If I had to develop such an electronic fuse, here's how I conceive the product.
We must start from the worst conditions, a short circuit, with a voltage source of low internal resistance and with a very low inductance in the circuit.
The electronic fuse is intended to protect the voltage source and possibly also the circuits it supplies.
It should be noted that in practice it is impossible to protect a semiconductor with a fuse, except when using an ultra fast fuse with i ² dt at least 30% lower than the semiconductor with diodes, thyristors, triacs and GTO's.
The electronic fuse can not change the operation of the circuit it protects.
For this reason, it must have a very low resistance as a fuse have.
I already deducted that the current sensor can not be done by a resistance, I would choose a Hall effect current sensor.
How does a fuse work?
When the current reaches several times the rated current , the fuse blows and the instantaneous power ( peak current x voltage ) is dissipated in the arc that occurs in the fuse.
This introduces an arc voltage drop and also a resistance which limits the current .
The arc is then extinguished either naturally ( elongation of the arc ) or by silica ( sand) that melt and isolates the electrodes.
If we want an electronic fuse , we must do the same .
First, it is obvious that we can not use a relay because the operating delay varies from 10 to 30 ms ...
In a circuit with low inductance and low resistance of the voltage source , the current will reach its highest value (U / Rint) well before the 10 ms.
The current to be interrupted will be very high and the relay will be damaged (and perhaps also other components of the circuit !) .
You have to choose a MOSFET to interrupt the current .
He must act very fast because the di / dt can be very high and the short circuit current may exceed the maximum peak current of the Mosfet.
However, such a high-speed electronic fuse may be annoying , for example, inadvertently triggering when charging a capacitor.
That is why I would choose another solution: Mosfet should limit the current to an adjustable value, and after an adjustable delay, (compatible with the power the Mosfet can dissipate), I would block it.
It should also provide an overheating protection to protect the Mosfet if the electronic fuse is reset several times.