An inter-temporal optimization of flexible nuclear plants operation in market based electricity systems: The case of competition with reservoir

In electricity markets where competition has been established for a long time, a nuclear operator familiar with the operation of such markets could be interested in the optimal long-term management of a flexible nuclear set (like the French) in a competitive market. To obtain a long vision of the optimal management of a nuclear set, we realize a full inter-temporal optimization of the production which results from the maximization of the value of generation over the whole game. Our model takes into consideration the periodical shut-down of nuclear units to reload their fuel, which permits to analyze the nuclear fuel as a stock behaving like a reservoir. A flexible nuclear reservoir permits different allocations of the nuclear fuel during the different demand seasons of the year. Our analysis is realized within a general deterministic dynamic framework where perfect competition is assumed and two flexible types of generation exist: nuclear and thermal non-nuclear. The marginal cost of nuclear production is (significantly) lower that the one of non-thermal production, which induces a discontinuity of producers' profit. In view of this price discontinuity, a "regularization" of the merit order price is achieved within our numerical model which leads to an alternative optimization problem (reglarized problem) that constitutes a good approximation of our initial problem. We also prove that in the absence of binding productions constraints, solutions are fully characterized by a constant nuclear production. However, such solutions do not exist within our numerical model because of production constraints that are active at the optimum. Finally, we study the maximization of social welfare in an identical framework. Similarly, we demonstrate that in the absence of binding production constraints a constant non-nuclear thermal production is a characteristic property of solutions of the social welfare maximization problem