Screenshots and analysis by Michael Gordon.
"Inrush" is a phenomenon with iron core transformers and induction motors when initially energized or turned on.
Ordinarily, an inductor opposes changes in current, and since alternating current is constantly changing, the inductor will normally also oppose the alternating current.
However, iron cored transformers and induction motors sometimes allow a huge current flow to exist for the first few cycles of alternating current. Here I explore this phenomenon with nothing connected to the secondary of a transformer.
Short version:
Over 40 amps briefly flows into this particular transformer in the first full half cycle (from positive to negative or negative to positive) of operation. This current magnetizes the core so strongly that the next dozen or so cycles gradually demagnetizes the transformer core and allows normal operation.
Test procedure
Oscilloscope: Keysight DSOX1202G. Transformer: Salvaged from APC2200 UPS; three taps on the primary, normal secondary voltage 14.6 volts. Probably rated 1100 KVA (two of them make the 2200 KVA rating of the UPS). Current sense resistor: 1 Ohm, 10 Watt ceramic. Voltage control: Variable autotransformer and a switched powerstrip.
On the neutral side of the transformer primary (white wire) solder the 1 ohm resistor then solder other end of the resistor to the neutral side of a 2 wire power cord. The hot side of the power cord goes to the yellow wire of the transformer. The plug goes to a switching power strip. The power strip is plugged into the output of the variable autotransformer ("variac" style) and that in turn goes to household mains power.
The oscilloscope is powered from a Goal Zero Yeti 400 Lithium to ensure the scope chassis is isolated. Bad things can happen if you clip the ground lead of a scope to the hot wire of "mains".
Channel 2 will measure current. Its ground clip goes on the white wire of the transformer, the probe clips to the other side of the resistor. Thus, one amp of current will produce one volt across the resistor. Measure the volts and there's your amps. Easy peasy! Anyway, set probe sensitivity to 1X and configure the scope accordingly for proper display. Invert the polarity so that positive voltage produces positive current. To capture the initial inrush, a sensitivity of 10 volts per division works well. To capture running or idle current, 500 mv per division works well.
Channel 1 measures voltage at the primary of the transformer. Since you will be measuring 168 volt peaks, set 50 volts per division vertical sensitivity. Clip the probe to the yellow wire. Do not use the ground clip at all. You need and want only one probe ground for this. Set the probe sensitivity to 10X and configure the scope accordinly. That way you get correct display of volts on channel 1 and correct display of amps on channel 2.
Set trigger to manual and voltage level anything you like; I used 10 volts more or less as the trigger and channel 1 as the trigger source. DC coupling throughout. We will be using single sweep mode to capture the first few cycles from turn-on. Horizontal time division 10 milliseconds per division works well; you will be adjusting this to zoom in on details.
Let the tests begin!
With the variable transformer energized, and the power strip energized, and thus the transformer being tested also energized, turn down the voltage on the autotransformer. Take one or two seconds to smoothly go to zero. What this does is elminate magnetic remanence or the residual magnetism. I imagine you have magnetized a screwdriver by wiping a magnet across it. To demagnetize it you must subject it to an alternating magnetic field of gradually decreasing intensity. This is important for each test as otherwise the residual magnetism from the previous test alters the next test. So I always start each test with a de-magnetized core.
Open the power strip switch. Turn the variable autotransformer to your desired voltage. Enable Single Sweep on the oscilloscope.
Energize! Turn on the power strip. You should get a sweep. While still energized, turn down the variable auto-transformer to zero to demagnetize the core, then turn off the power strip. You are now ready to turn up the voltage on the variable autotransformer for the next test cycle.
Meanwhile, make screenshot of the oscilloscope, zoom in on features and make more screenshots as desired.
Repeat the test a number of times so you get different moments in the incoming power cycle and observe the effect.
What I found is:
Energizing the transformer at a voltage peak produces no inrush current.
