We present a bilevel model for transmission expansion planning within a market environment, where producers and consumers trade freely electric energy through a pool. The target of the transmission planner, modeled through the upper-level problem, is to minimize network investment cost while facilitating energy trading. This upper-level problem is constrained by a collection of lower-level market clearing problems representing pool trading, and whose individual objective functions correspond to social welfare. Using the duality theory the proposed bilevel model is recast as a mixed-integer linear programming problem, which is solvable using branch-and-cut solvers. Detailed results from an illustrative example and a case study are presented and discussed. Finally, some relevant conclusions are drawn.Index Terms-Bilevel model, duality theory, electricity market, mixed-integer linear programming, transmission expansion planning.
NOTATION
This paper addresses the self-scheduling problem of a price-taker power producer. It focuses on risk modeling, emphasizing the tradeoff existing between maximum profit and minimum risk. The paper analyzes a self-scheduling model that considers simultaneously profit and risk. This model is formulated as a mixed-integer quadratic programming problem, which is solved using commercially available software. Relevant results from a realistic case study are discussed. Index Terms-Pool-based electricity market, price-taker power producer, profit versus risk tradeoff, risk-constrained self-scheduling. NOMENCLATURE Variables: Production cost during hour. Power production during hour. Total revenue. covariance matrix of random variables. Market-clearing price of hour (random variable). Vector of the (24) prices for day. Constants: Number of days for which true and estimate prices are available. Considered time periods in one day (typically 24). Factor used to estimate the covariance matrix. Weighting factor to incorporate risk into the expected profit objective function. Feasible operating region of the generating machine. Miscellaneous: Expected value operator with respect to random variables. Variance operator with respect to random variables. est Superscript that indicates estimate value. true Superscript that indicates true value. exp Superscript that indicates expected value.
In recent advances in solving the problem of transmission network expansion planning, the use of robust optimization techniques has been put forward, as an alternative to stochastic mathematical programming methods, to make the problem tractable in realistic systems. Different sources of uncertainty have been considered, mainly related to the capacity and availability of generation facilities and demand, and making use of adaptive robust optimization models. The mathematical formulations for these models give rise to threelevel mixed-integer optimization problems, which are solved using different strategies. Although it is true that these robust methods are more efficient than their stochastic counterparts, it is also correct that solution times for mixed-integer linear programming problems increase exponentially with respect to the size of the problem. Because of this, practitioners and system operators need to use computationally efficient methods when solving this type of problem. In this paper the issue of improving computational performance by taking different features from existing algorithms is addressed. In particular, we replace the lower-level problem with a dual one, and solve the resulting bi-level problem using a primal cutting plane algorithm within a decomposition scheme. By using this alternative and simple approach, the computing time for solving transmission expansion planning problems has been reduced drastically. Numerical results in an illustrative example, * Corresponding author: rominsol@gmail.com, tlfn.: 00 34 926810046
Preprint submitted to European Journal of Operational ResearchJuly 2, 2015 the IEEE-24 and IEEE 118-bus test systems demonstrate that the algorithm is superior in terms of computational performance with respect to existing methods.
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