# Electrical Motors and Frequency

I was musing about electric motors after seeing one randomly on TV, and there's something I'm must be remembering incorrectly.

It's just a thought experiment, so I'm imagining some theoretical DC electric motor, with a constant RMS current/voltage feeding in, and some constant load on it causing it to spin at some constant rpm and produce some constant torque.

Since voltage x current = electrical power = motor's mechanical power, that's the cap on how much you can get out of the machine.

But I remember that the greater the difference in rotational speeds between the rotor and stator fields (slip?), the more force/torque will be exerted on the rotor.

So in the hypothetical, if the motor is doing its thing and is stable with the load, if you suddenly increased the frequency of the input voltage/current, that in my mind would result in suddenly increasing the difference in relative rotational speeds of the stator/rotor, meaning the stator would feel more force/torque on it, which would make it want to speed up and catch up to the stator field, speeding up the load.

But only frequency changed and not how much electrical energy is entering the device, so there's no way that's possible! So I MUST be wrong, I just don't see where the error in my thinking is...

What's wrong with my thinking, and what would actually happen if you increased the frequency like that?

(I'm not an electrical person by trade, so there's a limit to my knowledge of concepts/terminology.)

[EDIT: I failed to mention that by "frequency", I'm referring to how DC motors can be controlled with pulse width modulation, and those pulses go in at some frequency. Otherwise it wouldn't make sense to talk about "frequency" with direct motors]

• Just to get this straight. You've got a DC motor and are supplying it with a DC voltage and you are conceptually now varying its frequency?
– jonk
Commented May 28, 2020 at 22:29
• You're confusing a DC motor with an AC induction motor. And in no case do any laws of physics get broken. (Sorry, no time to write a complete answer to this right now.) Commented May 28, 2020 at 22:30
• I think that trying to increase the frequency would result in higher loading on the energy source. This would result in either more current being drawn or (if the source is regulating the current) a lower output voltage. In other words, the power (and energy delivered) does go up if the energy source (i.e. battery or DC regulator) allows it. Commented May 28, 2020 at 23:03
• To put it a different way, what is missing from the analysis is what is known as back EMF, without which a "motor" is not far from a short circuit. Commented May 28, 2020 at 23:13
• "the difference in relative rotational speeds of the stator/rotor" - that only applies to induction motors. DC motors don't 'slip', they are synchronous. Commented May 28, 2020 at 23:50

The type of problem you are talking about might be be explained by an induction motor.

In a dc motor increasing the no of pulses would only increase the average voltage which would then lead to motor entering a transition state till the new steady state is achieved(if achievable). If a steady state is achieved in accordance to both load and motor torque the motor might work at a new speed and hence the frequency(actual not the pwm one) of the internal ac currents and voltages might increase.

As for an induction motor when you increase the frequency there are multiple factors(load characteristics and motor characteristics at that frequency) that govern what the new steady state might be and all are in agreement with the conservation of energy. If you keep the voltage constant, the current is governed by the motor load requirement. Hence it will under normal operation, increase the current intake if load speed is increased at same torque. Well you see things start getting a little tricky here, in case you are changing parameters such that input power remains constant( and trust me that is not done by just changing the frequency) Then to increase speed the torque would have to decrease and this new steady state(if the load allows it) will have same product of torque speed as before.

It's really good to see people trying to think deeply about motors.Normally people are just interested in the applications. You should do some serious study if you like the topic, it's really indulging.

I like your thinking on this. You see something about it that bugs you so you ask a question. Those little things that bug you because they don't fit, and the curiosity to pursue them are very positive traits in engineering and science.

But I think you are mixing up a few different motor types. Induction motors are the ones that have slip. If you run an induction motor at a fixed input frequency with no load it will spin up until it ALMOST matches the electrical frequency. There will only be a tiny bit of slip. When you add a mechanical load, three things happen at the same time to balance out the physics of it:

1. the motor slows down (increasing slip)
2. the current going into the motor increases (increases input power)
3. the output torque of the motor increases (increased output power)

At some point the motor will find a new equilibrium with the changed load (assuming the load does not overwhelm the motor or something like that).

