July 28 (Reuters) - U.S. energy company Southern Co on Thursday boosted the cost estimate a bit for its Georgia Power utility's share of two nuclear reactors under construction at the Vogtle plant in Georgia.

The Vogtle reactors, which are already billions of dollars over budget and years behind schedule, are the only nuclear power units under construction in the United States.

In an investor presentation of its second-quarter results, Southern boosted its capital cost estimate for its share of the new reactors by $52 million to roughly $10.5 billion.

Southern also narrowed its previously projected in-service dates to the first quarter of 2023 for Unit 3 and the fourth quarter of 2023 for Unit 4. Previously, company was looking at a wider window of the fourth quarter of 2022-first quarter of 2023 for Unit 3 and the third-fourth quarters of 2023 for Unit 4.

Over the past couple of months, two of the Vogtle partners - Oglethorpe Power Corp in June and Dalton Utilities in July - said they wanted to freeze their spending on the project. Their ownership in the project will be recalculated at a future time depending on the total cost to complete the reactors.

When Georgia approved the Vogtle expansion in 2009, the two 1,117-megawatt Westinghouse AP1000 reactors were expected to cost about $14 billion and enter service in 2016 and 2017.

Some analysts estimate total costs, including financing, have ballooned to more than $30 billion following delays related to the coronavirus pandemic, the nuclear accident at Japan's Fukushima plant in 2011 and the 2017 bankruptcy of Westinghouse, the project's former contractor.

The Vogtle owners include Georgia Power (45.7%), Oglethorpe (30%), Municipal Electric Authority of Georgia (22.7%) and Dalton (1.6%).

(Reporting by Scott DiSavino Editing by Nick Zieminski)