试推导两相任意旋转坐标系上以定子电流、定子磁链和转速为状态变量的感应电机状态方程,进而由此导出两相静止坐标系中的状态方程。
解: 根据教材式 [tex=3.571x1.357]Zrwm3YVK9ZdUFkTXJfmmcw==[/tex]、式[tex=3.571x1.357]pYQ+yG5obaZw7Ss256qvjQ==[/tex] 和式 [tex=4.071x1.357]3s1Gh3V49wqNEQCixo4m1A==[/tex], 不计零轴分量时两相任意旋转 坐标系上的定、转子电压方程和磁链方程为[tex=16.214x16.071]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[/tex]将电压方程改写为[tex=17.643x10.214]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[/tex]根据磁链方程, 将转子电汸和转子磁链用定子电流和定子礠链表达, 有[tex=15.429x11.214]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[/tex][tex=15.429x5.786]IfEG3NsBfGhtbCalasoF/1M/jEqIsTTtQVsL5SblxtJRm/D48Q1LA45XItW0gMwFhWQmy46ASC2GNGeySY6MfDYd2MQQR84pqwgrCzOgjOg9+N1zLVdwDan6mqTqqANO6Fs1eGL/jlniJeDsDqhkWbavPsbCkz/zRsJ7mvSk1SJiJhfzPmV7W9IbIKCPeY35Z00H6axSmHn3GRUyQZ5f4HpBbe66S9pMUEBKHb4qZFrHKZBq8N/9GewuS037H1i/UvaFnNIDiBsHu88E5SoSf1zG9YJN5/yOHZr0LUC++Hzr+jU938BAgQ7tTMvP9qgGQLX6ldSkvxusjeEHhziEKQ==[/tex]式中, [tex=0.571x0.786]G/buLKOLYVDEKMZ76t752w==[/tex]为电机的漏磁系数, [tex=5.071x2.714]SM1ZL0Dbwd2kRjl7tpFl+BGgUt7W4TMuhewvk+WuMRXOXZx6GvSaY3JjcpldLuwGtYMcDcYwmcHzEL/Cyn7Ssw==[/tex]将式 [tex=3.071x1.357]/Dl6x2DpwugvyMydEBDwNw==[/tex] 和式[tex=3.071x1.357]bw8jdNX5JaG3mH2LAUVNtg==[/tex]代入式 [tex=3.071x1.357]tjuTdN8DUmbrQXPDdg8zaw==[/tex] 第[tex=2.0x1.286]gY+MqJXDjropDYLZULobJg==[/tex]行, 并结合式 [tex=3.071x1.357]tjuTdN8DUmbrQXPDdg8zaw==[/tex] 第[tex=2.0x1.286]5v585gtVKM1zgBy9wzzJlQ==[/tex]行, 可得[tex=32.214x5.786]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[/tex]将习题 [tex=2.286x1.143]iV/hC5Pyb2bn2siC3Pl3/g==[/tex] 推导的用定子电流和定子磁链表达的转矩公式[tex=9.0x1.357]ag9rziklenT8jwX27UKOp5llAcCEPKTH9EJqgebXDWCEBa7Z1KLUQfh6BIpZGInKLpUgu1KPgcd+uJwEj+QKbNz19IKV1saDoFWT2Obdaag=[/tex]代入机械运动方程式, 整理得[tex=16.571x2.5]JmmlwdHFYNW4jG0CAfTgBtFJa88N2vaP97cMlxJ9lf5Qqz2D4RODG9TTy5NSpyzlRPqWvmEaLRHyiOBYAbPUgDUhQgrjwFDZZBRdORwgi3Biq6NyqM8AEf1Uoua/t/sSVei6gk8/8T39RYVc71Rqnm+aoCpY+EyXA0bb4Vg7H2XVL3GCBFcqvM9QAfahhOIQ[/tex]结合式[tex=3.071x1.357]tjuTdN8DUmbrQXPDdg8zaw==[/tex]前两行和式[tex=3.071x1.357]PNTNwTdZffLym+MaITzRkg==[/tex]、式[tex=3.071x1.357]o2gBGHsCfjPw9EbVXeznQw==[/tex], 在两相任意旋转坐标系上感应电机的 