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2.3.2 旋转坐标系数学模型
为了进一步简化机电能量转换平面的数学模型,采用以下形式的αβ平面向dq平面的变换矩阵T(θr):
![](https://epubservercos.yuewen.com/13B75A/23083816309814506/epubprivate/OEBPS/Images/46_02.jpg?sign=1739375060-RKuiNjX5ClcwyP9qOZmIdO5DcMgryl5n-0-13d07af095362b51349d87fc195f2161)
式(2-43)中ψs表达式左右两边同乘T(θr)变换矩阵,得出dq坐标系定子磁链如下:
![](https://epubservercos.yuewen.com/13B75A/23083816309814506/epubprivate/OEBPS/Images/46_03.jpg?sign=1739375060-IUyW5LUAoPUU1xDa9y1ym8NH09PgDTS5-0-f5523ed29ca8a21320175d821e86c667)
其中
![](https://epubservercos.yuewen.com/13B75A/23083816309814506/epubprivate/OEBPS/Images/46_04.jpg?sign=1739375060-vvxgMNo4Alb9uVWBbF0rDzQftqoEvtiP-0-f6bf3dc65cec3d49f80165e4f851bece)
把式(2-50)和式(2-51)代入式(2-49)中,式(2-49)进一步化简如下:
![](https://epubservercos.yuewen.com/13B75A/23083816309814506/epubprivate/OEBPS/Images/47_01.jpg?sign=1739375060-FMz9IIKPTRnxo3e9m679rYRFEiMOSMjg-0-5df36762a330d45947d3d45c50acbe70)
其中
![](https://epubservercos.yuewen.com/13B75A/23083816309814506/epubprivate/OEBPS/Images/47_02.jpg?sign=1739375060-7HIv499TK6nou9ARsbbZzoVqt8vhQrTM-0-b8b28a52af66ad4bcc658f78548cf817)
L d,Lq分别为电动机dq坐标系直、交轴电感。同理,根据式(2-44)中αβ平面电压方程,推导出dq平面定子电压平衡方程式如下:
![](https://epubservercos.yuewen.com/13B75A/23083816309814506/epubprivate/OEBPS/Images/47_03.jpg?sign=1739375060-NQ0Pg9azjWIUprnZqCXXk0tXvd3I8a7W-0-e1a9f34cc5d2eca870985a023ba3d972)
利用式(2-48)把式(2-46)的电磁转矩旋转变换至dq平面上
![](https://epubservercos.yuewen.com/13B75A/23083816309814506/epubprivate/OEBPS/Images/47_04.jpg?sign=1739375060-s51z983xtS9ZDOyBYrR9KCBW9MukBr71-0-991e7b621cd5443bc9daec0cb0233a66)
由式(2-52)和式(2-55),进一步推导dq平面电流表达式如下:
![](https://epubservercos.yuewen.com/13B75A/23083816309814506/epubprivate/OEBPS/Images/47_05.jpg?sign=1739375060-7jam3pfWF0N9oWO6lPwa1B7SHiM29TKJ-0-14804bd86e7e151b229cdabb7e9828ab)
根据图2-5所示的变量关系示意图可得
![](https://epubservercos.yuewen.com/13B75A/23083816309814506/epubprivate/OEBPS/Images/47_06.jpg?sign=1739375060-MfYx0wrM5J9LCSFx3tIdshXk2igeR2A5-0-79c63eae483eee2dcd7e409e3ecb3e64)
这样,把式(2-59)和式(2-58)代入式(2-57)中,可以建立电磁转矩与定子磁链幅值、永磁体磁链幅值及转矩角的关系如下:
![](https://epubservercos.yuewen.com/13B75A/23083816309814506/epubprivate/OEBPS/Images/47_07.jpg?sign=1739375060-XUeVxdP9BN1cTSbqGTnLLLFK2WcL5XVA-0-d96b6d3cfcacf41a80ff15ffd9c9d153)
式(2-60)表达形式与三相电动机一样,在定子磁链幅值|ψs|恒定的情况下,通过控制转矩角δ即可实现电磁转矩的直接控制。