(149b) Fast Zone-Model Predictive Control for Full Battery Pack of Electric Vehicles

Environmental concerns about carbon footprint and climate change have drawn interest in the development of hybrid electric vehicles (HEVs) and electric vehicles (EVs) in the automotive industry [1]. Lithium-ion (Li) batteries are mainly used in electric vehicles due to their high voltage and energy density. Therefore, the performance of lithium batteries is an important factor for the success of electric vehicles. The most important factor affecting battery performance is temperature. Lithium batteries have optimal efficiency and safety in the range of 15 to 40 [2]. Outside this temperature range, batteries experience significant degradation in efficiency, durability, and safety thermal runaway [2,3]. Therefore, it is necessary to control the optimum temperature of the battery so that the battery can operate within an appropriate temperature range during vehicle operation [3,4,5].

In order to keep the battery temperature within the optimal temperature range, the heat generation of the battery must be predicted. Therefore, model predictive control (MPC) approaches are suitable for considering future states and determining optimal control. There is an increasing number of studies applying the MPC approach for thermal management considering the pump power for coolant operation [1,3,5]. However, previous studies dealt with the entire battery pack as a single cell [5] or two subpacks (96 cells) [1]. Additionally, only the typical MPC, i.e. the setpoint MPC, was used to track the setpoint within the optimal temperature range [1,3,4].

In this paper, we propose a fast zone-MPC for temperature control of the entire battery pack. The zone-MPC strategy is much more efficient than setpoint MPC because the pump for coolant operation is turned off when the temperature of the battery pack enters the zone. The zone-MPC formulation requires mixed integer nonlinear programming (MINLP) solver. However, solving MINLP in real time in EV is not possible. Thus, introducing a soft plus function to approximate the objective function leads to nonlinear programming (NLP) formulation. Then, we declare the soft plus function as a new variable with the relevant dynamics. Finally, the continuous linearization method [6] can be used to transform NLP into a quadratic program (QP).

An equivalent circuit model (ECM) with integrated energy balance is used for battery dynamics and considers the heat exchange with the coolant. For model reduction, we introduce two representative cells for each 1 subpack (48 cells) and the total number of representative cells is 16 for full pack (360 cells). This is determined by examining experimental and simulation data. The cells contacting with air and cell are different from the cells contacting with cells; thus, we need two representative cells for one-subpacks (shown in the attached optional figure). In the objective function of MPC, we give the penalty if the temperatures of cells are outside the proper temperature zone and do not give any penalty if they are in the zone. Additionally, the pump power for the coolant circulation and the amount of heat exchange energy for cooling or heating the coolant temperature are considered in the objective function. The proposed zone-MPC maintains the battery temperature within an optimal temperature range and can reduce power consumption much more than the typical set-point MPC. When the driving simulation for 1 hour under 0.3C-rate with an ambient temperature of 38°C, the power consumption by the proposed zone MPC is 59% smaller than that of the set-point MPC.

References

[1] Yi Xie, Chenyang Wang, etc, “An MPC-Based Control Strategy for Electric Vehicle Battery Cooling Considering Energy Saving and Battery Lifespan”, IEEE Transactions on Vehicular Technology 69, no.12 (2020): 14657-14673.

[2] Garrow .Sarah Grace, “Dynamic modeling and control of transcritical vapor compression system for battery electric vehicle thermal management.”, Urbana, Illinois (2018).

[3] S. Park and C. Ahn, “Model Predictive Control With Stochastically Approximated Cost-to-Go for Battery Cooling System of Electric Vehicles”, IEEE Transactions on Vehicular Technology 70, no.5 (2021): 4312-4323.

[4] 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.

[5] C. Wei, T. Hofman, E. Ilhan Caarls, R. van Iperen, “Zone Model Predictive Control for Battery Thermal Management including Battery Aging and Brake Energy Recovery in Electrified Powertrains”, IFAC 52, no.5 (2019): 303-308.

[6] Jay H. Lee and N. Lawrence Ricker, “Extended Kalman Filter Based Nonlinear Model Predictive Control”, Ind. Eng. Chem. Res 33, no.6 (1994) :1530-1541.

Acknowledgement

This work was supported by Hyundai Motor Company as Mixed Integer Nonlinear Optimization Methodology Study for Nonlinear System Control Including Integer Variables.