Adelphia-One was a former Starfleet outpost built in the early 2270s in the Adelphous star system, and turned over to the government of the neutral planet Adelphous III in 2280. (Star Trek: Dauntless:"Paradox", Parts 1, 2 & 4)
Starfleet built Adelphia-One as Starfleet Outpost Epsilon-12, to support the Epsilon Outposts along the Klingon Neutral Zone in the 2270s. Rather than using standard fusion reactors to power the station, Epsilon-12 was designed with experimental pergium/durellium reactors, which were intended to provide power for up to 150 standard years without refueling. However, it was quickly discovered that the five reactors on board, besides power, were also generating dangerous byproducts, including chroniton radiation and isolytic particles. The reactors were scheduled to be replaced with ordinary standard fusion reactors shortly after the outpost was turned over to the government of Adelphous III, as a gesture of good will shortly after the planet decided to decline Federation membership.
Shortly after the station fell under the administration of Adelphous III, the designation was changed to Adelphia-One. Several months later, the station administration decided it would be more cost-effective to maintain the installed reactors, which could provide power for more than a century, than to replace them with new fusion reactors. The power core retrofit never occurred.
In 2382, after more than a century of the outpost reactors building up chroniton and isolytic particles and on the verge of overloading, the Adelphons issued a general distress call. The Federation starship USS Dauntless responded to the call and determined that the pergium/durellium reactors had to be shut down and replaced. An engineering team from the Dauntless which included the starship's commanding and first officers shut down three of the P/D reactors and replaced them with fusion reactors from the starship's own impulse engines. However, before the remaining two reactors could be shut down, a power spike in Reactor 4 caused the power core to explode, destroying the outpost and tearing open a rift in subspace which consumed a moon of Adelphous III and threatened to destroy both the planet and the Dauntless. The buildup of chroniton particles had the unexpected effect of sending the thirty-member engineering team back in time 106 years, where they were discovered in the engineering spaces of Epsilon-12 while it was still under construction.
In spite of the destruction caused by the explosion of Adelphia-One, there were relatively few casualties. The timely arrival of the Dauntless engineering team aboard the derelict starship Independence, which had been rigged with an isolytic trilithium device, sealed the subspace rift. The loss of the uninhabited moon Adelphous III-C caused adverse weather and tidal patterns on the planet which scientists predicted would correct themselves in less than a year. Records indicate that no other starbase or outpost was built using P/D reactors.