Efficient Unit Commitment Constraint Screening under Uncertainty

TL;DR

The paper tackles the challenge of solving day-ahead unit commitment under forecast uncertainty by introducing constraint screening methods tailored for robust and chance-constrained UC formulations. It leverages multi-parametric programming to convert screening problems into piecewise-affine mappings and extends screening to large-scale systems via a multi-area decomposition, achieving substantial online speedups while preserving feasibility. Key contributions include RO- and CC-screening formulations with theoretical guarantees, MPP-based acceleration that yields large reductions in screening time, and empirical validation across 39-, 118-, and 300-bus systems. The results demonstrate that efficient, reliable UC under uncertainty is feasible, enabling scalable operation and setting the stage for distributionally robust extensions and data-driven enhancements.

Abstract

Day-ahead unit commitment (UC) is a fundamental task for power system operators, where generator statuses and power dispatch are determined based on the forecasted nodal net demands. The uncertainty inherent in renewables and load forecasting requires the use of techniques in optimization under uncertainty to find more resilient and reliable UC solutions. However, the solution procedure of such specialized optimization may differ from the deterministic UC. The original constraint screening approach can be unreliable and inefficient for them. Thus, in this work we design a novel screening approach under the forecasting uncertainty. Our approach accommodates such uncertainties in both chance-constrained and robust forms, and can greatly reduce the UC instance size by screening out non-binding constraints. To further improve the screening efficiency, we utilize the multi-parametric programming theory to convert the underlying optimization problem of the screening model to a piecewise affine function. A multi-area screening approach is further developed to handle the computational intractability issues for large-scale problems. We verify the proposed method's performance on a variety of UC setups and uncertainty situations. Experimental results show that our robust screening procedure can guarantee better feasibility, while the CC screening can produce more efficient reduced models. The average screening time for a single line flow constraint can be accelerated by 71.2X to 131.3X using our proposed method.

Figures (10)

• Figure 1: Our intuition based on a two-node UC problem under net demand uncertainty. The deterministic UC model, based on predicted net demand, may yield infeasible solutions (Example 2-3). The RO-UC model and CC-UC model are developed to obtain solutions that can be reliably adjusted to feasible ones using predefined recourse policies $\boldsymbol{x}(\boldsymbol{\ell})$, typically linear decision rules when the exact net demand is known. We propose to conduct constraint screening for different formulations to reduce their complexity. The robust screening can be valid for all formulations and the RO-UC can be feasible under small-probability events (Example 3), while the CC screening may achieve a smaller reduced model equivalent to the original CC-UC model (Example 1-2).
• Figure 2: Redundant constraints identified by the screening models. Feasible regions are defined by all the UC model's constraints, while screened regions are defined by screening model constraints that are part of the UC model.
• Figure 3: Relationship among the UC-Models, Screening-Models, and Reduced-Models under different uncertainty settings.
• Figure 4: Critical regions of forecasted net demand $\hat{\boldsymbol{\ell}}$ corresponding to one screening model for line $j$. In each critical region, there exists an affine function mapping $\boldsymbol{\hat{\ell}}$ to $f^{*}_j$. The binding region means that the net demand here can cause maximum line flow to reach the line limit. The uncertainty representation $\omega$ can help make the solution more reliable but at the cost of intersecting with more regions $\mathbf{\Theta}$.
• Figure 5: Schematic of Whole-Screening and Area-Screening approaches. Compared to the whole-screening model, the area-screening models only involves the local variables and constraints, which can be small scale and solved in parallel. Lemma \ref{['lemma_area']} guarantees that the resulted model C is equivalent to model B.

Theorems & Definitions (9)

• Lemma 1
• proof
• Lemma 2
• proof
• Definition 1
• Lemma 3
• Theorem 1
• Lemma 4
• proof