In recent years, the global automotive industry has shifted focus towards sustainable transportation, with electric cars leading the charge due to their zero-emission capabilities and energy efficiency. The China EV market, in particular, has experienced rapid growth, driven by government policies and increasing environmental awareness. However, the widespread adoption of electric cars faces challenges, such as limited driving range and long charging times, primarily due to battery technology constraints. One promising solution to enhance the economic performance of electric cars is braking energy recovery, which converts kinetic energy into electrical energy during deceleration, storing it in batteries or other storage devices. Studies indicate that only 10% to 30% of braking energy can be effectively recovered, highlighting the need for optimized control strategies. This paper explores the optimization of braking energy recovery control strategies for electric cars, emphasizing the China EV context, to improve energy utilization and extend driving range.
Braking in electric cars involves a combination of mechanical braking and regenerative braking provided by the electric motor. The key to maximizing energy recovery lies in the distribution of braking force between the front and rear axles, while ensuring safety and stability. Based on the ECE-R13 regulations, a braking force distribution strategy is designed to define the proportion of regenerative braking under different braking intensities. For instance, during mild braking, the electric motor handles all braking force on the front axle, whereas in emergency braking, only mechanical braking is used. The ideal distribution follows curves such as the I-curve and f-curve to prevent instability, like rear-wheel lock-up. The braking force distribution for a front-wheel-drive electric car can be summarized as follows: for braking intensity \( z \) between 0 and 0.120, the front axle bears the entire force; for \( z \) between 0.120 and 0.525, a composite braking approach is used; and for \( z \) above 0.665, mechanical braking dominates. This strategy ensures that the electric car operates within safe limits while prioritizing energy recovery.
The mathematical formulation of braking force distribution is critical for optimizing electric car performance. Let \( m \) represent the vehicle mass, \( g \) the gravitational acceleration, and \( z \) the braking intensity. The front and rear axle braking forces, \( F_{uf} \) and \( F_{ur} \), are derived based on the ECE-R13 regulations. For mild braking (\( 0 < z < 0.120 \)):
$$ F_{uf} = m g z $$
$$ F_{ur} = 0 $$
For composite braking (\( 0.120 < z < 0.525 \)):
$$ F_{uf} = \frac{0.95 G (z + 0.07) (b + z h_g)}{0.85 L} $$
$$ F_{ur} = z G – F_{uf} $$
where \( G = m g \), \( b \) is the distance from the center of mass to the rear axle, \( h_g \) is the height of the center of mass, and \( L \) is the wheelbase. For higher braking intensities (\( 0.525 < z < 0.665 \)):
$$ F_{uf} = \frac{0.665 G (b + z h_g)}{L} $$
$$ F_{ur} = \frac{(L – 0.665 h_g) F_{uf}}{0.665 h_g} – \frac{G b}{h_g} $$
And for emergency braking (\( z > 0.665 \)):
$$ F_{uf} = \frac{z G (b + z h_g)}{L} $$
$$ F_{ur} = \frac{z G (a – z h_g)}{L} $$
Here, \( a \) is the distance from the center of mass to the front axle. This distribution ensures that the electric car maintains stability, such as avoiding rear-wheel lock-up, while maximizing the involvement of the regenerative braking system in the China EV context.
To further enhance the braking energy recovery for electric cars, a fuzzy logic controller is designed with three inputs—braking intensity \( z \), vehicle speed \( v \), and state of charge (SOC)—and one output—the regenerative braking force proportion coefficient \( k \). This approach accounts for real-time driving conditions and battery status, which is crucial for the dynamic environment of electric cars in China. The input variables are fuzzified into linguistic sets: for \( z \), the sets are Low (L), Medium (M), and High (H) over the range [0, 1]; for \( v \), Low (L), Medium (M), and High (H) over [0, 100] km/h; and for SOC, Low (L), Medium (M), and High (H) over [0, 1]. The output \( k \) is categorized as Very Low (VL), Low (L), Medium (M), High (H), and Very High (VH) over [0, 1]. The membership functions use triangular and trapezoidal shapes to reflect the motor’s external characteristics and battery constraints.
