Two-Stage Robust Unit Commitment for Co-Optimized Electricity Markets: An Adaptive Data-Driven Approach for Scenario-Based Uncertainty Sets

Abstract

Two-stage robust unit commitment (RUC) models have been widely used for day-ahead energy and reserve scheduling under high renewable integration. The current state of the art relies on budget-constrained polyhedral uncertainty sets to control the conservativeness of the solutions. The associated lack of interpretability and parameter specification procedures, as well as the high computational burden exhibited by available exact solution techniques call for new approaches. In this work, we use an alternative scenario-based framework whereby uncertain renewable generation is characterized by a polyhedral uncertainty set relying on the direct specification of its vertexes. Moreover, we present a simple, yet efficient, adaptive data-driven procedure to dynamically update the uncertainty set vertexes with observed daily renewable-output profiles. Within this setting, the proposed data-driven RUC ensures protection against the convex hull of realistic scenarios empirically capturing the complex and timevarying intra-day spatial and temporal interdependences among renewable units. The resulting counterpart features advantageous properties from a computational perspective and can be effectively solved by the column-and-constraint generation algorithm until -global optimality. Out-of-sample experiments reveal that the proposed approach is capable of attaining efficient solutions in terms of cost and robustness while keeping the model tractable and scalable.Index Terms-Adaptive data-driven approach, energy and reserve scheduling, renewable integration, robust optimization, scenario-based uncertainty set, unit commitment.

Distributionally Robust Transmission Expansion Planning: A Multi-Scale Uncertainty Approach

“…Not surprisingly, the optimal scenarios identified by problem (36) will be extreme points of the polyhedral support set Ξ ω , as this problem is a maximization of a convex function within a polyhedral set [35]. This fact also corroborates the result derived in section III-C that allows us to ignore all nonextreme points in problem (12)- (14) to achieve the equivalent formulation (19)- (21). To solve problem (36), we replace function g(x (j) , ξ, ω) with the dual objective function of problem (3), as it provides a tight upper bound under dual feasibility, resulting in the following bilinear mixed integer program:…”

“…It is worth mentioning that while part of the recent literature on ARO have considered probability agnostic models (see [11], [5], and [4]), relevant efforts have been made to account for the information extracted from data to devise more realistic descriptions of the short-term uncertainty. We refer the interested reader to [12], [13], and [14] for applications in short-term operational models and to [9] for a hybridrobust-and-stochastic approach applied to the TEP problem. Nevertheless, in long-term TEP applications, the use of scenario-based approaches relying on current data may be questionable, as the structure of the uncertainties in the target period may significantly differ from that found on data [3].…”

“…which constitutes a finite dual equivalent formulation for the distributionally robust recourse function defined in (12)- (14). The dual equivalent model (17)-(18) allows us to derive a primal finite equivalent formulation for the recourse function (12)- (14), namely,…”

Coordinated Planning With Predetermined Renewable Energy Generation Targets Using Extended Two-Stage Robust Optimization

“…This method can be used to estimate the power intervals of RES and load at different sample sizes and confidence levels. Unlike the scenario-based uncertainty set modeling method [24], the distribution information and confidence level are considered in the process of modeling a single uncertain set. We note that a systematic data-driven approach based on Dirichlet process mixture model to construct an uncertainty set is presented in [25].…”

“…All cases are the same as Scheme 1, and the total cost is 368352 $. When the uncertain budget is set to (24,24,12), the daily cost of five cases is 474 k$, 458 k$, 437 k$, 468 k$, and 453 k$, respectively. The uncertainty set is the largest, and the total cost is more sensitive to an uncertain budget.…”