We present a three-level equilibrium model for the expansion of an electric network. The lower-level model represents the equilibrium of a pool-based market; the intermediate level represents the Nash equilibrium in generation capacity expansion, taking into account the outcomes on the spot market; and the upper-level model represents the anticipation of transmission expansion planning to the investment in generation capacity and the pool-based market equilibrium. The demand has been considered as exogenous and locational marginal prices are obtained as endogenous variables of the model. The three-level model is formulated as a mixed integer linear programming (MILP) problem. The model is applied to a realistic power system in Chile to illustrate the methodology and proper conclusions are reached.

The current renewable-driven generation expansion wave, pushed by high renewable targets, is not accompanied by the same movement in the transmission expansion planning (TEP) side. In this context, new techniques are needed to balance the cost of relying in expensive reserve resources and the cost of building new lines to ensure least-cost reserve deliverability and foster new renewable projects. The situation is worsened in the presence of contingencies, where the interaction between the optimal reserve siting and deployment, the amount of renewable curtailment, the construction of new lines, and the selection of candidate renewable sites to be developed became even more complex. This paper presents a two-stage min-max-min model for co-optimizing the expansion of the transmission system and renewable generation capacity to meet renewable targets under high security standards and renewable uncertainty. In order to account for realistic reserve needs and its interaction with the expansion plan, correlations between renewables injection as well as generation and transmission (GT) outages are accounted for in a robust fashion. In order to ensure security within a flexible framework, the concept of compound GT n - K security criteria is presented. Three case studies are proposed to illustrate the applicability of the proposed model. A case study with realistic data from the Chilean system is presented and solutions obtained with different levels of security are tested against a set of 10 000 simulated scenarios of renewable injections and system component outages.

Intermittence and variability of renewable resources is often a barrier to their large scale integration into power systems. We propose a stochastic real-time unit commitment to deal with the stochasticity and intermittence of non-dispatchable renewable resources including ideal and generic energy storage devices. Firstly, we present a mathematical definition of an ideal and generic storage device. This storage device definition has some mathematical advantages: 1) it can be easily integrated within complex optimization problems, 2) it can be modeled using linear programming, suitable for practical large-scale cases. Secondly, a stochastic unit commitment with ideal and generic storage devices and intermittent generation is proposed to solve the joint energy-and-reserves scheduling and real-time power balance problem, reflecting the minute-by-minute intermittent changes and the stochasticity of renewable resources. We also compare our results with those obtained using a deterministic unit commitment with perfect information. The proposed model is illustrated with a 24-bus system.

This paper presents a new approach for the joint energy and reserves scheduling and unit commitment with n-K reliability constraints for the day-ahead market. The proposed method includes a novel n-K criterion where demand must be met with a specified probability under any simultaneous loss of K generating units. A chance-constrained method is proposed with an α-quantile measure to determine the confidence level to meet the demand under K simultaneous contingencies. The chance-constrained optimization problem is recast as a mixed integer linear programming optimization problem. Wind and demand uncertainty are included into the model. The methodology proposed is illustrated with several case studies where the effect of increasing wind power penetration is analyzed showing the performance of our model.