A low-carbon electricity supply for Australia was simulated, and the installed capacity of the electrical grid was optimized by shifting the electricity demand of residential electric water heaters (EWHs). The load-shifting potential of Australia was estimated for each hour of the simulation period using a nationwide aggregate EWH load model on a 90 x 110 raster grid. The electricity demand of water heaters was shifted from periods of low renewable resource and high demand to periods of high renewable resource and low demand, enabling us to effectively reduce the installed capacity requirements of a 100%-renewable electricity grid. It was found that by shifting the EWH load by just 1 hour, the electricity demand of Australia could be met using purely renewable electricity at an installed capacity of 145 GW with a capacity factor of 30%, an electricity spillage of 20%, and a generation cost of 15.2 ;/kWh. A breakdown of the primary energy sources used in our scenario is as follows: 43% wind, 29% concentrated solar thermal power, and 20% utility photovoltaic. Sensitivity analysis suggested that further reduction in installed capacity is possible by increasing the load-shifting duration as well as the volume and insulation level of the EWH tank.