報告學生 : 趙炫能 指導教授 : 秦純 教授. 1. 習題 6.7 2. 習題 6.13 3. 習題 6.15
TRANSCRIPT
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