Regenerative braking energy recovery control strategy for electric vehicles with battery temperature measurement

Aiming at the problems of short mileage and overheating and easy damage of the battery in electric vehicles, the fuzzy control regenerative braking strategy with vehicle speed, braking intensity, battery state of charge (SOC), and the introduction of battery temperature as fuzzy control input and regenerative braking distribution percentage as output are proposed; secondly, the ideal braking force distribution curve and ECE regulations are used as the boundary to determine the braking force distribution range of pure electric vehicles. Finally, the control strategy designed in this paper is simulated under selected working conditions by ADVISOR software, and the effectiveness and superiority of this control strategy are verified. The strategy can not only reduce the damage to the battery caused by high temperatures but also obtain more braking energy.


Introduction
With the development of technology, electric and hybrid vehicles are gradually replacing traditional cars.However, pure electric vehicles also have some disadvantages that cannot be ignored.Among them, insufficient battery capacity is particularly prominent.The capacity of the battery is not sufficient to support the long-distance driving of electric vehicles, and it needs to be charged several times during the driving process [1] .But frequent charging and discharging will cause the battery temperature to rise, thus affecting the battery life.These problems not only increase the cost of electric vehicles but also hinder the advancement of electric vehicles.
In [2], researchers combined supercapacitors with batteries to optimize the energy recovery efficiency of electric buses.In [3], scholars proposed the matching of different braking force distribution schemes for differences in braking intensity, which was verified to be simple to implement and effective in improving energy recovery efficiency.In [4], a simulation model with braking intensity as the distribution criterion was presented, and by conducting comparative experiments, it was concluded that the new simulation model had higher energy recovery efficiency.A predictive control-based braking force distribution strategy was proposed for hybrid vehicles in [5], which improved the tram efficiency and ensured the target of vehicle braking slip rate.
The core technology of pure electric vehicles lies in the reasonable distribution and recovery of electrical energy, and the storage capacity of the battery [6] .However, in this major technical difficulty of the onboard battery, no breakthrough has been made over the years.Therefore, the recovery of the regenerative braking energy of the driving motor is the most important direction of our research.

Structure and working principle of the pure electric vehicle braking system
The regenerative braking system has two components, in which the hydraulic braking system provides mechanical braking force for the vehicle and the electric motor braking system provides regenerative braking force for the vehicle, both of which work in concert to complete the braking process [7] .Figure 1 shows the overall structure of the regenerative braking system.Regenerative braking energy recovery means that when an electric vehicle brakes, the vehicle powertrain will adjust the operating mode of the motor, switching it from a drive state to a power generation state to charge the onboard battery.

The effect of temperature on the battery
New energy vehicles commonly choose lithium-ion batteries as the vehicle electrical energy reserve device, but many safety problems still occur in practice.According to the practical investigation between 2018 and 2022, there are hundreds of spontaneous combustion accidents caused by thermal runaway batteries.The root cause of these accidents is that the new energy power battery is in a state of efficient use for a long time, resulting in the gradual aging of some components, and the battery function is also declining, so overcharging and long-term idling in this state are likely to trigger a thermal runaway [8] .
The influence of temperature on the battery is mainly reflected in the available capacity of the battery.As shown in Figure 2, the available capacity of a certain type of lithium battery increases significantly with the increase in temperature, so the available capacity of a power battery is affected by temperature.However, a higher temperature doesn't mean better.Due to its internal electrochemical reaction, as well as material transfer, it will cause continuous heat production inside the battery, and if the heat production and heat dissipation cannot realize a thermal equilibrium, safety accidents such as fire and explosion may occur.Therefore, a suitable control strategy is needed to keep the battery in a safe working condition at all times.

Braking force distribution principles for electric vehicles
During the braking of a car, the body is subjected to a normal phase force on the ground by: where 1 Z F and 2 Z F are the force of the ground on the front and rear wheels (N); z is the braking strength, g h the height of the center of mass to the ground (m), and G is the gravity of the car (kg).Let z be the braking strength, and its calculation equation is: The normal force on the ground can be found by combining Equations ( 1) and ( 2).

