Learning to Optimize Joint Chance-Constrained Power Dispatch Problems

The ever-increasing integration of stochastic renewable energy sources into power systems operation is making the supply-demand balance more challenging. While joint chance-constrained methods are equipped to model these complexities and uncertainties, solving these problems using traditional iterative solvers is often time-consuming, limiting their suitability for real-time applications. To overcome the shortcomings of today's solvers, we propose a fast, scalable, and explainable machine learning-based optimization proxy. Our solution, called Learning to Optimize the Optimization of Joint Chance-Constrained Problems <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\mathcal{LOOP}-\mathcal{JCCP})$</tex>, is iteration-free and solves the underlying problem in a single-shot. Our model uses a polyhedral reformulation of the original problem to manage constraint violations and ensure solution feasibility across various scenarios through customizable probability settings. To this end, we build on our recent deterministic solution <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\mathcal{LOOP}-\mathcal{LC}\ 2.0)$</tex> by incorporating a set aggregator module to handle uncertain sample sets of varying sizes and complexities. Our results verify the feasibility of our near-optimal solutions for joint chance-constrained power dispatch scenarios. Additionally, our feasibility guarantees increase the transparency and interpretability of our method, which is essential for operators to trust the outcomes. We showcase the effectiveness of our model in solving the stochastic energy management problem of Virtual Power Plants (VPPs). Our theoretical analysis, supported by empirical evidence, reveals strong flexibility in parameter tuning, adaptability to diverse datasets, and significantly improved computational speed.