Bilevel Programming Models for Power Generation Capacity Expansion Planning with Revenue Adequacy Constraints

The evolution of electricity systems involves transformative changes aimed at reducing carbon emissions. This requires a high penetration of renewables that is already showing a strong impact on prices. The resulting missing money problem, for which generators fail to recover costs through market revenues, may lead to an inadequate system, incapable of meeting decarbonization targets. In this context, mathematical models are crucial for addressing the challenges in long-term planning. In this work, we focus on an innovative modeling development for the Generation Expansion Planning (GEP) problem, customized to address the forthcoming demand for decision support in the Italian electricity market. The GEP is formulated as a bilevel optimization problem, where Revenue Adequacy is ensured for different technologies by considering a detailed definition of market revenues with meaningful market clearing prices. This includes zonal distinctions as perceived by the Italian electricity market to account for price signals. In addition, the model incorporates side payments that can serve as indicators for Capacity Remuneration Mechanism-like auctions. To ensure the realistic operation of the model, we suggest two novel sets of constraints, designed to prevent withholding strategies and to deal with price indeterminacy. The problem's bilevel nature, combined with revenue modeling, results in bilinear components. In addition to examining state-of-the-art linearization techniques, we develop an exact linearization method for the product of two continuous variables, namely prices and quantities. To address the difficulty of finding feasible solutions, we introduce specialized cuts and develop auxiliary problems that effectively warm start the model by mimicking the hierarchical relationship between levels. Furthermore, to address the task of proving optimality, we propose a “hybrid” approach that combines different formulations for complementarity slackness conditions.