In the development of electric multi-purpose vehicles (electric MPV), achieving optimal performance in terms of dynamics and economy is crucial. As an engineer specializing in new energy vehicle powertrain systems, I focus on the parameter matching and optimization of key components such as the motor, battery, and final drive ratio for an electric MPV. This process involves detailed calculations, simulation modeling, and iterative refinements to meet design targets. The use of interval mathematics and simulation tools like Matlab/Simulink allows for robust analysis under uncertainties. In this article, I discuss the methodology for matching powertrain parameters, present simulation results based on the China Light-duty Vehicle Test Cycle (CLTC), and propose optimization strategies to enhance performance. The goal is to ensure that the electric MPV achieves high speed, acceleration, gradability, and range while minimizing energy consumption.
The electric MPV under consideration is derived from a conventional internal combustion engine model, with modifications to accommodate an electric powertrain. Key vehicle parameters include a length of 4,830 mm, width of 1,860 mm, height of 1,720 mm, curb weight of 1,995 kg, and gross vehicle weight of 2,520 kg. Aerodynamic and rolling resistance coefficients are critical for performance; the drag coefficient (Cd) is 0.34, frontal area (A) is 2.67 m², rolling resistance coefficient (f) is 0.0095, wheel radius (r) is 327 mm, and transmission efficiency (ηt) is 0.9. Performance targets for this electric MPV include a 30-minute maximum speed of at least 130 km/h, acceleration times of 0–50 km/h in ≤6 seconds, 50–80 km/h in ≤5 seconds, and 0–100 km/h in ≤12 seconds, a maximum gradability of ≥20% at a crawl speed of 6 km/h, a CLTC cycle range of ≥400 km, and an energy consumption rate of ≤15 kWh per 100 km. These targets guide the parameter matching process to ensure the electric MPV meets real-world demands.
To handle uncertainties in vehicle operating conditions and component characteristics, I employ interval mathematics for calculations. This approach replaces deterministic values with intervals, allowing for a range of possible outcomes. For instance, if A = [a1, a2] and B = [b1, b2], then operations like multiplication and division are defined as A · B = [a1·b1, a2·b2] and A / B = [a1 / b2, a2 / b1], respectively. Using the Intlab toolbox in Matlab, I perform these interval computations to derive parameter ranges that account for variability. This method is particularly useful in the early stages of electric MPV development, where precise data may not be available, and it helps in selecting components that can tolerate fluctuations in performance.
The motor is a core component of the electric MPV powertrain, and its parameters must satisfy dynamic performance requirements as per standards like GB/T 18385-2005. For this electric MPV, I select a permanent magnet synchronous motor due to its high efficiency and widespread use in electric vehicles. The motor power is determined based on three key scenarios: maximum speed, maximum gradability, and acceleration. The power required for sustaining the 30-minute maximum speed (Pv) is calculated using the equation:
$$ P_v \geq \frac{m_1 g f V_{\text{max}}}{3600} + \frac{C_d A V_{\text{max}}^3}{76140 \eta_t} $$
where m1 is the half-load mass (kg), g is gravitational acceleration (9.8 m/s²), and Vmax is the target speed (130 km/h). Substituting values, Pv ≥ 37.6 kW. For maximum gradability, the power (Pi) is given by:
$$ P_i \geq \frac{1}{\eta_t} \left( \frac{m_2 g f \cos \alpha_{\text{max}}}{3600} V_i + \frac{m_2 g \sin \alpha_{\text{max}}}{3600} V_i + \frac{C_d A}{76140} V_i^3 \right) $$
where m2 is the gross vehicle mass (kg), αmax is the slope angle corresponding to 20% gradability, and Vi is the climb speed (15 km/h). This yields Pi ≥ 23.5 kW. The acceleration power (Pa) for 0–100 km/h is derived from:
