基于频域小信号分析的永磁电机PWM谐波损耗建模方法研究

Pulse width modulation (PWM) voltage generated by the inverter will induce significant harmonic losses in permanent magnet machines, which are difficult to calculate fast and accurately. Since the PWM harmonic currents are too small to affect the saturation level of the silicon steel, original idea for fast and accurately calculating the harmonic losses is proposed as follows. (1) Based on the frozen differential reluctivity tensor method, the frequency-domain small-signal finite element model is constructed to investigate the mathematical model between the high-frequency components in the PWM voltage and the corresponding harmonic losses. The investigated losses consist of both eddy current loss in the permanent magnet and iron loss in the silicon steel. (2) Based on the model between harmonic losses and harmonic voltages, the PWM harmonic losses in the stator and the rotor at arbitrary working condition can be calculated with the spectra of the PWM voltage in the stator and rotor reference frame respectively. The influence of eddy current reaction effect in the permanent magnet and the silicon steel can be taken into consideration in the proposed method, which has equivalent accuracy with the method based on the transient FEA with small time steps, but much faster calculation speed because of replacing the nonlinear transient FEA having thousands of steps with the linear frequency-domain FEA having dozens of steps. The influence of the modulation type, carrier frequency, and permanent magnet segmentation on the PWM harmonic losses can be analyzed fast and accurately with the proposed method, which makes it applicable to the optimal design of permanent magnet machines and the optimal efficiency control of the system.

逆变器输出PWM电压会在永磁电机中感应出较大谐波损耗，难以快速准确计算。考虑到PWM谐波电流小，不足以影响硅钢片饱和状态，本项目提出快速准确计算该损耗的创新思路为：（1）基于冻结张量增量磁阻率法，构建频域小信号有限元模型，研究PWM电压中的高频分量与电机中高频交变磁密及损耗之间的关系，进而建立谐波电压与谐波损耗之间的数学模型。所研究的损耗既包含永磁体涡流损耗又包含硅钢片中铁耗。（2）基于谐波电压与谐波损耗模型，可将任意工况下的PWM电压分别在定、转子坐标系下分解，根据其频谱快速计算定、转子上的PWM谐波损耗。所提算法可考虑永磁体及硅钢片中涡流反应的影响，精度与基于小步长瞬态有限元法相当，且因采用数十步线性频域有限元计算取代数千步非线性瞬态有限元计算，计算速度显著提升。该模型能快速准确分析调制方式、载频、永磁体分段等诸多因素对PWM谐波损耗的影响，可应用于永磁电机优化设计及系统最优效率控制。

脉宽调制（PWM）电压源型逆变器会在永磁体电机被动注入一系列高频谐波电压，进而引起高频磁密波动和PWM谐波损耗。传统瞬态有限元法不得不采用非常小的时间步长分辨高频谐波、耗时过长。本项目基于PWM谐波电流很小不足以影响硅钢片饱和状态且高频谐波电压的频率远高于基波电流的两个事实，提出采用冻结增量张量磁阻率法将永磁电机模型线性化，进而结合线性时谐场-路耦合有限元分析研究高频谐波电压与永磁电机中高频磁密变化及谐波损耗之间关系，最后实现分别以定、转子坐标系下谐波电压为输入快速计算定、转子上的PWM谐波损耗。基于该思想，本项目（1）建立了内嵌式永磁同步电机永磁体、硅钢片与扁铜线中全工况PWM谐波损耗的快速计算方法；（2）应用双爱泼斯坦方圈系统对高频、偏磁情况下的硅钢片损耗特性进行了深入测量，建立了仅使用低频测量参数的硅钢片高频铁耗模型；（3）将所提PWM谐波损耗快速算法推广应用于集中/分布绕组表贴式、聚磁式场调制式等多种不同类型的永磁电机，证明了该方法的广泛适用性；（4）验证了PWM电压源输入法相较于含谐波电流源输法在计算PWM谐波效应上的优势。通过对比一台车用扁线永磁电机正弦电流供电下计算的效率图、考虑PWM谐波损耗计算的效率图和实测效率图，发现将所提方法计算的PWM 谐波损耗考虑在内，不仅在低速轻载时可将正弦电流供电下最大4个百分点的计算效率偏差降至1个百分点左右，而且有效提升了整个工作区内效率的计算精度。相比于传统瞬态瞬态有限元法，本方法将单一工况PWM谐波损耗的计算速度提升了20倍以上；全工况PWM谐波损耗计算速度提升数百倍以上。本项目的研究开辟了分析永磁体电机中高频PWM谐波效应的新思路，解决了长期以来永磁电机中PWM谐波损耗难以准确快速计算的难题，同时本项目所提方法有望被进一步拓展用于解决永磁电机中PWM谐波电流、边带电磁力及高频振动噪声的快速计算问题，也有望被推广应用于感应电机等其它类型电机中PWM谐波效应的分析、建模与优化抑制研究。

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