Question

Example 6C:

15. Calculate the actual rotor speed, in rad/s, at maximum steady-state torque for the machine given in Example 6C for operation as a motor when connected to an electric source of (a) 120 Hz with twice rated voltage, (b) 60 Hz with rated voltage, (c) 30 Hz with one-half rated voltage, and (d) 6 Hz with 10 percent rated voltage. Example 6C. The parameters for the equivalent circuit shown in Fig. 6.8-1 may be calculated by using electromagnetie feld theory or deterined from tests. The tests generally performed are a de test, no-load test, and blocked-rotor test. The following test data are given for a 3-hp, four-pole, 110-V (rins), two phase, 60-H, induction machine, where all ac voltages and currents are in rms values: test No loud test 4-13.0 A |In-3.86 Allir-16.1 A 134 WP-469 W -60 Hz -15 H7 During the de test, a de voltage i applied to oue piase while the machine is at standstill. Thus, V6.9 13 The no-load test, which is analogous to the transformer open-circuit test, is performed with balanced two-phase 1Hz voltages applied to the stator windings without mechanical load on the rotor (no load). The total power input during this test is the sum of the stator obmic losses per phase, the core losses due to hysteresis and eddy currents, and rotation loes due to friction and windage. The total stator ohmic losses (two phases) are P2Ri 2(3.860.531 158 W (6C-2) Therefore, the powerloss due to friction, windage, and core losses is Piwc--P131-15.8- 118.2 W (6C-3) In the equivalent circuit sbown in Fig. 6.8-1, the ore loss is negiected. It is generally small and, in most cases, little erTOr is introduced by neglecting it. It can be taken into account by placing a resistor in shunt with the magnetizing reactanceXme- The friction and windage loeses may be approximated with B in (64-5) It is noted from the no-load test data that the small since the total apparent power input to the motor is power factor is very Sal-2Vn2110) (3.86) 849.2 VA (6C-4) Therefore, the noload impedance is highly inductive, and its magni- tude is assumed to be the sum of the stator leakage reactance and the magnetizing reactance since the rotor speed is essentially synchronous, whereupon rs is much larger than Xm in Fig. 6.8-1. Thus, Xu+x,no--=-=28.5 Ω (6C-5) 3.86 During the blocked-rotor test, which is analogous to the transformer ehort-circuit test, the rotor is locked by some mechanical means and balanced two-phase stator voltages are applied. The frequency of the applied voltnges is often less than ted in order to obtain a repre sentative value of since during normal operation the frequeucy of the rotor currents is low and the rotor resistance of some induction machines vary considerably with frequency. During stall s1), the rotor impedance rs is much smaller in magnitude than whereupon the current owing in the mnagnetizing reactance may be meglected in these calculations. Hence, the total power input to the motor during the blocked-rotor test is eC-6) From which 469 (6C-7) (2)(16.1)2-0.531-0.374 Ω The magnitude of the blocked-rotor input impedance is e 23.5 12,.--1.46 Ω Ihr 16.1 (6C-8) Thus, (6C-9) from which -1.46. (0.531 + 0.374)2 = 1.31 Ω2 (6C-10) Thus (6C-11) Geelly, X, and Xir are assumed equal; however, in some types of induction machines a diffcrent tioissuggrsted We will asume X whereupon we have determined the machine parameters. In particular, for w, 377 rad/s, the parameters are r, = 0.531 Ω. Xu-229 Ω, Xm»-26.2 Ω1 r. : 0.374 Ω, and X,-2.29 Ω.

Answer 1

rma 0.53 ,962 924 +36 を.xe*..z 22 6 2 2.29+26 59 G98 38.u

O37 6 938(9.105+22) O37u 0.88(u 35) 2 0-374 V 08798ャAJ160 0374 20 15 O.37

3 Then he ooloo eed coll bo 377 (i- o-08) 377 (0317 cử the focqcrcraf lao Ha T.cn : Q#577 11-0083)