Nov 2 (Reuters) - U.S. electric and gas utility Southern Co on Thursday increased its cost estimates for its Georgia Power utility's share of two nuclear reactors but stuck with the previously announced timeline.

The Vogtle two-unit expansion project is billions of dollars over budget and years behind schedule.

Unit 3, one of the two reactors at Vogtle, became the newest reactor in the United States to enter commercial service in July. Unit 4 is slated for completion in the first quarter of 2024.

In an investor presentation, Southern Co forecast Georgia Power's costs to be at around $10.75 billion. In April, the company estimated the project to cost around $10.59 billion.

The company discovered a "motor fault" in one of the four reactor coolant pumps in Unit 4 during pre-operational testing, which will be replaced with one from its spare parts inventory, CEO Christopher Womack said during the presentation.

"After successful installation of the spare pump, we will recommence with start-up and pre-operational testing with a projected in-service date during the first quarter of 2024," he added.

The company beat third-quarter profit estimates on Thursday, helped by electricity demand surge and lower operating expenses.

Customer additions also helped Southern Co post a 2.1% rise in total retails sales at 42,364 kilowatt-hour during the quarter.

Its operating expenses fell about 21% to $4.87 billion in the three months ended Sept. 30, compared to a year earlier, primarily due to lower fuel costs.

Southern Co's shares rose 2.9% after its earnings release on Thursday.

Peers CMS Energy and Xcel Energy also posted a rise in their third-quarter profits.

Southern Co serves more than 9 million customers. Its electricity segment caters to the states of Alabama, Georgia and Mississippi. The gas segment provides services in the states of Illinois, Georgia, Virginia and Tennessee. (Reporting by Nicole Jao in New York and Tanay Dhumal in Bengaluru; Editing by Shilpi Majumdar and David Evans)