We examine the impact of policy choices, including a carbon tax, on the optimal allocation of power across different generation sources and on future investments in generating facilities. The main focus is on the Alberta power grid, as it is heavily dependent on fossil fuels and has only limited ties to other power grids, although the model could be extended to larger (and even multiple) grids. The results indicate that, as wind penetrates the extant generating mix characterizing the grid, cost savings and emission reductions do not decline linearly but at a decreasing rate. However, if flexibility is allowed, then, as the carbon tax increases to C40/tCO2 or above, existing coal plants start to be replaced by newly constructed wind farms and natural gas plants. If coal can be completely eliminated from the energy mix and replaced by natural gas and wind, substantial savings of 31.03 Mt CO2 (58% of total emissions) can result. However, this only occurs for carbon taxes of over C170/tCO2. The associated high capital costs of new generating facilities may thus not be an ideal use of funds for addressing climate change.