As the global shift toward sustainable transportation accelerates, battery electric vehicles have emerged as a pivotal technology, driving innovations in powertrain efficiency and performance. The heart of a battery electric vehicle lies in its electric drive system, where the permanent magnet synchronous motor (PMSM) has become the preferred choice due to its high power density, torque density, and operational efficiency. However, the diverse driving conditions of battery electric vehicles—such as frequent starts and stops, hill climbing, cruising, and high-speed overtaking—pose significant challenges to the PMSM control system, particularly in terms of acceleration performance, speed regulation range, and control precision. To meet the power demands of battery electric vehicles at high speeds, flux-weakening control strategies are essential for extending the speed range beyond the base speed. This paper delves into a novel advance-angle flux-weakening control strategy for PMSMs in battery electric vehicles, aiming to enhance the overall vehicle performance and ensure stable operation across the entire speed domain.
The proliferation of battery electric vehicles is reshaping the automotive industry, with a growing emphasis on extending driving range and improving dynamic response. In this context, the PMSM’s ability to deliver high torque at low speeds and maintain efficiency at high speeds is critical. Traditional vector control strategies, such as id=0 control, are effective in the constant torque region but fall short in the high-speed constant power region. Thus, flux-weakening control becomes indispensable for battery electric vehicles to achieve wide speed range operation. This research explores the underlying principles of flux-weakening control and proposes an innovative approach that leverages advance-angle adjustment for seamless transition between control modes. Through comprehensive modeling and simulation, we validate the efficacy of this strategy in real-world scenarios for battery electric vehicles.
A battery electric vehicle system is typically composed of three main modules: the electric drive system, the power supply system, and the auxiliary system. The power supply system includes the traction battery, energy management system, and charger, ensuring stable power delivery to the motor while monitoring usage and managing charging processes. The auxiliary system enhances vehicle handling, stability, and passenger comfort. However, the core of a battery electric vehicle is the electric drive system, which acts as the “heart” of the vehicle. Key components include the motor, motor controller, power electronic devices, and transmission mechanisms. The working principle involves the vehicle controller interpreting driver inputs—such as accelerator pedal position, brake pedal engagement, and steering angle—and sending target commands to the motor controller. The motor controller then adjusts PWM signals to regulate motor operation, thereby driving the vehicle. In most driving conditions, torque control suffices for normal operation; in specific modes like cruise control, speed control is employed. Consequently, a dual-loop control structure combining speed and current loops is widely adopted in battery electric vehicles to meet driver demands and ensure a smooth driving experience.
To optimize the performance of battery electric vehicles, it is essential to understand the mathematical model of the PMSM. Assuming ideal conditions—neglecting magnetic saturation, eddy current and hysteresis losses, cogging, and armature reaction—the PMSM model in the synchronous rotating d-q reference frame is established. The voltage equations are given by:
$$u_d = R_s i_d + L_d \frac{di_d}{dt} – \omega_e L_q i_q$$
$$u_q = R_s i_q + L_q \frac{di_q}{dt} + \omega_e L_d i_d + \omega_e \psi_f$$
where \(u_d\) and \(u_q\) are the d- and q-axis voltages, \(i_d\) and \(i_q\) are the d- and q-axis currents, \(R_s\) is the stator winding resistance, \(L_d\) and \(L_q\) are the d- and q-axis inductances, \(\omega_e\) is the electrical angular velocity, and \(\psi_f\) is the permanent magnet flux linkage. The flux linkage equations are:
$$\psi_d = L_d i_d + \psi_f$$
$$\psi_q = L_q i_q$$
The electromagnetic torque equation is:
$$T_e = \frac{3}{2} n_p (\psi_d i_q – \psi_q i_d) = \frac{3}{2} n_p [\psi_f i_q + (L_d – L_q) i_d i_q]$$
where \(T_e\) is the electromagnetic torque, and \(n_p\) is the number of pole pairs. The motion equation is:
$$J \frac{d\omega_r}{dt} = T_e – T_L$$
where \(J\) is the moment of inertia, \(\omega_r\) is the mechanical angular velocity, and \(T_L\) is the load torque. Combining these equations, the PMSM model highlights the coupling between d- and q-axes, which introduces nonlinearities that become more pronounced at higher speeds, posing challenges for control in battery electric vehicles.
