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Static controls and braking of  motors  6/101
         cheap,  robust  and  is  devoid  of  any  such  operating   6.3  Vlfcontrol (speed control at
          limitations  and,  has  an  obvious  advantage over  d.c.   constant torque)
          machines. It alone can provide an immediate answer to
          such limitations. With the advent of static technology as
         discussed later, it has now become possible to make use   This is also known as variable frequency control. Consider
          of cage motors with the same ease and accuracy of speed   the following equations from Chapter  1 :
         control and that are even better than d.c. machines. Static
          drives  response  extremely  fast  as  they  can  be  micro-
         processor  based.  They  can  compute  process  data  and
         provide system corrections almost instantly (called ‘real-
         time processing’) as fast as within  1-2  ms and even less.
         In Table 6.5 we show a broad comparison between a d.c.   and el = 4.44 KCL’ . $,,,  . Z, ‘,f,   (1 3)
          machine and a static drive using cage motors. It gives an
         idea  of  applying  static  technology  to  all  process   :.  for the same supply voltage  VI
         requirements  with more ease and even better accuracy.
          With the advent of this technology, the demand for d.c.
         machines is now in decline as noted  in  Section 6.19.

         6.2.1  Theory of application

         The application of  solid-state technology for the speed   i.e. for the  same  design  parameters  ($,,,  remaining  the
         control  of  a.c.  motors  is  based  on  the  fact  that  the   same)  and  ratio  ezlf,,  the  torque  of  the  motor,  T, will
         characteristics  and  performance  of  an  induction  motor   remain constant. Since both e2 andji are functions of the
         can  now  be  varied,  which  until  a  few  years  ago were   supply  system,  a  variation  in  V, and f  can  alter  the
         considered fixed and uncontrollable. This concept is now   performance  and  the  speed-torque  characteristics of  a
         a  matter  of  the  past.  With  the  advent  of  solid-state   motor  as  required,  at  constant  torque.  By  varying  the
         technology,  which  was  introduced  around  1970  for   frequency smoothly from a higher value to a lower one
         industrial application, the motor’s parameters and therefore   or vice  versa  (within zero to rated).  an  almost  straight
         its performance can now be varied by varying the supply   line torque  can  be  achieved  (Fig. 6.3). This type  of  a
         parameters  of  the system, for example the voltage  and   control  is  termed  variable  voltage,  variable  frequency
         frequency  in cage motors, and rotor resistance or rotor   (v.v.v.f or Vu)  control. At speeds lower than rated, the
         current  in  slip-ring motors,  as discussed  in  Chapter  1.
         This technology can also provide a varying resistance in   natural  cooling  may  be  affected, more  so  at very  low
                                                        speeds, and may require an appropriate derating of  the
         the rotor circuit of a slip-ring motor by varying the rotor   machine or provision of  an  external or forced cooling.
         current as discussed in Section 6.16.3 without the loss of   The  practice  of  a  few  manufacturers,  up  to  medium-
         power in the external resistance. It is thus also suitable   sized motors, is to provide  a cooling fan with separate
         to provide speed control in a slip-ring motor. Speed control   power connections so that the cooling is not affected at
         of slip-ring motors with the use of solid-state technology   lower speeds.
         is popularly known as dip recovery systems, as the slip
         power can also be fed back to the source of supply through   Note  The speed of the motor can be varied by varying the frequency
         a solid-state feedback converter bridge, discussed later.   alone but this does not provide satisfactory performance. A variation
                                                        in frequency causes  an inverse variation  in  the  flux.  $I,,,,  for the
                                                        same system voltage. The strength of magnetic field, $I,,,,  develops,
         6.2.2  Effects of variable supply parameters on   the  torque and moves  the  rotor,  but  at  lower speeds, f would be
              the performance of an induction motor     reduced,  which  would raise  $I,,,  and lead  the  magnetic  circuit  to
                                                        saturation.  For higher  speeds, f would be  raised,  but  that  would
         Here we analyse the effect of  variation in the incoming   reduce  @,,,,  which  would  adversely  diminish  the  torque.  Hence
         supply parameters (voltage and frequency) on the charac-   frequency variation  alone is not recommended  practice  for speed
         teristics and performance of an induction motor (such as   control. The recommended practice is to keep  Vlf as constant, to
         its flux density, speed, torque, h.p., etc). We also assess   maintain the motor’s vital operating parameters,  i.e. it\ torque and
                                                        &,,  within acceptable  limits.
         the effect of variation of one parameter on the other, and
         then  choose the most appropriate  solid-state scheme to   The above is valid for speed variation from zero to the
         achieve a  required  performance.  We  generally  discuss   rated speed. For speed variations beyond the rated speed,
         the following schemes:                         the theory of VI’’   will not work. Because to maintain the
                                                        same ratio of Vlfwould mean a rise in the applied voltage
          1  Vlfcontrol  (speed control at constant torque)   which is not permissible beyond the rated  voltage, and
         2  Phasor (vector) control                     which has  already  been  attained by  reaching  the rated
            ~  Single-phasor (vector) control           speed. The speed beyond the rated is therefore obtained
            - Field-oriented control (FOC), commonly known as   by  raising the supply frequency alone (in other words,
             double-phasor or phasor (vector) control and   by weakening the field, $,,,)  and maintaining the voltage
            - Direct torque control (DTC)               as  constant  at  its  rated  value.  We  can  thus  achieve  a
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