状态方程为[tex=13.571x7.5]xAc5qgoEjd5nDw/WWC9ZhUzIOZvdH4s51fRRCoEOSA8Fig4bX1hsCxoPetZ4kR75WUYPOq7tA4NwJudk8XkYIrHDwqcp/i4mg+75dq+XDlUz2Tyioag111fvrx89gcf1nq/AGhT9onprU/sU3x3y2XmSYD4mYpg2O7uA2U2ck+6SDwhUcHnvRnh6AATApOv79LAUCy9INt8JwbuUmgqOWCTqf7KZ4fjWSXUSbuUQyzyB/+eIWQsVWN2d0Gze7AHGR6KpmCfKtUQUw1kRlVFIASX0bkkd+lYymzKySBYAY47mbCEAowtsVRkeDvbUQQNo8h2zVSZ+5wvubTijHtsdbecEunDh1mn0G3wS0UW3jx+3Xdw1A4DF9kfmYK1wPhrU1nRTUu5EV8m1hzCq31RDRg==[/tex][tex=28.214x5.214]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[/tex][tex=3.071x1.357]0cMQkj6c76RbuAjtUoL8Vg==[/tex]令式[tex=3.071x1.357]0cMQkj6c76RbuAjtUoL8Vg==[/tex]中的[tex=2.929x1.286]j1Y8h2YZZk9Bbjdn12l1sNmMs+rKeA7Fws+8gwnAnv8=[/tex],并将下标[tex=2.0x1.286]/VrbIXzWoFY8JpzT4d52gQ==[/tex]分别换成[tex=1.929x1.286]PA88quloD+FDWgFFNXuSyQ==[/tex],可得两相静止坐标系中的状态方程为[tex=14.071x7.5]xAc5qgoEjd5nDw/WWC9ZhUzIOZvdH4s51fRRCoEOSA9IDu0/0v7uir4VNjPnonvJ//ZQGWQf9k5yDplfDIY47z8c2YFgVis7ljVkFFywvg0Y8QSAOihswYbbEUPui5aulh68nziK0k41oJfeiY6wfcwsij34GKGWidjMHnU6xLyeZ5XdhEhWCLiqXvV+uHVPnKBsKeS15MjoLfpqCkz1ToiywzqkCxRxI7MVbPR6J4YNBhOeO0Tlp18GrZqSEodgkBJpMWxLK1Bp0IjNSlSeoGDYnoh6hBdqFcmVObWSrBxS54HUBoBvHRYAXu8V0WyjaA/3T3yAyM1RjXT1Pk1jC28F4AWfWbbJndkN6NY5tI0=[/tex][tex=25.643x5.214]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[/tex]
举一反三
- 在采用SVPWM的三相异步电机矢量控制中,用到的坐标变换不包括 A: 三相静止坐标系到两相静止坐标系 B: 两相静止坐标系到两相旋转坐标系 C: 两相旋转坐标系到两相静止坐标系 D: 两相旋转坐标系到两相旋转坐标系
- 异步电机无论是三相静止坐标系、两相静止坐标系,还是两相旋转坐标系下其动态数学模型必须由磁链方程、电压方程、______ 和运动方程构成。
- 异步电动机的状态方程中,哪种状态变量的选取合理()。 A: 转速、转子磁链、定子磁链 B: 转速、定子电流、转子磁链 C: 转速、转子电流、定子磁链 D: 转速、转子电流、转子磁链
- 异步电动机在两相正交坐标系上的动态数学模型,采用状态方程式表示时,通常选取的状态变量有角速度、定子电流、((______ ))或者((______ ))。
- 与定子绕组和转子绕组的3/2变换相比,异步电动机定子和转子绕组变换到静止两相正交坐标系中,“磁链方程复杂了,电压方程简单了”。
内容
- 0
与定子绕组和转子绕组的3/2变换相比,异步电动机定子和转子绕组变换到静止两相正交坐标系中,“磁链方程复杂了,电压方程简单了”。 A: 正确 B: 错误
- 1
进行异步电机数字式矢量控制技术时,采用两相静止坐标系上的转子磁链模型比两相旋转坐标系上的转子磁链模型更为合适。
- 2
可选取异步电动机的哪些状态变量可用来组成异步电动机的状态方程 A: 转速 B: 转子电流 C: 定子电流 D: 转子磁链 E: 定子磁链
- 3
试根据同步电机在转子[tex=1.5x1.286]ia+h9MRF6wuxAjYmIBLwfQ==[/tex]坐标系上的动态方程导出其状态方程。
- 4
要得到异步电动机在在静止两相正交坐标系上的动态数学模型,只将定子绕组进行 变换就可以了,而转子绕组是旋转的,必须通过 变换变换到两相旋转的坐标系上,在经过 变换,才能变换到静止两相正交坐标系上。