Subject to various thermal boundary conditions such as liquid or air convection, battery cells can be thermally controlled at different surfaces, including the electrical connection tabs (terminals), cell surfaces, or both. Prior literature studies have investigated the impact of tab and surface cooling methods on battery thermal performance. Surface cooling can maintain lithium (Li)-ion pouch cells at a lower average temperature under high current rates than tab cooling. In a case study, it was demonstrated that using tab cooling rather than surface cooling extended the lifetime of a battery pack by three times. Similar results were achieved for cylindrical Li-ion cells, where tab cooling was shown to reduce the internal temperature inhomogeneities. It is clear that both surface and tab cooling have their individual strengths and weaknesses. However, to the best of our knowledge, there is no battery control framework in the state-of-the-art literature that systematically investigates the optimal integration of these two cooling methods for advanced battery temperature management.

To bridge the identified research gap, we propose new 2D battery thermal models that stem from the decomposition of the particular solution of the non-homogeneous PDE-based 2D heat equation. Our model decomposes the particular solution into four components, each representing a distinct side of the battery cell. This method and its resulting model formulation enable us to obtain independent control signals for each side of the battery, including the tabs and surfaces. Evaluation of the model shows that by using four states, the model accurately predicts the local thermal behaviour, even under aggressive vehicle driving and cooling scenarios. The model with only one state, in particular, is both more accurate and computationally efficient than the widely utilised two-state thermal equivalent circuit (TEC) model, with a 28.7% reduction in computational time. Even as the number of states increases, it remains in the same computational order of magnitude as the TEC model, suggesting it could readily replace the TEC model in existing battery management systems

We then formalise the integration of the two cooling strategies as an optimal control problem. The goal is to optimally split the coolant flow between the tabs and the surface of the cell to minimise both the average temperature rise and the thermal gradients within the battery cell, regardless of operating conditions. The problem is solved in a receding horizon fashion using the model predictive control (MPC)
framework, which also guarantees constraints to be satisfied.

The effectiveness of the proposed MPC scheme is evaluated under the urban dynamometer driving schedule, against two state-of-the-art cooling methods commonly employed in EVs. Typically, cylindrical battery cells are cooled either along their lateral surface (side) only or from the base only, but rarely are both approaches used simultaneously. These two conventional cooling schemes, serve as benchmarks for comparison with our MPC. The schemes are evaluated across the following key thermal performance metrics; maximum temperature, mean temperature, maximum thermal gradients, and temperature difference. Results indicate that our proposed MPC significantly outperforms the conventional cooling schemes in all the metrics above.

This optimised cooling approach holds significant potential for EVs and battery applications. By maintaining lower and more uniform temperatures across the battery, it effectively slows down degradation processes and potential thermal runaway hazards, ensuring safer battery operation.