At least in California, probably varies somewhat elsewhere. I know it seems weird, but so it is.
http://www.caiso.com/Pages/TodaysOutlook.aspx
As far as the rates go there are a lot of different factors and different utility programs but in general you have it backwards. Most utility companies charge more for electricity during peak and less for off-peak, and generation is coordinated on a fairly tight schedule by the independent system operator based on predicted usage - once a day ahead of time and fine-tuned an hour ahead of time. Transmission lines would burn up in a heartbeat if power was simply dumped into them with nowhere to go (see graph at link).
Residential solar costs utilities money because they're forced to buy excess energy back, but they still have to maintain capacity for when it's cloudy. They still have to pay for maintenance on the equipment and have it ready to go on a minute's notice - clouds moving over the sun and drops in wind can cause major shifts in line voltage, which have to be balanced dynamically. While equipment sits idle they lose money. These plants are usually natural gas because they can ramp up and shut down quickly.
I don't have a problem with paying more for clean energy. While my utility offered it I paid about 30% extra for a Green energy plan which was supposed to require the utility to purchase a corresponding amount from renewables. But because solar requires natural gas backup it's not carbon free and and won't be for the forseeable future.
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