Distributionally Robust Generation Expansion Planning With Unimodality and Risk Constraints

Abstract

As more renewables are integrated into the power system, capacity expansion planners need more advanced longterm decision-making tools to properly model short-term stochastic production uncertainty and to explore its effects on expansion decisions. We develop a distributionally robust generation expansion planning model, accounting for a family of potential probability distributions of wind forecast error uncertainty. Aiming to include more realistic distributions, we construct more informed moment-based ambiguity sets by adding structural information of unimodality. We include operational-stage unit commitment constraints and model the risk of operational limit violations in two distinct forms: chance and conditional value-at-risk (CVaR) constraints. In both forms, the resulting expansion planning model is a mixed-integer second-order cone program. Using a thorough out-of-sample numerical analysis, we conclude: (i) the distributionally robust chance-constrained generation expansion planning model exhibits a better out-ofsample performance only if sufficiently accurate information about the first-and the second-order moments as well as the mode location of potential distributions is available; (ii) conversely, if such accurate information is unavailable, the distributionally robust CVaR-constrained generation expansion planning model outperforms; (iii) these two models have a similar performance when unimodality information is excluded.

Distributionally Robust Chance-Constrained Optimal Transmission Switching Problems

“…which require each chance constraint to be satisfied under all probability distributions P ∈ P. Typical ambiguity sets studied in related DRO-based power system decision-making problems fall into the following categories: i) moment-based ambiguity set [22]- [24], ii) distance-based ambiguity set [25]- [28] and iii) structural-based ambiguity set [29]- [31]. We consider the DRCC reformulations using the moment-based ambiguity set (mean and mean absolute deviation) and the distancebased ambiguity set (Wasserstein distance).…”

From Generalized Gauss Bounds to Distributionally Robust Fault Detection with Unimodality Information

“…Remark 10: As an approximation, the pessimisim underlying Theorem 8 is closely related to the selection of τ 0 > 0. In order for a good approximation, gridding of τ 0 can be carried out around (25) efficiently and the best solution can be chosen from all suboptimal candidates. Given the optimal solution P * to (26), the projection matrix P * can be obtained from the Cholesky decomposition P * = LL .…”

“…We remark that unimodality has been adopted for uncertainty description in diverse fields including DRO [19], [20], control theory [21], [22], power system operations [23]- [25], and statistics [26]- [28]. Despite these efforts, resolving the DRFD design problem remains a challenge, which arises largely from evaluating the worst-case FAR over the ambiguity set.…”

Distributionally Robust Optimal Dispatch of Virtual Power Plant Based on Moment of Renewable Energy Resource

“…Reference [18] proposed a distributionally robust optimization method for real-time economic dispatch considering automatic generation control, which reduced the total cost of power generations and frequency regulation. Reference [19] developed a distributionally robust generation expansion planning model, so that the violation risk of operational limits arising from the uncertainties pertaining to wind power output was reduced.…”