Learning to Optimize Joint Chance-constrained Power Dispatch Problems

TL;DR

This work proposes a fast, scalable, and explainable machine learning-based optimization proxy, called Learning to Optimize the Optimization of Joint Chance-Constrained Problems (LOOP-JCCP), which is iteration-free and solves the underlying problem in a single-shot.

Abstract

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 models using the traditional iterative solvers is time-consuming and can hinder real-time implementation. 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 (LOOP-JCCP), 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 (LOOP-LC 2.0) 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 numerical findings complement our theoretical justifications and demonstrate great flexibility in parameter tuning, adaptability to diverse datasets, and increased computational speed.

Figures (6)

• Figure 1: Diagram of the VPP in this study, highlighting uncertainties from non-dispatchable sources like photovoltaic arrays and wind turbines, due to variations between actual and predicted renewable energy outputs.
• Figure 2: $\mathcal{LOOP-JCCP}$ model as an alternative to iterative solvers to deal with the task of repeatedly solving power dispatch optimization for VPPs.
• Figure 3: Schematic of the proposed $\mathcal{LOOP-JCCP}$ model, which integrates the $\mathcal{LOOP-LC}\space2.0$ structure li2023toward with a novel polyhedron reformulation. This model efficiently learns solutions to joint chance-constrained power dispatch problems within VPPs, delivering near-optimal approximations and ensuring feasibility with customizable probabilities. By incorporating XAI components, such as the set aggregate module and the closed-form feasibility module, it provides transparency and adaptability to diverse sample sizes and input sequences, enhancing interpretability and trust in the decision-making process.
• Figure 4: Flow chart of safe parameter selection for the proposed model.
• Figure 5: Comparative analysis of robust optimization, polyhedron reformulation, and $\mathcal{LOOP-JCCP}$ using varying safety parameters to evaluate objective cost rate, in-sample, and out-sample violation rates. The objective cost rates are normalized against the scenario approach, expressed as $f(\mathbf{u}^*_{\texttt{method}})/f(\mathbf{u}^*_{\texttt{SA}})$.