I have had some experience with starting big (relative) motors on small systems. The biggest issue is short contact life due to the system not being able to maintain the Pull-Up Voltage during a start.

I'd take a look at the NEMA standards for motor contactors. IIRC, per the NEMA standard, the contactor has to hold in down to 85% voltage. In reality, most will hold in at lower voltages. But any voltage drop in excess of 20% (80% voltage) is generally considered a problem. Also, the serving utility may impose requirements as well. Some utilities require reduced voltage starting if a motor exceeds a certain horsepower (regardless of actual voltage drop).

For what it's worth, IEC contactors are SIGNIFICANTLY more sensitive to damage from voltage dips.

Dear Mr. nhcf (Electrical)(OP)2 Dec 22 17:43
" .... #1. Is there an IEEE or similar standard for recommended max voltage drop on a 480 V distribution system during a motor start?..... we can figure out what the transient voltage is, but I'm not sure of what voltage transient is considered too low. ... #2. I've assumed a 15% drop is acceptable, but don't have a good basis for that".
#1. In the US, NEC is the Law. But, I was unable to locate any mention of the allowable (transient) voltage-drop [during starting].
I would assumed that it depends on the motor (transient) torque at lower voltage SHALL be > the load torque in order to accelerate within 10, 20 ---30s, i.e. the limits of the motor and the thermal over-load setting. Note: (a) the (motor torque) is very much lowered when the [source voltage is < the rated]. (b) the (load torque) is [independent of the source voltage].
#2. It is dependent on the motor (kW) rating and the load torque characteristic. The motor torque (with transient lowered voltage) shall be > than the load torque, and able to speed up within the time limit of the motor. In general, the (transient voltage-drop) not exceeding 15% [during starting] would be fine.
#3. FYI: (a) in case that transient VD is too much, consider connect the (contactor coil supply) from a UPS source, or use a DC coil, or electronic controlled coil; which are less sensitive to the voltage.
(b) An IEC AC3 rated contactor would be fine, i.e. without plugging/inching (see IEC for definition of AC3 application).
Che Kuan Yau (Singapore)

As per IEC, the electromagnetic contactors shall definitely pickup with 80% of rated voltage at its terminals and shall not drop off with voltage at its terminals of 75%.
I suppose the limits may be same in IEEE too.
The allowable voltage drop of 15% and 20% at busbars and motor terminals respectively during motor starting comes from the above requirement to ensure the contactors in the system do not drop-off. This is widely followed in the industry to my knowledge.

NEMA specs say pickup voltage is 85%, but does not specify the dropout voltage. UL is also 85% pickup, but drop it can be anywhere from 70% down to 20% of rated voltage. MIL specs call for 85% and 75% dropout, so most manufactures go for 70% following UL to cover all bases.

" We are all here on earth to help others; what on earth the others are here for I don't know." -- W. H. Auden

If we follow ANSI C84.1-2016 Voltage Range there are two range of voltage A and B. For steady supply and utilization, the range A will be followed. For limited duration the range B is permitted.
For 480 V the minimum of service voltage in Range A it is 95% that means not less than 480*0.95%=456 V is permissible for Utility supply voltage.
However, for limited time the Range B is permissible, that means 91.67% of 480 V [440 V].
On the other hand, as utilization-at motor terminals voltage- 86.67% it is permissible [416 V].

Dear Mr. nhcf (Electrical)
1. I noticed that there are numerous learned advice, but each targeting the VD at different locations: (a) at the point-of-coupling, i.e. the utility supply up your incoming receiving point,
(b) starter output terminal voltage, i.e. about equal to the contactor input voltage,
(c) the motor terminal voltage, i.e. the voltage measured at the motor terminals.
2. The motor terminal voltage is the most important. The motor output kW/torque is dependent on the voltage at its terminals. Motor does not know/care what are the VDs along the upper stream.
3. The basic requirement is that the motor (transient torque) shall be > (transient load torque) during starting; in order to speed up within the motor rating.
3.1. Attention: The motor (transient torque) is [lowered] due to the (transient VDs), caused by the high (transient starting current); during starting.
4. In general, the transient VD at the motor terminals < 15% than the motor rated voltage would be fine. That is irrespective of the various (transient VDs) on the upper stream, which are irreverent.
Che Kuan Yau (Singapore)

In the US the utilities publish Power Quality Standards for Electric Service, I attached the document entergy posts. See page 12 Voltage Fluctuations Caused By Customer.
This requirement is measured at the point of coupling to the utility, and is enforced to protect other customers.
As long as your motor starts without excessive heating you should be OK.
If relays drop out, see the answers above. If the load has too much inertia for the above to work, it may be necessary to disconnect the motor from the load with the use of a clutch.

IEEE Std 141-1993 IEEE Recommended Practice for Electric Power Distribution for Industrial Plants Power Systems

• https://files.engineering.com/getfile.aspx?folder=1b5d1c94-ff88-4a91-82bb-6

Thanks everyone. Good info and feedback to review.

P.U. Volts = pick-up voltage
D.O. Volts = drop out voltage

The contactors in that table have picked-up (65-78% coil voltage or more required) by the time they close and start powering the motor. The size 5 drop-out is the worst at 65% of the coil voltage. If your voltage is dropping 65% or more you likely are causing other system issues.

As this is a drop caused by a motor during the start sequence on a distribution system - you have three things to consider.

1) The allowable drop is limited by the torque requirement to successfully accelerate to rated speed operation.
2) The voltage "limits" of the protection elements (circuit breakers, etc.) and their sensitivity to transients.
3) The voltage limitations/sensitivity of the OTHER connected equipment - for example, dropping below nominal distribution voltage for some period of time might cause all your (connected) uninterruptible power supplies to kick in on under-voltage.

A properly set up system will likely work just fine for the duration of a typical motor start sequence if the distribution voltage remains at least 0.85*V ... in your case, 408 V. If the driven load takes a long time (> 15 seconds) to accelerate, you might want to limit your drop to around 10 % (bus voltage at least 432 V).

Converting energy to motion for more than half a century

Dear Mr. nhcf (Electrical)
1. I wish to submit per IEC 61947-4-1 for your consideration:
A electromagnetic contactor (a) Shall close satisfactorily between 85% and 110% of their rated supply voltage U_s.
(b) Shall drop out and open fully between 70% to 20% for a.c of their rated control supply voltage U_s.
1.1 Attention: this is the mechanical operation requirement with respect to the coil voltage without load.
2. FYI: (a) In general, a.c. electromagnetic contactors on the market would "chatter" when the coil voltage drop to > 60% of the rated voltage when the contacts closed, during starting.
(b) Caution: chattering with current flowing through the main contacts would damage the contacts and motor in a very short duration!
Che Kuan Yau (Singapore)

Most limits on motor starting have to do with contactor hold in voltage, motor stalling voltage, and customer flicker concerns. As far as voltage drop in a 480V system, I believe most US motors (at some time in the past) were rated for 460V, which would allow for a larger voltage drop.
But most utilities required a limit at the point of common coupling (normally the meter) to be in the allowed area of the flicker chart. Some of these also had a factor of how many starts would be required per day or hour.
This was important for larger motors like saw mills and crushers.
A flicker study would include a fault study (with the smallest source) to find the system impedance, and required the motor cold resistance, to find the total current draw from a start, and from there to calculate the voltage drop at the meter.