Energy imbalances due to power forecast errors have a significant impact on both the cost of operating the power system and the profitability of stochastic power generating units. In this paper, we propose a modeling framework to analyze the effect of the costs of these imbalances on the expansion of stochastic power generating units. This framework includes the explicit representation of a day-ahead and a balancing market-clearing mechanisms to properly capture the impact of forecast errors of power production on the short-term operation of a power system. The proposed generation expansion problems are first formulated from the standpoint of a social planner to characterize a perfectly competitive market. We investigate the effect of two paradigmatic market designs on generation expansion planning: a day-ahead market that is cleared following a conventional cost merit-order principle, and an ideal market-clearing procedure that determines day-ahead dispatch decisions accounting for their impact on balancing operation costs. Furthermore, we reformulate the proposed models to determine the optimal expansion decisions that maximize the profit of a collusion of stochastic power producers in order to explore the effects of competition at the investment level. The proposed models are first formulated as multi-level programming problems and then recast, under certain assumptions, as single-level mixed-integer linear or non-linear optimization problems using duality theory. The variability of the forecast of the stochastic power production and the demand level throughout the planning horizon is modeled using yearly duration curves. Likewise, the uncertainty pertaining to power forecast errors is characterized through scenario sets. The main features and results of the proposed models are discussed using an illustrative example and a more realistic case study based on the Danish power system.
- Generating expansion
- Stochastic generating units
- Imbalance cost
- Market clearing
- Stochastic bilevel programming