented by a thermal capacitance and interconnected by thermal resistances. The accuracy of this distributed model is entirely dependent on correctly identifying these lumped parameters for each segment.
The core innovation of our methodology lies in its experimental design. Instead of applying external heat via heating films—which adds complexity and may introduce contact resistance uncertainties—we use the Joule heat generated by one lithium-ion battery itself as the controlled heat source. A second, identical lithium-ion battery is placed in intimate thermal contact with the first. The first battery is subjected to a pulsed current profile, causing its temperature to rise. This heat conducts through the contact interface into the second, passive lithium-ion battery, and is also dissipated to the environment from the outer surfaces. By meticulously measuring the surface temperatures of both lithium-ion battery units and knowing the electrical heat generation power from the first, we construct a complete thermal system. The parameters of the distributed thermal model are then the unknowns that, when used in the model equations, best reproduce the measured temperature evolution. This setup naturally incorporates both “self-generated heat” and “external heat transfer” phenomena.
The distributed thermal equivalent circuit model for a single lithium-ion battery is foundational. We consider the battery to be homogeneous in the plane of its electrodes and focus on one-dimensional heat transfer through its thickness, which is the primary path for significant gradients. The cell is divided into N segments (e.g., N=7). Each segment i has a thermal capacitance \(C_{b,i}\) and experiences a portion of the total heat generation \(P_{b,i}\). Adjacent segments are connected by a thermal resistance \(R_b\), representing the conductive resistance between layers. The outermost segments interact with the ambient environment via convective resistances \(R_{air1}\) and \(R_{air2}\). The governing equations for the temperature \(T_{b,i}\) of each node are derived from energy balance, analogous to electrical circuit node analysis:
For the internal nodes (i = 2 to N-1):
$$C_b \frac{dT_{b,i}}{dt} = \frac{T_{b,i-1} – T_{b,i}}{R_b} + \frac{T_{b,i+1} – T_{b,i}}{R_b} + P_{b,i}$$
where we assume the thermal capacitance \(C_b\) and internal conductive resistance \(R_b\) are identical for all segments due to uniform material distribution.
For the surface nodes (i=1 and i=N):
$$C_b \frac{dT_{b,1}}{dt} = \frac{T_{b,2} – T_{b,1}}{R_b} + \frac{T_{a} – T_{b,1}}{R_{air1}} + P_{b,1}$$
$$C_b \frac{dT_{b,N}}{dt} = \frac{T_{b,N-1} – T_{b,N}}{R_b} + \frac{T_{a} – T_{b,N}}{R_{air2}} + P_{b,N}$$
Here, \(T_a\) is the ambient temperature. The total heat generation power \(P_{total}\) for the lithium-ion battery under operation is primarily irreversible Joule heating, given by:
$$P_{total} = I (U_{terminal} – U_{OCV})$$
where \(I\) is the current (positive for discharge), \(U_{terminal}\) is the measured terminal voltage, and \(U_{OCV}\) is the open-circuit voltage at the instantaneous state of charge (SOC). For high-frequency pulsed currents, the contribution from reversible entropic heat is negligible and can be ignored. This total power is assumed uniformly distributed among the N segments, so \(P_{b,i} = P_{total} / N\).
The parameter identification system involves two such lithium-ion battery models coupled at one surface. Let us denote the active cell as Cell 1 and the passive cell as Cell 2. Their contacting surfaces are Node 1 of Cell 1 and Node N of Cell 2. The thermal connection between them is the same internal conductive resistance \(R_b\). The full system of equations expands to 2N coupled ordinary differential equations. The known inputs are the ambient temperature \(T_a\), the heat generation profile \(P_{Cell1}(t)\) for Cell 1 (with \(P_{Cell2}(t)=0\)), and the initial temperatures. The measurable outputs are the outer surface temperatures of both cells: \(T_{Cell1, outer}\) and \(T_{Cell2, outer}\). The parameters to be identified are \(C_b\), \(R_b\), and the effective ambient resistance \(R_{air}\) (which may be dominated by insulation material in the experiment).
