Abstract: Reducing the losses of permanent magnet synchronous motor (PMSM) drive systems is of great significance for improving the performance of pure electric vehicles. Based on the analysis of traditional linear loss models, this paper constructs a novel nonlinear loss model tailored to the operating characteristics of PMSMs, enabling accurate estimation of system losses across any operating condition. Based on this novel nonlinear system loss model, this paper proposes a comprehensive nonlinear loss optimization control for PMSM drive systems. Through optimal matching of motor losses and driver losses, the overall system efficiency is optimized. Experimental results show that, compared to traditional maximum torque-to-current ratio control, the comprehensive nonlinear loss optimization control can effectively improve the system's loss characteristics across all operating conditions, increase the energy utilization rate of the motor drive system, and achieve energy savings.
1 Introduction
As the main power source for pure electric vehicles, the operating efficiency of the permanent magnet synchronous motor drive system directly affects the driving range of electric vehicles on a single charge, and thus seriously affects the application scope of electric vehicles [1-2]. In order to improve the efficiency of the permanent magnet synchronous motor direct drive system, considering the complexity of the operating conditions of electric vehicles, a variety of efficiency optimization control strategies have been applied to improve the efficiency of the permanent magnet synchronous motor drive system, and have achieved good results. References [3-4] proposed a maximum torque-to-current ratio control method based on the dynamic mathematical model of the motor. By adjusting the stator magnetic field of the motor, the stator current of the permanent magnet synchronous motor is minimized when the output torque is constant, thereby reducing motor losses. It has the advantages of fast response and easy implementation. References [5-7] proposed an efficiency optimization control strategy based on the loss model of the permanent magnet synchronous motor. Based on the copper loss and iron loss of the motor, an accurate loss model of the motor is constructed. Then, by real-time detection or estimation of the speed and current signal of the permanent magnet synchronous motor, the optimal magnetic flux value when the motor efficiency is the highest is derived based on the loss model of the motor. Reference [8] proposes an efficiency optimization control strategy based on minimum input power using online search technology. This method does not require a precise mathematical model of the loss of permanent magnet synchronous motors. It searches for the optimal current online by detecting the system input power, thereby achieving efficiency optimization of the motor drive system.
While minimum power control strategies offer advantages such as slow response to parameter changes and high adaptability, their optimization time is too long, making it difficult to meet the complex operating conditions required for pure electric vehicles, and their energy-saving effect is unsatisfactory. Traditional efficiency optimization control of permanent magnet synchronous motors (PMSMs) based on loss models struggles to construct accurate driver loss models, limiting it to efficiency optimization control of motor losses and failing to achieve optimal system efficiency control performance. Therefore, to meet the need for high-efficiency drive control of direct-drive systems of PMSMs under complex operating conditions, this paper proposes a nonlinear loss comprehensive optimization control for direct-drive systems of PMSMs based on a nonlinear system loss model, specifically addressing the complex operating conditions of pure electric vehicles. By accurately fitting the nonlinear conduction and switching characteristics of power components using nonlinear polynomials, accurate estimation of driver losses under different operating conditions is achieved. Furthermore, by analyzing the copper and iron loss characteristics of PMSMs, a system nonlinear loss model for the direct-drive system of PMSMs across the entire operating range is constructed. Based on the system loss model, this study investigates the relationship between the motor stator current and the optimal system loss using optimization theory. Through nonlinear loss comprehensive optimization control, the optimal allocation of motor and driver losses is achieved, effectively improving the loss characteristics of the permanent magnet synchronous motor direct drive system across all operating conditions. The proposed loss comprehensive optimization control is verified on a designed permanent magnet synchronous motor experimental platform. Experimental results show that, compared to traditional maximum torque-to-current ratio control, nonlinear loss comprehensive optimization control can effectively improve the efficiency characteristics and energy utilization of the permanent magnet synchronous motor direct drive system across all operating conditions, thereby increasing the driving range of pure electric vehicles.
