SCE began ordering the so-called Public Safety Power Shutoffs on Thanksgiving Day.
As of 9 p.m. Friday, 1,099 customers in L.A. County, 1,815 in Orange County, nearly 500 in Ventura County, 556 in San Bernardino County and 1,481 in Kern County were without power.
The utility says only about 3,000 are still at risk of having their power shut off, including 518 customers in mostly northern L.A. County and 2,130 in San Bernardino County.
A red flag warning went into effect at 2 p.m. Thursday and was expected to last until 6 p.m. Saturday for the Los Angeles County mountains and the Santa Clarita Valley.
Winds started picking up Thursday afternoon, with gusts topping out at 75 mph at the Magic Mountain Truck Trail, according to the National Weather Service.
They were expected to reach 65 mph hour in the mountains and Santa Clarita Valley on Friday.
The shutoffs could continue through 3 p.m. Friday, SCE stated.
"SCE does not shut off power based only on weather forecasts -- rather, based on actual conditions in the affected areas,'' said SCE's Jeff Monford, who said the power would be back on for affected customers "Hopefully, within 24 hours.''
Shutoffs are designed to reduce the risk of fires caused by electrical equipment when strong winds are forecast. Several large fires in the state have been linked to electrical equipment.
SCE set up mobile power trailers and generators for customers to use in the affected areas.
Customers can view a map of current SCE outages at www.sce.com/wildfire/psps, or call 1-800-655-4555.
Customers can also sign up for alerts to let them know if the power will be shut off.
The utility says it generally sends customers a notice of a power shutoff 48 hours in advance.
"If your power has been shut off, we will restore power as soon as the weather conditions permit, and crews have inspected the power lines to confirm it is safe to restore power,'' Edison said.
Some of the largest, most devastating wildfires in California history have been linked to electrical equipment.
Bobcat Fire possibly caused by tree branches hitting SoCal Edison equipment
Easy Fire: SoCal Edison equipment failure caused blaze that burned 1,860 acres in Ventura County
Silverado Fire: SCE equipment under investigation as a possible source
City News Service contributed to this report.