The fuzzy rule base, derived from expert knowledge and extensive testing, defines how the inputs map to the output. For example, if the vehicle speed is low, SOC is high, and braking intensity is low, the regenerative braking proportion is very low to prioritize battery protection. Conversely, if the speed is high, SOC is low, and braking intensity is medium, the proportion is high to maximize energy recovery. A subset of the fuzzy rules is presented in the table below, which guides the control strategy for electric cars to adapt to varying conditions in the China EV market.
| Rule No. | Vehicle Speed (v) | SOC | Braking Intensity (z) | Output (k) |
|---|---|---|---|---|
| 1 | L | H | L | VL |
| 2 | L | H | M | VL |
| 3 | L | H | H | VL |
| 4 | M | H | L | VL |
| 5 | M | H | M | VL |
| 6 | M | H | H | VL |
| 7 | H | H | L | VL |
| 8 | H | H | M | VL |
| 9 | H | H | H | VL |
| 10 | L | M | L | L |
| 11 | L | M | M | M |
| 12 | L | M | H | L |
| 13 | M | M | L | VH |
| 14 | M | M | M | H |
| 15 | M | M | H | VL |
| 16 | H | M | L | VH |
| 17 | H | M | M | H |
| 18 | H | M | H | VL |
| 19 | L | L | L | M |
| 20 | L | L | M | L |
| 21 | L | L | H | VL |
| 22 | M | L | L | VH |
| 23 | M | L | M | H |
| 24 | M | L | H | VL |
| 25 | H | L | L | VH |
| 26 | H | L | M | H |
| 27 | H | L | H | VL |
The fuzzy inference system uses the Mamdani method, and defuzzification is performed using the centroid method to compute the crisp value of \( k \). This controller dynamically adjusts the regenerative braking force based on real-time inputs, ensuring optimal energy recovery for electric cars without compromising safety. For instance, when the SOC is high, the controller reduces regenerative braking to prevent overcharging, whereas at low SOC, it maximizes recovery to extend the driving range—a key consideration for the China EV market, where charging infrastructure may be limited.
To validate the proposed control strategy, a co-simulation platform integrating AVL Cruise and MATLAB/Simulink is employed. The electric car model parameters, such as mass, wheelbase, and motor specifications, are based on a typical front-wheel-drive configuration relevant to the China EV industry. The simulation involves two control strategies: Strategy A, which incorporates the fuzzy logic-based braking force distribution, and Strategy B, which uses a conventional approach without fuzzy control or optimized force distribution. The models are compiled into DLL files and embedded in the Cruise environment to simulate driving cycles, including the New European Driving Cycle (NEDC) and the Federal Test Procedure (FTP-75), which represent urban and suburban driving conditions common in electric car testing.
The simulation results demonstrate the effectiveness of the optimized control strategy for electric cars. In the NEDC cycle, Strategy A reduces the energy consumption per 100 kilometers from 13.62 kWh to 11.71 kWh, representing a 14% improvement. Similarly, in the FTP-75 cycle, energy consumption decreases from 12.99 kWh to 9.95 kWh, a 23.4% enhancement. These improvements highlight the potential of the fuzzy logic-based approach to significantly boost the economic performance of electric cars, particularly in the China EV context, where energy efficiency is a critical selling point. The table below summarizes the comparative results, emphasizing the superiority of Strategy A in terms of energy savings and extended range.
| Parameter | NEDC Energy Consumption (kWh/100 km) | FTP-75 Energy Consumption (kWh/100 km) |
|---|---|---|
| Strategy A | 11.71 | 9.95 |
| Strategy B | 13.62 | 12.99 |
| Efficiency Improvement | 14.00% | 23.40% |
Further analysis of the simulation data reveals that the fuzzy controller effectively modulates the regenerative braking force proportion \( k \) based on varying conditions. For example, during low-speed braking with high SOC, \( k \) approaches zero, whereas in high-speed scenarios with low SOC, \( k \) reaches up to 0.8, indicating strong regenerative braking. This adaptability ensures that the electric car recovers more energy during frequent stop-and-go driving, which is typical in urban environments for China EV applications. The mathematical representation of the output \( k \) can be expressed as a function of the inputs:
$$ k = f(z, v, \text{SOC}) $$
where \( f \) denotes the fuzzy inference system. The overall braking force \( F_b \) is then distributed as:
$$ F_b = F_{\text{reg}} + F_{\text{mec}} $$
with \( F_{\text{reg}} = k \cdot F_{uf} \) for the regenerative component and \( F_{\text{mec}} \) as the mechanical braking force. This integration ensures that the electric car maintains stability while maximizing energy recovery, addressing key challenges in the China EV market.
In conclusion, the optimization of braking energy recovery control strategies for electric cars, particularly through fuzzy logic and ECE-R13-based force distribution, significantly enhances energy efficiency and driving range. The proposed strategy demonstrates notable improvements in both NEDC and FTP-75 cycles, with up to 23.4% reduction in energy consumption, making it highly relevant for the growing China EV sector. Future work could explore the integration of additional factors, such as road gradient or traffic conditions, to further refine the control approach for electric cars. This research contributes to the advancement of sustainable transportation and supports the global shift towards energy-efficient electric vehicles.