电机学I作业(5)

Ia?Ia?Ia0?????1?1?2?(Ia?aIb?aIc)?Ia33??1?1?2?(Ia?aIb?aIc)?Ia 33??1?1??(Ia?Ib?Ic)?Ia33由等值电路，原边电流(零序电流不能流通)：

1IA?IA??IA??IA0??(Ia??Ia??Ia0)??Ia??A2????????IB?IB??IB??IB0??(aIa??aIa??Ia0)?0IC?IC??IC??IC0??(aIa??aIa??Ia0)?0?????2??????2???

rkUA??xk?IA???Ia???Ua??rkIA???Ia???xk?Ua??r1x1r2Ia0??rm0UA0??E0???Ua0xm0

??2I??2A，I??I???1I???1A （b）边界条件：Iaxbycz3333???III11byax?????cz?A ??A，IB?IC??可直接由变比求：IA??kk6k3??2I??2A，I??I???1I???1A （c）边界条件：Iaxbycz3333?可直接由变比求：IAX???III111byax???A，ICZ??cz?A ????A，IBY??k6k3k6??I??I???1?1??1A，I??I??I??1?1?1A 线电流：IAAXCZBBYAX362632??I??I??1?1?0A ICCZBY66??I??1A，I??I??0A （d）边界条件：Iabc- 20 -

???IIIab?????0.5A，IBY?ICZ????c?0A 可直接由变比求：IAX??kkk??I??I??0?0?0A ??I??I???1?0??1A，I线电流：IBBYCZAAXBY22??I??I??0?(?1)?0.5A ICCZAX2- 21 -

第5章 特种变压器

例：一台型号为SFSL1-20000/110的三相三绕组变压器，YNynod11连接，额定电压为121/38.5/11kV；高压、中压、低压绕组的容量分别为20000kVA、20000kVA、10000kVA；最大短路损耗为151kW；归算到高压侧的短路电压标幺值为uk12*=0.105，uk13*=0.18，uk23*=0. 065，试求其等效电路中的各个参数（励磁电流略去不计）。

解：简化等效电路图如下图所示：

r2?r1?x1?r3??x?2???I2?U1?I1??I3????U2?x3???U3??

由题已知：rk12*?Pk12*?rk12*?r1*?r2* r1*?r2*?0.003775； r3*?0.00755；

1511?0.00755，r1*?r2*?r3* 200002Zk12*?Uk12*0.105??0.105 Ik12*1则xk12*?Zk12*2?rk12*2?0.1052?0.007552?0.1047

Zk13*?Uk13*0.18??0.18 Ik13*1rk13*?r1*?r3*?0.011325

则xk13*?Zk13*2?rk13*2?0.182?0.0113252?0.1796

Zk23*?Uk23*0.065??0.065 Ik23*1- 22 -

rk23*?r2*?r3*?0.011325

则xk23*?Zk23*2?rk23*2?0.0652?0.0113252?0.064 x1*?xk12*?xk13*?xk23*?0.11

2x*?xk23*?xk13*x2*?k12??0.00545

2x*?xk23*?xk12*x3*?k13?0.069

2Z1*?r1*?jx1*?0.00378?j0.11 Z2*?r2*?jx2*?0.00378?j0.00545 Z3*?r3*?jx3*?0.00775?j0.069

Z1b?Z1NU1N2??732.07 SNZ1?Z1*Z1b?2.77?j80.53??r1?jx1 Z2?Z2*Z1b?2.77?j3.99??r2?jx2 Z3?Z3*Z1b?5.53?j50.51??r3?jx3

p83：5-1需明白求所量uk?或uk?UkN，即短路电流为额定电流时的短路电压标UN幺值。经验证表中短路试验，Ik13?I1N，其它Ik?IN

k0VA 选择基值：电压电流以各次额定电压电流为基值，容量以SN?1500为

基值。

uk12?Zk12?Zk1211?10338.23???17.03% Z1N121215000?10312.7?10.49% 11uk13?Zk13???23?uk23??Zk23?ukZk231.54?1031503???6.0% Z2N38.5215000?103- 23 -

ua12?rk12?pk12?3915000?103?2??0.91% 2Ik12???38.2???150001213???pk13?132??0.879% 23Ik15000?1013?ua13?rk13??pk23?5415000?103?23?ua?23??rk23??2?ua?0.81% 2Ik23???150???1500038.53???（2）分离各电阻电抗按如下公式：

rk12??rk13??rk23?x?xk13??xk23??0.0049x1*?k12??0.107522r?r?rx?xk23??xk13?r2*?k12?k23?k13??0.0042 x2*?k12??0.062 522r?r?rx?xk23??xk12?r3*?k13?k23?k12??0.0039x3*?k13???0.00322r1*?Zm??U30*1??24.9 I30*31.615000113??rm??p30*60/15000?2I30*31.615000113????2?2.48

22xm??Zm*?rm*?24.79

（3）等效电路：

p83：5-2

解：该自藕变压器变比：KA?10/3?3.1510/3?1.546

（1） 自藕变压器额定容量和绕组容量之比：

SANKA??2.832 SaxNKA?1- 24 -

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