Time delay for power contactor

https://www.littelfuse.com/products/protection-relays-and-controls/time-delay-relays/delay-on-break.aspx

In a well-designed system, a <...fault at the motor...> should operate either its overload protection device, or the circuit protection device, and disconnect it.

If the bus is appropriately sized and the feeds to the motors are appropriately fused, that shouldn't be an issue as the breaker should trip out before the fault draws enough power to drop the voltage to a point where the contactor coils drop out.

I don't see how a time delay will add any additional latching time for the coils in the event this does happen, as that scenario is supply dependent not signal dependent.

If your concern is that the power fluctuations caused by such a fault could create this problem before the breaker trips out, then you need to isolate the power supply to the contactors so that can't happen. For a real band-aid fix, maybe a zener diode then capacitor before the contactor signal switching??

...or trickle-charge a battery off the <...110VDC bus...> and use that to power the circuits feeding the <...power contactors...>, thereby making an uninterruptible power supply for them.

If, that is, a suitable piece of equipment is not available off-the-shelf.

For large motors that you don’t want to disconnect during a transient event, it has been longstanding industry standard to use dc coils on the contactors, and adding time delay undervoltage release protection to the contactor control. The motor doesn’t separate from the supply during transient events.

If you have an ac coil for your contactor, you can count on it dropping out at 63% of its rated voltage in one cycle. If you use a time delay relay to hold the run signal on, the contactor can open and then reclose, likely out of synchronism, which may not be desirable. VFDs now will commonly resynchronize before connecting to a spinning motor, if you select it in the operation parameters.

For the same starter, a dc coil will drop out at about 20% of its rated voltage. For big dc coils, holding resistors are often added to reduce power dissipation after the contactor has closed, taking advantage of the increased mechanical holding capacity.

So there's any number of ways of solving the problem, as usual.

Things are a bit easier in the DC domain, too.

A fault involving only one of the poles (to ground) should not cause a problem to voltage profile as the fault current is low.

If the fault is between +ve and -ve poles, the current will be large and the MCB sizing is such that the MCB (upstream of the Contactor) opens the circuit faster than the Contactor.

Coordination between MCB and the Contactor is part of the design and ensures that for any current beyond the safe magnitude level for the contactor, the MCB interrupts even before the contactor opens.

If there is a limitation in terms of MCB operating speed, it is better to consider HRC fuse.

You can use a Time delay relay the contact of which can control the supply voltages to coils of the main contactors...

The time delay relays that are commercially available, depending on the models can have adjustable time delay as well...

A sample of similar time delay relay that I've used back in the 70's as shown...

That presupposes that the upstream supply is already resilient to the impact of a <...fault occurs at the motor terminals, the bus voltage may drop...>. Otherwise, there is nothing to gain by using them.