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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]

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]

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]