The current supply for electricity generation mostly relies on fossil fuels, which are finite and pose a great threat to the environment. Therefore, energy models that involve clean and renewable energy sources are necessary to ease the concerns about the electricity generation needed to meet the projected demand. Here, we mathematically model a hybrid energy generation and allocation system where the intermittent solar generation is supported by conventional hydropower stations and diesel generation and time variability of the sources are balanced using the water stored in the reservoirs. We develop a two-stage stochastic model to capture the effect of streamflows which present significant inter-annual variability and uncertainty. Using sample case studies from India, we determine the required hydropower generation capacity and storage along with the minimal diesel usage to support 1 GWpeak solar power generation. We compare isolated systems with the connected systems (through inter-regional transmission) to see the effects of geographic diversity on the infrastructure sizing and quantify the benefits of resource-sharing. We develop the optimal sizing relationship between solar and hydropower generation capacities given realistic cost parameters and real data and examine how this relationship would differ as the contribution of diesel is reduced. We also show that if the output of the solar power stations can be controlled (i.e. spill is allowed in our setting), operating them below their maximum energy generation levels may reduce the unit cost of the system.