Efficient Decision Making under Uncertainty in a Power System Investment Problem

The optimization of power systems involves complex uncertainties, such as technological progress, political context, geopolitical constraints. These uncertainties are difficult to modelize as probabilities, due to the lack of data for future technologies and due to partially adversarial geopolitical decision makers. Tools for such difficult decision making problems include Wald and Savage criteria, probabilistic reasoning and Nash equilibria. We investigate the rationale behind the use of a two-player Nash equilibrium approach in such a difficult context, and show that the approach is computationally efficient for large problems. Moreover, it automatically provides a selection of interesting decisions and critical scenarios for decision makers and is computationally cheaper than the Wald or Savage, thanks to the use of the sparsity of Nash equilibrium. It also has a natural interpretation in the sense that Nature does not make decisions taking into account our own decisions. The proposed approach was tested on instances of an artificial power system investment problem and can be applied to other problems, that can be modelled as a two-player matrix game or of which a payoff matrix can be built.