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Recently, several authors have reported specific criteria to support the widely accepted use of a convex operational model for bulk energy storage in the formulation of power system operation and planning problems involving binary variables. Using two counterexamples, we show that this modeling simplification may give rise to impractical solutions featuring simultaneous charging and discharging, even though the recently published criteria are satisfied. Thus, both counterexamples invalidate those criteria and demonstrate that the customarily used convex model may be unsuitable for the precise incorporation of bulk storage in such instances of mixed-integer programming. [ABSTRACT FROM AUTHOR]

The large-scale integration of wind power generation has significantly boosted the role played by conventional fast-acting generating units in power system operation. Due to their short response time, these relatively expensive devices are particularly suited to cope with the intermittency and volatility featured by uncertain wind-based generation. Within the context of network-constrained generation scheduling under wind-related uncertainty, this paper presents a new robust approach wherein the operation of both slow- and fast-acting generating units is precisely characterized in a day-ahead co-optimized energy and reserve market. As salient modeling features, the ramping-related effect of dispatch nonanticipativity and nonspinning reserve offers are both accounted for. The resulting robust counterpart is formulated as a challenging trilevel program with lower-level binary variables that is effectively solved by an exact nested column-and-constraint generation algorithm. Numerical results including a practical out-of-sample validation procedure demonstrate the operational advantages and the computational effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In the restructured power industry, bulk energy storage may play a crucial role to provide the flexibility required by system operators to cater for the unprecedented levels of uncertainty. Within the context of co-optimized electricity markets for energy and reserves under wind uncertainty, this paper addresses the incorporation of bulk energy storage units in day-ahead network-constrained energy and reserve scheduling. A novel two-stage robust optimization approach is presented whereby the nonconvex and time-coupled operation of storage devices is precisely modeled while accounting for the anticipativity of the two-stage setting. The resulting robust counterpart is cast as a mixed-integer trilevel program with lower-level binary variables. In order to address the nonconvexity of the recourse problem, this paper proposes the application of an exact nested column-and-constraint generation algorithm. Numerical results illustrate the effective performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Two-stage robust optimization has emerged as a relevant approach to deal with uncertain demand and generation capacity in the transmission network expansion planning problem. Unfortunately, the solution of practical large-scale instances remains a challenge. In order to address this issue, this paper presents an alternative column-and-constraint generation algorithm wherein the max–min problem associated with the second stage is solved by a block coordinate descent method. As a major salient feature, the proposed approach does not rely on the transformation of the second-stage problem to a single-level equivalent. As a consequence, bilinear terms involving dual variables or Lagrange multipliers do not arise, thereby precluding the use of computationally expensive big-M-based linearization schemes. Thus, not only is the computational effort reduced, but also the typically overlooked case-dependent, nontrivial, and time-consuming tuning of bounding parameters for dual variables or Lagrange multipliers is avoided. The practical applicability of the proposed methodology is confirmed by numerical testing on several benchmarks including a case based on the Polish 2383-bus system, which is well beyond the capability of the robust methods available in the literature. [ABSTRACT FROM AUTHOR]

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]

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]