基於查表之雙三相同步電機等效電路模型建立與應用

Abstract

近年來，新型電機，特別是雙三相同步電機，因其更高的性能和可靠度而在電動載具及航天航太等應用中愈發受到重視。為全面地評估電驅系統整體性能，特別是在精密運動控制應用中，在設計與分析階段，須綜合考量電機、驅動、控制造成的影響，因此需要進行磁電（電機-驅動）耦合模擬。其中，電機等效模型是影響磁電耦合模擬準確度與效率的關鍵要素之一。因此，本文提出一種基於查表之電機等效電路模型（LUT-ECM）建模方法。此方法是專為磁電耦合模擬應用而設計，可用於建立各式電機之等效電路模型，包括本文欲探討的雙三相同步電機。此方法首先透過有限元分析或實測等方式獲取磁交鏈的非線性訊息，接著從非線性磁交鏈訊息推算出增量電感訊息並彙整成與電流及轉子位置相關的查找表，再結合依據物理所推導出之電機數學模型，最後採用本文改良之預測型辛普森方法搭配相依電流源建立出可直接與驅動電路模型互動之電機等效電路模型。本文首先透過有限元素分析證此方法的模擬效率與準確性，結果顯示在誤差控制在 2% 以下時，模擬速度可以有超過一千倍的顯著提升。接著，本文透過實驗展示基於此方法所建立的磁電耦合模擬在電驅系統設計及性能評估中的應用價值。為針對雙三相同步電機進行更深入的探討與分析，本文首先提出一套系統化的雙三相電機繞線佈局設計方法，接著定義出雙三相偏移角（δ角）與其計算方法，歸納 δ 角與不同電機槽極組合之間的關係，並進一步探討 δ 角與雙三相向量空間分解法之間的關係。此外，本文提出一種考量電機繞線佈局的等效磁路解析模型建模方法，用於量化繞組對轉矩的影響。

In recent years, novel electrical machines, particularly dual three-phase synchronous machines, have gained increasing attention in applications such as electric vehicles and aerospace systems due to their superior performance and reliability. To comprehensively evaluate the overall performance of a motor-drive system, especially in precision motion control applications, it is essential to consider the influence of the motor, drive, and control during the design and analysis stages. This highlights the need for an accurate and efficient motor-drive co-simulation, where the machine model plays a crucial role. To address this need, this dissertation presents a look-up table-based equivalent circuit model (LUT-ECM) for electric machines. This method is specifically developed for motor-drive co-simulation and is applicable to various types of electric machines, including the dual three-phase synchronous machine examined in this dissertation. The proposed approach first obtains nonlinear flux linkage data through finite element analysis (FEA) or experimental measurements. Then, incremental inductance is derived from the nonlinear flux linkage and compiled into look-up tables (LUTs) indexed by current and rotor position. These LUTs are integrated with the mathematical machine model. To construct an equivalent circuit model for electrical machines that directly interfaces with drive circuit models, this dissertation employs an improved predictive Simpson’s method with dependent current sources. The functionality of this method is verified through FEA and experimental results, demonstrating its advantages in simulation efficiency and accuracy. According to the results, the computational speed can increase by more than 1000 times while the error is within 2%. The effectiveness of the proposed LUT-ECM-based co-simulations in motor-drive system design and analysis is then demonstrated. To further analyze the dual three-phase synchronous machine, this dissertation introduces a systematic winding layout design method. The dual three-phase displacement angle (δ angle) is defined along with its calculation method. This dissertation first summarizes the relationship between the δ angle and various slot-pole combinations. It then examines how the δ angle influences the dual three-phase vector space decomposition method. Furthermore, this dissertation presents a magnetic equivalent circuit analytical model to quantify the influence of winding layouts on torque production.