On the Solution of Large-Scale Robust Transmission Network Expansion Planning Under Uncertain Demand and Generation Capacity

Abstract

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, available solution methodologies for the resulting trilevel robust counterpart are unsuitable for largescale problems. In order to overcome this shortcoming, this paper presents an alternative column-and-constraint generation algorithm wherein the max-min problem associated with the second stage is solved by a novel 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 non-trivial 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. Index Terms-Block coordinate descent algorithm, primal column-and-constraint generation algorithm, transmission network expansion planning, two-stage robust optimization, uncertainty. NOMENCLATUREThis section lists the main notation used throughout the paper. Additional symbols with superscripts "(k)" and "(m)" are used to indicate the value of a specific variable at iterations k and m of the column-and-constraint generation algorithm, respectively. Similarly, superscript "(ν)" is used to denote results obtained at iteration ν of the coordinate descent method. A. Indicesi Generating unit index.

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