PoE Network Switch?

I have a panel containing all my ethernet runs to my entire house. I'm going to add a network switch to this panel to facilitate the internet getting to all the rooms. There is not a plug within the panel, although there is one below it. However, I'd like to use a PoE system to avoid having to plug that network switch into an AC plug. Is this possible? Do I need a PoE network switch upstream from the network switch that would be in the panel?

 

Modem -> Network Switch (PoE) -> Network Switch (Non-PoE)

 

Would that work? Thanks.