使用多相空間向量脈寬調變之五相馬達諧頻分析與控制

Abstract

本論文提出一通用的多相空間向量脈寬調變(Space Vector Pulse Width Modulation, SVPWM)方法，並成功的控制五相馬達。相較於先前許多研究所提出的向量映射方法，本論文所使用的方法為參考輸入訊號由大至小，再依序相減，所得的便為導通時間比(duty ratio)。因此無論相數為多少，都可以很迅速地得到其相對應的空間相量與導通時間比。而先前的方法均無法擴展至多相的情況，且計算複雜。其次，本論文將多相SVPWM與載波脈寬調變比較(Carrier-based PWM)，推導出兩者之間的關聯性。由此關聯性，可將調變訊號以雙重傅立葉轉換，得到其頻譜成分，以利分析。完成公式推演之計算後，藉由MATLAB進行求值。從所求可看出隨著相數上升，其相對應之總諧波失真也隨之減小，亦間接證明相數與總諧波失真之關係。在此完成多相空間向量脈寬調變之理論、與諧頻分析。最後則是將所提出多相的SVPWM運用於五相馬達的實現，並比較速度、頻譜分析、速度響應等。

This thesis is based on the theory of a novel duty-ratio calculating method for SVPWM. Many methods proposed before were using vector projection. For example, signal projects on two nearest neighbor vectors in 3-phase system, and four in 5-phase case. The method proposed by this thesis is rearrange the input signal increasingly and subtract in order to acquire duty ratios. Therefore, no matter how many phases the system is, it is a quick way to find the relative space vectors and duty ratio. It has to be notified that the signal must be operated in linear mode. To avoid the increasing in total harmonics distortion (THD) from over-modulation, this thesis elaborates the concept of modulation index. Besides, it also compares SVPWM with carrier-based PWM and exhibit the relationship between them. With the relationship, by using double Fourier Integral, the modulation signal can be transformed from time domain to frequency domain, so called the harmonic analysis. After completing whole equation deducing work, the final values can be calculated by MATLAB. It can be inspected that when phase number increases, the relative THD decreases. In the end, the realization on a 5-phase motor with proposed method is presented.