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Impact of Training Dataset Size for ML Load Flow Surrogates

Timon Conrad, Changhun Kim, Johann Jäger, Andreas Maier, Siming Bayer

TL;DR

The paper investigates how training dataset size affects the accuracy of load-flow surrogates on a fixed-topology grid. It compares an MLP and two GNN variants on a modified IEEE 5-bus network, finding that GNN1 with a Global Decoder achieves the lowest validation error, though the MLP offers more stable training dynamics. Inference speedups over Newton-Raphson are substantial, with the MLP delivering the fastest predictions and GNNs providing competitive accuracy at meaningful times. The study highlights data scale as the dominant factor over architecture in this context and suggests physics-informed losses and Known Operator Learning to mitigate data demands for future larger-grid applications.

Abstract

Efficient and accurate load flow calculations are a bedrock of modern power system operation. Classical numerical methods such as the Newton-Raphson algorithm provide highly precise results but are computationally demanding, which limits their applicability in large-scale scenario studies and optimization in time-critical contexts. Research has shown that machine learning approaches can approximate load flow results with high accuracy while substantially reducing computation time. Sample efficiency, i.e., the ability to achieve high accuracy with limited training dataset size, is still insufficiently researched, especially in grids with a fixed topology. This paper presents a systematic investigation of the sample efficiency of a Multilayer Perceptron and two Graph Neural Network variants on a dataset based on a modified IEEE 5-bus system. The results for this grid size show that Graph Neural Networks achieve the lowest losses. However, the availability of large training datasets remains the dominant factor influencing performance compared to architecture choice.

Impact of Training Dataset Size for ML Load Flow Surrogates

TL;DR

The paper investigates how training dataset size affects the accuracy of load-flow surrogates on a fixed-topology grid. It compares an MLP and two GNN variants on a modified IEEE 5-bus network, finding that GNN1 with a Global Decoder achieves the lowest validation error, though the MLP offers more stable training dynamics. Inference speedups over Newton-Raphson are substantial, with the MLP delivering the fastest predictions and GNNs providing competitive accuracy at meaningful times. The study highlights data scale as the dominant factor over architecture in this context and suggests physics-informed losses and Known Operator Learning to mitigate data demands for future larger-grid applications.

Abstract

Efficient and accurate load flow calculations are a bedrock of modern power system operation. Classical numerical methods such as the Newton-Raphson algorithm provide highly precise results but are computationally demanding, which limits their applicability in large-scale scenario studies and optimization in time-critical contexts. Research has shown that machine learning approaches can approximate load flow results with high accuracy while substantially reducing computation time. Sample efficiency, i.e., the ability to achieve high accuracy with limited training dataset size, is still insufficiently researched, especially in grids with a fixed topology. This paper presents a systematic investigation of the sample efficiency of a Multilayer Perceptron and two Graph Neural Network variants on a dataset based on a modified IEEE 5-bus system. The results for this grid size show that Graph Neural Networks achieve the lowest losses. However, the availability of large training datasets remains the dominant factor influencing performance compared to architecture choice.
Paper Structure (10 sections, 9 equations, 5 figures, 2 tables)

This paper contains 10 sections, 9 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Dataset
  3. Grid Model
  4. Data Generation
  5. Architectures
  6. Graph Neural Network (GNN)
  7. Multilayer Perceptron (MLP)
  8. Experiments
  9. Results
  10. Outlook

Figures (5)

  • Figure 1: Modified IEEE 5-bus system used in data generation. S = Slack bus, PV = Generator bus, PQ = Load bus.
  • Figure 2: Illustration of the architecture of the GNN Model with Bus-specific Decoder
  • Figure 3: Training and Validation Loss Curves. The best configuration for each model is highlighted; all others are displayed with lower opacity.
  • Figure 4: Boxplots of MSE across different hyperparameter configurations.
  • Figure 5: Inference time depending the number of samples on the best models (Run 1) or N-R algorithm