Scenario reduction heuristics for a rolling stochastic programming simulation of bulk energy flows with uncertain fuel costs

Abstract

<p>Stochastic programming is employed regularly to solve energy planning problems with uncertainties in costs, demands and other parameters. We formulated a stochastic program to quantify the impact of uncertain fuel costs in an aggregated U.S. bulk energy transportation network model. A rolling two-stage approach with discrete scenarios is implemented to mimic the decision process as realizations of the uncertain elements become known and forecasts of their values in future periods are updated. Compared to the expected value solution from the deterministic model, the recourse solution found from the stochastic model has higher total cost, lower natural gas consumption and less subregional power trade but a fuel mix that is closer to what actually occurred. The worth of solving the stochastic program lies in its capacity of better simulating the actual energy flows.</p> <p>Strategies including decomposition, aggregation and scenario reduction are adopted for reducing computational burden of the large-scale program due to a huge number of scenarios. We devised two heuristic algorithms, aiming to improve the scenario reduction algorithms, which select a subset of scenarios from the original set in order to reduce the problem size. The accelerated forward selection (AFS) algorithm is a heuristic based on the existing forward selection (FS) method. AFS's selection of scenarios is very close to FS's selection, while AFS greatly outperforms FS in efficiency. We also proposed the TCFS method of forward selection within clusters of transferred scenarios. TCFS clusters scenarios into groups according to their distinct impact on the key first-stage decisions before selecting a representative scenario from each group. In contrast to the problem independent selection process of FS, by making use of the problem information, TCFS achieves excellent accuracy and at the same time greatly mitigates the huge computation burden.</p>