# Speed Current Relationship in İnduction Motors

It is said that speed of an induction motor depends on its frequency and torque depends on current. But I will explain what i cant understand here.

Let’s think an induction motor runs with constant load and speed. When I increase its current (by varying voltage) but keeping the source frequency constant (by vfd) what happens ?

For me, when i increase current it will cause torque to increase , when torque increase and motor will start to accelerate aftet it gets high speed it will find another point source and load torque trades off each other. In this way I don’t change frequency but motor gets higher speed by increasing current.

Is this assumption correct ? Or do i miss something ?

• When they say that speed depends on voltage and torque depends on current, what they mean is that the speed at zero torque is directly proportional to voltage, and the torque at zero speed is directly proportional to current. If torque and speed are both nonzero, the relationship is a little more complicated, as I understand it. And of course if you vary frequency as well you have some additional complications. – Hearth Apr 27 '19 at 15:07
• Where does this "it is said" come from? Who says it? Do they have any authority in the field? Do you have links? – TimWescott Apr 27 '19 at 15:35

You miss something.

The synchronous speed depends on frequency, this is the 'zero torque output' speed. An induction motor typically runs at a little below synchronous speed.

The amount it runs slow is called the 'slip'.

For small values of slip, the current it draws is proportional to the slip, and to the voltage. This means the torque, which depends on current, is proportional to slip at constant voltage.

If a motor was running at some small value of slip (say 3%), and you increased the voltage while keeping the load on the motor constant, then the slip would reduce a little, perhaps to 2.5%. This means the speed would increase, but not by much. If the synchronous speed was (say) 1800rpm, it would increase from 1746 rpm to 1755 rpm.

It is said that speed of an induction motor depends on its frequency and torque depends on current.

Induction motors are mechanically simple, but theoretically complicated beasts. I think the non-attributed "them" that you are citing are oversimplifying.

Let’s think an induction motor runs with constant load and speed. When I increase its current (by varying voltage) but keeping the source frequency constant (by vfd) what happens ?

Then you start operating it outside of the parameters of whatever oversimplification is being made by your non-attributed "them", and "they" are no longer correct.

Like most motors, induction motors generate torque because a magnetic field in the rotor works against a magnetic field in the stator. What makes an induction motor complicated is that it's rotor field is generated by a winding whose current is induced (hence "induction motor") by the magnetic field of the stator. This current varies by the amount of slip (look it up) and the strength of the magnetic field generated by the stator. The relationship between these is complicated enough that it can take more than one book chapter to fully describe -- and it's been a while since I've studied the subject, so I'm going to shamelessly gloss over any details.

I do know that variable frequency drives are designed to more or less hold the motors at constant slip. I say "more or less", because I suspect that there are all sorts of trade-offs between slip and efficiency, and between the expense of the VFD and the difficulty of maintaining an intended slip.

Part of this is that a VFD doesn't just control frequency -- it controls the voltage to the motor. It's constantly juggling both to get that constant slip and maximum efficiency at the desired output frequency.

So here's what happens in your scenario:

Assume that your VFD is (A) capable of driving the motor at maximum efficiency, and (B) will allow you to fiddle with its settings. These are both pie-in-the-sky, because (A) humans built the thing and we aren't that good (although I wouldn't be surprised at a VFD that can come within a percentage point or two of that goal, and (B) the humans who built the thing don't trust the humans that'll use the thing not to screw things up. But I digress.

You set the motor up to run at maximum efficiency at some speed. This is happening because you told the VFD what you wanted, and it's got multiple control loops that are insuring just that. You then tell your VFD "OK, lock on to the frequency you're going, but increase the motor voltage".

When that happens, the stator current and magnetic field increases. This increases the current in the rotor, so the motor speeds up a bit. I say "a bit" because a typical induction motor that's perking along happily probably has a slip of around 3-5%. The slip goes down, but it won't go below 0%, so the increase in speed will be slight. I can't tell you the details, because I'm not a motor expert -- but remember that the VFD was doing a good job of keeping the motor at maximum efficiency.

At best, the motor efficiency will stay close to what it was before. Energy conservation laws demand that the real power to the motor will stay constant. This, in turn, demands that in-phase component of the motor current will go down. So you need to go back and check with your un-attributed "them" to see what simplifications they were making.

It is said that speed of an induction motor depends on its frequency and torque depends on current.

Torque does not depend on current, current depends on torque. The motor has a certain torque capability that depends on motor design and the application of a suitable voltage and frequency. A certain amount of current will flow even when nothing is connected to the output shaft. That is magnetizing current and current due to motor losses.

When I increase its current (by varying voltage) but keeping the source frequency constant (by vfd) what happens?

If you increase the voltage, likely the slip will decrease and the speed will increase slightly. For well designed and properly adjusted VFD, the voltage increase will likely increase the voltage above the optimum value causing the motor magnetizing current to increase, motor losses to increase and efficiency to decrease.

For me, when i increase current it will cause torque to increase...

No. You don't, or should not be increasing current. Only an increase in load torque should increase current. If you have a VFD, the VFD increases frequency and voltage together when you increase the speed command. To the extent that the load requires more torque to operate at a higher speed, the motor will draw more current from the VFD.