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Optimal battery thermal management for electric vehicles with battery degradation minimization
Yue Wu, Zhiwu Huang, Dongjun Li, Heng Li, Jun Peng, Daniel Stroe, Ziyou Song
TL;DR
Hot-weather EV battery cooling must balance thermal safety, battery degradation, and cooling-energy use, while prior work leaves gaps in robust BTMS modeling and online degradation-minimizing control. This paper builds a control-oriented BTMS model and derives an online rule-based strategy from dynamic programming. Simulations report near-optimal performance versus DP, with improved driving economy and reduced degradation when regenerative energy is used for cooling.
Problem
The paper identifies missing control-oriented BTMS models effective across operating conditions and a reported online cooling optimizer that minimizes battery capacity degradation.
Source: §1 · p. 2Method
The authors establish a control-oriented onboard BTMS model and derive a three-stage online cooling strategy from DP optimization of battery degradation and cooling costs.
Source: §1 · p. 2, §3.1 · p. 8, §6 · p. 16Results
The rule-based strategy achieves near-optimal performance compared with DP, and the study reports improved driving economy and reduced battery degradation through regenerative-energy cooling.
Source: §1 · p. 2, §6 · pp. 16–17Takeaways & Limitations
The study concludes that using as much regenerative energy as possible to cool the battery pack can improve driving economy and reduce battery degradation.
Source: §6 · p. 17The battery model assumes identical electrical and thermal parameters across cells and does not distinguish cell core from surface temperature.
Source: §2.4 · p. 4
Abstract
from arXiv · showhide
The control of a battery thermal management system (BTMS) is essential for the thermal safety, energy efficiency, and durability of electric vehicles (EVs) in hot weather. To address the battery cooling optimization problem, this paper utilizes dynamic programming (DP) to develop an online rule-based control strategy. Firstly, an electrical-thermal-aging model of the $\rm LiFePO_4$ battery pack is established. A control-oriented onboard BTMS model is proposed and verified under different speed profiles and temperatures. Then in the DP framework, a cost function consisting of battery aging cost and cooling-induced electricity cost is minimized to obtain the optimal compressor power. By exacting three rules "fast cooling, slow cooling, and temperature-maintaining" from the DP result, a near-optimal rule-based cooling strategy, which uses as much regenerative energy as possible to cool the battery pack, is proposed for online execution. Simulation results show that the proposed online strategy can dramatically improve the driving economy and reduce battery degradation under diverse operation conditions, achieving less than a 3% difference in battery loss compared to the offline DP. Recommendations regarding battery cooling under different real-world cases are finally provided.
1. Introduction
Battery cooling in hot-weather EVs must balance thermal safety, driving economy, and battery life, but existing control strategies leave gaps in accurate modeling and online degradation minimization. This paper develops a control-oriented BTMS model and a DP-derived online strategy, then analyzes its performance across operating conditions.
1. Introduction
- Battery cooling optimization must jointly address battery aging and cooling-energy consumption because battery electrical, thermal, and aging characteristics are coupled.Active BTMS control also involves refrigerant phase change and coupled electrical-thermal processes.Source: §1 · pp. 1–2
- Prior offline cooling optimization methods require the full traction-power or velocity profile in advance and carry heavy computation burdens that hinder practical use.The paper also reviews online approaches including look-up tables, fuzzy PID, and MPC.Source: §1 · p. 2
- The paper identifies three gaps: a broadly effective control-oriented BTMS model, online cooling optimization that minimizes battery degradation, and guidance across operating conditions.The proposed strategy and operating-condition analysis address these gaps.Source: §1 · pp. 2–3
- The control-oriented BTMS model is established through orthogonal experiments and data fitting, with high accuracy across specified velocity, ambient-temperature, and coolant-flow ranges.The ranges are 0–120 km/h, 26–40 °C, and 0.14–0.22 kg/s.Source: §1 · p. 2
- The proposed online strategy extracts three cooling rules from offline DP results to minimize battery capacity loss and cooling energy while leveraging regenerative power.The strategy is reported as near-optimal compared with DP in EV applications.Source: §1 · pp. 2–3
- The paper analyzes driving economy across driving conditions, ambient temperatures, and BTMS parameters, and provides battery-cooling recommendations.The introduction identifies urban, suburban, and highway conditions among the cases analyzed.Source: §1 · pp. 2–3
2. System Modeling
The section builds a coupled EV, battery, and onboard BTMS model for evaluating battery cooling and its effects on energy use and degradation. The BTMS cooling-rate fit is checked against model/experiment data, while the battery models track electrical, thermal, and aging states.
