Several methodologies exist for evaluating the economic potential of renewable energy sources. These methodologies either cannot capture how this economic potential depends on its embedding in the whole energy mix, or provide a single cost-optimal energy mix, which is not flexible enough for building consensus among the relevant stakeholders. This article addresses these two limitations and introduces a novel methodology EXPANSE (EXploration of PAtterns in Near-optimal energy ScEnarios) for evaluating the economic potential of renewable energy sources from an energy mix perspective. This methodology is based on generation of cost-optimal and multiple near-optimal energy mixes. These mixes show the maximum, technically feasible, cost-effective potential of a renewable energy source under consideration and how this potential depends on the other supply alternatives and energy savings in an energy mix. The methodology is illustrated with the example of the renewable energy use for heat supply in a Swiss region. The example shows that even a particular renewable energy source is costlier than the currently deployed alternatives such as oil, its economic potential in an energy mix can be as high as its full exploitable (theoretical) potential, when some deviation is allowed from the cost-optimal energy mix. However, the full economic potential of all renewable energy sources cannot be utilized simultaneously. The full deployment of the economic potential of one renewable energy source decreases the economic potential of others. EXPANSE provides basis for analyzing such interlinkages.