No, Power BI is not available as a private and internal cloud service. But, with Power BI and Power BI Desktop, you can connect to your own on-premises data sources securely. With the On-premises Data Gateway, you can connect live to your on-premises SQL Server Analysis Services and other data sources. Also, You can schedule refresh with a centralized gateway. If a gateway is not available, then you can refresh data from on-premises data sources using the Power BI Gateway – Personal.