If you have
a site collection and want to upgrade from SharePoint 2010 to SharePoint 2013
PowerShell, then this blog will give you step–step to do this a bit
easier.

Go to Central
Adminstration, create New Site and in Select Experience Version choose 2010.
(Example: My site is Home).

The Home page is created in SharePoint 2010 as:

Open SharePoint 2013 Management Shell and Run as Administrator.

Enter command: Upgrade-SPSite
http://server/sitecollection -VersionUpgrade (for example: Upgrade-SPSite
http://vngo15sql2/home -VersionUpgrade).

Wait until you see the following
message:

Then, go to your site and launch
it.