2. System Modeling
- The EV model accounts for battery energy storage, traction load, and BTMS auxiliary power from the compressor, pump, and fan.The battery, BTMS, and traction-system power balance is described, with detailed vehicle powertrain modeling referenced to prior work.Source: §2 · p. 3, §2.1 · p. 3
2.2. Battery electrical model
- The battery electrical model uses an Rint representation, with voltage, power, and state-of-charge dynamics parameterized for the LiFePO4 pack.The studied pack contains 250 cells arranged as 125 in series and two in parallel, with 120Ah capacity and 412V voltage.Source: §2.2 · pp. 3–4, Table 1 · p. 4
2.3. Battery aging model
- A calibrated LiFePO4 capacity-degradation model makes incremental capacity loss a nonlinear function of current and battery temperature.The model is applied at each sampling step, and incremental capacity reduction is incorporated into the cost function.Source: §2.3 · p. 4
2.4. Battery thermal model
- Battery temperature dynamics combine heat generation and BTMS cooling, with temperature fed back into the electrical and aging models.Heat generation includes resistance Joule heat and reversible entropy heat; cells are assumed to share electrical and thermal parameters, without cell-to-cell temperature variation.Source: §2.4 · pp. 4–5, Figure 2 · p. 5
2.5. Battery thermal management system model
- The BTMS comprises refrigeration and battery-cooling loops, with heat transferred between the battery and coolant and between coolant and refrigerant in the chiller.The model separates cooling-power/energy, battery-to-coolant heat exchange, and coolant-to-refrigerant heat exchange submodels.Source: §2.5 · pp. 5–7, Figure 3 · p. 5
- More than 80% of BTMS model/experiment data have error below 5%, and 97% have error below 10%.The fitted cooling-rate model uses compressor power, ambient and coolant temperatures, air and coolant flow rates, and EV velocity.Source: §2.5 · p. 6, Figure 5 · p. 7
- Compressor power is the BTMS control variable, with pump and fan power treated as a constant 200W and cooling set to zero below 500W compressor power.The compressor operating range is [500, 4500W]; the cooling-rate relationship is fitted from orthogonal simulation data to reduce model complexity.Source: §2.5 · p. 6, Table 2 · p. 7
3. Offline optimization of battery thermal management
The offline DP minimizes battery-aging and cooling-electricity costs, then reveals a staged cooling process under representative driving cycles. Its SC03 result divides cooling into fast, slow, and temperature-maintaining stages.
3.1. Dynamic programming development
- The DP minimizes battery capacity-loss cost plus accumulated cooling-electricity cost, using battery temperature as its state and compressor power as its control.The target is 25°C; temperature and compressor power are each discretized into 111 states.Source: §3.1 · pp. 7–8
3.2. Analysis of dynamic programming results
- NYCC, SC03, and US06 represent urban, suburban, and highway cycles; repeated to consume initial 95% SoC below 10%, their total distances are 314, 317, and 232 km.Each cycle lasts 600 s; repetitions are 165 for NYCC, 55 for SC03, and 18 for US06.Source: §3.2 · p. 8, Figure 7 · p. 9
- Under SC03, DP divides cooling into fast (0–580 s), slow (581–2600 s), and temperature-maintaining (2601 s–end) stages, with battery temperature reaching about 25°C.At the end of fast cooling the battery is about 28°C; it drops to about 25°C by 2600 s.Source: §3.2 · pp. 8–9, Figure 8 · p. 9
- Fast cooling runs the compressor continuously, while slow cooling uses intermittent operation and maintenance holds the battery near 25°C with low or zero compressor power.During fast cooling, compressor power ranges from 500 W to 4500 W; during maintenance, it is between 0 and a low value.Source: §3.2 · pp. 9–10
4. Online battery cooling strategy
The online strategy converts DP results into fast-cooling, slow-cooling, and temperature-maintaining rules. It uses regenerative power for cooling where possible and adjusts the fast-cooling threshold with driving conditions.
4. Online battery cooling strategy
- In fast cooling, regenerative braking power drives the compressor, capped at 4500 W, while traction-mode compressor power is mainly about 532 W.The authors state that using regenerative power this way can reduce battery degradation associated with high-rate charging.Source: Figure 9 · p. 10, §4 · p. 10
- In slow cooling, regenerative braking continues to power cooling, but the compressor is generally off during traction; in temperature maintenance it is off during traction and usually set to zero otherwise.The battery remains around 25°C, fluctuating within about 0.1°C; if its temperature rises, the strategy can return to slow cooling.Source: §4 · pp. 10–11
- The Tsw1 threshold reflects whether low cooling's battery-aging cost reduction exceeds its electricity cost; only Tsw1 varies across the three cycles.Higher vehicle speeds induce more battery heat and require a longer fast-cooling stage and a lower Tsw1.Source: §4 · p. 11
- NYCC, SC03, and US06 average traction powers are 1.30, 4.43, and 14.56 kW, respectively; higher average power corresponds to a lower desired Tsw1.NYCC has the highest Tsw1 and US06 the lowest, as the share of additional cooling power relative to traction power decreases with speed.Source: §4 · p. 12
5. Results and Discussions
The results compare the proposed rule-based strategy with DP, MPC, and no-cooling across urban, suburban, and highway driving. The rule-based strategy closely matches DP, while temperature, trip length, and driving conditions shape the benefits of cooling.
