Robust Optimization Methods for Improving Virtual Power Plant Reliability and Classification Fairness

Abstract

In this dissertation, we present three different robust optimization approaches: distributionally robust optimization (DRO), target-oriented robust optimization (TORO), and Rawlsian fairness. We apply DRO and TORO frameworks to address virtual power plant reliability, and Rawlsian fairness to address the fair binary classification problem. A virtual power plant (VPP) is an entity that aggregates smaller solar and wind farms with other heterogeneous distributed energy resources (DERs) to increase their visibility to Independent System Operators (ISOs) and allows them to participate in the energy market. Typically, smaller solar and wind farms are unable to participate in the wholesale energy market, so a VPP's ability to integrate them into the energy market is a crucial step for reducing the global carbon footprint and combating climate change. Our proposed multi-stage DRO framework allows us to schedule VPP operations in the presence of intermittent renewable energy output by dynamically coordinating the heterogeneous DERs in a reliable and cost-effective manner. Our proposed TORO method helps us address another challenge that arises from increased renewable energy penetration, which is the assessment of the VPP’s flexibility. The uncertainty brought by renewable energy makes it harder to balance energy supply and demand, and failing to do so can result in expensive renewable energy curtailment or blackouts. Our TORO method provides a flexibility assessment framework that identifies the maximum amount of net load deviation the system can tolerate. Traditional binary classification algorithms are prone to producing unfair results that favor certain demographic groups over others. This inequity is often exacerbated in unbalanced datasets where the number of entries from a majority group significantly outweighs the entries from a minority group. We use a MIP framework to formulate our Rawlsian fairness to address these inequities. Our methodology prioritizes the performance of the worst-off demographic group, and our specific formulation can produce interpretable solutions by directly optimizing sparsity. Additionally, it provides flexibility for users to achieve interpretable solutions in multiple ways.