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This paper proposes a flow-based approach for the transmission tariff allocation problem based on the notions of long-run marginal cost (LRMC) and nodal exchange factors (NEFs). A worst-case power flow, expressed in terms of NEFs, is formulated to characterize the system state. Additionally, the NEFs optimal values are determined considering a specific criterion to compute tariffs. The resulting problem is formulated as a bilevel program. The upper level is a worst-case power flow that maximizes line flows taking into account the transmission tariffs computed in the lower level. The criterion considered in the lower level aims to minimize the variation range of transmission tariffs, which is particularly desirable to provide incentives for renewable sources installed far away from load centers. The resulting bilevel problem may have multiple solutions. Here, the uniqueness in tariffs is preserved by solving an alternative problem once both the generation dispatch and the variation range of transmission tariffs are known. Numerical results are provided for a 6-bus system and the IEEE 118-bus system. [ABSTRACT FROM AUTHOR]

This paper presents the numerical analysis of the bilevel programming approach for revenue- and network-constrained market clearing developed in its companion paper. The impact of minimum revenue conditions and minimum declared profits on generation and consumption levels as well as on locational marginal prices for energy is examined in detail through three case studies. First, the results from an illustrative example including minimum revenue conditions are comprehensively analyzed. The second case study is based on the IEEE Reliability Test System and considers minimum declared profits. In the third case study, a modified version of the IEEE 118-bus system is tested while accounting for minimum revenue conditions. In addition, the computational behavior of the proposed approach is illustrated with several case studies including the IEEE 300-bus system. Numerical results show the effectiveness of the proposed approach to handle revenue constraints as well as its superiority over the heuristic currently implemented in the Iberian electricity market. Moreover, simulations reveal that, unlike previous works in the literature, generation revenue constraints can be precisely incorporated in day-ahead market clearing while explicitly considering the standard economic-dispatch-based marginal pricing scheme and without requiring price uplifts. [ABSTRACT FROM AUTHOR]

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]

In the restructured power industry, demand responsiveness is a key factor whose importance will be boosted due to the impetus provided by the development of smart grids. Within the context of pool-based electricity markets, this paper addresses the incorporation of price-responsive demand in multiperiod energy scheduling driven by consumer payment minimization. Although consumer payment minimization has drawn considerable attention mainly in an operational setting and also recently under a planning framework, available models and solution approaches typically neglect demand-side participation. The proposed scheduling model considers a marginal pricing scheme as well as the effects of both network constraints and intertemporal constraints associated with generation operation. Modeling demand-side participation leads to bilinear payment terms that significantly increase the mathematical complexity of the optimization process. The resulting problem is formulated as a mixed-integer nonlinear bilevel program for which no exact solution technique is currently available. This paper presents a novel methodology by which the original bilevel and bilinear problem is converted into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software. This transformation is based on the application of duality theory of linear programming, integer algebra, and Karush–Kuhn–Tucker optimality conditions. The proposed approach has been successfully applied to the IEEE 118-bus system. [ABSTRACT FROM PUBLISHER]

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]

Market clearing in restructured power systems is mostly implemented through an offer-based setting with the goal of maximizing social welfare. This approach leads to sound results from an economic viewpoint when generation offers reflect true production costs. However, offers may significantly differ from actual costs in practice, thus yielding undesired distortion. Under a marginal pricing scheme, this paper presents a general bilevel programming framework for alternative market-clearing procedures dependent on market-clearing prices rather than on offers. The resulting nonlinear mixed-integer bilevel programming formulation is transformed into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software. The bilevel formulation is investigated through a particular instance of price-based market clearing driven by consumer payment minimization. This problem has recently received considerable attention due to the open challenges posed from both modeling and computational perspectives. Numerical results are provided to illustrate the performance of the proposed approach. [ABSTRACT FROM PUBLISHER]

This paper addresses the vulnerability analysis of the electric grid under terrorist threat. This problem is formulated as a mixed-integer nonlinear bilevel program. In the upper-level optimization, the terrorist agent maximizes the damage caused in the power system, which is measured in terms of the level of system load shed. On the other hand, in the lower-level optimization, the system operator minimizes the damage by means of an optimal operation of the power system. The distinctive modeling feature introduced in this paper is that, among the different corrective actions available, the system operator has the capability to modify the network topology. Due to its nonconvexity and nonlinearity, the resulting bilevel programming problem cannot be equivalently transformed into a standard one-level optimization problem. Therefore, this paper proposes a new approach based on Benders decomposition within a restart framework. Some numerical results obtained by the proposed algorithm are provided and compared with those published, based on the IEEE Reliability Test System. [ABSTRACT FROM AUTHOR]