The 3rd harmonic currents are not in phase with each other, they are just at 150 Hz but still 120 degrees apart relative to their period now being 6.67 ms instead of 20 ms - i.e. the zero crossings on each phase now occur every 3.33 ms instead of every 10 ms and are spread apart as a normal 3-phase set of waveforms.

But that does not mean that the A phase @ 150 Hz is in phase with the B phase and in phase with the C phase.

Remember what a delta is doing - we generally refer to it as a zero sequence trap where only zero sequence currents flow. This is because when there is zero sequence, that means the 3 individual zero sequence phase components are vectorially in phase.

Hence when each phase of the TF winding is connected into a delta, the zero sequence currents in each phase are in phase and hence the zero sequence current happily flows around the delta.

However the Positive Sequence A phase Component is not equal to the angle of the Positive Sequence B phase component is not equal to the angle of the Positive Sequence C phase component … by definition – they are 120 degrees apart relative to a 6.67 ms period

Similarly the Negative Sequence Components are not at the same angle … by definition

Since the Delta connection still requires Kirchoff's Law to be satisfied at the connection node between A and B windings and between B and C and between C and A, also at the Sequence Component level, we see Positive and Negative Sequence cannot flow in a delta - as by definition the Positive Sequence Components are 120 degrees apart and the Negative Sequence components are also 120 degrees apart

If we have balanced 3rd harmonic, that is also pure Positive Sequence, just as balanced 50 Hz is pure positive sequence.

The thing is it is hard to imagine a fault that occurs on a balanced system that suddenly generates unbalanced 3rd harmonics - it is more likely to be a 50 Hz fault. Consequently we don't see 3rd harmonics as an unbalanced condition.

Since 3rd harmonics is therefore pure Positive Sequence, they will not flow in a delta winding.

I'm far more simple in my thinking on this as abstract maths of components and adding vectors can get very confusing

- at pure 50 Hz, you can have a 100% positive sequence set of 3-phase waveforms.

- at pure 150 Hz i.e. the 3rd harmonic, you can have a 100% positive sequence set of 3-phase waveforms.

When we mix the waveforms as combined 50 Hz and 150 Hz, we can consider them as basic Superposition theory of two different voltage sources, one 50 Hz and one 150 Hz. So applying those two voltages sources in parallel to the same balanced load will result in the 50 Hz voltage source as 100 % Positive Sequence and the 150 Hz voltage source also as 100% Positive Sequence

So fundamental theory would suggest that if you are generating only Positive Sequence into a Balanced load, Negative and Zero Sequence don't "magically" pop up from nowhere - you need a source of Negative and Zero Sequence voltage to drive Negative and Zero Sequence currents

So harmonics do not necessarily imply Negative or Zero Sequence.

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