My 3 kva generator carbon brush detoriate with in 30 minutes ?

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Did you make certain that the breaker on the unit isn't tripped?

A 5.5 KW draw needs a 5,500 kva generator. Think in thousands.

the unit has gone into over load
The total power requirement has exceed the output of the generator
for example if the generator is a 2.500 kw or kva then it will generate well at 1.8 kva or kw but it will not run forever at 2.5 kva -kw
When a ac is running the power requirement will be constant on the generator and with the fridge as well then the load will be at the maximum out put of the unit.
when the fridge starts again the extra load will exceed the max out put of the generator and it will slow down ( lights dimming ) and eventually go into overload mode
have an accredited electrician calculate your maximum load requirement for an external power supply and then get a unit that is at least 15.. kva kw better that required
generally fridges use 1000watts , ac conditions will draw over 3000watts and any thing else adds up . I am guessing that your generator is only 2500 unit

If the unit has sat a long time, the rotor may have lost its residual magnetism and then can no longer induce voltage in the stator. It will require flashing, a procedure where DC voltage is applied directly to the brushes for a few / 3 seconds (correct polarity a must) I also disconnect the brush wires. This will cause the field to rebuild. I would try that first, before suspecting rotor and stator

Generator replacement brush notice:
1, from the model and material needs and the original brush.
2.It is best to grind the new brush to the Radian size of the old brush.
3. pay attention to adjust the brush grip pressure.
4. the carbon brush size should be equal, not too big or too small. The carbon brush is not subject to force in the process of placement.
5. pay attention to the carbon brush and armature to have obvious contact, do not push the carbon brush in.


Generator brush replacement method:
1, the first with a special wrench loose brush braid fastening screws, loose fastening screws should not be loosened excessive, to prevent screw loosening and falling off.

2, take off the carbon brush braid, the carbon brush and the pressure-equalizing spring at the same time. When installing a carbon brush, put the brush into the brush grip.
3, then press the equalizing spring.
4.Use special wrench to fasten the brush and braid to fasten the screw. When fastening the screw, it is not necessary to exert too much force to prevent the screw from being damaged.
5. Check that the brush moves freely in the brush grip, and the spring can be pressed in the center of the brush.

kva = kilo-volt-amps

watts = volts x amps = va

Therefore, 5.8kva = 5800 watts

1. Check for any blown fuse and replace. It can be traced directly from the output lines.
2. Check field excitation. The field excitation is supplied by the battery to the excitation coil through a pair of carbon brushes. If the brushes are worn out, no excitation field is supplied and no output is generated. Replace carbon brush if found worn-out.
3. Use an analog multitester to check the continuity of the carbon brush and the field coil.
   

1. Check for any blown fuse and replace. It can be traced directly from the output lines.
2. Check field excitation. The field excitation is supplied by the battery to the excitation coil through a pair of carbon brushes. If the brushes are worn out, no excitation field is supplied and no output is generated. Replace carbon brush if found worn-out.
3. Use an analog multitester to check the continuity of the carbon brush and the field coil.