Approximately 2 out of 10 people in the world still live without access to electricity. The UN "Sustainable Energy to All - SE4All" initiative aims at eradicating this electricity access deficit by 2030. To estimate the financial effort required to achieve this target we analyse two long-term scenarios developed by the Paul Scherrer Institute and the World Energy Council, which describe two alternative economic and energy system developments. We focus on developing Asia, Latin America and Sub-Saharan Africa, which currently have the largest percentage of population without access to electricity. We couple a long-term energy system model with regional econometric models that forecast population electrification rates. We find that establishing universal electricity access by 2030 requires significant, but attainable investments in power generation infrastructure, and results in low impacts on primary energy demand and CO₂ emissions.