Robust transmission network expansion planning in energy systems: Improving computational performance

Abstract

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.

Robust Transmission Network Expansion Planning Problem Considering Storage Units

“…Constraints (2b) impose that uncertain variables (in our case demands and generation capacities) are characterized by uncertainty set U. It should be noted that we use a cardinality-constrained uncertainty set as described in [12]. In this reference, the uncertainty sets are modeled through the uncertainty budget Γ, representing the maximum number of random parameters that may reach their lower or upper limits.…”

Robust dynamic transmission and renewable generation expansion planning: Walking towards sustainable systems

“…A bi-level approach for transmission expansion planning within a market environment is proposed in [12]. In an attempt to improve computational tractability, several robust approaches are presented in [13], [14], [15], [16] by using ARO. They proved that computational tractability is possible for real-size systems.…”

“…This system is composed of 6 buses, 3 generators, 5 levels of inelastic demand and 6 lines. Data for generation and demand capacities, and supply and bidding prices are given in [16]. The load-shedding cost is equal to hundred times the bidding price for each level of demand.…”

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

“…Within an ARO-based setting [8]- [12], the robust counterpart is formulated as an instance of trilevel programming wherein the first stage is associated with the upper level and the second stage corresponds to the max-min problem characterizing the two lowermost optimization levels. The upper level determines the least-cost first-stage decisions, namely the optimal investment plan.…”

“…Similar to the heuristic applied in [8], the approaches presented in [9]- [12] are unable to acknowledge global optimality. This shortcoming results from the transformation of the subproblem into a mixed-integer linear equivalent relying on setting bounds for dual variables or Lagrange multipliers, which may be in general unbounded [14].…”