Power BI Premium - which SQL server edition for catalog ?

I don't believe any of the express versions will work as the back end store for Report Server since it requires SQL Agent for running report subscriptions and for scheduling data refresh. So you will need at least a standard edition instance.

Janithri wrote:
But nobody has clarified if an On Premises Power BI Report Server installation(licensed through Power Bi Premium license) requires a paid SKU of SQL Server edition to be installed.

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No if you have licensed PBIRS through purchasing a P-SKU you are not required to purchase a paid SKU of SQL Server.

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Janithri wrote:
 "Power BI Report Server does not require a separate SQL Server license unless you intend to use other components such as the SQL Server database engine or SQL Server Integration Services. A limited-use rights database engine comes with the Power BI Report Server for hosting the Report Server catalog and temporary databases". 

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So what this limited use license means is that you are entitled to install a full edition of SQL Server as long as it is ONLY used for Power BI Report Server. As soon as you put a single other database on this instance you would be violating the "limited-use rights" and would need to pay for a full SQL license, but as long as it only hosts the Report Server databases you are fine.

But this is just my understanding based on what has been explained to me - you should be able to confirm this with your local Microsoft account representative or the local Microsoft office.