You can use an external Tag Browse Tree Component, in conjunction with the filter extension function, to filter the tags. Just not the one that is embedded in the Power Chart. You have yet to explain how the Tag knows what department it belongs to, or how that can be determined other than just "its in a database".
You will also need to hide the Chart Settings as @pascal.fragnoud points out because from there, if a user knows the path to a tag, even one that is outside of their "department" they can access that tag.
Once you have selected a tag, through whatever method, you will need to use a script to add a new pen to the chart.