Ki suppression control So i was wondering does ki suppression drain energy from the user, since they always need to think about this and maintain focus to some extent.

To start things of we know that not everyone can hide their Ki since it is a skill that has to be learned. 
We saw an an example of that when the sayajins arrived on earth and were surprised  by the fact that the earthlings could control their power level and change it on will. Later on Namek, we saw that people are able to track down others who are unable to do that, that is why Dodoria and the others are always "powered up", and why the scouters were able to read their true power level ( i am not taking transformations into the account here).

Usually one of the common reasons besides trying to stay "low", is said to be to preserve energy but if you take into account the examples i mentioned above, that would mean that people are constantly losing energy without doing anything, which seems totally illogical. Even if that was the case somehow the loss should be minimal. 

Taking everything into account there just does not seem to be a reason to do that, besides if you want to hide yourself on purpose. I doubt this was anywhere explained in depth, or that there will ever be a 100% verified answer but i would like to see what others thinks about this.
No, suppressing your power level does not exhaust you.

The Z-Fighters keep their power levels low for two reasons:


To hide their true strength from their opponents
To be able to raise their power levels extremely high when a fight does break out.


It's never stated (as far as I know) whether suppressing your power level saves a significant amount of energy. It's also never stated whether it takes energy to do this, either. However, based on the fact that the Z-Fighters go about their day-to-day lives with suppressed power levels, I'd argue it takes little to no stamina to maintain this, and may potentially save your ki reserves (though this is speculation).

I would argue, though, that learning to suppress your power level gives you a greater ability to manipulate your own ki, and therefore raise and lower it as needed. For an example of this, look at Ginyu's fight with Goku.

According to the wiki, Goku's max power level when he fought the Ginyu Force without Kaio-Ken was 90,000. It was 5,000 when supressed. He used this deceptively low power level to decimate the Ginyu Force, since they constantly underestimated him. However, when Captain Ginyu managed to take over Goku's body, his max power level was merely 23,000. I would speculate that in addition to the fact that this was a new body, Ginyu had no training in manipulating his own power level, so he could not even begin to approach Goku's normal strength without Kaio-Ken. 

In summary, suppressing your power level has no notable disadvantages, and allows the user to both conceal their true strength and to utilize said strength to its maximum potential.