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# Electrical power drivers et3026 wb lecture 6-2

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### Electrical power drivers et3026 wb lecture 6-2

1. 1. March 5, 2009 1 Elektrische Aandrijvingen WTB Lokatie/evenement P.BAUER
2. 2. March 5, 2009 2 FIGURE 15-1 Equivalent circuit of a wound-rotor induction motor at standstill. Equivalent circuit of the IM
3. 3. March 5, 2009 3 FIGURE 15-2 Approximation of the equivalent circuit is acceptable for motors above 2 hp. Equivalent circuit of the IM • Locked rotor
4. 4. March 5, 2009 4 FIGURE 15-3 Equivalent circuit of a wound-rotor motor when it is running at a slip s. The frequency of the voltages and currents in the stator is f. But the frequency of the voltages and currents in the rotor is sf. • E2 = s E1 Equivalent circuit of the IM
5. 5. March 5, 2009 5 FIGURE 15-4 a. Equivalent circuit of the rotor; E2 and I2 have a frequency sf. b. Phasor diagram showing the current lagging behind the voltage by angle β. • I2 = s E1 / (R2+js x2) • I1 = I2 = s E1 /(R2+js x2)= E1 /z2
6. 6. March 5, 2009 6 FIGURE 15-6 Equivalent circuit of a wound-rotor motor referred to the primary (stator) side.
7. 7. March 5, 2009 7 FIGURE 15-7 The primary and secondary leakage reactances x1 and x2 are combined to form an equivalent total leakage reactance x. • P = Eg 2 / Rm+ I1 2 r1 +.. • Q = Eg 2 / xm+ I1 2 x. • S = Sqrt( P2 + Q2 ) • Pr = I1 2 R2./s • Pjr = I1 2 R2 • Pjr = s Pr • Pm = Pr- Prj
8. 8. March 5, 2009 8 Simpler phasor diagram
9. 9. March 5, 2009 9 . Maximum torque • Tb= 9,55 Eg 2 /(nsz1cos2 alpha/2)
10. 10. March 5, 2009 10 FIGURE 15-12 Equivalent circuit of a 5 hp, squirrel-cage induction motor. Because there is no external resistor in the rotor, R2 = r2.
11. 11. March 5, 2009 11 FIGURE 15-13 Equivalent circuit of a 5000 hp, squirrel-cage induction motor. Although this motor is 1000 times more powerful than the motor in Fig. 15.12, the circuit diagram remains the same.
12. 12. March 5, 2009 12 FIGURE 15-14 Torque-speed curve of a 5 hp motor.
13. 13. March 5, 2009 13 FIGURE 15-15 Torque-speed curve of a 5000 hp motor.
14. 14. March 5, 2009 14 Properties of Asynchr. generator • s = • R2/s = - 48 ohm • Z = • I1 = E/Z • Pjr = I1 2 r2 • Pm = Pr+ Prj • Pr = -1410 W
15. 15. March 5, 2009 15 FIGURE 15-17 A no-load test permits the calculation of Xm and Rm of the magnetizing branch. No load test • r1 = RLL/2 • ENL PNL INL • SNL=ENL INLsqrt(3) • QNL=Sqrt( SNL 2 – PNL 2) • PfV PNL-3r1INL 2 • RM=ENL 2 /(Pf +Pv)
16. 16. March 5, 2009 16 FIGURE 15-18 A locked-rotor test permits the calculation of the total leakage reactance x and the total resistance (r1 + r2). From these results we can determine the equivalent circuit of the induction motor. Locked rotor test • SLR=ELR ILRsqrt(3) • QLR=Sqrt( SLR 2 – PLR 2) • x =QLR / 3ILR 2 • 3ILR 2(r1+r2 )= PLR
17. 17. March 5, 2009 17 FIGURE 15-19 Determining the equivalent circuit of a squirrel-cage induction motor (see Example 15-1).