Pascal Gourdel

Electricity systems are quitting monopoly for an operation framed by competitive markets. It therefore questions how the operation of nuclear plants capable of load-following is expected to change at the transition stage in a challenging economic environment for nuclear producers given the high penetration of renewables and the increase of nuclear production costs for renovation and safety reasons. To answer this question, we are focusing on a month-by-month management horizon of the nuclear fuel given the technico-economical features of the operation of flexible nuclear plants. The resolution of the month-by-month profit maximization problem contributes to identify potential difficulties and limits of production optimization and provides us with an equilibrium which proves the existence of an optimal production path. This benchmark could serve as a reference providing valuable insight on the resolution of more complex optimisation problems.

We give a generalized version of the well-known Borsuk’s antipodal fixed point theorem for a large class of antipodally approachable condensing or compact set-valued maps defined on closed subsets of locally convex topological vector spaces. These results contain corresponding results obtained in the literature for compact set-valued maps with convex values.

The road towards the decarbonization of electricity leads to high deployment of low-carbon power sources including intermittent energy sources. In this context, flexible nuclear power plants could play a significant role because they do not produce CO2 emissions and under certain conditions flexible operation is necessary to ensure the stability of the electricity grid. Flexible nuclear reactors have the ability to load-follow the predicted fluctuations in demand. However, high fixed costs of nuclear production, tighter regulations since the Fukushima accident and the extensive participation of renewable sources in the energy mix challenge the economic profitability of nuclear production. Consequently, a question that arises is how nuclear power producers can manage flexible nuclear production in order to maximize their profits. We proved that optimal production behaviour is not characterized by constant nuclear production unless further investments in thermal capacity are realized. On the contrary, both nuclear and thermal production are flexible at the optimum level.

In the spirit of Michael selection theorem (Theorem 3.1′′′, 1956), we consider a nonempty convex valued lower semicontinuous correspondence φ : X → 2^Y . We prove that if φ has either closed or finite dimensional images, then there admits a continuous single valued selection, where X is a metric space and Y is a Banach space. We provide a geometric and constructive proof of our main result based on the concept of peeling introduced in this paper.

Flexible nuclear power plants can adjust their electricity production to the predicted evolution of demand. Under certain conditions, flexible operation is necessary to ensure the stability of the electricity system. However, despite the potential advantages of nuclear energy including the flexibility of nuclear reactors, the social acceptance of nuclear has reduced after the Fukushima accident, leading some countries to reduce or even phase out nuclear (e.g. Germany). So, a question that arises is how flexible nuclear power plants have to be operated in order to maximize social welfare. The French nuclear fleet gives an illustration of flexible management while social acceptance of nuclear is questioned; this was reflected in the new French Energy Transition law. Theoretically and numerically, we found that the production behavior that maximizes social welfare is characterized by a constant thermal production and a totally flexible nuclear production given sufficient nuclear capacity. Energy

We present an extension of Borsuk’s antipodal theorem (on the existence of a zero) to antipodally approachable correspondences defined on bounded, symmetric and balanced domains.