It could be your regulator rectifier. I have had them go out on motorcycles and had the same problems that you are having.
They are expensive, so do check the voltage if you can. It could also be a short someplace.
You will need a multimeter for this and a manual (see below).
Here is a replacement regulator rectifier:
http://www.scooterwest.com/item_details/P-PX-AC-DC-Regulator-Rectifier-12V-5-Pole/2589It could be your generator, but let's hope not...
Here is a sweet link to a people 150 user manual, which may help you find the problem:
Kymco People 125-150 ENAnd then it could be your battery, so test that yourself as mentioned in another post or have a motorcycle shop do it.
I hate electrical problems. Good luck.