An induction motor's synchronous speed Ns is given as:

Ns = frequency * 120 / number of poles

This formula is independent of the voltage applied to the windings.

On the other hand, I know from basic theory that if the voltage across a solenoid is increased its magnetic flux will increase. And more magnetic flux will create more force on a current carrying wire.

Would the speed of the induction motor's rotor change with delta or star connection? And is there a formula explicitly shows such dependency between stator winding voltage(delta or star) and rotor speed? Would a three phase fan motor rotate faster if connected delta instead of star?

  • \$\begingroup\$ this site had a lot of answers for your questions: electrical-engineering-portal.com/star-delta-motor-starter \$\endgroup\$
    – Bruce
    Commented Mar 11, 2019 at 15:18
  • \$\begingroup\$ I saw that but there is not a single formula related to my question. \$\endgroup\$
    – cm64
    Commented Mar 11, 2019 at 15:22
  • \$\begingroup\$ I saw a formula and not one mention of voltage in that equation. That's your answer. A solenoid is a not a synchronous machine. But voltage can affect load slip \$\endgroup\$ Commented Mar 11, 2019 at 15:41

3 Answers 3


As the formula says, the synchronous speed is determined only be the frequency and number of poles. The operating speed is reduced below the synchronous speed by slip. Slip at rated torque is about 2 to 3 percent for a standard squirrel-cage motor. A high-slip motor could have up to about 8% slip at rated torque. Slip with no load is nary zero. From no-load to rated load, slip is fairly linearly proportional to torque.

Induction motors are generally designed to operate close to saturation at rated voltage and will overheat if the voltage is too high. If the voltage is reduced, the maximum torque will decrease approximately proportional to voltage squared. The slip will increase. To the extent that the motor can tolerate operation at increased slip, the speed can be reduced by reducing the voltage. That method of reducing speed is of limited use.

Normally changing between delta and star connection is used only for accommodating two possible supply voltages and for star-delta starting as a means of limiting the starting current by reducing the voltage for a few seconds while the motor is coming up to speed.

If a motor is designed to operate at a certain voltage with the star connection, connecting the motor in delta at the same voltage will cause saturation and overheating.

A the rated voltage for the star connection is 1.732 x the rated voltage for the delta connection. The rated current for the star connection is .577 x the rated current for the delta connection. The input kVA is about the same for either connection to the proper voltage for that connection. The peak torque, rated torque, rated slip and other torque vs. speed parameters are the same for both connections.


The speed of the motor does not change with delta or star connection. The thing that changes is the voltage accros the stator windings, thus the motor maximum current depends on the delta or star connection. So, the motors maximal torque is affected depending on the type of the connection.

  • \$\begingroup\$ But wouldnt more torque cause more speed at the rotor? \$\endgroup\$
    – cm64
    Commented Mar 11, 2019 at 15:23
  • \$\begingroup\$ This answer is misleading. the torque and current are reduced if the star connection is used with the voltage for which the delta connection is rated. The delta connection can not be used with the voltage for which the star connection is rated. \$\endgroup\$
    – user80875
    Commented Mar 11, 2019 at 15:45
  • \$\begingroup\$ No, more torque causes the rotor frequency to catch up to the stator frequency in less time, faster if u will. \$\endgroup\$
    – Ziggy
    Commented Mar 11, 2019 at 15:46

As said, the reduction of torque will cause the motor to increase slip slightly, so there might be a slight change in unloaded speed. With load, the loss of torque can create a much GREATER loss of speed and increase in slip, to the point of possibly stalling the motor, depending on the AMOUNT of load applied. With an effective 57.7% voltage applied to the windings, peak torque is reduced to 33% of rated. If the LOAD on the motor is less than 33% of rated, you may never see the difference in working speed. But if the load ever increases, you run the risk of stalling.

In fact this is a technique used by some to "save energy" in motors that have been grossly over sized for the load. i.e. a machine was built for one purpose and later on, repurposed for a task with much less load on the motor, but it would be too expensive to install a smaller motor. So the old oversized motor is connected in Star (Wye) so that with the effective drop in phase voltage, there is less magnetizing energy consumed in the motor (so called "iron losses"). It doesn't make very much of a difference, but I've seen it used in places with very high tariffs or where power is generated on site and every watt counts.


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