Changing the frequency is similar. In your scenario, you have a motor in steady state, and you increase the frequency by a small amount. Instantaneouslythe slip, torque and current will increase, balancing out all the terms for conservation of energy. Of course motors are less than 100 percent efficient, so the output power will always be less than the input power. Also, current * voltage is power, but you also need to consider power factor (search power factor if interested...). We are glossing over a lot of details.

But there is a bit of a catch here. For an induction motor, if you change the frequency more than a little bit, you really want to change the voltage in unison. For example, if the motor is happy running at 240V and 60Hz, it will also be happy at 120V and 30Hz or 60V and 15 Hz. As long as the Volts over Frequency (V/F) remains at that ratio of 4, the motor will be happy and will be able to supply its rated output torque.

There are a lot of exceptions and qualifications to what I said here. For the most part it doesn't apply readily to single phase induction motors. And anyway this is the sketch version. If you need to actually get into motor drives there are a lot more details to learn about.

Some cars do use three-phase induction motors. Their motor controllers are very sophisticated and highly optimized for power efficiency.

But other cars may use BLDC motors or permanent magnet synchronous motors. Everything is pretty much the same except that slip must be maintained at zero. The motor controller must maintain the rotating electrical field produced by the stator in phase with the rotor. But when the load increases, the motor drive control will either reduce the frequency and voltage to allow the motor to slow down or it will increase the voltage a bit to compensate for the increased load and maintain constant speed (if that is what it is trying to do). If the controller is maintaining constant speed, then when the load increases, the current will also increase to compensate. The voltage may increase a tiny bit but not as much as the current. And if the controller wants to speed up the motor it will ramp up the voltage and frequency.

To start with, just think about a classical DC motor, one with brushes. It is operating at some speed and the load requires some torque to operate at that speed. The mechanical power required to drive the load is speed multiplied by torque. Some voltage is applied to the motor and the motor draws some current. The power into the motor is current multiplied by voltage. Forget about whatever method is used to control the voltage. The input electrical power is equal to the mechanical output power plus the electrical and mechanical losses.

The motor speed is proportional to the voltage. The motor torque is proportional to the current. If you increase the voltage, the motor needs to go faster to satisfy the principal that speed is proportional to voltage. You can imagine that the motor has an excess voltage that drives more current into the motor giving it more torque. That torque is applied to accelerating the inertia of the motor and the load. As the speed increases, more torque may or may not be required to drive the load. That depends on the nature of the load, but all types of passive loads require the same torque or more torque to operate at higher speeds.

You don't need to think in detail about what mechanism in the motor makes it work the way it does. To learn about that, you should really start at the beginning and learn about everything involved in an order that covers each principal building on those that precede it.

All types of motors are generally similar. AC motors have the extra frequency dimension, but the underlying principals are essentially the same.

[EDIT: I failed to mention that by "frequency", I'm referring to how DC motors can be controlled with pulse width modulation, and those pulses go in at some frequency. Otherwise it wouldn't make sense to talk about "frequency" with direct motors]

PWM frequency has no direct effect on motor operation, it is effectively the same as the equivalent (average) DC voltage.

if the motor is doing its thing and is stable with the load, if you suddenly increased the frequency of the input voltage/current, that in my mind would result in suddenly increasing the difference in relative rotational speeds of the stator/rotor, meaning the stator would feel more force/torque on it, which would make it want to speed up and catch up to the stator field, speeding up the load.

A DC motor (brushed or brushless) is synchronous, the rotational speeds of the rotor and stator fields are always equal. The only thing that may change is the phase. You can increase the voltage (either with a DC source or PWM) but the motor itself decides what current it draws and how fast it spins.

How does it do this? When the rotor (BLDC) or armature (brushed motor) spins it generates a voltage which subtracts from the supply voltage. The voltage difference is impressed across the resistance of the windings, with a current flow determined by Ohm's law. This current produces torque, speeding the motor up or slowing it down depending on whether the supply voltage is higher or lower than the generator voltage. When the applied and generated voltages match (less voltage drop in the windings) the motor speed stabilizes.

But only frequency changed and not how much electrical energy is entering the device, so there's no way that's possible! So I MUST be wrong, I just don't see where the error in my thinking is...

Increasing PWM frequency does not affect the average supply voltage, so it has no effect. Increasing PWM ratio does increase voltage, so the motor will draw more current, create more torque, and speed up. Again, the motor (and its load) determine how much current is drawn, so the electrical energy entering the device is not constant.