報告學生 : 趙炫能指導教授 : 秦純 教授

1. 習題 6.72. 習題 6.133. 習題 6.15

• 6.7 Figure 6.23 shows a system consisting of a three-phase wound-rotor induction machine whose shaft is rigidly coupled to the shaft of a three-phase synchronous motor . The terminals of the three-phase rotor winding of the induction machine are brought out to slip rings as shown. With the system supplied from a three-phase , 60Hz source , the induction machine is driven by the synchronous motor at the proper speed and in the proper direction of rotation so that three-phase , 120Hz voltages appear at the slip rings. The induction motor has four-pole stator winding. Interconnected induction and synchronous machines.

圖 6.23 感應電動機與同步電動機的連接

a. How many poles are on the rotor winding of the induction motor?答 : 四極

b. If the stator field in the induction machine rotates in the clockwise direction, what is the rotation direction of its rotor?答 : 逆時針方向

c. What is the rotor speed in r/min ?

答 :d. How many poles are there on the synchronous motor?

答 : 四極e. It is proposed that this system can produce dc voltage by reversing two of

the phase leads to the induction motor stator. Is this proposal valid?答 : 不，這將會是直流通量連接感應電動機的轉子，但這不會是在集電環產生的電壓。

rpmp

f1800

4

60*120120

• A 15-kW 230-V three-phase Y-connected 60-Hz four-pole squirrel-cage induction motor develops full-load internal torque at a slip of 3.5 percent when operated at rated voltage and frequency. For the purposes of this problem, rotational and core losses can be neglected and cord losses can be neglected . The following motor parameters , in ohms per phase , have been obtained ： R1 = 0.21 X1 = X2 = 0.26 Xm= 10.1 Determine the maximum internal torque at rated voltage and frequency , the slip at maximum torque , and the internal starting torque at rated voltage and frequency.

• 答 :在題目中所給的 R1 、 X1 、 X2 、 Xm 下代入 P339-P340 的 matlab 程式經由 R2 的變化來達到最大轉矩與啟動轉矩。再把答案中所提供的R2=0.0953 代入得到最大轉矩 177N-m 及轉差率為 18.2% 、起動轉矩為 71.6N-m 。

• A three-phase induction motor, operating at rated voltage and frequency, has a staring torque of 135 percent and a maximum torque of 220 percent, both with respect to its rated-load torque. Neglecting the effects of stator resistance and rotational losses and assuming constant rotor resistance, determine:

a. The slip at maximum torque.

b. The slip at rated load.

c. The rotor current at starting (as a percentage of rotor current at rated load).

根據 6.34式

從 6.36式

從 6.33式中可得 S=1

得

)( 2,1max

2 XXTS

Rq

)(

5.0

2,1

2,1

max XX

VnT

eqs

eqph

])([ 22,1

22

22,1

XXR

RVnT

eqs

eqphstart

63.135.1

20.2max startT

T

可以從上式的方程式：

因此

可以得到最大轉差率

2,1

2

2

2,1

22

2,12

22,1

22

1)(

)(

)(63.1

XX

R

XX

R

XXR

XXR

eq

eq

eq

eq

63.1)1(5.0

max

2

T

matT

S

S

%3.34343.0max TS

從 6.33式 得知等效電阻 and with

所以

所以

習題 6.15 解答 (b.)01, eqR ratedss

])()/[(

)/(2

2,12

2

22,1

XXsR

sRVnT

eqrateds

ratedeqPhrated

ratedT

ratedT

rated ss

ss

T

T

/

])/(1[5.01.2

max

2maxmax

%24.80824.0240.0 max Trated ss

所以

習題 6.15 解答 (c.)

)/)(()(/ max21,

,1

21,2

,1

,2 jssXXXXjsR ratedTeq

eq

eqrated

eq

rated

VVI

%40505.4343.0

16.4/

max

max

,2

,2

j

j

js

jss

T

ratedT

rated

start

I

I