How to manage a large and flexible nuclear set in a deregulated electricity market from the point of view of social welfare?

In the case of a large nuclear set (like the French set), nuclear production needs to be flexible to adjust to the predicted evolutions of the energy demmand. Consequently, the dominant position of nuclear in the national energy mix makes it responsible for the overall equilibrium of the electricity system which is directly intertwined with social welfare. In a previous work, we looked at producers own profits (short-term, inter-temporal) considering the equality between supply and demand. Here, we proceed with a full optimization of the social welfare in an identical framework. Theoretically, the optimal production behaviour that maximizes social welfare is characterized by a constant thermal production and a totally flexible nuclear production given that the nuclear capacity is sufficient. Numerically, the significant amount of nuclear capacities compared with thermal capacities in the French electricity market leads to the same "paradoxical" production behaviour. Therefore, we conclude that social optimum is ensured within our model by investing sufficiently in nuclear capacity. The optimal production scheduling determined by the social welfare maximization problem and the optimal inter-temporal production problem are totally opposite.