How to calculate stepper motor power requirement?

I just want to calculate the max power requirements of my stepper motors so I can factor that into my power supply choice. It sounds like a simple question (P = V x I), but I've found so many conflicting answers on the web that I'm not sure who to believe any more. Some people use the rated voltage (rather than the actual voltage), some multiply the current by the number of phases (and some don't), and some say the current should be some fraction of the current limit set in the driver (see this article from Geko), can any of the electrical engineers here provide a definitive answer?

Lets take a real world example with this 4 wire stepper 17HS19-2004S1

Rated Current/phase 2.0A
Rated Voltage/phase 2.8V
Recommended Voltage 12-24V

Lets say I'm using a 24V power supply, and I limit current to 1.5A in my stepper driver.

At first sight it would seem simple, the worst case is when both phases are energised, so that's 36W per phase = 72W, is that the figure I should base my power supply choice on?

Using normal constant current drivers, the total power consumed by the motor at rest is always equal to the square of the phase current times the phase resistance (this is because sin^2 + cos^2 = 1). So 1.5 x 1.5 x 1.4 W in your example. The drivers are not 100% efficient, also there may be some iron losses because of the chopper drive, so the actual power taken from 24V will be somewhat greater than this.

When the motor is moving, and especially when it is accelerating or otherwise driving a load, the power consumption will be higher because of the back emf of fhe motor. So it's hard to be precise about the power requirement.

Edited 1 time(s). Last edit at 02/19/2016 07:43AM by dc42.

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Large delta printer [miscsolutions.wordpress.com], E3D tool changer, Robotdigg SCARA printer, Crane Quad and Ormerod

Disclosure: I design Duet electronics and work on RepRapFirmware, [duet3d.com].

For my purposes when building a printer, "precise figures" are not really required, I'm only really interested in a max power usage figure (in order to understand the potential power supply requirements), and the max current per phase (in order to choose the correct wire gauge).

From your equation we have 3.15W for this motor at rest (much less than I expected), would I be safe to multiply that by about 1.5 to get an idea of max power consumption under all conditions (so let's say 5W)?

You also mention back EMF, I've been choosing my wire gauge based on the max current I expect my stepper driver to supply (so 1.5A in this example), is back EMF ever going to be significant enough to need factoring in?

The motor back emf is one reason why you need a supply voltage to the drivers much higher than the nominal voltage of the motors. It does not affect the gauge of wire you need.

Bear in mind that if you decide to increase the motor current above 1.5A, then the increase in current from the 24V supply will be much more because the 24V current goes as the square of the motor current. So I think your factor of 1.5 is rather low. Also, I suggest you allow a higher factor for the X and Y motors (or all three motors if it is a delta) because of the back emf during travel moves.

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Large delta printer [miscsolutions.wordpress.com], E3D tool changer, Robotdigg SCARA printer, Crane Quad and Ormerod

Disclosure: I design Duet electronics and work on RepRapFirmware, [duet3d.com].

Alright, so back EMF is only affecting voltage, not current.

Agreed that for this estimate I probably would use the max motor rated current of 2A, rather than my expected current limit of 1.5A, so that gives 5.6W when stationary, what would be a reasonable multiplication factor to account for movement and back EMF? I'm not looking for an exact figure any more, when I first asked the question I expected to find a simple equation to say that a stepper will use x watts (peak) at a set voltage and current, clearly it's not as simple as that, so I'll be happy with just a ballpark figure with a reasonable safety margin built in.

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plankton
Alright, so back EMF is only affecting voltage, not current.

It doesn't affect the motor current (unless he back emf is too higher for the supply voltage to overcome), but it does affect the power drawn by the motor, and therefore the current drawn from the 24V supply.

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plankton
Agreed that for this estimate I probably would use the max motor rated current of 2A, rather than my expected current limit of 1.5A, so that gives 5.6W when stationary, what would be a reasonable multiplication factor to account for movement and back EMF? I'm not looking for an exact figure any more, when I first asked the question I expected to find a simple equation to say that a stepper will use x watts (peak) at a set voltage and current, clearly it's not as simple as that, so I'll be happy with just a ballpark figure with a reasonable safety margin built in.

I'm guessing here, but if you allow 10W per motor, I think that will be more than enough in practice.

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Large delta printer [miscsolutions.wordpress.com], E3D tool changer, Robotdigg SCARA printer, Crane Quad and Ormerod

Disclosure: I design Duet electronics and work on RepRapFirmware, [duet3d.com].