More than 80 firefighters fought the fire which broke out in a storage vault containing 50,000-60,000 gallons of mineral oil.
Local people reported the sound of an explosion but this has not been confirmed.
Much of the blaze on Saturday was out within two hours but firefighters were expected to stay at the scene to monitor possible flare-ups.
Drivers in the area were advised to take extra care as many roads would be without lights due to the power outage.
Officials were not able to say when power might be restored at the plant which serves 1.6 million customers in Los Angeles.
An employee said work was going on around the clock to restore power. He said: "It's got to be done. People are without power."
In a statement, the plant said: "The fire affected one portion of the receiving station, but as an emergency precautionary measure, power to and from the facility has been shut off while Los Angeles fire department personnel work to put the fire out.
"As soon as possible, crews will assess damage at the station and begin the work of restoring power to affected customers."
The incident happened as Los Angeles recorded a second day of record high temperatures that exceeded 90F (32C).
SKY News.
