I have found instructions for 2010 but I cannot find the 2013 instructions. I can delete a project but I cannot find how to archive.
From Daily Schedule Backup (Project Server 2013)
This article describes how to use the Daily Schedule Backup settings page to select the Project Server 2013 objects that you would like to schedule for back up on a daily basis. This procedure does not back up the physical files of a database (.mdb), but creates backups of specific items in the database. These items are backed up from the Published section to the Archive section in the Project Web App database.
Check the article in Technet
Hope it will be helpfully.
There is no option in Project Server to archive completed Projects. As mentioned by jpussacq You can schedule daily backup so that you can have good copy of Project Plan.
If you are using Project Server Permission mode you can do follow below steps:
- Create new Manage Catagory and only add people who should see the Archive Projects.
- Move completed Projects to newly created Catagory.
This way only few set of people like Project Manager and Portfolio Managers can see the Project.