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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]

This paper presents an alternative day-ahead auction based on consumer payment minimization for pool-based electricity markets. This auction is an instance of price-based market clearing wherein market-clearing prices are explicitly modeled as decision variables of the optimization. The auction design includes network constraints, inter-temporal constraints associated with generation scheduling, and marginal pricing. Hence, consumer payment is expressed in terms of locational marginal prices. The proposed solution approach is based on bilevel programming. In the upper-level optimization, generation is scheduled with the goal of minimizing the total consumer payment while taking into account that locational marginal prices are determined by a multiperiod optimal power flow in the lower level. In this bilevel programming setting, locational marginal prices are the Lagrange multipliers or dual variables associated with the nodal power balance equations of the lower-level problem. The resulting mixed-integer linear bilevel program is transformed into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software. This transformation relies on the application of results from duality theory of linear programming and integer algebra. The proposed methodology has been successfully applied to several test systems including the IEEE 118-bus system. Numerical results have been compared with those obtained from declared social welfare maximization. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of price multiplicity in network-constrained pool-based electricity markets under marginal pricing. This problem consists in the existence of multiple vectors of locational marginal prices for the same optimal market-clearing dispatch solution. As a consequence, delicate conflicts of interest may arise among market participants. Price multiplicity may take place even in auction designs based on convex formulations for the market-clearing procedure. An effective duality-based solution approach is proposed in this paper to handle the issue of price multiplicity. Once the optimal market-clearing dispatch is known, we propose the subsequent solution of a simple pricing problem in order to determine the vector of locational marginal prices. Unlike previously reported methodologies, the proposed approach presents two salient features: 1) it is based on sound mathematical programming, and 2) it is computationally inexpensive since it relies on the solution of a linear program. Numerical results are provided to illustrate the performance of the proposed tool. [ABSTRACT FROM PUBLISHER]

This paper presents a risk-based approach for the transmission network expansion problem under deliberate outages. Malicious attacks expose network planners to a new challenge: how to expand and reinforce the transmission network so that the vulnerability against intentional attacks is mitigated while meeting budgetary limits. Within this framework network planners face the nonrandom uncertainty of deliberate outages. Unlike in previous approaches, the risk associated with this uncertainty is explicitly addressed in the proposed model. Risk characterization is implemented through the minimax weighted regret paradigm. The resulting mixed-integer nonlinear programming formulation is transformed into an equivalent mixed-integer linear programming problem for which efficient commercial solvers are available. Numerical results illustrate the performance of the proposed methodology. The risk-based expansion plans are compared with those achieved by a previously reported risk-neutral model. An out-of-sample assessment is carried out to show the advantages of the risk-based model over the risk-neutral approach. In addition, the tradeoff between risk mitigation and cost minimization is analyzed. [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]

Highlights: [•] We examine the consumer payment minimization problem by mixed-integer linear programming. [•] Quadratic and piecewise linear supply offers, and inter-temporal constraints are modeled. [•] As a salient feature, no heuristic manipulation or control parameter tuning are required. [•] Optimal or high-quality near-optimal solutions are attained in moderate computing times. [•] Inter-temporal constraints enlarge payment reductions with slight cost increases. [ABSTRACT FROM AUTHOR]