Houses with solar systems consume less than half as much utility-delivered electricity as ordinary houses, the study found. But from about 4 p.m. through the night, they consume more, and they add to the system’s peak demand, which comes around 5 p.m.

Pointing panels to the west means that in the hour beginning at 5 p.m., they produce 55 percent of their peak output. So a 10-kilowatt system would make 5.5 kilowatts. But point them to the south to maximize total output, and when the electric grid needs it most, they are producing only 15 percent of peak, or 1.5 kilowatts.

Why wouldn’t everyone point the panels west? Some homeowners have their panels face south because that is the direction of the roof. While some solar panel owners are paid time-of-use rates and are compensated by the utility in proportion to prices on the wholesale electric grid, many panel owners cannot take advantage of the higher value of electricity at peak hours because they are paid a flat rate, the energy analysts said. So the payment system creates an incentive for the homeowner to do the wrong thing. The California Energy Commission recently announced a bonus of up to $500 for new installations that point west. A new solar installation is completed every 3.2 minutes, according to the authors of the analysis.

Solar panels do not have to be pointed in just one direction; a homeowner can buy a device called a tracker that will pivot them, over the course of the day, like a sunflower, so they always face the sun. A tracker can raise the output of a panel by 45 percent. But adding trackers can cost hundreds or thousands of dollars, and a cheaper way to get the same number of kilowatt-hours may be simply to buy a few extra panels.