There is increasing urgency towards integration of renewable sources into electricity generation so as to minimize greenhouse gas (GHG) emissions. Renewable power sources are highly specific in prevalence, both regionally and temporally, and their utilization at utility-scale for round-the clock power supply poses the problem of matching power generation capacity and power demand at every instant of time. In the present work, we propose a model that integrates (geographically) distributed and (technically) diverse power sources with geographically spread-out power consumption centres and distributed and diverse electrical energy storage systems through transmission and storage loss models. For a regional electricity grid, the model computes, over a given day, the minute-by-minute power demand from and power generation in all districts, extracts matching power from a hierarchy of power sources so as to minimize transmission and storage losses, and stores excess power in a variety of power storage options. For the specific case of the South Indian Power Grid (catering to about 285 million people in South India), the model shows that 235 GWh of new electrical storage is required for round-the-clock power supply from nonGHG power sources.