This paper proposes a bilevel model to assist a generation company in making its long-term generation capacity investment decisions considering uncertainty regarding the investments of the other generation companies. The bilevel formulation allows for the uncoupling of investment and generation decisions, as investment decisions of the single investing generation company are taken in the upper level with the objective to maximize expected profits and generation decisions by all companies are considered in the lower level. The lower level represents the oligopolistic market equilibrium via a conjectured-price response formulation, which can capture various degrees of strategic market behavior like perfect competition, the Cournot oligopoly, and intermediate cases.The bilevel model is formulated as an MPEC, replacing the lower level by its KKT conditions and transformed into a MILP. Results from a study case are presented and discussed.Index Terms-Bilevel programming, generation expansion planning, mathematical program with equilibrium constraints (MPEC).

This paper analyzes different models for evaluating investments in energy storage systems (ESS) in power systems with high penetration of renewable energy sources. First of all, two methodologies proposed in the literature are extended to consider ESS investment: a unit commitment model that uses the "system states" (SS) method of representing time; and another one that uses a "representative periods" (RP) method. Besides, this paper proposes two new models that improve the previous ones without a significant increase of computation time. The enhanced models are the "system states reduced frequency matrix" model which addresses short-term energy storage more approximately than the SS method to reduce the number of constraints in the problem, and the "representative periods with transition matrix and cluster indices" (RP-TM&CI) model which guarantees some continuity between representative periods, e.g., days, and introduces long-term storage into a model originally designed only for the short term. All these models are compared using an hourly unit commitment model as benchmark. While both system state models provide an excellent representation of long-term storage, their representation of short-term storage is frequently unrealistic. The RP-TM&CI model, on the other hand, succeeds in approximating both shortand long-term storage, which leads to almost 10 times lower error in storage investment results in comparison to the other models analyzed.Index Terms-Energy storage systems, power system planning, power system modeling, system states, representative days.

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