Mathematical contributions for the optimization and regulation of electricity production.

Summary We present our contribution on the control and optimization of electricity production. The first part concerns the optimization of the management of a micro grid. We formulate the management program as an optimal control problem in continuous time, then we solve this problem by dynamic programming using a solver developed for this purpose: BocopHJB. We show that this type of formulation can be extended to a stochastic modeling. We end this part with the adaptive weights algorithm, which allows a management of the micro network battery integrating its aging. The algorithm exploits the two time scale structure of the control problem. The second part concerns networked market models, and in particular those of electricity. We introduce an incentive mechanism to decrease the market power of energy producers, to the benefit of the consumer. We study some mathematical properties of the optimization problems faced by market agents (producers and regulators). The last chapter studies the existence and uniqueness of Nash equilibria in pure strategies of a class of Bayesian games to which some network market models belong. For some simple cases, an equilibrium computation algorithm is proposed. An appendix gathers a documentation on the numerical solver BocopHJB.