13章电机学作业

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0??U22?(I?x)???s?2?1.414

E?U%?0?UI??U??x??100%?41.4%

??arctans?U??45

??（2）I?0.9

???31.79

??E?U?jI?x0???s???

?1?j0.9??31.79?1.474?j0.765?1.66?27.43??

?E0??1.66??27.43

??U%?1.66?11?100%?66%

?（3）I?0.9

???31.79

??E?U?jI?x0???s???

?1?j0.9?31.79?0.526?j0.765?0.928?55.49??

?E0??0.928??55.49

??U%?0.928?11?100%??7.2%

13-2解：

???1?0则I?1?0（1）设UN???????jI??xq??1.0?j0.6

UN???arctan0.61??30.96

?????????0?30.96?30.96

Id??I?sin??0.514

Iq??I?cos??0.857

?E?U?cos??I?x0??Nd?d??1?cos30.96?1.3721.372?11E?U??0.514

?U%??100%?37.2%

U2(x?x)?d?q?2xd??xq?

PM??0???sin??xd?sin2?

?1.372sin??0.333sin2???1?0则I?0.9（2）设U?N???

??I?0.765?j0.474?0.9?31.79????jI??xq??1.284?j0.459??19.67

???

UN???arctan0.4591.284??????31.79?19.67?51.46

Id??I?sin??0.704

Iq??I?cos??0.561

?E?U?cos??I?x0??Nd?d??1?cos19.67?1.6461.646?11E?U??0.704

?U%??100%?64.6%

U2(x?x)?d?q?2xd??xq?

PM??0???sin??xd?sin2?

?1.646sin??0.333sin2???1?0则I?0.9（3）设U?N???

??I?0.765?j0.474?0.9??31.79????jI??xq??0.716?j0.459??32.66

???

UN???arctan0.4590.716??????32.66?31.79?0.87

Id??I?sin??0.014

?E?U?cos??I?x0??Nd?d??1?cos32.66?0.8560.856?11E?U??0.014

?U%??100%??14.4%

U2(x?x)?d?q?2xd??xq?

PM??0???sin??xd?sin2?

?0.856sin??0.333sin2?

13-3解：

U（1）U??N3?1050003?6.06KV

I??Il?P3UN?240003?10.5?1.32KA

U

故Zb?I??6.06?4.6??x?1.32x所以xd?E2.76qd???0.6??1.09xq?Zb4.6Zb4.65

P??0???sin??xd??UU2(x?x)?d?q?2xd??xq?sin2?

?1.376sin??0.375sin2?（2）P??20MKVA24MKVA?0.833

解方程1.376sin??0.375sin2??0.833得??23.8

E?0??Ux??cos??1.5?1?cos23.81.09??0.537

?（3）Id?d?UIq???x?sin??q?1?sin23.80.6??0.673

I??I22?I?0.86d?q?I??arctand?q?I??38.57

??????14.77

?所以Q?S?UIsin??24MVA?1?0.86sin14.77??dP??1.376cos??0.75cos2??0

??5.256MVA

（4）

d?由于1?cos??1，解这个方程得cos??0.3842

即??67.4

所以sin??0.923sin2??0.71故Pmax??1.376?0.923?0.375?0.71?1.54

?P?1.54?24MW?36.96MWmax13-4解：

???/?U?jI?x（1）E，U?jI?x?E0?0???s???s??

?/??所以E0??2U?E

?0??令U?1?0?，P?0.5

??E

则P???U?0??sin??0.5???24.62

xs?

???U?jI?x?1.2?24.62所以E0???s??

?/????E0??2U?E?2?1.2?24.62?1.038??28.81

?0?E?U0??sin??0.5xs?（2）P??

E0??/?1.1时E0??1.038不变

11.1?1.04?E??arcsin()?61.24

?2I??xs?/2??E2?2EE/cos61.24?1.090?0?0?0?

???/222U?0.52?E?E0??(2I?x))??0.92

?0??0??s?????

13-6解：

???设U?1?0I?0.8?j0.6

D???I??0.8?j0.6?U?jIx?1.36?j0.48?1.44??19.44??q???故???19.4