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The first of this two-paper series addresses a practical day-ahead auction model, where generation revenue constraints are explicitly incorporated in the problem formulation, as routinely done in several national electricity markets across Europe. The revenue-constrained market-clearing procedure includes the effect of the transmission network, inter-temporal constraints associated with generation scheduling, demand-side bidding, and marginal pricing. This auction design is an instance of price-based market clearing which features two major complicating factors. First, locational marginal prices become decision variables of the optimization process. In addition, producer revenues are formulated as bilinear and highly nonconvex products of power outputs and market-clearing prices. The resulting problem is formulated as a mixed-integer nonlinear bilevel program with bilinear terms for which available solution techniques rely on heuristics, approximations, or modeling simplifications. This paper presents a novel and exact methodology whereby the original problem is recast as an equivalent single-level mixed-integer linear program. As a consequence, finite convergence to optimality is guaranteed and the use of standard commercial software is allowed. The proposed transformation is based on duality theory of linear programming, Karush-Kuhn-Tucker optimality conditions, and integer algebra results. In the second part of this two-paper series, numerical results from several case studies illustrate the effective performance of the proposed solution approach. [ABSTRACT FROM AUTHOR]

Abstract: The reasons why the transmission network is a potentially attractive target for deliberate outages are twofold: (i) its crucial importance as a critical infrastructure for the society welfare, and (ii) its high level of vulnerability due to the current operation close to its static and dynamic limits. This new context where destructive agents come into play has been recognized by several agencies in Europe and North America, and various initiatives have been launched worldwide in order to assess and mitigate the vulnerability of transmission. Within this framework, this paper proposes the reinforcement and expansion of the transmission network as a way of mitigating the impact of increasingly plausible deliberate outages. The network planner selects the new lines to be built accounting not only for economic issues, as traditionally done, but also for the vulnerability of the transmission network against a set of credible intentional outages. The resulting vulnerability- and economic-constrained transmission expansion planning problem is formulated as a mixed-integer linear program. A number of case studies numerically illustrate the tradeoff between economic- and vulnerability-related issues and its impact on the expansion plans. In addition, we compare the results with those achieved by a traditional expansion planning model based on cost minimization. [Copyright &y& Elsevier]