How does this iPhone app measure the power flowing through an AC appliance cord?

Question

My electric utility released an iPhone app called "DTE Insight" which (among other things) measures the amount of power flowing through an appliance's power cord by asking you to hold the cord against a specific part of the iPhone at a specific angle. I tested this app against the measurements from my Kill-a-Watt, and the app seems remarkably accurate to the point where I don't really understand how it works.

I understand that current flowing through a conductor creates a magnetic field around the conductor, and I imagine that this app is using the phone's magnetic field sensor to try to measure the magnetic field caused by the current flowing through the cable, then multiplying the calculated current by an assumed voltage of 115 or 120 or whatever in order to estimate power.

What confuses me is that household appliance cables contain two current-carrying conductors. Wouldn't the opposing magnetic fields from the two conductors interfere with and almost completely cancel out their respective fields out in the area around the cable? The app does ask whether the cord being tested is a two- or three-pronged cord, and whether the cord is round or flat. Can anybody explain to me how this might work?

Data

I did some tests using the app and my Kill-a-Watt to measure power draw of the same loads. I did five trials of each of the four loads using the app. The loads were:

1. Assorted computing equipment sharing a power strip
2. An electric fan on low
3. An electric fan on medium
4. An electric fan on high

The results are as follows:

Compute Load:

Kill-a-Watt: 632 W, 757 VA

App: 678 W, 667 W, 623 W, 662 W, 644 W

Fan on Low:

Kill-a-Watt: 56 W, 57 VA

App: 75 W, 75 W, 75 W, 75 W, 77 W

Fan on Medium:

Kill-a-Watt: 75 W, 75 VA

App: 103 W, 101 W, 98 W, 100 W, 97 W

Fan on High:

Kill-a-Watt: 97 W, 102 VA

App: 132 W, 129 W, 131 W, 128 W, 131 W

Reproducibility

If you want to try this yourself, you have to select "Tools" and then "Take a Power Scan" from the main menu of the app.

Answer 1

Not having used said app I believe it is a master of assumptions and averages.

The far field of a transmission line with two opposite current conductors is essentially zero. However the near field on anything other than a solid screen co-ax will always have a unbalanced component around it.

The maximum unbalance will be when the two current conductors are 'eclipsed' and the near field will be mostly due to the nearer conductor.

What I suggest for better trials is that you take a mains cable and carefully remove the outer covering for 12 inches or so to separate the internal wires (do this with a spare kettle cord if you like). Then run your tests with the phone placed next to just one of the live wires and see if it has repeatable results.

It is also important to remember that the magnetic field sensor in the phone should be a 3 axis device so it can determine the magnetic field 'direction' and infer the conductor placement to a degree and correct a bit.

Accuracy of 30% compared to a somewhat more predictable device I think is pretty phenomenal like you have found. Getting better will obviously be much harder given the loose test conditions required.

It does remind me of a totally passive DC ammeter that my friend had that was over 50 years old. It was merely placed against a (single) conductor (such as the alternator charging lead in a car) and would deflect its needle to indicate the local induced magnetic field proportional to the current. Orientation was important and it would not have read accurately if a return conductor was nearby, however the principal is pretty much the same.

Answer 2

I suspect that the current flowing in the cable deflects the "compass" reading. Even though the opposing current flows diminish the magnetic field strength, the magnetic field strength is non-zero in close proximity. The stronger the current flow, the stronger the deflection. Software can distinguish between the alternating (or pulsating) magnetic field and Earth's non-alternating magnetic field, each with different "headings". The relative magnetic strengths between the two help calculate the current flowing in the wire.