現今，交流馬達廣泛應用在日常生活與工業中，尤其電動車在近年來銷量逐漸上升，馬達與驅動器市場需求跟著日益增加，為了降低開發成本和實現高性能馬達與驅動器，物理意義明確的馬達模型是必要的。因此本論文通過使用一致的座標軸定義對永磁同步馬達、感應馬達進行數學建模來做出貢獻。該建模方法結合了與尤拉公式有著相同性質之二維轉換矩陣，增強了馬達數學模型的清晰度和簡潔性。此外，在永磁同步馬達、感應馬達數學模型的基礎上，本論文將其擴展到架構較為特殊的內藏式齒輪電機數學模型，並且建立各馬達的控制方塊圖，以利於分析各馬達之特性。
本文在馬達模型模擬架構上使用雙端網路(Two-port network)，該架構有助於馬達模型模組化與可視化，隨後將此架構建立於MATLAB/Simulink中進行數學模型模擬，分析馬達的動態行為，繪製出各馬達扭矩速度曲線(TN curve)，最終解釋各馬達的特性。

AC motors have become ubiquitous in daily life and industry, with a notable surge in their demand, particularly due to the widespread adoption of electric vehicles worldwide. To achieve cost-effective and high-performance AC drives, the utilization of a physically explicit motor model is necessary. This thesis attempts contributing to this solution by employing a consistent definition of the coordinate system to mathematically model both the permanent magnet synchronous motor (PMSM) and the three-phase induction motor (IM). The modeling approach incorporates a two-dimensional transformation matrix with properties similar to Euler's formula, which enhances the clarity and conciseness of the motor's mathematical representation. Moreover, this approach is extended to include the pseudo direct drive motor (PDDM) with its unique structure, building upon the foundation of its original mathematical model. To ensure accuracy and comprehensiveness, the control block diagram for each motor is established and subjected to simulation and analysis, facilitating a detailed comparison of their respective characteristics.
This thesis adopts a two-port network for each motor model. This strategy helps in creating a modular and visually engaging motor model framework, that can be implemented in MATLAB/Simulink for simulation purposes. Using this framework, the dynamic behavior of each motor is evaluated, drawing the torque-speed curve (TN curve) for comprehensive insights into their individual characteristics.

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