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### Non Linear Load

09/15/2012 1:49 AM

Why the non linear load producing more neutral current.

can anybody tell the reason and formula to calculate

that neutral current?

Pathfinder Tags: Non linear load
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#1

### Re: Non linear load

09/15/2012 9:01 AM

All of your non-linear loads will load one phase and return with the neutral current. So how evenly distributed these loads will be across the three phases will not be known. So current sharing will not be known. Additionally each non-linear device will start and stop drawing current at different points of the sine wave depending on the circuit topology and the changing load provided by the supply. So even if one lucks into each phase drawing the same RMS current level, the current waveform is likely not identical in shape so that current sharing will not exactly match. Remember a linear load will have only a sine wave form. In theory one could apply a statistical approach to all of these different factors to get an anticipated neutral current but this will just be a formal guess.

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#2

### Re: Non Linear Load

09/15/2012 1:57 PM

In=√((Ia²+Ib²+Ic²)-((Ia*Ib)+(Ia*Ic)+(Ib*Ic)))

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#3

### Re: Non Linear Load

09/16/2012 5:40 AM

The neutral current is the sum of the three phase currents. Three pure sine waves 120 degrees separated in phase add up to zero. If the loads are balanced and linear, then the current return in the neutral from each phase adds up to zero. If your loads are nonlinear, for example fluorescent lighting, then the current waveform will not be sinusoidal and the three phase currents to not cancel.

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#4

### Re: Non Linear Load

09/17/2012 9:32 AM

Not all non-linear loads would cause more neutral current. Only triplen harmonics generating non-linear loads (typically, all single phase power electronic loads) cause high neutral current.

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#5

### Re: Non Linear Load

09/17/2012 7:18 PM
1. A non-linear load energised from a sinusoidal voltage source will draw a non-sinusoidal current.
2. According to Fourier's theorem, any non-sinusoid regularly repeating waveshape can be replaced by a component at the fundamental frequency plus components at integral multiples [1, 2,3, 4, 5,... times fundamental frequency]. The arithmetic sum of the components at any time gives the non-sinusoid total (or a good approximation to it, since an infinite number of components is not practical to calculate).
3. The diagram below [courtesy of M.G. Say's book "Performance and Design of Alternating Current Machines"] shows how fundamental and third harmonic can be summed to get a non-sinusoidal "peaky" or "flat peaked" waveform. The example a) is applicable to the magnetising current of transformers, which usually has a strong third harmonic (3 times the fundamental frequency), say 150Hz for 50 Hz power system.
4. The third harmonic is interesting, since it is easy to see it can cause a neutral current. If you have 3 phases with equal currents containing fundamental and third harmonic then you know, for a conventional system, that the fundamental currents in successive phases are 120 degrees or 1/3 period displaced in time.
5. However, if each third [3rd] harmonic has the same time displacement from its fundamental in its phase, then the harmonic in the next phase is displaced by 3 times 1/3 or 1 cycle from the first.
6. So from 5/, all three 3rd harmonic phase currents are displaced whole cycles from each other.
7. When the 3rd harmonic currents are combined in the neutral, they are all whole cycles [of 3 x fundamental frequency] apart - so they always add to each other, rather than cancelling part of the time. So if the 3rd harmonic current in one phase is I3 , then the neutral current is 3 x I3.
8. So harmonics have the bad effect of often causing neutral current, even if the phases are symmetrical. Note some harmonic currents do cancel in the neutral(and others will not, like the third), but since 3rd harmonic is often the strongest, neutral current is common when harmonics are present.
9. Note: the advantage of a balanced 3 phase sinusoidal system is that the neutral currents balance out to zero all the time.

There is not any easy formula for neutral current, because the harmonic amplitudes and their phase displacements depend on the non-linear function of the load resistance. If you add the complication of unequal phase currents or different non-linearity in the phases the work is greater. An analytical function is possible for some loads, but the real world refuses to be easy. Fortunately, modern numerical computing methods make it possible to deal with practical cases when the practical cost in the system makes the calculation effort worthwhile.

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#6
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### Re: Non Linear Load

09/17/2012 9:37 PM

Nicely summarised 67. GA.

Just one nit-pick... non-linear function of the load resistance..... if it's non linear it isn't a resistance.

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### Re: Non Linear Load

09/18/2012 7:34 AM

If it is non-linear, it is not a fixed resistance. But consider a 24 volt tungsten filament lamp - it is certainly a resistance and has negligible capacitance and inductance (it makes a good resistance load even at 50 MHz).

I measured a 24V 1.2 watt panel lamp with DC, result was...

Volts Ohms milliamps

3.02 195 15.5

6.02 266 22.6

12.04 356 33.8

24.01 462 52

That is not linear. But I expect you could approximate the resistance with a function which made current increase about 50% for each doubling of voltage.

The modern fixed resistor, with its value changing little with time or temperature or voltage, is the gift of 200 years electrical development.

Voltage dependent resistors - VDR - are well used for overvoltage protection.

Electric arcs are not linear, but they are resistive - By arranging a magnet coil fed with arc current to deflect the arc and make it longer, they can have a "negative resistance" characteristic where increasing voltage reduces current - they were used for "Poulsen Arc" continuous sine wave radio transmitters of about 100 years ago, as much as 1000 kW.

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