$$ P_a \geq \frac{1}{\eta_t t_j} \left( \frac{m_1 g f t_j}{1.5 \times 3600} V_j + \frac{C_d A t_j}{2.5 \times 76140} V_j^3 + \frac{\delta m_1}{2 \times 3.6 \times 3600} V_j^2 \right) $$
where tj is the acceleration time (12 s), Vj is the final speed (100 km/h), and δ is the rotational mass factor (1.08). This results in Pa ≥ 103.2 kW. The peak motor power (Pp) must exceed the maximum of these values, with an additional redundancy ε (10–20%) to account for full-load conditions, leading to Pp = [113.5, 123.8] kW. The rated power (Pr) is based on the maximum speed requirement and the overload ratio λ (Pp/Pr), typically between 2 and 2.5, giving Pr = [45.4, 61.9] kW. For motor speed, the maximum speed (nmax) is set to 9,000 rpm for cost-effectiveness, and the base speed ratio β (nmax/nr) ranges from 2 to 2.5, resulting in a rated speed nr = [3,600, 4,500] rpm. The peak torque (Tp) and rated torque (Tr) are calculated as:
$$ T_p = 9550 \frac{\beta P_p}{n_{\text{max}}} $$
yielding Tp = [241, 328] Nm, and
$$ T_r = 9550 \frac{P_r}{n_r} $$
giving Tr = [96, 164] Nm. Based on these intervals and market availability, I finalize the motor parameters for the electric MPV as peak power of 120 kW, rated power of 55 kW, peak torque of 280 Nm, rated torque of 131 Nm, maximum speed of 9,000 rpm, and rated speed of 4,000 rpm.
| Parameter | Interval Calculation | Final Value |
|---|---|---|
| Peak Power (kW) | [113.5, 123.8] | 120 |
| Rated Power (kW) | [45.4, 61.9] | 55 |
| Peak Torque (Nm) | [241, 328] | 280 |
| Rated Torque (Nm) | [96, 164] | 131 |
| Max Speed (rpm) | N/A | 9,000 |
| Rated Speed (rpm) | [3,600, 4,500] | 4,000 |
The battery pack is another critical component for the electric MPV, directly influencing range and power delivery. I opt for a ternary lithium-ion battery due to its high energy density and common use in electric vehicles. The single cell has a nominal voltage U0 of 3.65 V and capacity C0 of 180 Ah. According to GB/T 31466-2015, the battery pack nominal voltage Ub should be in the range [328.7, 363.3] V, leading to a series cell count nS = [90, 100]. The depth of discharge ξ is set to 90% for maximum range. The total energy required for the CLTC range (Qb1) and the battery pack energy (Qb2) are calculated as:
$$ Q_{b1} = \frac{L_{\text{CLTC}} W}{100 \xi} $$
where LCLTC is the target range (400 km) and W is the energy consumption rate ([12, 15] kWh/100 km), giving Qb1 = [53.3, 66.7] kWh. The battery energy is:
$$ Q_{b2} = \frac{U_b C_b}{1000} = \frac{U_0 C_0 n_P n_S}{1000} $$
where Cb is the pack capacity, and nP is the parallel cell count. With C0 fixed at 180 Ah, nP is 1, and solving for nS gives a target of 92 cells for a total energy of 60.4 kWh. Thus, the battery parameters are nominal voltage of 335.8 V, capacity of 180 Ah, configuration of 1 parallel and 92 series, and total energy of 60.4 kWh. This setup ensures that the electric MPV meets the range requirements while maintaining a compact design.
| Parameter | Value |
|---|---|
| Single Cell Voltage (V) | 3.65 |
| Single Cell Capacity (Ah) | 180 |
| Pack Nominal Voltage (V) | 335.8 |
| Pack Capacity (Ah) | 180 |
| Series Cells | 92 |
| Parallel Cells | 1 |
| Total Energy (kWh) | 60.4 |
The final drive ratio (i0) is essential for translating motor output to wheel torque and speed. It must satisfy both the maximum speed and gradability requirements. For maximum speed, the ratio is bounded by:
$$ i_0 \leq 0.377 \frac{n_{\text{max}} r}{V_{\text{max}}} $$
and for gradability:
$$ i_0 \geq \frac{r (m g f \cos \alpha_{\text{max}} + m g \sin \alpha_{\text{max}})}{T_p \eta_t} $$
Substituting values, i0 ranges from [6.59, 8.53]. Considering supplier options, I select a single-stage reduction gear with a ratio of 7.81 for initial simulations, as it balances performance and cost for the electric MPV. This choice ensures that the vehicle can achieve the target speed while providing sufficient torque for acceleration and climbing.