The experiment is designed with meticulous attention to detail. Two identical commercial 8 Ah NCM (Nickel Cobalt Manganese) soft-pack lithium-ion battery cells are used. Their key specifications are summarized below:
| Parameter | Value |
|---|---|
| Nominal Voltage | 3.6 V |
| Rated Capacity | 8 Ah |
| Voltage Limits | 2.75 V – 4.2 V |
| Mass | 300 g |
| Dimensions (L x W x Thickness) | 142 mm x 115 mm x 8.5 mm |
The cells are preconditioned to a nominal 50% State of Charge (SOC) to minimize SOC variation during the short test. High-thermal-conductivity grease is applied to ensure good thermal contact between the large faces of the two lithium-ion battery cells. The assembly is then thoroughly insulated on all sides except the two outermost faces, which are left to exchange heat with the controlled environment of a thermal chamber. Fine-wire thermocouples are attached to the centers of the outer surfaces of both lithium-ion battery cells to record temperature history. The active lithium-ion battery is connected to a programmable battery tester that delivers the precise current profile.
The current profile is a bidirectional pulse sequence. For example, a 20A charge pulse for 5 seconds followed by a 20A discharge pulse for 5 seconds, repeated continuously. This symmetric profile ensures the net change in SOC over a full cycle is nearly zero, justifying the neglect of entropic heating and keeping the cell’s OCV relatively constant for accurate heat calculation. The pulse magnitude is adjusted for different ambient temperatures to maintain a measurable temperature rise without exceeding safe limits. The experiment is conducted at multiple ambient setpoints (e.g., 0°C, 10°C, 20°C) to observe parameter consistency or variation.
With the measured current, voltage, and temperature data, the next step is parameter identification via optimization. The system of discretized thermal ODEs is simulated in time using a forward-Euler or similar method. This simulation produces predicted outer surface temperature histories, \(\hat{T}_{Cell1,outer}(t)\) and \(\hat{T}_{Cell2,outer}(t)\), for a given guess of the parameter set \(\theta = [C_b, R_b, R_{air}]\). The objective is to find the parameter set that minimizes the difference between these predictions and the actual measurements. We define a root-mean-square error (RMSE) cost function:
$$F(\theta) = \sqrt{ \frac{1}{M} \sum_{k=1}^{M} \left[ (T_{Cell1,outer}(t_k) – \hat{T}_{Cell1,outer}(t_k; \theta))^2 + (T_{Cell2,outer}(t_k) – \hat{T}_{Cell2,outer}(t_k; \theta))^2 \right] }$$
where M is the total number of time samples.
To efficiently search the parameter space and find the global minimum of this cost function, we employ an Adaptive Particle Swarm Optimization (APSO) algorithm. APSO is a robust, population-based stochastic optimization technique inspired by social behavior. A swarm of particles (each representing a candidate parameter set \(\theta\)) flies through the search space. Their positions and velocities are updated based on their own best-known position and the best-known position of the entire swarm. The “adaptive” component often involves dynamically adjusting parameters like inertia weight to improve convergence speed and accuracy. The algorithm iterates until the cost function converges to a minimum, yielding the optimal identified parameters for that test condition.
The results from applying this methodology at three different temperature setpoints are compelling. The following table summarizes the identified thermal model parameters for the lithium-ion battery:
| Ambient Setpoint (°C) | Heat Capacity, \(C_b\) (J/K) | Internal Conductive Resistance, \(R_b\) (K/W) | Ambient Resistance, \(R_{air}\) (K/W) |
|---|---|---|---|
| 0 | 41.66 | 0.0985 | 5.11 |
| 10 | 43.51 | 0.0995 | 5.63 |
| 20 | 43.05 | 0.0995 | 6.79 |
The consistency of \(C_b\) and \(R_b\) across temperatures is notable. The small variations are within expected measurement and optimization tolerances. The ambient resistance \(R_{air}\) shows an increasing trend with temperature, which is physically plausible as the thermal chamber’s convective conditions (like fan speed for temperature uniformity) might change slightly with setpoint, and the insulation’s effective properties may have a mild temperature dependence.
