圆线图

圆线图（circle diagram）是由图形方式表示电机性能的方式，最早是由A. Heyland及B.A. Behrend在1894年、1895提出^[1]^[2]^[3]。是由电机输入电压及电流的轨迹来绘制^[4]。圆线图可以用来表示交流发电机、同步马达、变压器及感应马达的性能。Heyland图是圆线图应用在感应马达上的近似表示法，其中假设定子输入电压、转子电阻及转子电抗为定值，定子电阻及铁损为零^[3]^[5]^[6]。另一种常见的圆线图是针对固定气隙的感应马达，描述如下^[7]^[8] 其中

R_s, X_s：定子电阻及定子漏电抗
R_r^', X_r^', s：转子电阻及转子漏电抗、转子滑差
R_c, X_m,：铁损及机械损，磁化电抗
V_s：定子电压
I₀ = OO^', I_BL = OA, I₁ =OV：无载电流、堵转电流，工作作电流
Φ₀, Φ_BL：无载功因角，堵转功因角
P_max, s_Pmax, PF_max, T_max, s_Tmax：最大输出功率及对应气隙，最大功因、最大转矩及对应气隙
η₁, s₁, PF₁, Φ₁,：工作电流下的效率、滑差、功因及功因角
AB：表示转子功率输入，除以同步转速后为启动转矩

圆线图是根据开路测试以及变压器的短路测试或是马达堵转测试所得，会得到一个符合O^'和A点的半圆。

圆线图因为假设气隙为定值，因此会引入误差，其他的误差有因为磁饱和对转子磁阻及电抗的影响，以及从无载到工作速度范围之间的转子速度变化，对转子磁阻及电抗的影响

参考资料

^ Behrend, B.A. The Induction Motor and Other Alternating Current Motors, their Theory and Principles of Design. McGraw-Hill. 1921: ix [4 January 2013]. （原始内容存档于2019-07-08）.
^ Heyland, A. A Graphical Method for the Prediction of Power Transformers and Polyphase Motors) (PDF). ETZ: 561–564. 1894 [4 January 2013]. （原始内容存档 (PDF)于2020-03-20）. 参数|journal=与模板{{cite web}}不匹配（建议改用{{cite journal}}或|website=） (帮助); |volume=被忽略 (帮助)
^ ^3.0 ^3.1 Terman, Frederick Emmons; Freedman, Cecil Louis; Lenzen, Theodore Louis; Rogers, Kenneth Alfred. The General Circle Diagram of Electrical Machinery 49. American Institute of Electrical Engineers, Transactions of the. Jan 1930.
^ S.K.Bhattacharya. Electrical Machines 2008. Tata McGraw-Hill Education. : 359. ISBN 0-07-066921-X.
^ Heyland, Alexander. A Graphical Treatment of the Induction Motor. G.H. Rowe, R.E. Hellmund (trans.). McGraw Publishing Company. 1906 [10 January 2013].
^ Phase to Phase BV. The Asynchronous Motor Model (PDF): 5–6. 2006 [10 January 2013]. （原始内容 (PDF)存档于2014年8月10日）.
^ Alger, Philip L.; et al. 'Induction Machines' subsec. of sec. 7 - Alternating-Current Generators and Motors. A.E. Knowlton (Ed.) (编). Standard Handbook for Electrical Engineers 8th. McGraw-Hill: 710–711. 1949.
^ Fernandez, Francis M. Construction of Circle Diagram (PDF). College of Engineering Trivandrum. [10 January 2013]. （原始内容 (PDF)存档于2014-08-08）.

[Behrend_(1921)-1] Behrend, B.A. The Induction Motor and Other Alternating Current Motors, their Theory and Principles of Design. McGraw-Hill. 1921: ix [4 January 2013]. （原始内容存档于2019-07-08）.

[Heyland_(1894)-2] Heyland, A. A Graphical Method for the Prediction of Power Transformers and Polyphase Motors) (PDF). ETZ: 561–564. 1894 [4 January 2013]. （原始内容存档 (PDF)于2020-03-20）. 参数|journal=与模板{{cite web}}不匹配（建议改用{{cite journal}}或|website=） (帮助); |volume=被忽略 (帮助)

[circle-3] 3.0 ^3.1 Terman, Frederick Emmons; Freedman, Cecil Louis; Lenzen, Theodore Louis; Rogers, Kenneth Alfred. The General Circle Diagram of Electrical Machinery 49. American Institute of Electrical Engineers, Transactions of the. Jan 1930.

[4] S.K.Bhattacharya. Electrical Machines 2008. Tata McGraw-Hill Education. : 359. ISBN 0-07-066921-X.

[Heyland_(1906)-5] Heyland, Alexander. A Graphical Treatment of the Induction Motor. G.H. Rowe, R.E. Hellmund (trans.). McGraw Publishing Company. 1906 [10 January 2013].

[Ph-to-Ph_(2006)-6] Phase to Phase BV. The Asynchronous Motor Model (PDF): 5–6. 2006 [10 January 2013]. （原始内容 (PDF)存档于2014年8月10日）.

[Knowlton_(1949)-7] Alger, Philip L.; et al. 'Induction Machines' subsec. of sec. 7 - Alternating-Current Generators and Motors. A.E. Knowlton (Ed.) (编). Standard Handbook for Electrical Engineers 8th. McGraw-Hill: 710–711. 1949.

[Fernandez_(nodate)-8] Fernandez, Francis M. Construction of Circle Diagram (PDF). College of Engineering Trivandrum. [10 January 2013]. （原始内容 (PDF)存档于2014-08-08）.

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