Smart Grids (SGs) are emerging as a promising technology meant to cope with the energy efficiency issue, currently witnessed in legacy electrical grids, by disseminating relevant information in a real-time mode among the different SG components. The SG Advanced Metering Infrastructure (AMI) form s a central SG component, and consists basically of meters/sensors that are regularly communicating data towards the Control Plane. Much of these communicated data emanates from wireless sensors, and falls in the realm of Big Data. The latter needs substantial high-performance compute (HPC) power for processing and mining. In this paper, we shed further light into a syne rgetic interface between SGs and the Cloud. We propose the use of Cloud computing to provide HPCaaS fo r SG Big Data processing, and delineate a suitable architecture. We present the blue print for deployi ng a real world private cloud testbed using OpenStack, Hadoop, and the MapReduce progra mming model. To assess the test bed functionalities, we run extensive experiments using benchmarked Big Data sets.