These lumped parameters can be converted into the more fundamental thermophysical properties. The specific heat capacity \(c_p\) is calculated from the heat capacity and mass:
$$c_p = \frac{C_b}{m}$$
The average thickness-direction thermal conductivity \(k\) is derived from the internal conductive resistance. For a slab of cross-sectional area A and total thickness L divided into N segments, the resistance for one segment is related by:
$$R_b = \frac{(L/N)}{k A} \quad \Rightarrow \quad k = \frac{L}{N A R_b}$$
Using the average values from the identification (\(C_b \approx 42.74 J/K\), \(R_b \approx 0.0992 K/W\), m=0.3 kg, L=0.0085 m, A=0.142m*0.115m), we obtain:
$$c_p \approx \frac{42.74}{0.3} \approx 1.0 \, J/(g·K)$$
$$k \approx \frac{0.0085}{7 \times (0.142 \times 0.115) \times 0.0992} \approx 0.377 \, W/(m·K)$$
To validate the methodology, these average identified parameters are used in the distributed model to simulate the thermal response of the lithium-ion battery under completely different current excitation profiles and at ambient temperatures not used for identification (e.g., 5°C, 15°C). The simulated outer surface temperatures are compared to new experimental measurements. The agreement is excellent across all validation tests. The maximum error between simulation and experiment remains below 0.1°C, even for temperature rises exceeding 4°C. This high level of accuracy strongly confirms the validity and robustness of the identified parameters and the underlying thermal model.
A critical analysis involves comparing our derived thermophysical properties with values reported in the literature for similar lithium-ion battery chemistries and formats. This comparison provides context and reinforces the credibility of our results.
| Source / Reference | Cell Chemistry | Specific Heat Capacity, \(c_p\) (J/(g·K)) | Thermal Conductivity, \(k\) (W/(m·K)) |
|---|---|---|---|
| This Work (Average) | NCM Pouch | ~1.00 | ~0.38 |
| Literature A | NCM Pouch | 0.928 | 0.354 |
| Literature B | NCM Pouch | 1.243 | 0.48 |
| Literature C | NCM Pouch | 0.90 | 0.335 |
| Literature D | LFP Pouch | 1.114 | 0.284 |
| Literature E | LFP Pouch | 1.39 | 0.35 |
The derived specific heat capacity of approximately 1.0 J/(g·K) and thermal conductivity of 0.38 W/(m·K) for our NCM lithium-ion battery fall well within the range reported for similar cells. The variations among literature values stem from differences in exact cell chemistry, electrode loading, stack pressure, and measurement technique. Our results align closely with typical values, providing strong evidence that the proposed identification method yields physically reasonable and accurate parameters for the lithium-ion battery.
The advantages of this methodology are manifold. First, it is cost-effective, requiring only standard battery testing equipment, temperature sensors, and basic insulation materials—no ARC or specialized thermal analyzers are needed. Second, it is rapid; the entire identification process for a given temperature can be completed within a few hours, including experiment time and optimization computation. Third, it is non-invasive and representative; it uses the lithium-ion battery’s own Joule heating, which is the actual heat generation mechanism during operation, avoiding potential artifacts from external heaters. Fourth, it naturally identifies system-level parameters like the effective ambient resistance, which encapsulates combined convection and radiation in the actual application environment. Finally, the method directly provides parameters for a ready-to-use distributed thermal equivalent circuit model, which can be easily integrated into broader battery management system (BMS) algorithms for real-time temperature estimation and thermal control.
In conclusion, we have successfully developed and demonstrated a practical, accurate, and efficient method for identifying the key thermal model parameters of a laminated soft-pack lithium-ion battery. By ingeniously leveraging the intrinsic heat generation of one lithium-ion battery cell and its subsequent transfer to a neighboring cell, we create a self-contained thermal system from which parameters can be extracted via optimization. The identified parameters show excellent consistency and, when converted to thermophysical properties, align well with established literature values for lithium-ion batteries. Most importantly, validation tests using independent current profiles confirm the model’s high predictive accuracy. This methodology provides researchers and engineers with a powerful, accessible tool for characterizing the thermal behavior of lithium-ion batteries, facilitating the development of more accurate thermal models, advanced BMS algorithms, and ultimately, safer and more efficient energy storage systems.