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Solid-State Reduced Voltage Starters and Starting Torque
Copyright © 2002 Francis J. Martino

The torque of a three phase motor is proportional to the internal air gap
flux which consists of two components: 1) stator winding voltage and
2) rotor voltage that is created through the generator action of the field
voltage cutting the rotor bars of the stator and thus inducing current into
the bars. Thus, with a 50% drop in motor terminal voltage, the rotor
voltage will also be reduced by 50%. That condition will hold true when
the motor inrush is allowed to flow freely on start-up.

Therefore, the torque produced is proportional to both the field and
rotor voltages. For rated voltage at per unit volts, the torque will be
(field volts x rotor volts), or, 1.0 x 1.0 = 1.0 which is 100% of rated
torque. With a 50% reduction in terminal voltage, torque will be
0.50 x 0.50 = .25, or, 25%. For that reason the torque of the motor is
proportional to the square of the voltage with normal inrush
current allowed.

A reduced voltage starter will allow a “soft” start by virtue of the
torque being reduced. The soft start will lower shock loading throughout
the mechanical system of the load.

The inrush current that a motor will draw at any particular reduced
voltage will be allowed up to the solid state starter’s limiting peak of
600% of full load amps.

If the inrush current must be reduced to accommodate a weak
distribution system or to gain a decrease in kW demand, the inrush current
may be limited by the programming of the starter.

Since the rotor voltage is proportional to the IR drop within the rotor
(IR = current in amps x rotor resistance in ohms), the rotor voltage
achieved will be proportional to the rotor current.

The following relationships exist between motor voltage, inrush
current and developed torque: [1]

* Starting torque will vary approximately with the square of the
applied voltage.

* Inrush current will vary approximately with the applied voltage.

* Rotor inrush amps, which is dependent upon rotor design, will be
approximately 50% of the total motor inrush.

* Running torque will be approximately proportional to the rotor current.

A typical motor will draw 500% FLA and develop approximately 180%
of full load torque with a full voltage start. Based on the above relationships,
the first five columns of the following table will hold for that motor during
reduced voltage starting with no limitations on inrush current. Maximum
starting torque with a limited inrush is given in the column on the right.
The data given in the table is an approximation that neglects core losses
within the motor, i.e., stator copper losses, friction, windage, and stray
load losses, etc. The data is reasonably close to that encountered in a
solid state or autotransformer starter.


Applied Motor Volts At Start % Rated Motor Volts At Start Inrush Current % FLA Amps Torque % FL Torque Inrush Rotor Amps % FLA 460 VAC Applied, % Full Load Torque On Start With Inrush Current Limited [2]
460 100 500 180 250 180
414 90 450 146 225 160
368 80 400 115 200 144
322 70 350 88 175 126
276 60 300 65 150 108
230 50 250 45 125 90
184 40 200 29 100 72
138 30 150 16 75 54
92 20 100 7 50 36
46 10 50 2 25 18

[1] Ralph A. Millermaster, “Harwood’s Control of Electric Motors,”
John Wiley & Sons, Inc., New York, 1970, Pages 352-353, 406-409.
See also pages 380-382.

[2] With 460 VAC applied to the motor terminals after ramp-up, the
maximum starting torque available with a reduced voltage starter that
has been programmed to limit current to the values shown in the column
labeled “Inrush Current % FLA” is roughly approximated in the column
labeled “460 VAC Applied, % Full Load Torque On Start With Inrush Current
Limited.” Thus, with 460 VAC on the motor terminals and with inrush
current limited to 150% of FLA, the maximum starting torque will not
exceed 54% of the Full Load Torque rating of the motor.

Using the voltage to torque relationship as described above, the 54%
is derived as follows: (460/460) x (138/460) x 180% = 54% of full
load torque.

With a high inertia load, a momentary impulse of current that is
greater than the maximum programmed inrush may be required initially to
develop “break-away” torque. In most applications, with current limited
to 150% of full load amps the motor will not develop enough torque to
start rotating. In general, machinery will require anywhere from 120% to
600% of full load torque on start.

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