Modeling Uncertainty Processes for Multi-Stage Optimization of Strategic Energy Planning

This paper deals with the modeling of stochastic processes in long-term multi-stage energy planning problems when little information is available on the degree of uncertainty of such processes. Starting from simple estimates of variation intervals for uncertain parameters, such as energy demands and costs, we model the temporal correlation of these parameters through carefully constructed autoregressive (AR) models that respect the intervals defined in each period. We introduce a coefficient for 'zigzag' effects in the evolution of uncertain processes that controls the correlation across periods and also the likelihood of extreme scenarios. To preserve the convexity of the stochastic problem, we discretize the AR models associated with the cost parameters involved in the objective function by Markov chains. The resulting formulation is then solved with a Stochastic Dual Dynamic Programming (SDDP) algorithm available in the literature that handles finite-state Markov chains. Our numerical experiments, performed on the Swiss energy system, show a very desirable adaptation strategy of investment decisions to uncertainty scenarios, a behavior that is not observed when the temporal correlation is ignored. Moreover, the solutions lead to better out-of-sample cost performances, especially on extreme scenario realizations, than the non-correlated ones which usually yield overcapacities to protect against high, but unlikely, parameter variations over time