To address these challenges, flux-weakening control strategies are employed to extend the speed range of PMSMs in battery electric vehicles. The basic principle revolves around the limitations imposed by the inverter’s voltage and current capacities. The maximum stator phase voltage \(u_{smax}\) and current \(i_{smax}\) constrain the motor’s operational envelope. For an inverter with DC-link voltage \(U_{dc}\), the maximum output voltage under SVPWM is \(U_{dc}/\sqrt{3}\). The voltage limit circle and current limit circle define the feasible operating regions. For a salient-pole PMSM (where \(L_d \neq L_q\)), the voltage limit circle is expressed as:
$$(u_d)^2 + (u_q)^2 \leq u_{smax}^2$$
Substituting the voltage equations and neglecting stator resistance, we derive:
$$(L_d i_d + \psi_f)^2 + (L_q i_q)^2 \leq \left( \frac{u_{smax}}{\omega_e} \right)^2$$
The current limit circle is given by:
$$i_d^2 + i_q^2 \leq i_{smax}^2$$
For simplicity, consider a non-salient PMSM where \(L_d = L_q = L\). The voltage limit circle centers at \((-\psi_f/L, 0)\) with radius \(u_{smax}/(L\omega_e)\), shrinking as speed increases. The operational regions are divided into three zones, as summarized in Table 1.
| Region | Speed Range | Control Strategy | Current Trajectory | Characteristics |
|---|---|---|---|---|
| I: Constant Torque | \(\omega \leq \omega_b\) | id=0 or MTPA | O → A | High torque output, minimal current for maximum torque |
| II: Constant Power | \(\omega_b \leq \omega \leq \omega_{mtpv}\) | Flux-weakening along current limit circle | A → B | Decreasing torque, constant power output |
| III: Deep Flux-Weakening | \(\omega_{mtpv} \leq \omega \leq \omega_{max}\) | MTPV curve operation | B → C | Voltage-limited, further speed extension |
Here, \(\omega_b\) is the base speed, \(\omega_{mtpv}\) is the speed at the intersection of the voltage limit circle and the maximum torque per voltage (MTPV) curve, and \(\omega_{max}\) is the maximum achievable speed. This division ensures that battery electric vehicles can handle varied driving scenarios efficiently.
In this study, we propose an advance-angle flux-weakening control strategy for PMSMs in battery electric vehicles. This strategy adjusts the phase angle of the stator current vector to achieve smooth transition into the high-speed region. The control system structure, as illustrated in Figure 4 (conceptual representation), incorporates multiple loops: a speed loop for precise speed regulation, current loops for dynamic response and decoupling, and a voltage loop for flux-weakening implementation. The advance angle \(\gamma\) is dynamically regulated based on voltage feedback. When the motor operates below base speed, the voltage loop PI controller saturates positively, setting \(\gamma = 0\), and the motor runs in constant torque mode. Above base speed, the PI controller desaturates, producing a negative \(\gamma\) (where \(-\pi/2 \leq \gamma < 0\)), leading to a negative d-axis current \(i_d = i_s \sin \gamma < 0\) that weakens the rotor flux. This enables the PMSM to operate safely in the constant power region, extending the speed range for battery electric vehicles. The control law can be expressed as:
$$\gamma = -K_p (U_{dc} – U_{ref}) – K_i \int (U_{dc} – U_{ref}) dt$$
where \(K_p\) and \(K_i\) are PI gains, \(U_{dc}\) is the DC-link voltage, and \(U_{ref}\) is the reference voltage limit. This approach minimizes torque and speed fluctuations during mode transitions, enhancing the driving experience in battery electric vehicles.
