
You don't seem to get the idea
at all. I don't know how to try to explain it any better, but I'll try one last time, very clearly, then I'm out, the OP is free to do their own analysis. This is frustrating, since this is exactly what I've been doing many times, and seen the issues myself, and you don't even seem to have an idea what we are talking about.
1) OVP is an active circuit that detects a voltage over certain threshold, then stops the converter action completely, so no more energy flows. It's very similar to voltage control loop, only that it's not trying to regulate, but shut down completely.
2) There already are (or should be) enough output capacitance so that by dumping the energy in L, the voltage only changes a little [compared to component ratings]. (Otherwise, there would be huge voltage ripple over the caps in normal operation.)
Maybe a numerical example helps you:
Say, the nominal maximum output voltage is 10V.
The output caps are rated to 16V, the switching components to 20V (quite tight design).
The OVP is set to activate at 12.0V.
Load is suddenly disconnected - output voltage exceeds 12.0V, OVP comparator detects this and shuts down the PWM generation, energy in L is dumped to the caps, now the voltage is at maybe 12.1V, maybe even 13-14V if the OVP is slow and crappy and inaccurate and there were a few cycles of normal operation into open load before it reacted. Let's say it's at 14V. No big deal!
With a latch, highly recommended, everything will shut down until power is cycled, and the voltage at the output slowly fades in leakages.
Without a latch, the voltage will slowly fade in leakages, until it goes below the OVP activation level minus hysteresis, let's say it would be at 10V, then there is a short operating cycle which brings the voltage back to the peak, let's say 14V. This doesn't happen too often, because the leakage is small. This is a hiccup mode CV regulator, running every few seconds, consuming almost no power, keeping the output inside a range.
Now how do you add a zener to this? Use a 10V zener? Not going to work, it's going to conduct well before 10V, under normal conditions. Maybe a 13V zener would be "off enough" at 10V, and thus usable under normal conditions. You know what? A 13V zener would start properly conducting at maybe 15-16V. It wouldn't do much anything! Finally, if you manage to find a zener that does
anything in this circuit, then all it does is that it speeds up the discharge. And in this case, it causes the circuit to dump more and more energy to the zener. The formula you posted has nothing to do with this whatsoever. It doesn't even model the curve of the zener. You just assume some duty cycle of "over voltage fault time", but your zener is going to define that duty of fault time, and it's not too trivial to calculate! Yes, if you have enough hysteresis in OVP, then the zener only conducts very shortly, only eating tiny amount of the voltage peak, but why bother?
Then you might think: what if the OVP circuitry isn't working properly? Maybe the zener is a good safety device! No. If the OVP misbehaves and doesn't limit the overvoltage actively, then you are injecting huge amounts of energy in the zener. It needs to be massively overrated and heatsinked. Not going to happen.
You see, the problem with zeners are that they are very inaccurate. An active OVP does
everything that is needed, and, as you admitted, it's needed
in any case, because your zener solution depends on it. In
best case, your zener does absolutely nothing. In the worst case, it blows up, most likely in a short circuit, waiting for a battery to be inserted.
And adding a zener to the hickup CV controller (the OVP controlled converter) is nothing more than adding an unnecessary, random load. And, because it's an inexact, not perfectly regulated voltage source that can deliver a lot of current, a zener is the worst type of load.
You should expect that the OVP
works. And if it doesn't, the zener is not going to save your ass.
And even a crappy OVP is more accurate at clamping the voltages than a zener.
Crowbar type of OVP in a battery charger is generally a horrible idea!
You are seeing some limited part of the issue, but not the big picture.