DS9 had a fusion reactor to power all of it systems. The reactor is located at the bottom of the central core (the part that glows red). It is unclear whiether it is one large reactor or several small reactors working in tandem (more likely) but the overall output from the reactor is much larger than that of a starship's warp core.DS9 has a fusion reactor. Since it has no real need to move at warp speed, the kind of matter/antimatter reactor that provide the power a starship's warp engines need is not necessary.Deep Space 9 has fusion reactors, check out episode "Civil Defense", they are mentioned there. These fusion reactors should provide plenty of power. Impulse engines on most starships are fusion reactors and can supply much of the power for ship systems in low alert conditions. The warp power is used primarily for warp travel or the large power requirements of Red Alert, etc. My understanding is with anti-matter (for the core) being harder to have large quantities, it is preferred to power systems off of impulse reactors (running off deuterium or hydrogen picked up by the Busard collectors). Running all systems and warp drive requires more power than these reactors provide though on starships. DS9 has several reactors, however, and is designed to run off them.
The above is correct. However a warp engine produces theta radiaition from matter/antimatter. The by product is absorbed through a series of radiometric convertors and it is broken down into energy which is not harmful. This is used to power up all the systems on the ship. Environmentally sound and recycled on a continuous loop. This is why the plasma grids need to be cleaned out on a regular cycle. This is mentioned in the Episode Night. It is possible that DS9 operates on the same principle where all radiation is turned into useful kinetic and plasma energy.
Additional information to supplement the above: according to the DS9 Tech Manual, DS9 has a total of six fusion reactors located in the lower core. Of these, four are fully operational, one is destroyed (or at least permanently nonfunctional), and the last one can be used as an emergency reserve. Canon may or may not have stated what Starbases tend to use, so it may be different (it might be, for instance, matter/antimatter, akin to a warp core). An interesting note is that, at least in theory, the energy provided by a starship's warp core should be vastly superior, and as such a single ship might be able to win a battle of energy attrition with DS9 without much difficulty, but this does not seem to be the case according to canonical evidence (in the battles involving DS9, it successfully repels a great many ships in extremely intense combat), which raises questions on just how starships actually consume their energy in battle.