The cost recovery problem in power generation expansion planning models

The evolution of the electricity system in Italy towards decarbonization targets involves a significant increase in installed generation capacity from renewable sources, which are currently bidding at zero price on the day-ahead market (Mercato del Giorno Prima – MGP). This has several consequences: firstly, thermal plants, typically gas-fired plants that incur production costs, produce in a reduced number of hours and incur higher operating costs due to the higher number of startups and shutdowns caused by the non-programmability of renewable power plants. In addition, the higher expected contribution of renewable sources leads to an increase in the number of hours when the market price of energy is low or even zero. In this context, the inability of thermal power plants to recover their costs (in particular investment and fixed costs) through market payments may lead to the decommissioning of existing plants and discourage investment in new plants. This ultimately leads to the risk that the electricity system will not be able to meet peak demand. Several countries have adopted different strategies to address this challenge, seeking to ensure the adequacy of the electricity system while promoting a shift towards more sustainable energy sources. In particular, to ensure the recovery of fixed costs for thermal generators, Italy has introduced a type of capacity market based on an auction mechanism that results in additional payments outside the spot market, known as side-payments. More recently, the government is considering auctions involving various forms of Contracts for Difference to support investment in renewable generators. Generation Expansion Planning (GEP) models are used to determine the optimal configuration of the electricity system in the long run, i.e., the configuration that minimizes investment and operating costs and ensures the achievement of policy objectives: adequacy and decarbonization. Most GEP models proposed in the literature do not address the issue of cost recovery and thus provide projections that do not necessarily reflect the real economic viability of the system: in this case the investment decisions envisaged by the model may not be implemented by private investors. Only a few papers deal with cost recovery in GEP, of which only Guo et al. [1] use an optimization approach, but the market price determined by their model does not represent the cost of satisfying an additional unit of demand. We therefore propose a GEP model in which a central planner determines the optimal configuration of the system, both spatially and technologically, while minimizing the total cost to consumers and ensuring the economic sustainability of thermal and renewable power plants and the necessary storage. This is achieved by introducing revenue adequacy constraints, where revenues come both from the market and potentially from side payments. Our optimization model is structured as a bilevel problem to allow accurate estimation of revenues and costs: at the lower level, the market operator solves the dispatch problem to satisfy the load and determines the MGP zonal hourly price as the cost of meeting an additional unit of demand; at the upper level,the central planner determines the optimal investment, thermal plant operation and side payments,while imposing policy targets for renewable penetration. The resulting optimization model is a Mixed Integer Quadratic Constrained Problem (MIQCP), since physically based characteristics (such as lumpy investments, technical minimum and start-up decisions for thermal plants) are modelled by integer variables, and revenues are represented by bilinear terms. The MIQCP model is solved using a specialized solver. In addition, MIP versions of the model have been developed by means of linearization techniques for bilinear terms.