(372b) Battery Thermal Management of Electric Vehicles through Optimal Control of Battery Cooling and Refrigerant Circuits

As the demand for eco-friendly power resources grows, there has been a significant increase in interest in electric vehicles (EVs). [1]. Lithium-ion batteries are widely used for EVs because of their high energy density and specific power. However, they are sensitive to temperature, so it’s crucial for the batteries in electric vehicles to operate within an appropriate operating temperature range of 15-35°C. The battery properties, such as efficiency and durability, can be degraded in the outer range [2]. When the battery is at high temperatures, thermal runaway can occur, and the electrolyte conductivity decreases at low temperatures [3].

In our previous study [4], a zone model predictive control is proposed to determine the coolant inlet temperature and the coolant flow rate to control battery temperature within the desirable range and minimize power consumption. The heat exchange with refrigerant at the chiller (Q_{required,chiller}) is required to achieve the optimal coolant inlet temperature. To this end, it is necessary to control the refrigerant circuit, which includes a compressor, condensers, an expansion valve, and a battery chiller. Thus, we use static optimization with a proposed simple static heat exchange model for refrigerant operation condition determination.

The heat exchanger model is especially important for refrigerant circuit modeling. In addition, the model simplification is significant for real-time decisions and real implementation. The finite volume method (FVM) and the moving boundary method (MBM) have been proposed. The FVM is the method that discretizes the heat exchanger into many control volumes and solves the mass and energy balance equations, consisting of differential equations [5]. The MBM tracks the phase change boundary dynamically [6]. These methods are generally used to construct dynamic models, which are comprised of differential equations.

Static models are sufficient to optimize the operation point (set-point). In Ref. [7], a static model with a calculation strategy for the phase change points in the heat exchangers is proposed using iteration algorithms. We improve this algorithm with a maximum heat transfer rate recalculation strategy in accuracy. In addition, we propose phase length functions that do not require iteration algorithms and are algebraic equations. It is necessary because the static heat exchanger models are used with the optimization solver to determine the optimal operation points of the refrigerant circuit.

We construct the heat exchanger model with phase length function using the effectiveness-NTU (ε-NTU) method. The ε-NTU method first calculates the theoretical maximum heat transfer rate (Q_max) from the inlet conditions. Then, the effectiveness of the equipment with the fluid properties, heat transfer area (A), and overall heat transfer coefficient is calculated and the actual heat transfer rate is calculated as Q=Q_max × ε. In particular, the effectiveness depends on the phase. Thus, the phase change points, i.e., the phase lengths with the constant duct area, are significant to calculate the accurate effectiveness. These phase lengths can be determined considering the enthalpy changes required from the current state to the phase change state. For example, if the current phase is vapor-phase, the enthalpy change required to be two phase is H_current - H_{saturated vapor}. H_current means the enthalpy at the current condition, and H_{saturated vapor} denotes the enthalpy at the saturated temperature.

The phase length calculation problem can be formulated with a convex optimization problem only with bounds on the decision variable (the phase length). Thus, the optimality condition for the phase length can be expressed with the first-order optimality condition, and then enforcing the bounds on the solution is sufficient to find the phase length. To enforce the bounds on the solution, the smooth minimum and maximum functions are used to ensure the differentiability of the heat exchanger model. This is because the heat exchanger model is finally used to determine the operation points of the refrigerant circuit, such as the compressor and fan rotational speeds.

Regarding the theoretical maximum heat exchange amount (Q_max), it is recalculated at the phase change points. It is recalculated by subtracting the heat exchange amount for the phase change from the initially calculated maximum heat exchange amount using the inlet conditions. The improvement of the model accuracy with this strategy is validated with rigorous simulation program GT-suite data.

Finally, the three-step procedure for battery thermal management is proposed to comprehensively consider the coolant and refrigerant circuits, as shown in Figure. The first step is calculating the maximum heat transfer rate of the battery chiller (Q_max,chiller) under current conditions. This information is used as the constraint when determining the coolant inlet temperature and flow rate by MPC for the coolant circuit. This can ensure that the heat transfer rate determined by MPC does not exceed the maximum capacity of the chiller. In the second step, the MPC determines the coolant circuit operation in real time. The determined required heat exchange amount in the chiller is then used to determine the optimal setpoint of the refrigerant circuit. To achieve the required heat exchange at the chiller (Q_{required,chiller}), the optimal compressor and fan rotational speeds are determined with the proposed simple heat exchange model and optimization solver. When simulating under the charging scenarios, it was confirmed that the battery temperature was maintained within an appropriate operating range.

Acknowledgments

This work is supported by Hyundai Motor Company as "Mixed Integer Nonlinear Optimization Methodology Study for Nonlinear System Control Including Integer Variables" and as “Development of Model Predictive Control for Battery Thermal Management.”

References

[1] Y. Masoudi and N. L. Azad, “MPC-based battery thermal management controller for Plug-in hybrid electric vehicles.” 2017 American Control Conference (ACC) (2017): 4365-4370

[2] S. Park and C. Ahn. "Computationally Efficient Stochastic Model Predictive Controller for Battery Thermal Management of Electric Vehicle." IEEE Transactions on Vehicular Technology 69(8) (2020): 8407-8419.

[3] L. He, et al. " Review on Thermal Management of Lithium-Ion Batteries for Electric Vehicles: Advances, Challenges, and Outlook." Energy & Fuels 37(7) (2023): 4835-4857.

[4] C. Hong, et. al., "Fast Zone-Model Predictive Control for Full Battery Pack of Electric Vehicles," AIChE Annual Meeting 2023.

[5] X. Liu and A. Yebi, et al. “Model Predictive Control of an Organic Rankine Cycle System.“ Energy Procedia 129 (2017):184-191

[6] R. Sangi, P. Jahangiri and D. Müller, “A combined moving boundary and discretized approach for dynamic modeling and simulation of geothermal heat pump systems.” Thermal Science and Engineering Progress 9 (2019):215-234

[7] I. Lu, N.A. Weber, P. Bansal, and D.E. Fisher, "Applying the effectiveness-NTU method to elemental heat exchanger models." ASHRAE Transactions. 113 (2007): 504-513.