THREE-PHASE INDUCTION MOTORMarch 2007A. PREPARATIONC. REPORTC. REPORTTHREE-PHASE INDUCTION MOTORMarch 2007A. PREPARATION1. Introduction2. The Rotating Field3. Rotor Currents4. Induction Motor Equivalent Circuit5. Torque and Power Characteristics6. Operation Beyond the Range 0 < s < 1 7. Determination of Motor Constants8. BibliographyB. EXPERIMENT1 . Equipment List2. Speed and Direction of Rotation3. Starting Current4. No Load Test5. Locked Rotor TestC. REPORTInduction Machines - 1Induction Machines - 2Induction Machines - 3Induction Machines - 4Induction Machines - 5Induction Machines - 6Induction Machines - 7Induction Machines - 8Induction Machines - 9Induction Machines - 10Induction Machines - 11Induction Machines - 12Induction Machines - 13Induction Machines - 14Induction Machines - 15Rather than the equivalent circuit of Fig. 10, we choose one more akin to Fig. 9 to yield the result shown in Fig. 13. Based on past experience, the following simplifying assumptions can be made for this model:X0 >> X1 , │R0 + jX0│ >> │R2 + jX2│, and X1  X2 . NOTE WELL: This is based upon a WYE model and therefore represents but one of the three phases.For the rotor locked, s = 1 so that the following equations can be written from the equivalent circuit of Figure 13 assuming │R0 + jX0│ >> │R2 + jX2│:Z11 = (R1 + R2) + j(X1 + X2), │Z11│ = V1/I1 , and PPH = (R1 + R2)I12 These equations can be solved for R2, X1 , and X2 as follows: R2 = (PPH/I12)  R1 and (by assumption)X1 = X2 = ½ .Assuming that the stator resistance R1 is measured at DC and that phase powerPPH , phase voltage V1 , and phase current I1 are measured, R2, X1, and X2 can be calculated for the motor from the locked rotor test data. From the data obtained from the no-load test, we can determine the values for the series circuit elements R0 and X0. To find these values, we draw graphs of power and line current versus applied voltage as shown in Figure 14. First the measured I1 and the measured phase power PPH are used to calculate PC + PFW = PPH  I12R1 , where I12R1 is the copper loss in this no-load case, PC [W] is the per-phase core loss and PFW [W] is the per-phase friction-and-windage. The derived values are then appropriately plotted and a suitable approximating curve put through them; this curve is then cleverly extrapolated backwards to the voltage origin, and because core loss varies as V1, its intercept gives the friction-and-windage power loss. This will be explored further on the next page.  The observant student will note the italicized and bold-face material in this sentence and realize that brainpower may be more important than computer power in getting this right. Induction Machines - 16For no load, s = 0 so that the following equations can be written from the equivalent circuit of Figure 13: ZIN = (R1 + R0) + j(X1 + X0) │ZIN│ = V1/I1. PPH = PCu + PC + PFW = I12(R1 + R0) + PFW . Thus: R0 = [PPH  PFW]/I12 - R1 X0 =  X1. Assuming that phase power PPH, phase voltage V1, and phase current I1 are measured and that friction-and-windage loss PFW has been obtained as shown in Figure 14, R0 and X0 can also be calculated for the motor from the no-load test data. 8. Bibliography (1) A.S. Langsdorf, Theory of Alternating Current Machinery, 2nd. ed., New York, McGraw-Hill, 1955. (2) T.S. Reynolds and T. Bernstein, "The Damnable Alternating Current", Proceedings of IEEE, (64) pgs. 1339-1343, Sept. 1976. (3) P.L. Alger and R.E. Arnold, "The History of Induction Motors in America", Proceedings of IEEE, (64), pgs. 1380-1383, Sept. 1976. Induction Machines - 17Figure 14B. EXPERIMENT1. Equipment ListOne Instrumentation Rack with the usual test equipment One 208 Volt, 0.75 HP, 3-phase induction motor One dynamometer with torque controller One Phase Sequence IndicatorOne single-phase wattmeter plus miscellaneous apparatus as needed2. Initial DataRecord all nameplate information for the induction motor. You should also make a DC measurement of stator winding line-to-line resistance using a DMM.3. Speed and Direction of RotationThe motor is mounted in a test rig that allows one to control the torque applied to the motor shaft and to measure both rpm and torque. The rpm sensor operates on a Hall effect principle and consists of a disk bearing on its periphery two magnetic pole-pairs and a detector that pulses once each time a pole-pair is rotated past it. Observe that, by counting the output of the detector, you will get afrequency, φ [Hz] , that is twice the actual rotational frequency of the motor. Therefore motor rpm = n = 60×(½φ) = 30φ .To observe the rpm sensor in operation, proceed as follows. Energize the detector with 20 VDC ; and attach its output to the oscilloscope, the torque controller, and frequency counter. Power up the motor normally and determine the no-load* rpm when the motor, as viewed from the front, is rotating clockwise (CW); repeat with the motor spinning counter clockwise (CCW). A successful salesman for General Electric's motor division once remarked to one of your instructors that, when asked by a customer how a motor actually worked, he invariably replied "Very well, indeed.". This attitude is typical * The “no-load” condition is that which obtains when the controller knob is fully counter-clockwise. Induction Machines - 18BE CAREFUL !! It can hurt to tangle with a three-phase motor.of a technologically mature discipline: one really can afford to treat the device asif it were a black box. Therefore, in addition to determining the short circuit and open circuit characteristics of your motor you will also have to determine its input and output powers. To this end, it will be assumed that the motor is a balanced three phase wye connected load and that you will therefore need to measure only one line-neutral voltage, only one line current, and only one phase power to characterize Pin completely. That is,Pin = 3Pline-neutral = 3Pphase = 3IrmsVrmscos. Take note that Vrms is the phase voltage Vline-neutral = Vline-line/. Further,Pout = 2πfT = T = πφT,where T is the shaft torque, measured with the dynamometer in-oz, which must be converted to N.m in order to obtain power in watts. 4. Starting Current Wire up the motor for CW motion so that starting current can be measuredaccurately using the oscilloscope#. With no load on the motor and 120 Vrms, line-line,turn on the power and observe and