SearcharxivSearch

arXiv · 1701.08649

Robust Dynamic Transmission and Renewable Generation Expansion Planning: Walking Towards Sustainable Systems

Abstract

Nowadays, the transition from a conventional generation system to a renewable generation system is one of the most difficult challenges for system operators and companies. There are several reasons: the long-standing impact of investment decisions, the proper integration of renewable sources into the system, the present and future uncertainties, and the convenience to consider an integrated year-by-year representation of both uncertainties and investment decisions. However, recent breakthroughs in Dynamic Transmission Network Expansion Planning (DTNEP) have demonstrated that the use of robust optimization might render this problem computationally tractable for real systems. This paper intends to consider not only the capacity expansion of lines, but the construction and/or dismantling of renewable and conventional generation facilities as well. The Dynamic Transmission Network and Renewable Generation Expansion Planning (DTNRGEP) problem is formulated as an adaptive robust optimization problem with three levels. First level minimizes the investment costs of transmission network and generation expansion planning, the second level maximizes system operational costs with respect to uncertain parameters, while the third level minimizes those operational costs with respect to operational decisions. The method is tested for two cases: i) an illustrative example based on Garver IEEE system and ii) a case study using the IEEE 118-bus system. Numerical results from these examples demonstrate that the proposed model allows making optimal decisions towards reaching a sustainable power system, while overcoming problem size limitations and computational intractability for realistic cases.

Explore related subjects

Keep this discovery

BibTeXRIS

Cristina Roldán, Agustín A. Sánchez de la Nieta, Roberto Mínguez, Raquel García-Bertrand. 2017-01-30. Robust Dynamic Transmission and Renewable Generation Expansion Planning: Walking Towards Sustainable Systems. https://doi.org/10.1016/j.ijepes.2017.09.021

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Deterministic and Random Bipartite Matching on General Networks: Convex Flow Reformulation, Asymptotic Properties, and Fast Algorithms

Minimum-distance bipartite matching on general networks has numerous applications various fields. This paper first focuses on deterministic problems and presents an exact edgewise-separable convex-flow reformulation. By introducing a smooth monotone rearrangement approximation of the edge-wise imbalance profiles, the convex-flow reformulation's can be solved efficiently. If we further conduct a first-order resistance-based approximation of the convex program, a one-step Laplacian-based estimator can be analytically derived in closed forms. The paper also studies random problems where supply and demand points are randomly distributed. We show that the expected optimal matching distance scales with the square root of the number of points if the supply/demand point distributions are identical, or linearly otherwise. In the former case, the optimal flow is proven to be centered, symmetric, and sub-Gaussian. In the latter case, the limiting resistance network characterizes how supply-demand imbalance is redistributed and motivates a fast algorithm that approximate the optimal flow based on the limiting resistance. Numerical experiments show that the proposed estimators closely approximate the exact matching cost while substantially reducing computation time. The proven theoretical properties of the random matching solution are numerically verified by large-scale Monte Carlo simulations.

math.OC

Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set

Data-driven distributionally robust optimization (DRO) typically treats the conditional outcome law as fixed and uses ambiguity sets to capture estimation error. This paper studies latent distributional heterogeneity, where each instance has an unobserved law but contributes only one observation, so uncertainty persists even if the mixture law is known. We propose Conformal-DRO, which uses nested conformal regions to construct an ambiguity set for the future latent law. Under exchangeability, the set covers this law with probability at least $1-\alpha$ in finite samples, without estimating underlying latent laws or their mixing mechanism. The conformal path induces a data-driven transport geometry, while $\alpha$ determines the radius. The worst-case problem reduces to a finite linear program over conformal shells and admits sparse adversarial solutions. The resulting robust value provides a finite-sample certificate for the selected decision's expected cost.

math.OC

The best approximation tuple: an extension of the Cheney-Goldstein algorithm and results to the multiple sets case

In this paper we extend the algorithm and several results published in the celebrated 1959 paper of Cheney and Goldstein about the best approximation pair (BAP) problem in two separate directions. One is the consideration of more than two sets. The other is the ability to handle each set as an intersections of a finite family of sets. We call the resulting problem the "Best Approximation Tuple (BAT) problem". The fundamental observation that leads to this generalizations is to recognize and handle one set (the "pivot set") as different from the remaining sets (the "satellite sets") instead of seeking cycles as the minimizers of a target functional. This enable us to overcome a certain theoretical obstacle related to cycles and minimizers of general functionals. We prove the convergence of the algorithm to the unique solution of the problem in the Euclidean case with strictly convex and compact satellite sets. Because of the lack of Fej\'er monotonicity, our convergence analysis is not standard, and is based on almost unknown properties of orthogonal projections regarding equality and inequality in the definition of nonexpansiveness.

math.OC