報告學生 : 趙炫能 指導教授 : 秦純 教授

1. 習題 習題 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。

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= 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

可以從上式的方程式： 因此 可以得到最大轉差率

從 6.33 式 得知等效電阻 and with 所以 習題 6.15 解答 (b.)

所以 習題 6.15 解答 (c.)