考虑交叉耦合影响的内置式永磁同步电机电感计算及转矩分析

Inductance Calculation and Torque Analysis of Interior Permanent Magnet Synchronous Machine Considering Cross-Coupling Effects

内置式永磁同步电机的电磁转矩主要包括永磁转矩和磁阻转矩两种成分,转矩成分的准确分离和分析有助于进一步优化设计电机拓扑结构,提高电机的功率密度,而电磁转矩成分精确分析的关键在于交直轴电感的准确计算。该文针对内置式永磁同步电机的交直轴电感求解与转矩成分分析的实际问题,以一台8极11 kW的内置式永磁同步电机为例,对其进行建模仿真计算;通过对采用静磁场求解电感与瞬态场求解电感两类求解电感的方法进行对比分析,在此基础上提出了一种改进的静磁场快速求解交直轴电感的方法,并实现了对电机转矩组成的高精度分离提取和在电磁设计阶段对电磁转矩成分的预测。改进的静磁场求解电感的方法既能精确考虑交叉耦合效应,又能考虑不同负载下饱和效应的影响。此外,相较于瞬态场求解电感的方法,该方法有效减少了仿真步数从而缩短了仿真时长。最后,构建实验测试平台对目标样机进行了转矩测试,并与预测模型结果进行比较,实验结果验证了所提方法的准确性和有效性。

The electromagnetic torque of an IPMSM(Interior permanent magnet synchronous machine)mainly consists of two components:permanent magnet torque and reluctance torque.The accurate separation and analysis of the torque components can optimize the topology and improve the power density of the machine.The key to accurate analysis of the components of the electromagnetic torque is the accurate calculation of the d-q-axis inductance.This paper uses an IPMSM with 8 poles and 11 kW as an example to solve the d-q-axis inductance and analyze the torque components.By comparing and analyzing two kinds of inductance solving methods,static magnetic field solving inductance and transient field solving inductance,an improved method for fast solving the inductance by the static magnetic field is presented,which achieves high-precision separation and extraction of machine torque components and prediction of electromagnetic torque components in the stage of electromagnetic design.The improved method determines the current lead angle according to different d-q-axis current combinations,converts the mechanical angle of the machine to the current lead angle,and transforms the relative mechanical position of the stator and rotor to control the machine operation under different current amplitudes or current lead angles.Then,the three-phase flux linkage under different d-q-axis current combinations is obtained by finite element calculation,and the d-q-axis flux linkage is obtained by Park's transformation of the three-phase flux linkage.Finally,the d-q-axis inductance is obtained by solving the d-q-axis flux linkage,and the permanent magnet flux linkage is obtained using the frozen permeability method.The improved method can consider both the cross-coupling and saturation effects under different loads.In addition,the d-q-axis inductance calculated by the above method is combined with the electromagnetic torque equation considering the effect of magnetic saturation and cross-coupling.The d-q-axis inductances of the target prototype are solved by the transient field method and the improved static magnetic field method,respectively.The relative errors of the d-q-axis inductances solved by the two methods are within 6%.Compared with the transient field method,the improved static magnetic field method reduces the simulation steps by 96.08%and the calculation time by 96.14%.It shows that the improved method can effectively reduce the number of simulation steps and shorten the simulation time.Finally,an experimental test platform is built to test the torque of the target prototype under different operating point currents.The relative errors between the measured torque and the predicted torque are within 3%.Taking the working condition of the prototype under the rated current as an example,the electromagnetic torque of the machine output at different current lead angles of 0°to 180°is separated.At the same time,the composition of the maximum electromagnetic torque obtained by the maximum torque current ratio control logic is analyzed.In the composition,the value of the reluctance torque is 2.55 N·m,accounting for about 3.72%;and the value of the permanent magnet torque is 66.07 N·m,accounting for about 97.20%.Moreover,the maximum reluctance torque of the prototype can reach about 11 N·m,while the actual reluctance torque at the maximum electromagnetic torque point is 2.55 N·m,which shows that the magnetic barrier design of this prototype still has a large space for optimization.The torque density of the target machine can be further improved by optimizing the rotor structure combined with the fast torque analysis and the prediction model in this paper.The experimental results verify the accuracy and validity of the new method.