An Optimal Scenario Reduction Method for Stochastic Power System Problems

Modern power systems problems recognize the value of using stochastic information to model renewable generation operations properly. Many optimal operation and planning problems can be formulated as two-stage stochastic optimization problems, typically employing discrete probabilistic scenarios to describe stochastic information. Large discrete scenario sets increase the computational complexity of these problems. Therefore, it is essential scenario reduction techniques that provide a good representative scenario set yielding the same or similar optimal results as the original probabilistic set.This paper describes a generalized adaptive partition-based method (GAPM) for finding an optimal representative scenario set for two-stage stochastic optimization problems. The iterative methodology obtains the optimal partition for a scenario set while providing the optimality gap at each iteration. Numerical tests are performed to compare the GAPM with popular scenario reduction techniques employed in the power systems literature. We show that even for a simple small problem, popular scenario reduction techniques based on the Kantorovich distance exhibit optimally gaps of more than 5%, performing even worse than vanilla methods of scenario reduction. Our methodology, in principle, can guarantee any optimality gap between the original problem and the reduced one.