Joe, which ones are you referring to? And which one is the oddball? I see three jpg's named "fun", and you talk about laying all three phases on top of each other, but I'm not sure I understand.
No problem.
IMO, the second one is very likely an 8-cycle fault on a remote circuit, which is pretty typical for high speed relay clearing on a power system. So you're just catching the voltage dip due to a remote fault. This kind of trace is extremely common, and happens every time you get a ground fault on a power system line (eg, tree branch gets into the line, etc.). I assume this was captured from an automatic disturbance recording device, and you weren't incredibly lucky to happen to capture an electrical fault when your scope was connected. 
First, you are correct. I am not attaching my hand held meter or scope to the mains. I use a specialized bit of equipment for this. The cost is a bit on the high side but it's paid for itself. Not to mention that I trust it in this sort of environment.
It's common to have small transformers located inside a building to convert the various voltages. In this case there is a small step down transformer. What had happened over time is loads were continued to be added without doing a calculation on the size. Eventually the transformer gave up. They wouldn't always run enough of a load to cause a problem so it was intermittent.
I assume the first one was due to some sort of inverter failure (all that sawtooth yumminess...), but without knowing the system configuration and what you're measuring it's tough to guess. And IMO, since those inverter systems are generally proprietary designs, it's tough to figure out exactly what's going on.
This is what I consider the odd ball. If you look at the wave and visually plot the three phases in your head or on paper, you can see these triangle waves are the rising edges of the three phases. You can also see that the frequency was off when the event happened. I am not sure what this bit of equipment was but suspect it may be some sort of a load balancing system.
The last one needs some more background on what the system configuration was and what you're measuring. I agree it's very strange. If it was connected to the utility, it seems strange to have so much distortion. Lots of harmonics like that makes me think there's some iron-core transformer overvoltage causing saturation, but that would more likely cause flat-topped voltage waveform. Was it an ungrounded system? Were there inverters or other industrial equipment connected? Was this running isolated from the utility, served by a diesel or something?
You will see people trying to tout a one technology solution for all AC line disturbances. Don't ask me why. In this case we see what happens when a large resonate system is presented with a stepped load on it's output.
By the way, never underestimate the likelihood that what you're measuring may not be what's actually on the system As you know, there's always the possibility that the measurement system has a problem. Also, I've found that the more strange an event is, the more likely it's caused by multiple issues at the same time, not just one. Which makes it even tougher to diagnose.
And I assume these aren't individual traces of three phases of a 3 phase system?
Normally I can trace the problems down to the root cause easy enough if I can capture it. In my case I have not seen too many multiple issue problems. I was told about how a device was having problems at a site and they could not figure out the cause. It was very time dependent but there were no large loads being switched at these times. Eventually the discovered the site had these old time clocks that you would find in schools. These clocks were synchronized by a signal that was superimposed on the mains... I can't remember what the device was but found the story amusing.
If I have to get involved with the mains, it's because something is causing a problem. I will take my measurements at the location where the problem is. I have not ran into a problem with the test equipment not working or causing errors in my data. That would be a major problem.
To give you some sort of idea, the product I use would set you back around $10K. Unlike what you see a lot posted here about handheld DMMs need to be safe and don't need to survive things like surge, in this case we not only want the equipment to be safe and survive, we want to capture the event and we want to do this over and over.... When I was looking for a new unit, I had the major companies bring in their products for a demonstration. I had them leave them with me and then with their permission, I exposed them to the real IEC standards.
If you watch any of the videos where I show damaging cheap handheld meters and people go all crazy about how these transients will never happen in real life and they are so overkill not even a Fluke will survive....(trying to add some drama). Well, as I have said many times, that's a toy in comparison to an actual combo generator, specifically designed to test a DMMs electrical robustness. The test I was running on these demo units were the real deal.
Once I knew the products could survive, were safe and that I could capture the events I was looking for, we procured one.
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