High 3rd harmonic on the neutral

It’s over twenty years since I did three phase theory, so feel free to add a few sketches and notes to jog my memory, as I’m not getting a picture in my head of where the neutral current is supposed to cancel in this installation.

If it helps any, and all the sine wave stuff isn't exactly obvious, try thinking of a simpler situation as a means of introduction...


Say we had a 3-wire d.c. system - +12V - 0V - 12V say with two sets of 12V loads - some connected between +12V and 0V and the rest connected between 0V and -12V.  Say the first group of loads were drawing a total of 10A and the second group 8A. Hopefully it should be 'obvious' that the +12V supply line needs to deliver 10A, the -12V line 8A. If you then think about the point where the -v side of the first group of loads and the +ve side of the second group of loads meet (at the load end of the 0V supply wire) then we have 10A 'in' and 8A 'out' to/from the loads - and as we know that the total of currents into and out of a point must sum to zero, you should be able to deduce that the 0V wire must carry 2A back to the supply. (Probably helps to draw a diagram). So that's a simple example of currents cancelling in a common conductor. If both sets of loads drew 10A then you'd have 0A flowing in the 0V conductor.


I struggled with sine waves cancelling until it eventually dawned on me that the result of adding two pure sine waves of the same frequency together was always a pure sign wave - it doesn't matter if they're out of sync with each other or of different amplitudes you still get a pure sign wave. Nothing I've read seemed to clearly state that, but without that observation much of the rest of the explanations didn't make much sense to me. Shifting a sine wave by 180 degrees is the same as negating it - so adding two sine waves 180 degrees out of phase with each other is the same as subjecting one from the other. So subtracting one pure sine wave from another (of the same frequency) also always produces anther pure sign wave. Those with mathematical training probably find such things obvious, but it took me a long while to figure it out.


Add two sine waves together - one offset by 120 degrees (L2) and the other offset by 240 degree (L3) and you end up with a sine wave offset by 180 degrees - i.e. the exact opposite of one with a 0 degree offset (L1) so adding in L1 brings to total to a pure zero-amplitude sine wave (or nothing at all, if you prefer).


   - Andy.

It’s over twenty years since I did three phase theory, so feel free to add a few sketches and notes to jog my memory, as I’m not getting a picture in my head of where the neutral current is supposed to cancel in this installation.

If it helps any, and all the sine wave stuff isn't exactly obvious, try thinking of a simpler situation as a means of introduction...


Say we had a 3-wire d.c. system - +12V - 0V - 12V say with two sets of 12V loads - some connected between +12V and 0V and the rest connected between 0V and -12V.  Say the first group of loads were drawing a total of 10A and the second group 8A. Hopefully it should be 'obvious' that the +12V supply line needs to deliver 10A, the -12V line 8A. If you then think about the point where the -v side of the first group of loads and the +ve side of the second group of loads meet (at the load end of the 0V supply wire) then we have 10A 'in' and 8A 'out' to/from the loads - and as we know that the total of currents into and out of a point must sum to zero, you should be able to deduce that the 0V wire must carry 2A back to the supply. (Probably helps to draw a diagram). So that's a simple example of currents cancelling in a common conductor. If both sets of loads drew 10A then you'd have 0A flowing in the 0V conductor.


I struggled with sine waves cancelling until it eventually dawned on me that the result of adding two pure sine waves of the same frequency together was always a pure sign wave - it doesn't matter if they're out of sync with each other or of different amplitudes you still get a pure sign wave. Nothing I've read seemed to clearly state that, but without that observation much of the rest of the explanations didn't make much sense to me. Shifting a sine wave by 180 degrees is the same as negating it - so adding two sine waves 180 degrees out of phase with each other is the same as subjecting one from the other. So subtracting one pure sine wave from another (of the same frequency) also always produces anther pure sign wave. Those with mathematical training probably find such things obvious, but it took me a long while to figure it out.


Add two sine waves together - one offset by 120 degrees (L2) and the other offset by 240 degree (L3) and you end up with a sine wave offset by 180 degrees - i.e. the exact opposite of one with a 0 degree offset (L1) so adding in L1 brings to total to a pure zero-amplitude sine wave (or nothing at all, if you prefer).


   - Andy.