A stochastic network equilibrium model for electric power markets with uncertain demand

We use the theory of stochastic variational inequalities to develop a network equilibrium model of the whole supply chain of electricity markets: power generation, supply, transmission, and consumption. In particular, we take into account the case where the market demand functions are not exactly known but are affected by some kind of uncertainty. A discretization and truncation procedure is used to numerically solve the stochastic variational inequality model. Monotonicity properties of the operator are investigated and the affine case is analysed in detail. Finally, numerical experiments show the impact of different probability densities of the random variables on the approximated solutions and the scalability of the proposed numerical method for real-world sized problems.