This study newly develops a recursive-dynamic global energy model with an hourly temporal resolution for electricity and hydrogen balances, aiming to assess the role of variable renewable energy (VRE) in a carbon-neutral world. This model, formulated as a large-scale linear programming model (with 500 million each of variables and constraints), calculates the energy supply for 100 regions by 2050. The detailed temporal resolution enables the model to incorporate the variable output of VRE and system integration options, such as batteries, water electrolysis, curtailment, and the flexible charging of battery electric vehicles. Optimization results suggest that combing various technical options suitable for local energy situations is critical to reducing global CO₂ emissions cost-effectively. Not only VRE but also CCS-equipped gas-fired and biomass-fired power plants largely contribute to decarbonizing power supply. The share of VRE in global power generation in 2050 is estimated to be 57% in a cost-effective case. The results also imply economic challenges for an energy system based on 100% renewable energy. For example, the average mitigation cost in 2050 is 69USD/tCO₂ in the cost-effective case, while it increases to 139USD/tCO₂ in the 100% renewable case. The robustness of this argument is tested by sensitivity analyses.