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EXAMPLE 1714 Induction Motor Analysis
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Determine the following quantities for a three-phase induction motor using the circuit model of Figures 1739 to 1741 1 Stator current
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Known Quantities: Motor ratings; circuit parameters Find: IS ; pf; T Schematics, Diagrams, Circuits, and Given Data: Motor ratings: 500 V; 3 ; 50 Hz; p = 8; s = 005; P = 14 hp Circuit parameters: RS = 013 ; RR = 032 ; XS = 06 ; XR = 148 ; Ym = GC + j Bm = magnetic branch admittance describing core loss and mutual inductance = 0004 j 005 1 ; stator to rotor turns ratio = 1 : = 1 : 157 Assumptions: Use per-phase analysis Neglect mechanical losses Analysis: The approximate equivalent circuit of the three-phase induction motor on a
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per-phase basis is shown in Figure 1741 The parameters of the model are calculated as follows: R2 = RR X 2 = XR Z = RS + 1 1
= 032
1 157 1 157
= 013
= 148
= 06
R2 + j (XS + X2 ) S 013 + j (06 + 06) = 273 + j 12 = 013 + 005 Using the approximate circuit, (500/ 3) 0 V VS = = 888 j 39 A I2 = Z 273 + j 12 IR = VS GS = 2887 V 0004
= 115 A = j 144 A
Im = j VS Bm = 2887 V ( j 005) I1 = I2 + IR + Im = 8995 j 534 A Input power factor = Torque = Re[I1 ] 8995 = = 086 lagging |I1 | 1046 3I 2 R2 /s 3P = 2 = 935 N-m S 4 f/p
Part III
Electromechanics
Performance of Induction Motors The performance of induction motors can be described by torque-speed curves similar to those already used for DC motors Figure 1742 depicts an induction motor torque-speed curve, with ve torque ratings marked a through e Point a is the starting torque, also called breakaway torque, and is the torque available with the rotor locked, that is, in a stationary position At this condition, the frequency of the voltage induced in the rotor is highest, since it is equal to the frequency of rotation of the stator eld; consequently, the inductive reactance of the rotor is greatest As the rotor accelerates, the torque drops off, reaching a maximum value called the pull-up torque (point b); this typically occurs somewhere between 25 and 40 percent of synchronous speed As the rotor speed continues to increase, the rotor reactance decreases further (since the frequency of the induced voltage is determined by the relative speed of rotation of the rotor with respect to the stator eld) The torque becomes a maximum when the rotor inductive reactance is equal to the rotor resistance; maximum torque is also called breakdown torque (point c) Beyond this point, the torque drops off, until it is zero at synchronous speed, as discussed earlier Also marked on the curve are the 150 percent torque (point d), and the rated torque (point e)
T,% 300 a b 200 e No-load speed c
Figure 1742 Performance curve for induction motor
A general formula for the computation of the induction motor steady-state torque-speed characteristic is mVS2 RR /s 1 T = e [(RS + RsR )2 + (XS + XR )2 ] (1782)
T D 300 C 200 A 100 B
where m is the number of phases Different construction arrangements permit the design of induction motors with different torque-speed curves, thus permitting the user to select the motor that best suits a given application Figure 1743 depicts the four basic classi cations, classes A, B, C, and D, as de ned by NEMA The determining features in the classi cation are the locked-rotor torque and current, the breakdown torque, the pull-up torque, and the percent slip Class A motors have a higher breakdown torque than class B motors, and a slip of 5 percent or less Motors in this class are often designed for a speci c application Class B motors are general-purpose motors; this is the
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