To validate the parameter matching, I develop a full vehicle simulation model in Matlab/Simulink. This model incorporates the powertrain components, vehicle dynamics, and CLTC driving cycle for economic analysis. The top-level structure includes blocks for the motor, battery, transmission, and vehicle body, with inputs for driver commands and environmental conditions. The CLTC cycle, which includes urban, suburban, and high-speed segments, is used to simulate real-world driving patterns. The model’s ability to track the CLTC speed profile is verified, as shown in the simulation where the actual speed closely follows the target, confirming that the electric MPV powertrain can handle the dynamic requirements of the test cycle. This simulation approach allows for iterative testing and optimization without physical prototypes, reducing development time and cost.
Initial simulation results for the electric MPV indicate that most performance targets are met, but two areas require improvement: the 0–100 km/h acceleration time and the CLTC range. The acceleration time is 12.3 seconds, slightly above the 12-second target, and the range is 367 km, below the 400 km goal. Other parameters, such as maximum speed (141 km/h) and gradability (25%), exceed targets. The energy consumption rate is 14.8 kWh/100 km, within the limit. These results highlight the need for optimization to fully achieve the design goals for the electric MPV.
| Performance Parameter | Simulation Result | Target | Status |
|---|---|---|---|
| 30-min Max Speed (km/h) | 141 | ≥130 | Met |
| 0–50 km/h Acceleration (s) | 5.4 | ≤6 | Met |
| 50–80 km/h Acceleration (s) | 4.6 | ≤5 | Met |
| 0–100 km/h Acceleration (s) | 12.3 | ≤12 | Not Met |
| Max Gradability (%) | 25 | ≥20 | Met |
| CLTC Range (km) | 367 | ≥400 | Not Met |
| Energy Consumption (kWh/100 km) | 14.8 | ≤15 | Met |
To address the deficiencies, I propose two optimization strategies for the electric MPV powertrain. First, I adjust the final drive ratio to improve acceleration. Using supplier-provided ratios of 8.07, 8.26, and 8.51, I run simulations to evaluate their impact. A ratio of 8.26 reduces the 0–100 km/h acceleration time to 11.9 seconds while maintaining the maximum speed at 134 km/h, which is acceptable. Second, to increase the range, I enhance the battery pack by increasing the series cells to 100, raising the total energy to 65.7 kWh and nominal voltage to 365 V. Additionally, I reduce the drag coefficient to 0.32 and switch to low-rolling-resistance tires (f ≈ 0.008). Re-simulating with these changes, the CLTC range improves to 410 km, and all acceleration targets are met. These optimizations ensure that the electric MPV achieves all performance goals without compromising other aspects.
| Final Drive Ratio | Max Speed (km/h) | 0–100 km/h Acceleration (s) | CLTC Range (km) |
|---|---|---|---|
| 8.07 | 137 | 12.1 | 367 |
| 8.26 | 134 | 11.9 | 366 |
| 8.51 | 130 | 11.8 | 366 |
In conclusion, the parameter matching and optimization process for the electric MPV powertrain is a multifaceted task that requires careful consideration of motor, battery, and transmission components. By applying interval mathematics and simulation modeling, I derive robust parameter sets that meet dynamic and economic targets. The optimizations, including final drive ratio adjustment and battery enhancement, successfully address initial shortcomings, resulting in an electric MPV that fulfills all design requirements. This methodology not only accelerates development but also provides a framework for future electric MPV projects, emphasizing the importance of iterative analysis and component integration.