This thesis introduces a computer model for simulating worldwide deployment of wind and solar power technologies at high spatial and temporal resolution. The Spatiotemporally-Explicit Power and Transmission (SEXPOT) model integrates global meteorological, geophysical, and socioeconomic data to identify cost-minimizing strategies for utilizing available renewable resources. SEXPOT is unique, because it allows for low-cost, large-scale analyses while providing local-scale results. Model output includes the preferred locations for wind and solar power technologies and transmission lines and shows how variable power sources can be integrated with conventional technologies to meet demand hour-by-hour. NASA climate model output is used to predict the performance of onshore and offshore wind turbines and utility-scale and rooftop solar photovoltaic (PV) panels, and a statistical model is developed to predict the distribution of electricity consumption across space and time. Linear programming techniques are then used to optimize the deployment of generating technologies. This paper describes the development of model components and associated input data and demonstrates functionality with an illustrative model run. Application to a variety of research questions is explored and areas for model improvement identified. SEXPOT is presently a working prototype that, it is hoped, will be improved over time.