Can or can't negative sequence current, 5th harmonic, flow in neutral line ?

Question

please prove me that

Answer 1

The assumptions here are important.

By mentioning sequences, it is understood that you are dealing with a 3-phase circuit.  Thus, all the deprecated cases of single-phase and two-phase conditions don't matter.

The other significant implicit assumption you've made is that 5th harmonic currents have the characteristics of negative sequence current.

Balanced 5th harmonic currents do behave the same as negative sequence fundamental frequency currents.  In a balanced 3-phase circuit, neither positive nor negative sequence current components will flow in the neutral.  This is key to the definition of sequence components.  Positive and negative sequence components are, by definition, balanced in magnitude and phase, but have opposite rotation.  Thus, they sum to zero at the neutral point.

Back to the 5th harmonics in the neutral...

Phase currents of any frequency, including the fundamental and harmonics, can be unbalanced.  And, they can be represented with sequence components.  Obviously, if the 5th harmonic phase currents contain a zero sequence component, that 5th harmonic zero sequence component will appear in the neutral, but not the positive or negative 5th components.

Similarly, if triplen harmonics (3rd, 6th, 9th, etc) are unbalanced, they will contain positive and/or negative sequence components that will not be blocked by the typical zero sequence 'traps' such as the delta-connected transformer.

Answer 2

If you use a live and a neutral and you complete the circuit with an inverter then the current will flow through the live and neutral (return) as it is a completed circuit. If you generate harmonics on your live or neutral it will be in the return line or the live. If you want to prove it put a power analyser or a scope on the neutral wire to earth.