Ideal braking force distribution curve
During the braking process, instances of wheel lock and dragging generally occur when the force of ground breaking surpasses the ground traction.If the vehicle is braked with both the front and rear wheels locked, the relationship between the front and rear axle braking forces is known as the ideal brakeforce distribution curve (I-curve).In this case, the relationship between front and rear axle braking forces is:

ECE Regulations
The braking force distribution of electric vehicles during braking must reach the relevant standards.According to the ECE regulations, when the road surface adhesion coefficient is between 0.2 and 0.8, the relationship between the road surface adhesion coefficient  and braking strength is: The front and rear braking force relationship can be expressed as follows: ) ) ( 0 .0 7 ) 0.07 0.85 0 ( ( The braking force region of the electric vehicle should be between the I curve and the ECE regulations, at the same time, the brake distribution curves of the front and rear brake axles should be as close as possible to the ECE regulations thus recovering more energy from braking.

Fuzzy controller design
There are many nonlinear factors affecting the efficiency of energy recovery, among which vehicle speed, SOC, and braking intensity have a larger impact on recovery efficiency.Considering the effect of temperature on battery life, a battery temperature factor has also been added, so we will design a four-variable input fuzzy controller, which realizes the reasonable distribution of regenerative braking force through the fuzzy logic algorithm.Figure 3 shows the braking force distribution area.
Reasonable fuzzy rules play an effective role in achieving the desired control effect.In this paper, IF-THEN fuzzy rules are adopted.Fuzzy rules are analyzed as follows: The rule base is set to four input variables and one output variable, and a total of 55 fuzzy logic control rules are established.Some of the rules are shown in Table 1.
Table 1.Partial rules of fuzzy controller When the braking intensity is large, the proportion of motor braking should be reduced; when the braking intensity is small, the braking force should be provided by the motor as much as possible.The theoretical domain of braking intensity is [0, 1], and the fuzzy subset is {L, M, H}.
(2) When driven at a low speed, the brake energy recovery is very low; as the vehicle speed increases, the brake energy recovery increases.When the vehicle speed is very high, safety should be guaranteed first.The fuzzy set of the car's driving speed is {L, M, H}; the theoretic domain is {0, 100}.
(3) When SOC > 0.8 or SOC < 0.2, there is no need to recover this part of braking energy; when 0.2 < SOC < 0.8, the motor should be involved in car braking as much as possible.The battery SOC fuzzy set is {L, M, H}; the theoretical domain is {0, 1}.
(4) When the battery temperature is low, we will increase the regenerative braking distribution proportionality coefficient and decrease the proportionality factor as the temperature increases.The battery temperature temp fuzzy set is {L, H}; the theoretical domain is {0, 70}.
Membership function of fuzzy controller input is shown in Figure 4.The simulation cycle condition selected in this paper is the U.S. urban cycle condition (CYC_UUDS).The specific parameters are shown in Figure 6. Figure 6.UUDS working condition Figure 7 shows the change of motor output torque and battery current with time.The tram is driven when the vertical coordinate is greater than zero, the motor torque is positive, and the battery is discharged.When the vertical coordinate is less than zero, the car is in a braking state, and the motor in power generation mode, thus completing regenerative braking energy recovery.

Figure 2 .
Figure 2. Temperature dependence of a lithium battery capacity

Figure 4 .
Fuzzy input affiliation functionAs shown in Figure5.Output is regenerative braking percentage K.As the value-K increases, more energy is generated by motor braking.The theoretical range of the regenerative braking percentage coefficient is [0, 1] and the fuzzy subset is {SL, L, M, H}.

Figure 5 .
Figure 5. Regenerative braking scale factor affiliation function 6. Modelling and Simulation ADVISOR (Advanced Vehicle Simulat OR) is a simulation software developed by NREL, USA, which can be run under a Simulink environment.It has features such as modularity, hybrid simulation, and open-source code, which provides convenience for users to analyze various aspects of vehicle performance.The simulation cycle condition selected in this paper is the U.S. urban cycle condition (CYC_UUDS).The specific parameters are shown in Figure6.
(a) Motor output torque (b) Battery charge/discharge current Figure7.Variation of energy recovery system A comparison of the battery SOC value changes for the two strategies is shown in Figure8.The overall battery SOC value shows a decreasing trend with simulation time, and the local rise is at the point where the motor performs regenerative braking energy recovery.Under the same operating conditions, the fuzzy control designed in this paper increases the braking energy recovery rate by 25.68% compared to the control strategy that comes with ADVISOR; the effective energy recovery rate increases by 6.25%.

Figure 8
Figure 8 Comparison chart of battery SOC change7.ConclusionIn this paper, a fuzzy control-based braking energy recovery system for an electric vehicle is designed and a safe braking range for a short-range pure electric vehicle is planned.The electric vehicle control strategy is modeled by ADVISOR software and simulated under UUDS operating conditions.The