34.3.3.2 Slip Power Control

P 2 34.3.3.2 Slip Power Control

The developed torque, T =

Variable-speed, three-phase, wound-rotor (or slip-ring) induc- tion motor drives with slip power control may take several

The slip frequency, sf 1 , is the frequency of the rotor current forms. In a passive scheme, the rotor power is rectified and

and the airgap voltage E 1 is given by

dissipated in a liquid resistor or in a multi-tapped resistor that may be adjustable and forced cooled. In a more popular

(34.17) scheme, which is widely used in medium- to large-capacity pumping installations, the rectified rotor power is returned to where λ m is the stator flux linkage due to the airgap flux. If the the ac mains by a thyristor converter operating in a naturally stator impedance is negligible compared to E 1 , which is true commutated inversion mode. This static Scherbius scheme is when f 1 is near the rated frequency f o ,

E 1 =ω 1 L m I m =ω 1 λ m

indicated in Fig. 34.15. In this scheme, the rotor terminals are connected to a three-phase diode bridge which rectifies the

V 1 ≈E 1 = 2πf 1 λ m

(34.18) rotor voltage. This rotor output is then inverted into mains fre- quency ac by a fully controlled thyristor converter operating

and from the same mains as the motor stator.

2 The converter in the rotor circuit handles only the rotor slip 3P

sR 2 V 2 3P sR 2 1 λ 2 m

(34.19) power, so that the cost of the power converter circuit can be

2 + (sω ω 1 R 2 2 + (sω 1 L 2 ) 2 much less than that of an equivalent inverter drive, albeit at

34 Motor Drives 925

Speed, V A rev/min

Load T- w V =1 pu

V B IM V =0.75 pu

V =0.5 pu V C

Motor T- w e c

FCC Torque, Nm

(a)

(b)

FIGURE 34.14 (a) Stator voltage controller and (b) motor and load torque–speed characteristics under voltage control.

AC MAINS

DC Reactor I

FIGURE 34.15 The static Scherbius drive scheme of slip power control.

the cost of the more expensive motor. The dc link current, where ω s and ω r are the angular frequencies of the voltages in smoothed by a reactor, may be regulated by controlling the the stator and rotor circuits, respectively, and n is the ratio of firing angle of the converter in order to maintain the developed the equivalent stator to rotor turns. The dc-link voltage at the torque at the level required by the load. The current controller rectifier terminals of the rotor, v d, is given by (CC) and speed controller (SC) are also indicated in Fig. 34.15.

The current controller output determines the converter firing

3 6V R

angle α from the firing control circuit (FCC).

From the equivalent circuit of Fig. 34.13 and ignoring the stator impedance, the RMS voltage per phase in the rotor

Assuming that the transformer interposed between the circuit is given by

inverter output is and the ac supply has the same turns ratio n as the effective stator-to-rotor turns of the motor,

v d (34.21)

926 M. F. Rahman et al. The negative sign arises because the thyristor converter rotor circuit, allowing the motor to operate at a rate higher

develops negative dc voltage in the inverter mode of operation. than synchronous speed. For very large drives, a cycloconverter The dc-link inductor is mainly to ensure continuous current may also be used in the rotor circuit with direct conversion of through the converter so that the expression (34.21) holds for frequency between the ac supply and the rotor and driving the all conditions of operation. Combining the preceding three motor above and below synchronous speed. equations gives

sω s = −ω s cos α so that, s = −n cos α

34.3.3.3 Variable-voltage, Variable-frequency (V–f )