I don't know if there is an answer. Most dehumidifiers operate by cooling the air till the water condenses out of it, then allowing it to warm up again. So they have to pay the cost of refrigerating the air. The only other way I can think of to dehumidify would be to use some chemical that adsorbs moisture, such as silica gel; but you'd need a lot of it, and you'd need to heat it up outside from time to time to drive the moisture out again. If you can get your hands on a huge amount of silica gel, and rig up some sort of fan to blow your room air through it, and also a system to move it outside and spread it out in the sun to bake off the moisture every few days, this might be your cheapest route. Unfortunately, there's no simple, cheap way.