Generation of multivariate scenario trees to model stochasticity in power management

Modern electricity portfolio and risk management models represent multistage stochastic programs. The input of such programs consists in a finite set of scenarios having the form of a scenario tree. They model the probabilistic information on random data (electrical load, stream flows to hydro units, market prices of fuel and electricity). Since the corresponding deterministic equivalents of multistage stochastic programs are mostly large scale, one has to find significant tree-structured scenarios. Our approach to generate multivariate scenario trees is based on recursive deletion and bundling of scenarios out of some given (possibly large) scenario set originating from historical or simulated data. The procedure makes use of certain Monge-Kantorovich transportation distances for multivariate probability distributions. We report on computational results for generating load-inflow scenario trees based on realistic data of EDF Electricite de France.