Power cycle is definitely not necessary. The exact method you use will depend on your OS, and whether you start as a service or not.
Centos service:
service openvpn restart
Debian service:
/etc/init.d/openvpn restart
In your case:
openvpn new_config.config
are you stopping the old instance first? (ctrl+c)
If yes, then you are doing all that is required. Nothing further required.