I posted an answer on this last night and then woke up thinking "Oh no! That doesn't make sense!" so here goes again in the spirit of trying to help. . Is the AVR a separate box - one of the clickety-click types on the market there or is it more sophisticated? . How does the generator behave when loaded by a more straightforward resistive kind of load like a heating element when the AVR (if a separate item) is not in the loop? Put a couple of different resistive loads on it and check the voltage and frequency. Why do you need an AVR if using a small generator or do you sometimes have mains power that is unreliable? . Have you checked the voltage and frequency coming from the generator? (I was under what may be a false belief that these small portable generators used speed regulation to maintain voltage so if you see a frequency rise on increasing load I would suspect the generator speed regulation to be at fault.)
The chaps on this forum may be able to help: http://www.fieldlines.com/index.php?topic=147381.0
Don't forget to let us know how you get on! Tricky one this!
All the best //Steve
some AVR has current compensation . positive or negative. may be you have positive . these means that when load increase you increase voltage setting to compensate for the drop. if so reduce this setting or put it to negative.
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