Limited data on global power infrastructure makes it difficult to respond to challenges in electricity access and climate change. Although high-voltage data on transmission networks are often available, medium- and low-voltage data are often non-existent or unavailable. This presents a challenge for practitioners working on the electricity access agenda, power sector resilience or climate change adaptation. Using state-of-the-art algorithms in geospatial data analysis, we create a first composite map of the global power system with an open license. We find that 97% of the global population lives within 10 km of a MV line, but with large variations between regions and income levels. We show an accuracy of 75% across our validation set of 14 countries, and we demonstrate the value of these data at both a national and regional level. The results from this study pave the way for improved efforts in electricity modelling and planning and are an important step in tackling the Sustainable Development Goals.