Fig. 3

Exemplary schema illustrating the two modeling approaches to include equality in the model: first, the quadratic characteristic of the objective function (blue) for the Min var modeling approach when a region’s capacity potential utilization deviates from the global mean. A negative utility induces inequality costs in our model. Second, a limitation of the deviation from the global mean (orange) is implemented as a model constraint, representing the Lim d modeling approach (no utility or inequality costs considered). Note: due to the dependency of the two variables \({\gamma}_{k}\) and \(\overline{\gamma}\), the length of the available interval for the resulting deviation is always < 1