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中国电机工程学报 2008, 28(27) 126-130 DOI:
ISSN: 0258-8013 CN: 11-2107/TM |
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| 电机与电器 |
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感应电机不对称暂态分析中一类一元三次特征方程及其近似求解 |
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罗炜 崔学深 罗应立 |
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浙江大学理学院数学科学研究中心 华北电力大学电气与电子工程学院 华北电力大学电气与电子工程学院 |
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摘要：
对于旋转状态的感应电机，在短暂断电后重新接入电源时，为了限流，经过晶闸管开关首先接通两相电源施加部分电压，然后逐步过渡到全压。该文研究接入两相电源后的不对称电磁过渡过程。对微分方程进行拉普拉斯变换得到一元三次特征方程；然后，基于牛顿切线法得到近似求解一元三次特征方程的简化方法，进而应用于分析感应电动机的不对称过渡过程问题，导出时间常数近似公式。通过与繁杂且难以实际应用的精确卡丹公式对比，该文公式简单明了，便于应用，对于功率5.5 kW以上一般用途的感应电动机，其误差不超过5%。 |
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关键词：
牛顿切线法
一元三次方程
时间常数
感应电机
不对称运行
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Approximate Solutions of a Class of Cubic Characteristic Equations in One Variable in Asymmetric Transient Analysis of Induction Machines |
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LUO Wei CUI Xue-shen LUO Ying-li |
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Abstract:
In order to limit currents, a two phase voltage is applied to an induction machine in rotating state after a brief power outage before full voltages are gradually provided via thyristor switch. The asymmetric electromagnetic transient process after switching-on two phase supply is studied in the paper. Firstly, a cubic characteristic equation in one variable is obtained via Laplace transforms on corresponding differential equations. Secondly, the cubic equation is solved via Newton's method, and then applied to asymmetric transient process analysis of induction machines. Lastly an approximate formula of time constant are derived and compared to the accurate but complicated Cadarno formula. The suggested formula is simple and easily applicable, with an error less than 5% in application to general induction machines of power over 5.5 kW. |
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Keywords:
Newton's method
cubic equations in one variable
time constants
induction machines
asymmetric running
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收稿日期 2008-07-01 修回日期 1900-01-01 网络版发布日期 |
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DOI: |
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基金项目:
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通讯作者: 罗应立 |
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作者简介: |
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作者Email: luoyingli@china.com |
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| Copyright by 中国电机工程学报 |
