Nov 2 (Reuters) - American Electric Power on Thursday beat profit estimates for the third quarter, as the utility benefited from higher electricity rates and customer additions.

That helped the company, one of the largest electricity producers in the United States, to cushion the impact of soaring costs driven by higher interest rates.

Operating earnings in its transmission and distribution unit, which includes Ohio Power, rose to $206 million for the quarter, from $165 million last year.

The company had filed for a rate case increase in Ohio earlier this year that went into effect in June. A rate case is the formal process used to determine what customers need to pay for the electricity, natural gas, private water and steam services provided by regulated utilities.

Its sales volumes declined, however, due to storms in certain territories such as Michigan and Tennessee.

"We've added nearly 30,000 new residential customers in our service territory this year, which has helped offset lower average usage in the residential segment," said CEO Julie Sloat.

The Columbus, Ohio-based company reported an adjusted profit of $1.77 per share for the quarter ended Sept. 30, beating analysts' average estimate of $1.70 per share, according to LSEG data.

The utility firm narrowed its full-year adjusted operating earnings forecast to between $5.24 and $5.34 per share, from an earlier outlook of $5.19 to $5.39. (Reporting by Kabir Dweit; Editing by Shweta Agarwal and Devika Syamnath)