After you make your way through the Lumiose Badlands, you find a Team Flare Grunt's pass and enter the Kalos Power Plant.
Go toward the Main Room
There are no wild pokémon or hidden items in the power plant. Just go north until you reach the next room. From there, go north. A Team Flare Grunt will challenge you. The Grunt has a level 32 Scraggy and a level 32 Croagunk. You get 1280 Pokédollars for winning. The Grunt says that they are "redirecting" (a.k.a. stealing) the power.
Go to the right and into the room. There is a guy in a black suit who will sell you Fresh Water for 300 Pokédollars. Don't bother. After you deal with Team Flare in the Power Plant, he'll lower the price. In the right side of the room, you find a Zap Plate.
Leave the room and go northwest. There's another Team Flare Grunt up here. She has a level 31 Croagunk and a level 33 Golbat. You get 1320 Pokédollars for winning.
Go north from the Grunt and through the door.
This is the main room of the power plant. If you go right from the entrance, a Team Flare Grunt runs up to you. This Grunt has a level 34 Mightyena. The Grunt will block the path to the right, so go left.
The next Grunt you encounter has a level 32 Scraggy and a level 32 Golbat.
Go northwest and you'll encounter another Grunt. This one has a level 32 Golbat and a level 32 Mightyena.
Go northeast from there and you'll reach a Grunt who has a level 34 Swalot.
Continue east to find a Grunt who has a level 31 Liepard and a level 33 Swalot.
Southeast from there is a Grunt who has a level 31 Croagunk, a level 31 Scraggy, and a level 31 Liepard.
After this, you finally can reach the center by using the walkway to the left.
Battle the Admin and Aliana
Go up to the two people in the center. Aliana speaks of a device that Team Flare is trying to power up. Then the Team Flare Admin will battle you. He has a level 36 Houndoom.
After you win, the Admin asks Aliana to battle you. You can heal up before the battle. When you're ready, talk to Aliana to start the battle. She has a level 38 Mightyena.
After the battle, two mysterious masked kids come up to you. They heal your pokémon and give you some Full Restores. They say that the power is back on in Lumiose City, and you can go to the north part of Lumiose City by going south from Lumiose Badlands.
Go back to the small room in the Power Plant. Talk to the worker near the entrance to receive TM43 Flame Charge. Talk to the female researcher to get a Magnet. Talk to the guy in the black suit to buy Fresh Water. Now that you restored the power, he sells them for 100 Pokédollars each.
Now leave the Power Plant and go east, then south. After you go down the stairs, you encounter a really tall, white-haired guy who mumbles something about a flower Pokémon that has eternal life. Then he walks south.
Before going to Lumiose City, go east. There is a rock that you can break with Rock Smash. After you break it, use the Dowsing Machine to find Stardust to the south.
Go east and break the rock, then go south to find a Rare Candy.
Now go to the west again, and go south to reach the northern part of Lumiose City.