對傳統馬達解析解之公式，乃是透過設定一預期之轉速，透過相關之公式解出該轉速下之轉矩及其效率，然而此方法僅能得知該轉速之工況，並無法得知該顆馬達之最大效率點為何及該操作點之轉矩以及其轉速。因此本研究基於電路學之基礎上，透過簡易之電路模型並利用雙埠網路矩陣進行最大效率公式之推導，亦可同時求得最大效率操作點之性能參數，並透過電路範例經由模擬軟體驗證公式之正確性，確定無誤後將會對直流有刷馬達以及交流無刷馬達進行數學建模，透過將其等效為電路之模型後再轉為控制方塊圖，並會對馬達之各項損失進行說明並定義，並將過往傳統理想情況之馬達模型進行修正，化為較為實務之馬達模型，接著將進行馬達實例之驗證，透過一直流有刷馬達以及一表貼式永磁同步馬達之範例，藉由推導出之最大效率公式進行該馬達範例之性能預測，並在之後將會與經由馬達模擬軟體分析後之結果進行比較驗證，並探討其之間誤差來源。

Traditional analytical formulas for motors requires a known speed to be able to calculate the torque and efficiency of the motor at that speed using related formulas. However, this method can only obtain the motor performance at the known speed, and not the maximum efficiency of the motor. To obtain the maximum efficiency, this thesis utilized the circuit theory, using a simple circuit model, and the two-port network matrix to derive the maximum efficiency formula. Also, the performance parameters of the maximum efficiency operating point can be obtained at the same time. The circuit example is verified by simulation software. A mathematical model
of a DC brushless motor and an AC brushless motor is developed and used to create a control block diagram through the analogies of an equivalent circuit model. The various motor losses were explained and defined. The traditional ideal motor model is revised into a more practical motor model, and the correctness of the model is verified using a DC brush motor and a SPM (surface-mounted permanent magnet) motor as example. A performance prediction of the motor examples using the derived maximum efficiency formula is carried out. Its results are compared with the obtained simulation results explaining the reason for differences among them.

[1] 台灣綠色生產力基金會(2014)，檢自https://www.tgpf.org.tw/main6-1_detail.asp?id=74.(Sep.27,2021).
[2] 經濟部能源局能源統計手冊(2020),檢自 https://www.moeaboe.gov.tw/ECW/populace/content/SubMenu.aspx?menu_id=6975(Sep.27,2021).
[3] IEEE Guide Test Procedures for Synchronous Machines, ANSI/IEEE std 113-1985.
[4] IEC，https://www.iec.ch/energies/energy-efficiency
[5] D. Collins. (2020). What are international efficiency (IE) standards for motors and gearmotors? Retrieved from https://www.motioncontroltips.com/what-are-international-efficiency-standards-for-motors-and-gearmotors/
[6] Hanselman, Duane C. Brushless permanent magnet motor design. Lebanon, Ohio: Magna Physics Publishing, 2006.
[7] Dorf, Richard C., and James A. Svoboda. Introduction to electric circuits. Hoboken, NJ: John Wiley & Sons, Inc, 2014.
[8] S. Morimoto, Y. Tong, Y. Takeda and T. Hirasa, "Loss minimization control of permanent magnet synchronous motor drives," in IEEE Transactions on Industrial Electronics, vol. 41, no. 5, pp. 511-517, Oct. 1994.
[9] J. S. Hsu and B. P. Scoggins, "Field test of motor efficiency and load changes through air-gap torque," in IEEE Transactions on Energy Conversion, vol. 10, no. 3, pp. 477-483, Sept. 1995.
[10] M. Al-Badri, P. Pillay and P. Angers, "A Novel In Situ Efficiency Estimation Algorithm for Three-Phase IM Using GA, IEEE Method F1 Calculations, and Pretested Motor Data," in IEEE Transactions on Energy Conversion, vol. 30, no. 3, pp. 1092-1102, Sept. 2015.
[11] T. Ohira, "Angular expression of maximum power transfer efficiency in reciprocal two-port systems," 2014 IEEE Wireless Power Transfer Conference, Jeju, 2014, pp. 228-230.
[12] P. J. Ko, “Study on monitoring technology of PM motor and its applications”. PhD thesis, Cheng Kung University, 2009.
[13] Tsai M.C., Gu D.W. Robust and optimal control : a two-port framework approach. London: Springer, 2014.
[14] 路昌工業，永磁馬達實務系統架構分析(2012)檢自: https://lutron1980.pixnet.net/blog/post/23849985.
[15] Kenjo T., and Nagamori S., “Permanent-Magnet and Brushless DC Motors,” Oxford University Press, Feb. 1986.
[16] 源自[Online]:https://www.sphs.hc.edu.tw/ischool/public/resource_vie-w/open.php?file=5c19f945ac13021f881d8aad2f551e48.pdf.
[17] 源自[Online]:https://electronics.stackexchange.com/questions/17786-3/can-anyone-explain-why-a-b-h-curve-with-hysteresis-doesnt-result-in-a-highly-no.
[18] C. Canudas, K. Astrom and K. Braun, "Adaptive friction compensation in DC motor drives," Proceedings. 1986 IEEE International Conference on Robotics and Automation, 1986.
[19] Lee S. C., Tsai M. C., Wang M. S., and Mao. S. H., “Characteristics Measurement of DC Motors without Dynamometer,” Proceedings of 2nd International Forum on Systems and Mechatronics, Tainan, Taiwan, Dec. 2007.
[20] 吳建諭，永磁馬達特性快速檢測系統設計，國立成功大學機械工程學系碩論文，2010。
[21] 劉昌煥，交流電機控制:向量控制與直接轉矩控制原理，東華書局，2008。
[22] 陳俊霖，謝易儒，淺談交流馬達d-q軸轉換，馬達電子報，成大馬達科技研究中心，第750期，2017。.
[23] Ohm D. Y. “Dynamic model of PM synchronous motors.” 2000.
[24] Miller, T. J. E. Brushless permanent-magnet and reluctance motor drives. Oxford New York: Clarendon Press Oxford University Press, 1989.
[25] R. J. Hamilton, "DC motor brush life," in IEEE Transactions on Industry Applications, vol. 36, no. 6, pp. 1682-1687, Nov.-Dec. 2000.
[26] 新竹科技園區，電機能效提升應用實務(2019)，檢自: https://web.sipa.gov.tw/WEInfoWeb/index.do.