Energizing the transformer near a zero crossing produces a huge peak; but curiously, the peak does not happen immediately, but starts happening a quarter cycle later when the voltage goes "over the top" and starts back down. It is when the voltage starts to reduce that the current starts to rise, and the current peaks when the voltage crosses zero. That very first surge magnetizes the core and it stays magnetized for the next 10 cycles or so, gradually reducing current spikes.
Once things settle down, the transformer requires little pulses of current, 0.6 amps per pulse, and the current spikes are aligned exactly with voltage crossover. I haven't yet figured out why this is.
Implication for inverters such as Goal Zero. Performing the experiment with a Goal Zero Yeti1000x was interesting. Somewhat unexpected results. The Goal Zero does not like current being pushed from the load when the pushing is the wrong polarity. A small push of an amp or two can be absorbed but more than that causes problems with the voltage regulator and probably snubber diodes.
A typical test. The voltage turned on nearly at the end of the first half cycle, about 30 volts left to go to zero crossing. The current does not start until the bottom of the next half-cycle when voltage goes from most negative and starts back up to most positive. The peak current is aligned with the zero crossing and is over 20 amps. The next surge one cycle later is about 7 amps, then 3 amps, then 2 amps.
Here the energizing happens near the negative peak. Again, no current starts to flow until the voltage starts going the other way. The first peak is 8 amps; which is much less than the 20 amp peak. It rapidly dwindles on successive cycles.
A lucky shot; energized at the peak. You might think this is a bad thing but as you can see, the transformer is perfectly happy to be slammed with 168 volts suddenly. No current surge! It goes immediately into the idle mode of small currents positive and negative.
A detailed view of a high inrush current surge, first cycle. For the first quarter cycle, going to maximum negative, the top of the transformer, yellow wire, is becoming negative which means it is pushing electrons to the bottom of the transformer, the white wire. This tiny magnetizing current is barely detectable because the transformer is opposing it as it builds a magnetic field. This property I think is called Lenz Law; the expanding magnetic field is simultaneously a consumer of current but also a generator of current, the generation is almost enough to oppose the applied voltage. So, no visible current flow from turn-on to voltage peak (either positive or negative).
When the voltage goes over the top (or bottom), the inductor magnetic field starts to collapse and by doing that, pushes current along the same direction and as the applied voltage decreases so does the opposition to this magnetically generated current. So, the current rises rapidly reaching maximum when voltage reaches zero. Then as the voltage goes positive pulls it along BUT the current has exhausted the stored magnetic field. Consequently, the magnetic field has finally collapsed when the voltage reaches its next peak.
Worst Case Scenario. For this test, I allowed the previous test magnetic field to remain. That is, just abruptly turn off the supply voltage somewhere mid-cycle. The magnetism that is left in the core is thus added to the magnetizing current of the first quarter cycle and the resulting current surge when the voltage changes direction is about double, or in this case, over 40 amps but clipped before revealing exactly how many amps.
40 amps on the 1 ohm sense resistor is a 40 volt drop and changes the voltage waveform slightly, but nowhere near as much as one would expect. A smaller value sense resistor would have less voltage distortion.
Idling voltage and current on an unloaded transformer. The current ought to be a sine wave, but it isn't. That is because of hysteresis in the core. It takes time for the magnetic domains to switch orientation and start to magnetize in the opposite direction; it lags voltage. The distortion of shape from a sine wave means that some "real power" is consumed as heat in the transformer but most of this current is returned to the source.
See "power factor" for more information on inductive current being out of phase with voltage
Using a Goal Zero Yeti 1000x as the supply for the next test of inrush current. Observe the glitching voltage. When the transformer forces the current, it hits the MOSFETs in the inverter but they are already on the other half-cycle and along comes 20 amps of current; where does it go? Since it doesn't produce a voltage spike it is probably being dumped in the snubber diodes of the MOSFETs or external snubber diodes just for this purpose. Obviously it also confuses the voltage regulator which rapidly oscillates at 3.8 kilohertz.