Running PowerShell scripts in a user context without any window being displayed at all is not possible.
The closest way is the WindowStyle hidden switch available from PowerShell version 2 onwards:
PowerShell.exe -WindowStyle hidden Run-Script.ps1
This will still display a temporary PowerShell window.
To completely remove the window from the use context use this vbs to call the PowerShell script:
wscript.exe PsRun.vbs Run-Script.ps1
The most common use case for this operation is a scheduled task that needs to run in the user context and needs to not display an annoying pop-up.