电机学课后习题答案

本文格式为Word版，下载可任意编辑——电机学课后习题答案2-1一台单相变压器，SN=5000kVA,U1N/U2N=35/6.0kV,fN=50HZ,铁心有效面积A=1120cm2，铁心中的最大磁密Bm=1.45T，试求高、低压绕组的匝数和变比。解:高压绕组的匝数U1NU1NN1??4.44f?m4.44fBavA35?103??152424.44?50?1.45?1120?10?4?N1U1N35kV??5.83变压器的变比k?N?U6kV22NN11524??261低压绕组的匝数N2?k5.832-2有一台单相变压器，已知r1=2.19Ω，x1σ=15.4Ω，r2=0.15Ω，x2σ=0.964Ω，

rm=1250Ω，xm=12600Ω，N1=876匝，N2=260匝，当cosφ2=0.8滞后时，二次侧电流I2=180A，U2N=6000V，试用“Г〞形近似等效电路和简化等效电路求u1及i1。

22122

2222?1?

k1222k1?2?22

下面用“Г〞形近似等效电路求解。

N876r??kr?3.369?0.15?1.703?k???3.369N260x??kx?3.369?0.964?10.94?r?r?r??2.19?1.703?3.89?x?x?x??15.4?10.94?26.3?11I??180?53.4Ak3.369U??kU?3.369?6000?20235VI??令

?????U2?U2?0?20235?0由于cosφ2=0.8，则φ2=36.87°，所以

???I???36.87??53.4??36.87?I22

???r?jx??U?????IU2kk21

??53.4??36.87??3.89?j26.3??20235?0???42.7?j32.04??3.89?j26.3??20235????21226?j1001?21249.6?182.7???U121249.6?182.7?Im??

rm?jkm1250?j12600

m2

而用简化等效电路求解：

21249.6??182.7??84.33??1.678?98.37?12661.852???????I1?I?I??1.678?98.37?53.4??36.87???0.2443?j1.66???42.744?j32.058???42.988?j33.718?54.63?141.89??rk?jxk??U2??21249?182.7U1??I2

可见用简化等效电路求解与用“Г〞形近似等效电路求解的一致；

???????53.4?143.13I1??I2画出折算后的矢量图和T形等效电路。

∨2-8一台三相变压器，SN=750kVA,U1N/U2N=10000/400V,Y,d接法，f=50HZ。试验在低压侧进行，额定电压时的空载电流I0=65A，空载损耗p0=3700W；短路试验在高压侧进行，额定电流时的短路电压Uk=450V，短路损耗pkN=7500W（不考虑温度变化的影响）。试求：11)折算到高压边的参数，假定R1=R?2=Rk,x1σ=21x?2σ=xk；22)绘出T形电路图，并标出各量的正方向；3)计算满载及cos?2=0.8（滞后）时的效率?N；4)计算最大效率?max。解：1)p0?I06511??37.53A?p0??3700W?1233WI0??3333,Z'm?Z'0?UI2N?0??400V?10.66?37.53Rm?'p?1233W?I?(37.53A)0202?0.875?xm?'22??(10.66?)?(0.875?)?10.62?Z?mR?m22折算至高压侧的激磁参数：k?U1N?U2N??100003?14.434002=14.43×10.66mZm=k2=2219.7ΩZ?ΩRm=k2R?m=14.432×0.875Ω=182.2Ω?=14.432×xm=k2xm10.62Ω=2211.3Ω短路参数计算：Uk?Uk450V???259.8V3311pk??pk??7500W?2500W33SN750?103Ik?I1N???43.3A3U1N3?10000Uk?259.8V?6?Zk==Ik43.3ARk=Pk?Ik22500W??1.33?2(43.3A)2222Z?R(6?)?(1.33?)?5.85?Xk=kk=11R?R1=R?2=2k2?1.33??0.665?11x1σ=x?2σ=2xk?2?5.85??2.93?2)T形电路图如下：4)满载时的效率?mp0pkN?3700W7500W?0.702?max?(1?2p0)?100%?mSNcos?2?2p02?3.7kW?(1?)?100%?98.27%0.702?750kVA?0.8?2?3.7kW

7.2有一三相电机，z=48,2p=4,a=1,每相串联导体数N=96,f=50Hz,双层短距绕组，星型接法，

?21，0?3?0.365?10?2Wb，?5?0.24?10?2Wb，每极磁通?1?1.1?15Wb?7?0..93?10?2Wb，试求：

（1）力求减弱5