Hi,
PowerPivot doesn't work with Office 2007 and workbooks that were created with Data Model from later versions of Excel will not be refreshable on Office 2007.
Your Office 2010 users can install the PowerPivot Add-in here. The Add-in is free for these versions.
In Office 2013 the PowerPivot is included in Excel, but you can only refresh it with the licenses you have. The PowerPivot manage windows can only work with Office 2013 Professional Plus.
In addition, you should note that there are forward compatibility issues between Excel version 2013 and 2010. if your Office 2010 users will create Data Models with the PowerPivot Add-in, and will share the workbooks with their Office 2013 peers, during
the refresh of the Data Model on Excel 2013, the users will get a prompt to ask them to upgrade the Data Model. Once upgraded, these Data Models cannot load on Excel 2010.
To summarize - You will need to ensure that all your users are on the same Excel version - 2010 or 2013. If you go with Excel 2013, the authors will need to use Professional Plus version.