Your dehumidifier and your air conditioner are very nearly the same machine and probably use about the same amount of electricity.
The air conditioner cools the air by removing heat from it, then transfers that heat outside. When it cools the air below dewpoint, the excess humidity in the air condenses on the cooling coils and drains to the outside.
The dehumidifier cools the air by removing heat from it, which causes the same condensation, but instead of transferring the heat outside, it transfers it back to the cooled air stream to reheat it.
Because of the laws of physics, more net heat is always generated by these machines than is removed from the air when cooling it, in other words, the hot side always rejects more energy than the cold side absorbs, i.e., there is always more heat "left over" that has to go somewhere.
For this reason, your dehumidifier is always adding heat to your room when you run it. It probably cools the air about the same amount that your air conditioner does in order to remove the water from it, but it adds all that heat plus more back to that same air once the water is removed, so the room gets hotter.
Easiest fix: control moisture with the AC during the Summer, and with the dehumidifier during the Winter.
Best fix: an air conditioner, appropriately sized, with modulating hot gas reheat.
Google Daikin Quaternity.
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