# Motors: Active, Reactive, and Apparent Power

by on November 10, 2014

There are a bunch of confusing powers involved when we look at motors, especially with DC brushless motors. When your boss comes and asks you to measure the electrical power that your motor is using, it is often not straight forward. Typically the easiest way to get the current used by a motor is to measure the current draw going into the amplifier. If you have a brushed motor you can put a current clamp over the wire going to the motor, measure the voltage and you can get power. However with a DC brushless motor you can not just put an amp clamp on it. With a DC brushless motor you need to worry about the varying trapezoidal or sinusoidal voltages that are spread over multiple phases and the corresponding phase currents.

So in a DC brushless motor if you need current and you are using a digital drive you can often query the current with a software command. For example with an Elmo motor controller you can send a serial command of ID (for reactive current) or IQ (for active current). Now if you compare those numbers to the current entering your amplifier to spin the motors they will not line up at all. Whats up with that? Further you can not easily get the corresponding sinusoidal voltages corresponding with those currents in order to get motor power.

There are generally 3 different types of current/power that we care about when we discuss motors.

### Active

Active current which is also called “real” or “true” current is the current in the active phase. When we discuss Active power the units is in watts.
The active magnetic field component is perpendicular to the magnetic direction of the rotor and produces the mechanical torque for the motor operation

Following an analogy I heard in college (way back when) and in the image above. The active power corresponds to the actual beverage in a pint of beer (or soda), the part that you want and can do something.

### Reactive

Reactive current is the magnetic energy of the fields. It is 90degrees out of phase from the active current. Pretty much if you picture a sinusoidal wave as the wave increase and the field is growing the reactive current grows. As the wave decreases the reactive current decreases. This has the effect that the reactive current keeps surging up and down with the sin wave. This reactive current is important and needed to sustain the magnetic fields to spin the motor. You typically want the reactive current to be close to 0. When we talk about power it is still power=volts x amps, however the reactive power has the units var.

The reactive power is equivalent to the beer head. The head is important and we need/want it. However it does not provide the real work that we want from the drink.

### Apparent

Apparent current is the combination of the Active and Reactive current elements.
$I=\sqrt{I_{Active}^{2} + I_{Reactive}^{2}}$
Apparent power has the units of voltampers or written as VA. This is represented in the image above from the combination of the active and reactive parts of the drink.

Just like with a glass of beer you need a cup large enough to hold the liquid and the head, when you choose your conductors they need to be sized based from the apparent current.

Putting that all together active power and reactive power function independent of each other and can not be converted into the other. The active power produces our physical result (motor torque and heat) and the reactive power only represents power that oscillates back and forth as the magnetic field builds and switches direction.

So after all of that how would I get the power used by the motor?

### DC Brushed

This is the easy case you can measure the input voltage and measure the current using an amp clamp on the main power wire to the motor. The Power = Volts X Amps and you have your solution.

### DC Brushless

The most accurate way is to measure the input voltage and the current going into the amplifier (motor drive). If that is not possible and you need to use the reported current from the drives then you need to approximate the power. The way I do this is based on things I have experienced, but I have not actually seen documented anywhere else. For voltage I compute the RMS value of the voltage (VRMS=VPeak X 0.707). And then for current if I want to know current draw of the motor I will use the apparent current from above. If I want to know the current that the motor has for producing torque I will use the active current value. I will also average together the reported current values over several motor rotations when possible for the above calculations. The results are not perfect, but I think they are close.

As reader chaimav mentioned below you can also get a meter to measure your 3 types of power. The Fluke 43b looks like a nice tool that can get you motor information. It is designed for really large really large currents and voltages which puts most robot motors on the very low-end of its performance spectrum.

Note: Fluke released the Fluke 345 Power Quality Clamp Meter which can act as a replacement for the Fluke 43b in cases with low switching frequencies (as pointed out by Rob below). Possibly not of use but the video clip is informative about this class of instrument.

Do you have a better way to get motor power? Please leave it in the comments below!

I know I am switching from current to power to beer a lot. I tried to pick the better one for each example. Sorry if I confuse or annoy you with my switching.

Main image from Wikipedia and modified based on an example from old college notes.

Much of the material above is based from my old college text-book titled “Electrical Machines, Drives, and Power Systems” from Theodore Wildi.

Nevers saw the beer analogy before, but I believe I had the same textbook.

As for measuring current, we had one of these in our power lab at schoolen-us.fluke.com/products/power-quality-tools/fluke-43b-power-quality.html
I even convinced the lab at work to buy one.

Reactive power is very important to remember because while it doesn’t consume energy – it still needs to be accounted in wire sizing. Remember losses are I^2R so even reactive current will heat up your wiring.

David Kohanbash says:

The other analogy the professor mentioned but is less interesting is to a bag of chips. It has the chips, the air, and the entire bag.

I am going to add the meter to the post above. I have never used one but it does seem really nice!

Rob says:

Are you sure the above will work for BLDC motors? The BLDC motors I use have switching frequencies in the 8kHz-32kHz range. The ratings on the above Fluke meters are in the 40-70Hz range you would expect for a device intended to work with mains power.

Rob says:

The 43B says 10.0 to 15.0 kHz in the Frequency Range under the V/A/Hz display heading — but, under Power display, H2 frequency fundamental 40.0 to 70.0 Hz. I’m not sure what to make of that.

Have you used either of these instruments to measure the 3-phase power between a BLDC controller and a motor? Considering motors and controllers typically used by R/C cars and planes?

I am not completely sure. I think for measuring volts/current it has the wider frequency band, but not for the actual power measurements/calculations.

I would also generally measure the input to the controller and not the output. Measuring the input lets you get a better picture of the system and not require you to deal with the alternating phases and trying to estimate the voltage/current at a given point. It also lets you avoid the switching issue.

If you are working on “small” motors I would not use this tool. This tool is more for large motors in industrial applications.

Rob says:

Thanks for the comments and suggestions.

I’m working a project with a student of mine — the express point of it is to try to isolate and understand the efficiency of the controller. He has developed an instrument to measure instantaneous power, but that is getting us apparent power, and we need to figure out how to get back to active power.

A handheld and affordable instrument that did the job would be great, but I don’t think such a thing exists.

Yes unfortunately that is tough to do and I do not know of an instrument that will do that for you? You can try calling a motor controller vendor and ask how they get their efficiency specs.

You can also build your own niche instrument… I have wanted one on many occasions.