It is normal and acceptable for an overload condition to exist on a power 
circuit. Examples are motor starting currents and initial charging of power 
supply capacitors. Some standards have tests specifically for this 
situation. IEC 950 requires that the steady state current shall not exceed the
rated current by more than 10% under normal load. In North America, for some
types of equipment such as electric discharge lighting (fluorescent, metal
arc), computers, and most continuous loads, the rated current may not exceed
80% of the branch circuit (plug) rating. 

You understood correctly that it is the overheating which is the critical
point of concern. That is what overcurrent protection is designed to control. 
>From a practical design point, your biggest problem may be the avoidance of 
tripping overcurrent devices, but careful measurement of conductor and 
connector temperatures is important.

You mention several minutes of overload per hour, but are not clear about the 
duty cycle. Several minutes at 30 amps is not going to work on a 20 amp 
circuit. If these overloads are short and well distributed, you may have no
problems. It may be necessary to specify special overcurrent protection such
as time delay fuses or HACR rated circuit breakers. Start by consulting the
fuse and circuit breaker manufacturers for their performance curves and allow
a sufficient margin to avoid nuisance tripping. 

Connector quality and tight connections may be a significant issue for you 
since it appears you will see significant temperature cycling in you 
connections. Loose screws or contacts will quickly lead to oxidized surfaces, 
more heating and burnout of the connection. 

Some startup or surge situations can be helped by a series resistor which is
shorted out by a time delayed relay. 

If you need to go to a larger connector, the twist lock series is a less 
expensive solution in North America, but the IEC 309 is the only common
solution for the rest of the world. 

Bob Johnson

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