Efficient reformulations of ReLU deep neural networks for surrogate modelling in power system optimisation

2026-01-21

AI Summary

This work addresses the computational challenges arising from embedding ReLU-based deep neural networks (DNNs) as surrogate models in power system optimization, which typically yield nonconvex and intractable formulations. Focusing on a convexified ReLU DNN architecture with nonnegative weights beyond the first layer, the study proposes a compact linear programming (LP) reformulation that enables, for the first time, efficient and scalable integration of such structures into optimization frameworks. The approach preserves model fidelity while substantially outperforming conventional mixed-integer programming (MIP) and penalty-based methods. Validated on a Danish tertiary reserve market bidding case, the method achieves solution quality comparable to piecewise linearization and MIP approaches but with markedly improved computational speed, demonstrating its practicality and computational efficiency.

Technology Category

Search and Optimization: Non-convex OptimizationConstraint Satisfaction and Optimization: Mixed Discrete/Continuous OptimizationMachine Learning: Deep Neural Architectures and Foundation Models

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsEconomics, Online Markets and Human Computation: Cost models of using LLMs in production systemsSystems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

The ongoing decarbonisation of power systems is driving an increasing reliance on distributed energy resources, which introduces complex and nonlinear interactions that are difficult to capture in conventional optimisation models. As a result, machine learning based surrogate modelling has emerged as a promising approach, but integrating machine learning models such as ReLU deep neural networks (DNNs) directly into optimisation often results in nonconvex and computationally intractable formulations. This paper proposes a linear programming (LP) reformulation for a class of convexified ReLU DNNs with non-negative weight matrices beyond the first layer, enabling a tight and tractable embedding of learned surrogate models in optimisation. We evaluate the method using a case study on learning the prosumer's responsiveness within an aggregator bidding problem in the Danish tertiary capacity market. The proposed reformulation is benchmarked against state-of-the-art alternatives, including piecewise linearisation (PWL), MIP-based embedding, and other LP relaxations. Across multiple neural network architectures and market scenarios, the convexified ReLU DNN achieves solution quality comparable to PWL and MIP-based reformulations while significantly improving computational performance and preserving model fidelity, unlike penalty-based reformulations. The results demonstrate that convexified ReLU DNNs offer a scalable and reliable methodology for integrating learned surrogate models in optimisation, with applicability to a wide range of emerging power system applications.

Problem

• ReLU deep neural networks
• surrogate modelling
• power system optimisation
• nonconvex formulations
• computational tractability

Innovation

• ReLU DNN
• linear programming reformulation
• convexified neural networks
• surrogate modelling
• power system optimization