2 Loss Model of Permanent Magnet Synchronous Motor Direct Drive System
To achieve optimal control of the nonlinear losses in a direct drive system of a permanent magnet synchronous motor (PMSM), it is necessary to construct an accurate system loss model for the PMSM drive system. The losses in a PMSM drive system mainly consist of two parts: PMSM losses and driver losses. Motor losses primarily include copper losses and iron losses, while driver losses mainly include conduction losses and switching losses of the power devices.
2.1 Loss Model of Permanent Magnet Synchronous Motor
The dynamic mathematical model of the permanent magnet synchronous motor is shown in Figure 1.
From Figure 1, we can see that the voltage equation of the permanent magnet synchronous motor can be expressed as follows:
In the formula, L1d and L1q are the leakage inductances of the dq axis of the permanent magnet synchronous motor, Lmd and Lmq are the inductances of the dq axis of the motor, id and iq are the stator currents of the dq axis, ud and uq are the stator voltages of the dq axis of the motor, Rs is the stator winding resistance, ωr is the motor speed, and np is the number of pole pairs of the motor.
According to equation (1), the stator copper loss of the permanent magnet synchronous motor can be expressed as:
Stator iron loss per unit volume can generally be estimated using the following formula.
In the formula, kh is the hysteresis loss coefficient of the material, ke is the additional loss coefficient of the material, σ is the conductivity of the material, kd is the thickness of the material lamination, Bm is the peak value of the magnetic induction intensity, and f is the frequency of the magnetic field change.
According to equation (3), the stator iron loss of the permanent magnet synchronous motor can be expressed as:
In the formula, khd is the stator equivalent hysteresis loss and eddy current loss coefficient of the motor considering the stator tooth and stator yoke shape, and kep is the stator additional loss coefficient of the motor considering the stator tooth and stator yoke shape.
Furthermore, from equations (2) and (4), the motor loss of the permanent magnet synchronous motor direct drive system can be expressed as follows:
2.2 Loss Model of Permanent Magnet Synchronous Motor Driver
In direct drive systems of permanent magnet synchronous motors, the conduction and switching characteristics of the power components in the driver exhibit strong nonlinearity. Currently, in the analysis of driver loss characteristics in direct drive systems of permanent magnet synchronous motors, linear models are often used to fit the conduction and switching characteristics of the power components, as shown in equation (6).
As shown in Figure 3, traditional linear models for power devices can only approximate the conduction characteristics of power devices well at the rated operating point. However, when the power device current is far from the rated operating point, the linear model struggles to accurately fit the conduction characteristics. To achieve accurate estimation of the conduction and switching losses of power devices across the entire operating range, this paper proposes a nonlinear loss model to accurately fit the conduction and switching characteristics of power devices. The nonlinear conduction model of the power device can be expressed as follows:
In the formula, ac, bc, and cc are nonlinear fitting coefficients for the conduction characteristics of the power device.
In a permanent magnet synchronous motor, the stator current is a sinusoidal current, and its magnitude changes constantly. Therefore, in the drive control system of a permanent magnet synchronous motor, the average conduction loss of a power element during the current cycle can be expressed as:
In the formula, I0 is the amplitude of the phase current, φ is the power factor angle, and m is the modulation ratio of SVPWM modulation.
The switching characteristics of power devices can also be expressed as
In the formula, aon, bon, and con are the nonlinear fitting coefficients for the turn-on characteristics of the power device, and aoff, boff, and coff are the nonlinear fitting coefficients for the segment characteristics of the power device. Udc_test is the DC bus voltage value used when testing the switching characteristics of the power device.
Therefore, the nonlinear switching loss model over one current cycle can be expressed as follows:
In the formula, fsw is the PWM switching frequency of the power device.
