That's not entirely true. A given generator will have a minimum running fuel consumption at idle, but generally more fuel is used under loaded conditions. If this is not the case for your generator you should investigate its throttle settings. Systems designed to incorporate battery storage capacity into your home electrical system are commercial available (
http://www.oksolar.com/abc/solar_systems_sta.htm) or you can put one together yourself with a charge/genset controller, interter, and a battery bank. Just get ready to fork over lot of cash...