To validate the proposed strategy, we developed a simulation model in MATLAB/Simulink tailored for battery electric vehicle applications. The parameters used in the simulation are summarized in Table 2, reflecting typical values for a PMSM in a battery electric vehicle.
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| DC-link voltage | \(U_{dc}\) | 800 | V |
| Base speed | \(\omega_b\) | 8000 | r/min |
| Maximum current | \(i_{smax}\) | 200 | A |
| Stator resistance | \(R_s\) | 0.05 | Ω |
| d-axis inductance | \(L_d\) | 0.5 | mH |
| q-axis inductance | \(L_q\) | 0.5 | mH |
| Permanent magnet flux | \(\psi_f\) | 0.2 | Wb |
| Pole pairs | \(n_p\) | 4 | – |
| Moment of inertia | \(J\) | 0.01 | kg·m² |
The simulation scenarios were designed to emulate real-world driving conditions for battery electric vehicles. Initially, the target speed was set to 8000 r/min with a load torque of 70 N·m. At t = 0.5 s, the target speed increased to 14000 r/min, and at t = 1 s, it further rose to 18000 r/min. The results, depicted in waveforms, demonstrate the control system’s performance. In the interval 0–0.5 s, the motor operates below base speed; the stator voltage magnitude remains within limits, \(\gamma = 0\) rad, and \(i_d = 0\) A, indicating non-flux-weakening operation. From 0.5–1 s, as speed exceeds base speed, the voltage limit is approached, and the flux-weakening loop generates a negative \(\gamma\), producing a negative \(i_d\) to weaken the flux and maintain stable high-speed operation. From 1–1.5 s, at even higher speeds, the stator voltage magnitude stays at the maximum, and a larger negative \(i_d\) sustains operation. Key performance metrics are summarized in Table 3.
| Time Interval (s) | Speed (r/min) | Advance Angle \(\gamma\) (rad) | d-axis Current \(i_d\) (A) | Voltage Magnitude (V) | Operation Mode |
|---|---|---|---|---|---|
| 0–0.5 | 8000 | 0 | 0 | < \(U_{dc}/\sqrt{3}\) | Constant Torque |
| 0.5–1 | 14000 | -0.2 | -40 | ≈ \(U_{dc}/\sqrt{3}\) | Flux-Weakening |
| 1–1.5 | 18000 | -0.5 | -100 | = \(U_{dc}/\sqrt{3}\) | Deep Flux-Weakening |
These results confirm that the advance-angle flux-weakening control strategy enables smooth mode transitions and stable operation across a wide speed range, which is crucial for battery electric vehicles facing dynamic driving conditions. The rapid response and minimal torque ripple contribute to improved vehicle performance and energy efficiency.
The advancement of battery electric vehicles hinges on continuous improvements in motor control technologies. Our proposed advance-angle flux-weakening strategy addresses several limitations of traditional methods, such as parameter dependency and instability in deep flux-weakening regions. By integrating voltage feedback and PI control, this strategy ensures robust performance even under varying load and speed conditions in battery electric vehicles. Future work could explore adaptive tuning of PI parameters or incorporation of machine learning techniques for further optimization. Additionally, real-time implementation on hardware-in-the-loop platforms would validate practical applicability for battery electric vehicles.
In conclusion, this research contributes to the evolving landscape of battery electric vehicle technology by presenting a novel flux-weakening control strategy for PMSMs. The mathematical modeling, simulation validation, and comprehensive analysis underscore the strategy’s effectiveness in extending speed range and enhancing operational stability. As battery electric vehicles become more prevalent, such innovations will play a vital role in achieving higher efficiency, longer range, and superior driving dynamics. The insights gained here provide a foundation for further engineering advancements in the electric drive systems of battery electric vehicles.