A diagram sometime helps ...
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In magnetics, as in electricity, one can ask whether it's the current through a resistor that causes a voltage drop across it, or if it's an applied voltage that causes the current.Basically I'm wondering if either the DC current is very small due to very small offsets or whether most transformers are just so well below saturation. Or I have something fundamentally messed up in my understanding...
Magnetizing current is directly related to the flux, because it's the current that creates the H.
The core, through permeability, defines B. Permeability changes with H of course.
Which goes back to my question...
In general we have one of:
- Small DC offset voltage, so small DC current
- Significant DC offset voltage, fairly high resistances
- Transformers are generally well below saturation so even a moderate DC current doesn't lead to saturation
- I'm missing something.
[That was some serious Latex abuse]
As I said in another post:So, uhh, I think that's about it.
Magnetizing current is directly related to the flux, because it's the current that creates the H.
The core, through permeability, defines B. Permeability changes with H of course.
So, the magnetizing current is not directly proportional to flux; μ is involved. That's why the magnetizing current in the first scope image shows the flux (blue trace) being sinusoidal, but the magnetizing current (orange) is not; it is non-linearly related to the flux.\(H = \frac{I_{enc}}{l}\)
Why would there be huge DC currents? As I've explained, only a few special loads such as hair dryers draw DC anyway, and it's isolated from the grid at large by the distribution transformer at homes. These half-wave loads are usually only active a small fraction of the time, and constitute only a small fraction of total loads.So now that we have concluded transformers are in fact near saturation and it is easy to shift the curve even further into saturation, why doesn't it ruin everything? Why aren't the grid voltages all distorted and why aren't there huge currents (AC and DC), since in saturation μ is reduced and the magnetizing inductance appears smaller which is of course a shunt.
I didn't really expect to be able to measure it, but I thought I'd give it a try anyway.I suspect you can't measure the DC offset from your neighbour because you have very little common impedance between your homes. If your hair dryer is taking that 1 A DC from the transformer you might have 100 mlliohm resistance, giving you that 100 mV offset.
The resistance of AWG 14 is about 8 milliohms per meter from the table I looked at and that's what my house has at least.
Your neighbour's house will have its own lines from the transformer, so you might share only 10 milliohms from the transformer itself and a short length of wire, giving you a lot less offset in your house.
t_n_k's example is not applicable to typical actual transformers. They are already somewhat in saturation when excited with rated voltage, so any DC will push then further into saturation in one direction.t_n_k, your example does cut through to the issue. I have not convinced myself yet that the offsets are low enough and the resistances high enough in general to prevent high DC currents and saturation. This then makes me doubt everything else.
Is half an Ohm a reasonable value for a transformer DC winding resistance? If it is that high then it things make more sense.
It's funny, I've done those calculations too but you never get an idea of how reasonable the numbers are until you get more experience.
The procedure looks good to me, I didn't re-calculate to check though.
Your point is well made Electrician. Indeed the expectation is that mains transformers always operate into the saturation region - for sound economic reasons. Imagine the cost of transformers which only operated in the quasi-linear region of their cores' B-H characteristic.t_n_k's example is not applicable to typical actual transformers. They are already somewhat in saturation when excited with rated voltage, so any DC will push then further into saturation in one direction.
It's interesting to note that the peak in magnetizing current occurs as a particular half sine of applied voltage is coming to an end. Since the flux is proportional to the integral of the applied voltage, those volt-seconds max out as the applied voltage is about to change polarity. You would think that the increased IR drop occurring at that time might be visible on the waveform, but I can't see it.To take up Ghars' point on AC waveform distortion - it's worth emphasising the point that large mains transformers do operate into the saturation region and there is very little observable sinusoidal waveform distortion. My expectation is that the applied voltage and resulting core flux are mutually related and therefore sinusoidal for a sinusoidal voltage system. It's the excitation mmf (and hence primary exciting current) that shows increasing distortion with increasing saturation. However, I presume the series impedance drop on the primary side [with a situation of high primary harmonic current distortion] is what contributes to distortion of the transformed "sinusoidal" waveform. Perhaps this is what we observe in cheaper low power mains transformers which may be designed to operate even further into the saturation region than a well engineered high capacity mains transformer.
Sorry I meant AC, not sure why I said "AC and DC".Why would there be huge DC currents? As I've explained, only a few special loads such as hair dryers draw DC anyway, and it's isolated from the grid at large by the distribution transformer at homes. These half-wave loads are usually only active a small fraction of the time, and constitute only a small fraction of total loads.
I mentioned in post #33 that the transformer loss (almost all core loss; eddy current and hysteresis loss) was 5 watts.Let's try it...
Here's the schematic
I searched my transformers and found one with a very high quality, low loss, high permeability core.Adding that resistor just adds a noticeable sinusoidal current which I don't see in your measurement.