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

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.

A New Time Series Similarity Measure and Its Smart Grid Applications

Many smart grid applications involve data mining, clustering, classification, identification, and anomaly detection, among others. These applications primarily depend on the measurement of similarity, which is the distance between different time series or subsequences of a time series. The commonly used time series distance measures, namely Euclidean Distance (ED) and Dynamic Time Warping (DTW), do not quantify the flexible nature of electricity usage data in terms of temporal dynamics. As a result, there is a need for a new distance measure that can quantify both the amplitude and temporal changes of electricity time series for smart grid applications, e.g., demand response and load profiling. This paper introduces a novel distance measure to compare electricity usage patterns. The method consists of two phases that quantify the effort required to reshape one time series into another, considering both amplitude and temporal changes. The proposed method is evaluated against ED and DTW using real-world data in three smart grid applications. Overall, the proposed measure outperforms ED and DTW in accurately identifying the best load scheduling strategy, anomalous days with irregular electricity usage, and determining electricity users' behind-the-meter (BTM) equipment.

IRMAC: Interpretable Refined Motifs and Binary Classification for Rooftops PV Owners

In this paper, we seek to identify residential rooftop solar PV owners using imported energy data. To solve this problem with an interpretable, fast, secure, and maintainable solution, we propose Interpretable Refined Motifs And binary Classification (IRMAC) method, which includes a shape-based dimensionality reduction technique we call Refined Motif (RM), and a classification technique with linear complexity to identify solar owners. Furthermore, with the real data from Australia and Denmark, the proposed method is tested and verified in identifying PV owners as well as identifying electrical heating system users. The performances of the proposed method is studied and compared with various of state-of-the-art methods, where the proposed method outperformed the alternatives.