Bilevel Flexible-Robust Optimization for Energy Allocation Problems

A common issue in energy allocation problems is managing the tradeoff between selling surplus energy to maximize short-term revenue, versus holding surplus energy to hedge against future shortfalls. For energy allocation problems, this surplus represents resource flexibility. The decision maker has an option to sell or hold the flexibility for future use. As a decision in the current period can affect future decisions significantly, future risk evaluation of uncertainties is recommended for the current decision in which a traditional robust optimization is not efficient. Therefore, an approach to flexible-robust optimization has been formulated by integrating a real options (RO) model with the robust optimization framework. In the energy problem, the real option model evaluates the future risk, and provides the value of holding flexibility, whereas the robust optimization quantifies uncertainty and provides a robust solution of net revenue by selling flexibility. This problem is solved using bilevel programming and a complete general mathematical formulation of bilevel flexible-robust optimization model is presented for multireservoir systems and results shown to provide an efficient decision making process in energy sectors. To reduce the computational expense, mathematical techniques have been used in the proposed model to reduce the dimension in the quantification and propagation of uncertainties.