Feature-based scenario clustering and selective degrees of freedom reduction for two-stage stochastic optimization of Power-to-Methanol

Abstract

Power-to-X processes can be operated flexibly to exploit electricity price fluctuations or renewable power availability, reducing production costs. Ideally, the process design should be optimized simultaneously with the scheduling or operation. To address the uncertainty in electricity prices or availability, several scheduling scenarios can be simultaneously considered in two-stage stochastic optimization problems. However, these problems, especially when nonlinear, become challenging to solve when the scenario number and scheduling horizon increase.

To tackle this challenge, we combine feature-based scenario clustering with reducing the degrees of freedom (DoF) related to the scheduling variables. The latter maintains time step chronology memory, thus ensuring optimal solution feasibility even if storage is present. For a Power-to-Methanol process, we show that DoF reduction should not be applied to all scheduling variables when there is intermediate storage, since it strongly correlates the variables, thus affecting the optimal process design. In a sensitivity analysis concerning the scenario cluster number, we show that scenario clustering based on interpretable features can represent the original space and estimate the objective function with a few scenarios, performing similarly to k-means and k-medoids clustering regarding the objective function. However, despite similar objective values, different optimal designs are identified for different scenario cluster numbers.