5.1. Comparative results of battery cooling process
- The evaluation compares the online rule-based strategy with offline DP, MPC, and BTMS-off cases, using an MPC horizon of 10 and perfect velocity/traction-load prediction.The passage notes that perfect prediction is almost impossible in real-world implementations and that uncertainty can worsen MPC performance.Source: §5 · p. 12, §5.1 · p. 12
- 2.46% higher battery capacity loss than DP, while the rule-based strategy reduces degradation by 1.8–3.8% and consumed SoC by 0.55–6.34% versus MPC.The numerical comparison also reports the strategy’s loss as identical to DP under US06, at 0.0380.Source: Table 5 · p. 12, §5.1 · pp. 12–13
- 18.83%, 18.75%, and 19.83% lower battery degradation than no-cooling under NYCC, SC03, and US06, respectively, with driving range barely reduced.The associated consumed SoC is 2.35%, 2.14%, and 2.84% more than no-cooling under those cycles, respectively.Source: Table 5 · p. 12, §5.1 · p. 13
5.2. Comparative results of driving economy and battery life
- The rule-based strategy’s capacity-loss, cooling, and total costs almost overlap DP’s; cooling lowers total cost even on short trips, while its benefit accumulates on longer trips.MPC has higher costs during the first 6, 3, and 1 cycles under NYCC, SC03, and US06, respectively, and is not cost-effective for short-term driving.Source: §5.2 · pp. 13–14, Figure 12 · p. 14
- Approximately 20% battery-life extension is achieved as temperature stabilizes, with the rule-based strategy close to DP; MPC can shorten battery life on short trips.The comparison covers different cooling strategies, driving conditions, and distances.Source: Figure 13 · p. 14, §5.2 · p. 14
- For DP and the rule-based strategy, life extension first rises then falls with cycle count in NYCC, is less clearly non-monotonic in SC03, and rises monotonically in US06.Urban gains initially reflect reduced accumulated charging current; highway gains mainly reflect lower temperature, while SC03 falls between these patterns.Source: §5.2 · pp. 14–15
5.3. Parameter sensitivity analysis
- Across NYCC, SC03, and US06, capacity loss is mainly determined by average battery temperature (Tair), rather than cooling area or coolant flow; for NYCC, Case 3 ends 0.96–1.34°C hotter and with 16–19% higher final loss than Cases 1 and 4.Source: §5.3 · p. 15
- Higher ambient temperature yields greater long-trip reductions in total cost and degradation, but Case 3 can raise total cost on a 600-second urban trip; cooling is recommended for long trips.For Case 3 at two NYCC cycles, the cost reduction is only 0.67 USD/100 km; the parameter and cycle comparisons are summarized against no-cooling.Source: §5.3 · p. 16, Table 7 · p. 16
6. Conclusion
The paper develops an online, three-stage cooling strategy from DP optimization of battery degradation and cooling costs. Simulations report near-optimal performance relative to DP and identify regenerative-energy cooling as central to the reported economy and degradation benefits.
6. Conclusion
- The online rule-based strategy’s battery degradation differs from DP by less than 3%.The strategy uses fast cooling, slow cooling, and temperature-maintaining stages derived from DP results.Source: §6 · p. 16
- The BTMS model characterizes compressor power and battery cooling rate across operating conditions, while DP minimizes battery degradation and cooling costs.The paper adopts an electrical-thermal-aging model for commercial LiFePO4 batteries.Source: §6 · p. 16
- Using as much regenerative energy as possible to cool the pack is reported to improve driving economy and reduce battery degradation.The reported comparisons cover urban, suburban, and highway conditions; different BTMS parameters affect cooling speed but have no significant impact on driving economy.Source: §6 · p. 17
Appendix: BTMS orthogonal experiment and model parameters
The appendix describes an orthogonal-experiment-based onboard BTMS model and its parameterization. The experiment relates compressor power and operating conditions to battery cooling rate, then fits the relationship in regions.
Appendix: BTMS orthogonal experiment and model parameters
- The BTMS model uses a Magna onboard air-conditioning system implemented in KULI, with R-134a refrigerant and a 50% ethylene glycol-water battery coolant.The model assumes constant fan air mass flow and assigns all cooling capacity to the battery, excluding cabin effects.Source: Appendix: BTMS orthogonal experiment… · p. 17
- The experiment varies coolant outlet temperature and flow, ambient temperature, vehicle speed, and compressor power, with battery cooling rate as its target.Vehicle speed affects condenser inlet airflow; the total condenser airflow also includes fan-supplied air.Source: Appendix: BTMS orthogonal experiment… · pp. 17–18
- Because a single high-precision correlation was judged impractical, the model fits data sequentially by regions divided using ambient temperature and coolant flow.Figure A presents the relationship between cooling rate and compressor power; the resulting BTMS model incorporates compressor power, ambient temperature, coolant outlet temperature, and air and coolant flow rates.Source: Appendix: BTMS orthogonal experiment… · pp. 17–18