# Does Back EMF change according to stator current in SM?

The concept of Back EMF always confuses me in Synchronous Machines. If I have a synchronous machine and I manually rotate at "x" rpm, do I get the same back EMF as when I excite the stator with 3 phase AC and have it operate at the same "x" rpm?

• Yes. But some synchronous motors have a winding in the rotor (field winding) that can be excited. The back EMF of such a motor can be adjusted by adjusting the current in the field winding. This also applies to generators. It is common for alternators and generators to use field windings in the rotor. Dec 12, 2022 at 22:20

## 1 Answer

First of all, the answer to your question is "yes."

Back EMF is the voltage that would appear on your motor terminals if you rotated it at "x" rpm with no current - that is if it were a generator without any load. When you apply the three phase AC to make the motor turn, you must have current in the phases to generate torque. But if the AC signal was exactly the same as the back EMF, there would be no current flowing. Therefore, the drive voltage waveform must exceed the back EMF in a motor to make it spin. In a lossless world, an unloaded motor would coast if the back EMF voltage were present. In the real world, the supply voltage must exceed the back EMF by at least an amount equal to the phase current times the phase resistance. As the motor takes on load, the rotor position will lag the AC supply creating a further (phase) difference between the back EMF and the AC supply.

• I understand. Thank you. So, is there a relationship in terms of phase difference between AC Current and back EMF? Does Lenz's Law have any significance here? Dec 12, 2022 at 21:18
• @Zelreedy ideally the back EMF and AC current should be in phase for maximum efficiency. Only the current that is in phase with the back EMF produces torque. But this is not the only possible way to run a motor. The motor can run with the current and back EMF somewhat out of phase. Dec 12, 2022 at 22:23
• @mkeith 915 Can you explain the theory behind this? Also how can we make sure that the AC current is in phase wih the EMF, since it seems that the EMF has no relation with the current, but is more about the magnetic flux's interaction with the stator. I'm a bit lost about the concept. Dec 12, 2022 at 23:35
• @Zelreedy it is a very big topic. You can search on this term: "Field-oriented control" or "FOC." In the synchronous machine, the current and voltage are both synchronous to the back EMF. Maybe this video will help. youtube.com/watch?v=cdiZUszYLiA Dec 13, 2022 at 5:32
• @mkeith Thank you for this link. Just another question on something I remembered now. In the university, we work on drawing the phasor diagram for the machine, and the three parameters are never in phase with each other. So which one is correct? Dec 13, 2022 at 9:21