Therefore, the power device losses in a direct drive system of a permanent magnet synchronous motor can be expressed as:
Comprehensive optimization control of nonlinear losses in 3 permanent magnet synchronous motor direct drive systems
From equations (5) and (12), the system loss of the direct drive system of the permanent magnet synchronous motor can be expressed as:
As can be seen from equation (13), the losses of the direct drive system of the permanent magnet synchronous motor can be expressed as a function of the motor stator current, motor speed, switching frequency, and DC bus voltage. Since the PWM switching frequency and DC bus voltage of the system remain constant during motor operation, the system losses are only functions of the motor speed and current.
According to the electromagnetic torque equation of the motor, the q-axis current can be expressed as:
Equation (15) indicates that, under constant motor speed and torque, the losses of the permanent magnet synchronous motor drive system are only related to the d-axis current of the motor. Therefore, for any fixed operating condition (where the motor speed and torque remain constant), there must exist an optimal d-axis current that optimizes the matching between the system motor losses and the driver losses, ultimately minimizing the system losses. The optimal d-axis current can be expressed as follows:
In the formula, id* is the optimal d-axis current under a certain fixed operating condition.
As shown in Figure 4, based on the command torque signal given by the electric vehicle throttle, the nonlinear system loss comprehensive optimization controller can control the stator current of the motor to remain in the optimal state under any operating condition, thereby achieving the optimal matching of motor loss and driver loss and improving the operating efficiency of the permanent magnet synchronous motor direct drive system within the operating range.
4. Experimental Results and Analysis
Based on the above principles, an experimental platform for a direct drive system of permanent magnet synchronous motors was established, as shown in Figure 5.
On the experimental platform, a 400kW induction motor was used as a mechanical load to drive a 30kW permanent magnet synchronous motor under test, simulating the operating load characteristics of an electric vehicle under different working conditions at different speeds. A designed 45kW motor driver was used to drive the 30kW permanent magnet synchronous motor under test. The superiority of the proposed control strategy was verified by comparing the system efficiency characteristics under traditional maximum torque-current ratio control and the proposed nonlinear loss-efficiency integrated optimization control. The parameters of the 30kW permanent magnet synchronous motor under test are shown in Table 1.
The efficiency cloud diagrams of the permanent magnet synchronous motor direct drive control system under the traditional maximum torque-current ratio control and the proposed nonlinear loss integrated optimization control are shown in Figures 6 and 7.
As shown in Figures 6 and 7, compared to traditional maximum torque-to-current ratio control, nonlinear loss comprehensive optimization control effectively improves the operating efficiency of the permanent magnet synchronous motor direct drive system across the entire operating range while meeting the system's dynamic characteristic requirements. Furthermore, Figure 8, showing the system efficiency difference between the two control strategies, demonstrates that nonlinear loss comprehensive optimization control significantly improves the system operating efficiency of the motor drive system under light loads, making it more suitable for the needs of pure electric vehicles operating in urban traffic.
5. Conclusion
Based on the analysis of efficiency optimization control strategies for permanent magnet synchronous motors (PMSMs), this paper proposes a comprehensive optimization control strategy for nonlinear losses in direct-drive systems of PMSMs. A loss model for PMSMs is established based on the analysis of their electromagnetic characteristics. After analyzing and comparing the shortcomings of traditional linearized power device models, a polynomial-based nonlinearized power device model is proposed, effectively improving the accuracy of the power device conduction and switching loss models across the entire operating range. Based on the motor loss model and the driver loss model, an accurate loss model for the direct-drive system of PMSMs across the entire operating range is constructed. Based on the system loss model, the nonlinear loss control of the PMSM drive system achieves optimal system efficiency across the entire operating range by comprehensively optimizing and matching motor and driver losses under any operating condition. This effectively improves the energy utilization rate of the PMSM drive system and increases the driving range of electric vehicles. Experimental results show that, compared with traditional maximum torque-to-current ratio control, the comprehensive optimization control of nonlinear losses effectively improves the system's operating efficiency across the entire operating range, verifying the correctness and rationality of the theoretical analysis.
