BART’s second batch of sleek new rail cars — another 10-car train — will be rolling onto the transit system’s tracks by next week, officials said.

The state Public Utilities Commission approved the new train for service in a letter to BART officials Tuesday, four days after the train passed a systemwide test in which it stopped at every station and its doors successfully opened and closed under automatic controls.

The letter, signed by Roger Clugston, the commission’s deputy director of rail safety, said the tests “demonstrate the cars are acceptable and ready for revenue service.”

BART’s first 10 cars rolled into service in January, but months behind schedule, after problems with the doors emerged during a test by commission inspectors.

Normally that initial test of new cars would have sufficed. But the commission ordered BART to put its second train of 10 cars through similar tests because of those problems.

Now that the new rail cars have twice passed the test, the commission said, BART will need only to conduct its own readiness tests and provide proper paperwork for any new cars it receives from manufacturer Bombardier over the next several years.

“Going forward, no specific operational field runs will be required for placing the cars in service,” Clugston wrote.

Bombardier is expected to produce and deliver 16 to 20 cars per month to BART over the next several years until the entire fleet is replaced. For the time being, BART has 26 of the new cars in its Hayward yard, and has been running as many as 10 of them in a single train on the Richmond-Fremont line. Some days, however, BART runs a shorter collection of the new rail cars, removing some for routine maintenance or to fix what agency officials have described as minor problems.

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The new rail cars have three doors on each side, compared with two on current cars, and feature wider aisles, fewer seats and bright green and blue colors. They’re also outfitted with automated announcements and signs that display the name of the next station.

While the new train runs daily, most passengers haven’t ridden one yet since, unlike most BART riders, they don’t go into San Francisco. Those who have been aboard the new cars give mostly favorable reviews, though some complain about the reduced seating.

With the approval of the second set of rail cars, BART will run new trains on both the Richmond-Fremont line and the Warm Springs-Daly City line. Officials expect to have 80 new cars in service by the end of the year, and 176 by the middle of 2019.

Michael Cabanatuan is a San Francisco Chronicle staff writer. Email: mcabanatuan@sfchronicle.com Twitter: @ctuan