• The relative difference between mmf speed n1 = f1/p1 and the rotor speed n is called slip, S = 1-np1/f1.
• The frequency of the emf induced by the stator mmf field in the rotor is f2 = Sf1.
• The rated slip Sn, corresponding to rated nn, Sn = 0.08 – 0.01; larger values correspond to smaller power motors (under 1 kW).
• At zero slip (S = 0), for short-circuited rotor, the rotor current and the torque is zero; this is called the ideal no-load mode n = n1 = f1/p1.
• When the rotor windings are fed by balanced three-phase voltages Vr′ of frequency f2 = Sf1, the zero rotor current and zero torque is obtained at a slip S0 = Vr′/E1, where E1 is the stator phase emf. S0 may be positive (subsynchronous operation) or negative (supersynchronous operation) depending on the phase angle between Vr′ and E1.
• The active power traveling through an airgap (related to Pointing’s vector) is called the electromagnetic power Pelm.
• The electromagnetic torque, for a short-circuited rotor (or in presence of a passive, additional, rotor impedance) is
Te = Pelm ωP11
• At ideal no-load speed (zero torque), the value of Pelm is zero, so the machine driven at that speed absorbs power in the stator to cover the winding and core loss.
• Motor no-load mode is when there is no-load torque at the shaft. The input active power now covers the core and stator winding losses and the mechanical losses.
• The induction motor operates as a motor when (0 < S < 1).
• For generator mode S < 0 and for braking S > 1.
• In all operation modes, the singly fed IM motor “absorbs” reactive power for magnetization.
• Autonomous generating mode may be obtained with capacitors at terminals to produce the reactive power for magnetization.
• At zero speed, the torque is nonzero with stator balanced voltages. The starting torque Tes = (0.5 – 2.2)Ten. Ten – rated torque; starting current at rated voltage is Istart = (5 – 7(8))In; In – rated current. Higher values of starting current correspond to high efficiency motors.
• At high currents (S >> Sn), the slot leakage flux path saturates and the short-circuit (zero speed) inductance decreases by 10 to 40%. In the same time the rotor frequency f2 = Sf1 = f1 and the skin effect causes a reduction
of rotor slot leakage inductance and a higher increase in rotor resistance. Lower starting current and larger starting torque are thus obtained.
• The closed-slot rotor leakage inductance saturates well below rated current. Still, it remains higher than with half-closed rotor slots.
• No-load and short-circuit (zero speed) tests may be used to determine the IM parameters–resistances and reactances.
• The electromagnetic torque Te versus slip curve has two breakdown points: one for motoring and one for generating. The breakdown torque is inversely proportional to short-circuit leakage reactance Xsc, but independent of rotor resistance.
• Efficiency and power factor also have peak values both for motoring and generating at distinct slips. The rather flat maxima allow for a large plateau of good efficiency for loads from 25 to 150%.
• Adequate phasor diagrams evidentiating stator, rotor, and airgap
(magnetization) flux linkages (per phase) show that at steady-state, the rotor flux linkage and rotor current per phase are time-phase shifted by 900. It is +900 for motor and –900 for generating. If the rotor flux amplitude may also be maintained constant during transients, the 900 phase shift of rotor flux linkage and rotor currents would also stand for transients. Independent rotor flux and torque control may thus be obtained. This is the essence of vector control.
• Unbalanced stator voltages cause large imbalances in stator currents. Derating is required for sustained stator voltage imbalance.
• Higher than rated balanced voltages cause lower efficiency and power factor for rated power. In general, IMs are designed (thermally) to stand ±10% voltage variation around the rated value.
• Unbalanced rotor windings cause an additional stator current at the frequency f1(1 – 2S), besides the one at f1. Also an additional rotor-initiated backward torque which is zero at S = ½ (n = f1/2p1), Geörge’s torque, is produced. A saddle in the torque versus slip occurs around S = ½ for IMs with relatively large stator resistance (low-power motors). The machine may be “hanged” (stuck) around half the ideal no-load speed.
• In this chapter, we dealt only with the single-cage rotor IM and the fundamental mmf and airgap field performance during steady state for constant voltage and frequency. The next chapter treats starting and speed control methods.
7.19 REFERENCES
1. P.T. Lagonotte, H.Al. Miah, N. Poloujadoff, Modelling and Identification of Parameters of Saturated Induction Machine Operating under Motor and Generator Conditions, EMPS: Vol.27, No.2, 1999, pp.107 – 121.
2. J. Kneck, D.A. Casada, P.J. Otday, A Comparision of Two Energy Efficient Motors, IEEE Trans Vol.EC – 13, No.2., 1998, pp.140 – 147.
3. A.H. Bonnett, G.C. Soukup, NEMA Motor-Generator Standards for Three Phase Induction Motors, IEEE – IA Magazine, Vol.5, No.3, 1999, pp.49 – 63.