I can enable "allow users to connect remotely using remote desktop services" manually in Local Group Policy. Is there simple way to use Powershell to do it, not by changing Registry key?

Essentially, no matter how it is done, it will change a registry key. So only way I know of doing it is through GPO, right click Computer --> properties, Remote Desktop Tab, and enable, or modifiy the registry

HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Terminal Server

Set fDenyTSConnection = 0 to enable

Have a look at the below script -

http://gallery.technet.microsoft.com/scriptcenter/089bd25e-6900-45b7-8a8d-8d71bba88b2f

And also below

http://gallery.technet.microsoft.com/scriptcenter/Remotely-Enable-RDP-855c3842

But personally, if you are in a domain enviroment - i would use group policy.