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         speed variation beyond the rated speed by sacrificing its   Vlfis a concept to vary the speed, maintaining a constant
        torque  and  maintaining  the  product  T  . f  as  constant.   torque. Through a static drive, however, it is possible to
        Since P  = T . N, and N, = h, therefore speed variation   vary one parameter  more than the other, to obtain any
        can now be achieved at constant power output (see Figure   speed-torque  characteristic to meet a particular duty cycle.
        6.4). We have combined Figures 6.3 and 6.4 to produce   By varying the rectifier and inverter parameters, a whole
        Figure 6.5 for more clarity, illustrating the speed variation   range of Vlfcontrol is possible. High-inertia loads, calling
        at constant torque below the base speed and at constant   for a slip-ring motor for a safe and smooth start, can now
        h.p. above the base speed.                     make  use of  a  standard  squirrel cage  motor.  Open- or
          Vlfis the most commonly used method to control the   closed-loop control systems can be employed to closely
         speed of a squirrel cage motor. The fixed frequency a.c.   monitor and control the output voltage and frequency so
         supply,  say,  at 415  V,  50 Hz  from  the  mains,  is  first   that the ratio of  Vlfis always maintained constant.
        rectified to a constant or variable d.c. voltage, depending
        upon the static devices being used in the inverter circuit   Limitations of V/f control
         and their configuration. This voltage is then inverted to
         obtain the required variable-voltage and variable-frequency   Figure 6.1 illustrates theoretical speed-torque  curves. In
         a.c. supply. The basic scheme of a Vlfcontrol  is illustrated   fact at very low speeds, say, at around 5%  of N, (at 5%
         in Figure 6.6. The approximate output voltage, current   f) or  less,  the  motor  may  not  be  able  to  develop  its
         and torque waveforms are shown in Figure 6.7(a). The   theoretical torque due to a very low stator voltage, on the
         torque  curve  is  now  almost  a  straight  line, with  only   one hand, and relatively higher proportion of losses and
         moderate  pulsations,  except  for  some  limitations,  as   a lower efficiency of the machine, on the other. Figure
         discussed later, enabling the drive to start smoothly. When,   6.2 illustrates a realistic torque characteristic at different
         however, a higher starting torque is required to start the   supply frequencies. They display a sharply drooping and
         motor  quickly, it is  also possible  to  boost the  starting   rather unstable performance at very low speeds. For more
         torque to a desirable level (up to the designed T,, of the   accurate  speed  controls  at  such  low  speeds,  one may
         motor) by  raising  the  voltage to  V,,  through  the pulse   have  to  use  phasor-controlled  drives,  discussed  later.
         width  modulation  (PWM), discussed in  Section 6.9.2.   Phasor-controlled drives are available at reasonable cost
         The starting current can also be reduced  to only  100-   and can provide extremely accurate speed controls even
         150% of  the  rated  current or as  desired,  to  the  extent   at very low speeds, 5% of N, and less, or cyclo-converters,
         possible,  by  suitably  varying  the  Vlf. The control  can   which are relatively very costly, for large drives. Typical
         thus also provide a soft-start switching. It may, however,   applications calling for such a high torque at such low
         be noted that there is no control over the starting current,   speeds could  be  a  steel plant  process  line or material
         which  is  a  function  of  the  applied  voltage,  and  the   handling  (e.g. holding  a  load stationary at a particular
         minimum voltage during start-up will  depend upon the   height  by  the  crane,  while  shifting  material  from  one
         motor, the load characteristics and the thermal withstand   location to another).
         time of  the motor (Section  2.8). With the use of  static
         control  drives,  it  is however, possible  to minimize  the
         starting inrush current to a reasonable  level but with a
         loss of starting torque. To do so, it is advisable to match
         the  load  and  the  motor  starting  characteristics  and
         determine the minimum starting torque required to pick
         up the load. For this starting torque is then adjusted the
         starting voltage. The magnitude of  the starting current
         will then depend upon this voltage.
           The static drives too are defined by  their overcurrent
         capacity and its duration. EC 60146-1-1 has defined it
         as  150-300%,  depending upon  the type of application,
         for a maximum duration of one minute. For instance, for
         centrifugal drives,  which  are  variable  torque  drives
         (Figures  2.10  and  2.1 I)  such  as  pumps,  fans  and
         compressors etc. an overcurrent capacity of the order of
         1 10% for one minute would be adequate. For reciprocating
         drives, which  are constant torque  drives (Figures  2.12
         and 2.13),  such  as ball  mills  and conveyors, a  higher
         overcurrent capacity say, 15&300%  for one minute, would   At Ns = 5%     f= 1
         be essential. For higher starting currents or longer durations   and less, the   v= 1
         of  start, the  drive  may  have  to  be  derated,  which  the   motor is not   f decreasing   f rising
         manufacturer of the drive alone will be able to suggest.   able to maintain   Speed or frequency
         Drive ratings are basically selected on the basis of motor   its Tstand  Tpo
         rating and the starting currents and are rated for a starting   levels
         current of  150% for one minute.  If  more than  150% is
         required, then the rating of the drive is worked out on the   Figure 6.1  Approximate theoretical representation of speed
         basis of the starting current requirement and its duration.   versus torque for  V/f control of  a motor at different values of  f
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