How can I tell how many power supply's it is safe to put in series?

So at university, to provide both negative and positive supply rails for op amps, we were told to set two independent supplies to a required voltage, lets say 15V, then plug the positive terminal of one of them to ground, and the negative terminal of the other to ground and thus achieve -15V and +15V.

This is a diagram of the sort of thing we did:

My question is this, if you wanted to achieve a higher voltages by adding even more power supplies, what would be the limiting factor at which point you could no longer add supplies safely (Without blowing them up)? What specs on the data sheets of my power supplies determine this and I should look out for?

Also does the relative voltage to ground have any effect, or just total potential difference. For example does it matter if I do this:

or this:

• One limitation will be the potential difference between a PSU's outputs and ground. The outputs are floating but that does not mean they can be at +/- 1000 V relative to ground. A practical limit could be 200 V. So that would limit you to +/- 200 V. Jan 4, 2017 at 16:08

It depends on the isolation potential each supply is capable of. That's the maximum allowed voltage difference from any output to any input. For most commercial power supplies, that's often in the 1.5 to 2.5 kV range.

Let's say you have a bunch of 15 V supplies running from 120 VAC, and they are rated for 2 kV isolation. Since the input is a sine, it will range from ±170 V from ground, so let's use 200 V. If one of the outputs is grounded, then we have up to 215 V difference from any output to any input.

From the above, there is (2 kV)-(215 V) = 1785 V of isolation potential left. For each supply from the one that is grounded, another 15 V is used up. That comes out to 119 supplies pn either side of one that is grounded. Since two supplies in the middle can share a ground connection, the absolute maximum in this example just from isolation voltage is 119 + 2 + 119 = 240.

So basically, the answer is "a lot". Note that in the maximum string of supplies above, the total end to end voltage would be 3.6 kV. You'd of course have to be very careful with that, and make sure any insulation you are using can handle that. Ordinary off the shelf wire doesn't usually have 3.6 kV insulation rating.

I also want to make it clear I'm not actually recommending or endorsing this. This is a bad idea. One problem is that the isolation from output to case is probably less than output to input. This means that effectively the cases of the string of power supplies must be considered "live". You can't, for example, have the string of 240 supplies sitting on a metal rack. All but a few of the supplies in the middle would be unsafe to touch. The math above also doesn't leave any margin for voltage spikes on the power line and the like. Again, more than "a few" supplies in series is a bad idea.

The insulation transformer breakdown rating might be one limit if approaching 1kV and this is degraded if the DC output is earthed due to leakage capacitance stress across insulation.

The other is DC load regulation of the worst power supply will limit the amount of load current in order to prevent overloading the weakest link. This is similar to series batteries.

Finally short circuit protection might in fact exceed device OCP capability due to the possible reverse voltage on the weakest series device, from a short circuit. The same is true for back EMF say from a large motor or negative resistance arc.

Otherwise you can string as many as you want in series if you observe the above potential failure modes.

The data sheet ought to give this information. I've had a quick look through a well known online supplier at PSUs from £40 to £800, and none of them do.

Generally, if you want to stress a component, and the datasheet stays silent about how much you can stress it, then prudence says you shouldn't, until you've conducted your own tests.

In order to be able to be connected to mains, most instruments will survive the mains input going to +/- 1.5kV with respect to ground. Unfortunately, this tolerance is rarely matched on the output side. As the output is designed to handle only low voltages, the clearances between tracks and grounded elements on the PCBs may only be appropriate for hundreds of volts, not thousands.

If you do contemplate connecting several PSUs in series, then buy one, strip it down and examine the clearances. Power it up taking the output to 50% more than your target voltage above ground/chassis. Check that nothing breaks down to chassis, to programming connectors, to any accessible metalwork on the case. You may be pleasantly surprised. You may save yourself the cost of buying many supplies to find they weren't suitable.

Since most floating output power supplies (the only type you could connect in series) have a limited breakdown potential to mains Earth, this would appear the only safety issue. It's unlikely that you'd ever hit this since it's typically in the 1500+ V range. The other issue that you more likely would hit is that short circuit and fold-back protection is now a cascading series of partial events, and the overload voltage may not be non-zero.
For example, if you had just two 30 V supplies that fold-back from a set 1 A maximum output value. The current trigger levels will be different by some small amount, so one supply will fold-back first taking you from 60 V to (30 + fold-back voltage). So your output voltage no longer follows the expected fold-back or constant current voltage profile.
This could mean you burn rather than protect your external circuits you are powering. As you connect more supplies in series, the problem gets worse.