The electricity cost will mainly be the one coming from your lamp, regarding the watts you use. I say that because in its simpliest way, the hydro is just a water filled tank on which you place a table. Then it’s the water pump that will make your fertilisers to go up where your plants are. Thus, a water pump doesn’t cost a lot to use and maintain in an automatic cycle system.
You’ll just gain the advantage to be able to put a timer on your pump so you’ll be able to automate your watering.
So in terms of expenses, if you follow the JoshawaM’s DIY way, it won’t cost you much!
Besides, during the grow, you may use a little bit more of fertilizers, so think about that.
Also, the pH and the ppm of your water, other habits to get but once in place, everything will be easier!
Don’t hesitate if you have other questions!